UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Cognitive and noncognitive correlates of statistics achievement Selkirk, Sheena Ann 1982

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


831-UBC_1982_A8 S44.pdf [ 6.14MB ]
JSON: 831-1.0054636.json
JSON-LD: 831-1.0054636-ld.json
RDF/XML (Pretty): 831-1.0054636-rdf.xml
RDF/JSON: 831-1.0054636-rdf.json
Turtle: 831-1.0054636-turtle.txt
N-Triples: 831-1.0054636-rdf-ntriples.txt
Original Record: 831-1.0054636-source.json
Full Text

Full Text

C O G N I T I V E AND N O N C O G N I T I V E C O R R E L A T E S OF S T A T I S T I C S ACHIEVEMENT  by SHEENA  ANN S E L K I R K  O.T.Dip., McGill B.A.(Hon.), University  A THESIS THE  SUBMITTED  University, 1965 of Saskatchewan,  IN  REQUIREMENTS  PARTIAL  FULFILMENT  FOR T H E D E G R E E  M A S T E R OF  1969  OF  OF  ARTS  in THE Department  of  We  F A C U L T Y OF G R A D U A T E  Educational  accept to  this  the  Psychology  thesis  required  THE U N I V E R S I T Y  Sheena  and  Special  conforming  standard  OF B R I T I S H  September  ©  as  STUDIES  COLUMBIA  1982  Ann S e l k i r k ,  1982  Education  In  presenting  requirements  for  Columbia,  I  available  for  permission  this an  agree  advanced  without  Department  of  study.  I  extensive granted  this  by  thesis  my w r i t t e n  Educational  September,  1982  copying the  Head  It  is  for  make  further thesis  this  of  my D e p a r t m e n t  understood  of  British  it  freely  for  that  gain  the  agree  of  financial  of  University  and  The U n i v e r s i t y of B r i t i s h 2075 W e s b r o o k P l a c e V a n c o u v e r , Canada V 6 T 1W5  Date:  the  reference  representatives.  allowed  at  shall  or  of  degree  fulfilment  Library  may  publication  partial  the  purposes her  in  that  for be  thesis  scholarly  or  by  copying  shall  not  permission.  Psychology Columbia  and  Special  that  Education  his or be  i i  Abstract This  thesis  is  observed  variance  within  population  of  a  twelve  in  a  as  the  research  variable  the  was  on a  The  original  intent  modeling  Unforseen  delays  independent  in  and  Alberta  questions  were  any  common  at  latent  pools  the  at  the  and  statistics,  of  self-concept  were  motivation,  utility. measured  by  of  The  twelfth  the  number  completed.  The  achievement,  was  examination. the  variables" the  University  data.  subjects  facility,  determinants  application  differences of  toward  investigate the  the  comprehension,  number  statistics  of  Victoria.  previously  administering  redeveloped  and  to  through  significant  Columbia  LVM a p p r o a c h  was  with  variables  statistically  one-hour  basis  classes  achievement  courses  the  Measures  volunteer  academic  as  for  statistics,  the  verbal  perceived  variable,  obtained  "causal  of of  of  statistics  achievement  of  experience,  dependent  on  four  attitude  measures  score  statistics  of  visualization, of  account  Education.  C o l u m b i a and  and  and  in  selected  each  British  Measures  or  students  of  to  introductory  collected-from  spatial  were  mathematics of  were  attempt  in  i n c l u d e d measures  motivation  independent  an  variables,  Alberta,  toward  specific  graduate  session  learning.  collected,  measure  of  reasoning,  attitude  of  of  of  achievement  area,  variables  logical concept  the  class  Universities The  in  report  independent  literature during  a  of  Bentler's  (LVM)  approach.  measures of  Alberta  between  Consequently,  so as  to  exclude  exploration  of  potential  of  of  the  resulted  the the  British research  consideration latent  in  of  the  variables  from  the  then,  to  analysis the  plan.  examination  The  of  zero-order  computation  of  Columbia  and  Alberta  samples  of  exploratory  nature  the  adopted  as  the  exploratory  criterion  Correlational revealed  visualization  Two  experiential the  Application experience of  the  and  first of  toward  and  analysis  a  to  with  be  stepwise  achievement variables. statistics  was  correlations  and  regressions.  the  and  a  of  in  related  to  regression accounted  were  55.5% of  toward  achievement.  that  the  past  set  of  12  variance. that  spatial  learning,  attitude  significantly  Cognitive-attitudinal independent  matrix.  The  54.9% of  the  for  the  set  12  of  learning, contributed  variables  Both  that  visualization)  only  The  achievement.  (concept  with  proportion  revealed by  spatial  achievement.  research  of  sample  identified.  revealed  concept  statistics  was  (cognitive-  significant  data  clusters  level  correlated  revealed  correlation  variables  spatial  Alberta  British  reasoning,  achievement.  facility,  the  0.10  statistics  for  the  Because  intercorrelations  accounted  attitude  The  Columbia  significantly  statistically  the  the  British  to  to  significance.  verbal  of  limited,  separately.  analysis,  regression  statistics  Three and  of  statistics  number  identified  appeared  the  related  attitudinal-motivational  were  of  for  in  statistics  correlated  was  together  visualization,  was  analyzed  learning  stepwise  accounted  Similar  analysis  statistical  clusters  cluster  taken  of  of  attitudinal-motivational)  variance  variables  were  experience,  and concept  achievement.  Only  of  forward  analysis  that  method  clusters results  variance  in  independent  attitude  toward  significantly  iv  to  the  two  samples  the  order  in  the  explained  two  The  were of  variance  subjected  entry  of  the  in to  achievement. regression  variables  was  When  the  analyses, not  similar  samples. were  reported  in  literature  different  administration  research.  exploratory  independent  results  terminated  statistics  the  by  a  discussed and  times  presentation  in of  of  the  the of  terms  of  possible tests.  some  the  findings  effects The  suggestions  of  the  thesis  is  for  future  V  Table  of  Contents  L i s t of T a b l e s L i s t of F i g u r e s Acknowledgement I.  Introduction  .....ix xi xii  to  the  Problem  1  Background  1  Statistics Statement  of  A Plausible Research  the  Review  of  Problem  of  8 10  the  Thesis  10  Literature of  Path  Analysis  with  Latent  12  Statistics  Motivational  III  7  Questions  Prediction  Three  3  Model  Organization II.  Achievement  Achievement  Variables  and C a u s a l  20  Modeling  Variables  Exploratory  13  21  Models  25  . Method  31  Instruments Measures  31 of  Verbal  the  Variables  Comprehension  Logical Number  Independent  Reasoning Facility  ....31 32 33 34  Spatial  Visualization  Concept  Learning  35 ...35  Attitude  Toward  Statistics  Attitude  Toward Research  37 40  vi  Academic  Self-Concept  Achievement Perceived Specific  42  Motivation  -  Utility  44  Motivation  45  Experience The  Measure  of  45 the Dependent  Variable  Subjects Population  Accessible  47  Population  .47  Sample  47  Collection  and P r e p a r a t i o n  47  Data  Collection  47  Data  Preparation  49  Scoring Preliminary  Procedures  50  Analysis  51  Item A n a l y s i s Equivalence Columbia IV.  46 47  Target  Data  43  Preliminary Results  of  the  British  and A l b e r t a  Results of  51  the  and F i n a l  Analytic  Preliminary  Analysis  Description Integrity  Samples  of  of  the  Sample  the Data  Pool  Item A n a l y s i s British  Columbia  The  Alberta  Sample  of  Procedures  53 53 53 55 56  The  Equivalence  52  the  Sample  Samples  56 60 63  vii  Recasting  of  Methodology  the of  Correlational  V.  Results  Research  the  Final  Columbia  The  Alberta  Sample  Final  Correlational The  Sample  Analysis  71  Intercorrelations  The  Alberta  Forward  Regression  VI.  Summary  and  Summary  Forward  Forward  Discussion  the of  Results  85 90  One  92  Research  Question  Two  94  Research  Question  Three  96  of  Conclusions  and  the  Study  Implications  98 100 103  Literature  Cited  104  A.  Initial  Form  Concept  Learning  Task  Task  82  Question  Notes  the  80  Research  Limitations  Appendix  Regression  85  Investigation the  76  Regression  Conclusions of  75 76  Intercorrelations  Exploratory  71 71  Sample  Parsimonious  68  .71  C o l u m b i a Sample  Parsimonious  68  69  Analyses  British  66  68  British  the  Analysis  Analyses  The  of  Questions  Instructions  of 108 108  vi i i  Concept Test Appendix  Description  Questions B.  Letter  of  Concept  Statement  Measure  Academic  Self-Concept  116 ...119  Motivation  120 121  Utility  ..121  Experience C.  121  Initial  Form of  Attitude  Scales  Instructions-  Statements  About  122 1 22  Statistics  122  Statements  of  Positive  Polarity  122  Statements  of  Negative  Polarity  123  Statements  Appendix  114  Motivation  Perceived  Task  ...112  L e a r n i n g Task  Specific  112  113  Attitude  Appendix  Materials  Consent  Achievement  109 111  Non-Copyright Test  Introductory  Past  .  About Research  124  Statements  of  Positive  Polarity  ..124  Statements  of  Negative  Polarity  125  D.  Administration Instructions  127  ix  List  Table  1.  Latent  Investigated Table  2.  Table  3.  and Table For  and M a n i f e s t and  their  Correlations  Variables  with  4.  of  the  Underlying  Item and  The  of  Attitude  Variables  Cognitive  Definitions  and  Manifest  Variables  Variable  39  5.  Obtained  Table  6.  Scale  Statistics  (British  Columbia  Table  7.  Scale  Statistics  (Alberta  Sample)  Table  8.  Inter-correlations  Table for  Table  (British  Partial  the  Non-Contributory  10.  11.  for  the  (Alberta  (Alberta  Sample) and  Sample)  56 61  the 72  F-Ratios  Variables 75 among  the  Sample)  77  Correlations  Non-Contributory Sample)  55  Sample)  Inter-correlations  Partial  ..  among  Correlations  Columbia  Variables Table  Sizes  Columbia  9.  (British  32  Statistics  Table  Variables  19  Scales Sample  9  Noncognitive  Achievement  Latent  Scale  Tables  Substantive  Statistics  Measures the  of  and  F-Ratios  Variables 80  X  Table for  12.  Beta  Correlations  9 Non-Contributory  (Alberta Table  Partial  13.  and  Independent  F-Ratios Variables  Sample) Order  Weights  of  for  82 Entry,  R-Square  Exploratory  Change,  Forward  and  Regressions  83  xi  List  Figure  1.  Path-Analytic  Vocabulary  LVM M o d e l  Figure  3.  Exploratory  of Figure of Figure  Statistics 4.  (Less Figure  7.  (More  Adult  Model  Model  Vocabulary  Score  Model  Model  28 "B" 29 "C"  Achievement of of  24  "A"  Achievement  Achievement  Experienced Model  Adult  Achievement  Exploratory  Statistics 6.  of  Exploratory  Statistics 5.  of  23  2.  Figure  Model  Figures  Score  Figure  of  of  Student)  30 ( 101  Achievement  Experienced  Student)  101  xi i  Acknowledgement  I  would  supervisor, with  first Dr.  tolerance  committee,  Dr.  patiently;  I  Dr.  D.  T. for  and  am  their  materials.  of  Ratzlaff grateful  to  their  I  would  completed expressed  my  has The  ,  to like  I  Alberta  to  me  E.  deserve  rather  such  interest  problems  bore like  Skakun  my  with  me  to  thank  and  Dr.  test to  forms  study.  for  thanks  missing  my g r a t i t u d e  the  of  special  tedious in  many  my  Randhawa  locate  express  the  would R.  Dr.  to  members  Sherrill,  and D r .  help  with  other  J.  classes. of  gratitude  dealt  them b o t h .  Layton  efforts  Finally,  and  who  and D r .  University  heroic  industriously  D.  utilize  who  express  Rogers,  Dr.  the  to  understanding.  H.  me t o  McGuire  subjects,  T.  Bateson,  allowing  like  the so  1  Chapter Introduction  I.  to  the  Problem  Background In has  the  been  among  educational  paid  to  college  the  psychology  patterns  students.  general  academic  academic  subjects  (e.g.,  example  of  An Hackman  and Taber  students,  each  of  or  "least  and  institutional  twelve of  profiles  Hackman  by  is,  Test  in  a  focused  both  achievement  in  group  of  nominated  "most  student  variables,  defined and  the  community  of  seven  nomination.  sort and  average  include  a  expectancy power  setting  study  the  (Mathis,  revealed  characteristic students.  rather  globally.  were  been  selected a  single  selected  Examples of  beliefs of  successful"  commonly, has  of  interpersonal  students  achievement".  predictive college  being  success  More  that  analysis  "unsuccessful"  academic  is  undergraduate  personal,  "unsuccessful"  grade-point  this  academic,  as  Multivariate  five  particular  studies  been  along  on  statistics).  whom h a d  achievement of  success  from  "academic of  has  attention  academic  examined data  as  investigations  determination  on  of  They  peer  operationalize  academic  and  former  students,  and  such  research  much  (1979).  "successful"  variable  of  the  and Taber  faculty  The  dimensions.  of  correlates  mathematics,  successful"  "successful"  That  success  and  literature,  the  of  relationship  (Henson, American 1972),  to  and  1976),  a  College a  meta-  2  analysis  of  over  achievement  to  Among in  a  cognitive  school  subject  that  were  high  college  board  grades  in  a  of  of  various  average,  correlates  investigation  by  mathematics and  number  of  and  college  grades,  high  mathematics  reports  Risser  in  on a  in  college  grades.  of  for  test A  He  in  second  reported  intelligence,  ranks a  both  secondary  placement  class  of  (1965),  grades,  a measure  courses  achievement  are  (1978).  school  academic  variables,  algebra  Troutman  of  achievement  independent  scores  of  1979).  mathematics and  of  finite  the  Davis  previous  scores  (White,  substantial  predictive  school  relationship  status  noncognitive.  found  an  the  relationship  measures  and  is  area,  the  grade-point  example that  of  to  mathematics  of  investigations  investigations mathematics  studies  socio-economic  the  specific  example,  100  predicted  college  freshman  population. Among  the  mathematics Keeling  appears  (1978),  predictive  among to  mathematics, occupations.  number  of  that,  their  sample  was  a  the  was  on  college  predictor (1980)  and  of  found  anxiety  attitudes taken,  and  selected,  mathematics  courses  Sepie  differential  for  better  achievement,  towards  anxiety  Austin-Martin  freshmen,  mathematics  the  specific  found  anxiety.  mathematics  extensively.  versus  which  college  anxiety  investigated  anxiety  general  female  studied  They  from  mathematics than  been  general  achievement.  achievement  related  have  variables,  instance,  of  population  specific  that,  to  for  power  mathematics student  noncognitive  was  towards parents'  3  Several gender  difference  Recently, measures  a  of  five  although  appeared  at  differences In others than  of  some the  were  Grade  such  have  suggested se  supported  results  gender-related found  that  degree  of  the  support  to  elementary  in  this  those  literacy)  gender  He  found  differences  12 s i g n i f i c a n t  found  1977). by  Fox  mathematics  usefulness  significant  operations,  children.  by  gender  of  others These  mathematics  as  Robitaille,  differences  determinants  achievement.  the  large  statistics  often-heard  correlates  and  on  measures.  earlier  of  differences  of  This  rather  mathematics suggestion  (1976),  who  studied  performance. mathematics correlated  variables a male  is  She  and  the  strongly  were,  in  turn,  domain.  Achievement  Despite  reported  Grade  the  explored.  computer  socio-cultural  affecting  of  and  which  been  (numbers  school  Sherman,  perception from  as  important  reported  perceptions  Statistics  five  and  factors  mathematics  related  on a l l  that  has  significant by  in  gender  topics,  Columbia  results  are  (Fennema  by  mathematics  4 level,  obtained  conducted  achievement  statistically  of  per  been  examined  algebraic  spite  gender  of  British  achievement  with  (1981)  domains  sample  have  mathematics  measurement,  large  that,  in  Robitaille  geometry, in  investigations  lament  in  the of  area,  numbers courses  that  two  in  college the  "statistics  literature  course  of  are  reports  in  who  behavioral  sciences  is  me",  address  achievement  students  not  for  directly  statistics. of  few  the Of  enter and  studies  area the  investigations  the  of  studies of  the  4  relationship  of  achievement,  while  examinations  a  single the  of  the  independent  variable  to  remaining  five  are  contributions  of  several  statistics  reports  of  independent  variables. Michael  and  Michael  arithmetic  and  algebraic  accounted  for  slightly  performance (1980)  in  a  examined  statistics". they  basic  observed  scores  and  classes  correspond  to  a  were  course  achievement related. related attempted  in  a  of  of  34  of  variable  and  0.54  in  Bilderback  "attitude  statistics  29%  basic  variance  5-point  and  in  this  the  Roberts  These  examined  two  eight  potential  calculus, an  toward  Likert  items,  between  scale  course  three  for  three  correlations  the  variance  in  each  of  several  cognitive  previous  overall  course  cognitive Of  and M a t h e m a t i c s  the  basic  tests  with  average and  students  who  statistics  the  proved  exception  coursework  commonly  were  was  by  one  of  examining  found  discriminate  not  (1975)  obtained  Record  and  positively  Smith  course,  Graduate to  the  course  Huberty  discriminators eight,  multiple-variable  mathematical  grade-point  among t h e a  the  statistics  achievement.  in  of  found t h a t ,  introductory  levels  record.  in  (1972)  discriminate  grade  Verbal  in  and  30%  0.48  of  course  four  student  0.33,  contributions  However,  to  that  found  variable  scale  earned  23%,  and  class.  students.  Giambra  in  to  own of  ability  respectively.  investigations. of  of  11%,  potential  variables  their  examined  than  noncognitive  points  successive  The  more  correlations  total  achievement,  operations  statistics  the  Using  (1969)  in  the  Examination best,  but  5  even  they  addition, various  did  accuracy  of  statistics  and  reasoning,  verbal  of  technical  of  grades,  scores  psychology.  of  variance the  attitude  Feinberg towards  included reading  each  statistics of  and as  the  five  scales  measures  grade  concepts,  state  anxiety  course  grade,  previous  mathematics  courses  achievement  in  correlations  exceeded  mathematics  statistics 0.40  speed,  essay-writing  the  course  oral  subjective course  attitudes for  51.3%  self-ratings 5.9%,  that  measured basic  and  the  attitudes during  a  and  gender  of  success  in  correlated  However,  for  mathematics  ability,  courses,  course.  at  assessing  significantly  (between  algebra,  reported  mathematical  were  reading  for  (1978)  abstract  possible  the  Halperin  of  of  accounted  achievement,  entered regression  skill  four  three  and  were  and  of  (1976)  vocabulary,  course  expected  remaining  measures  18.5%.  a  the  predictors  stepwise  aptitude,  of  of  the  comprehension  included,  cognitive  perceptions  number  block  ability  each  in  for  class,  achievement,  previous  The  quantitative  statistics  subject,  in  on  a  retention,  also  predictions  scales  In  for  and  and H a r t l e y  arithmetic  attaining  towards  in  writing  were  probabilities  the  Hartley  reasoning,  comprehension,  and  widely  correlates  considered  variables  Self-ratings  presentation  10.5%,  were  variables  Cognitive  ability,  classification.  varied  noncognitive  studies.  procedure.  logic,  classification  achievement  independent  speed.  "satisfactory"  levels.  cognitive  multiple-variable 23  allow  grade-score  Both of  not  none  achievement  and  with of  the  basic  6  mathematics 0.35.  and  attempt  to  The  regression by  skills),  the  was  so  correlation of  the  of  Elmore  previous  Attitudes  Gender  visualization  ability  Towards  grade be  0.32  using  reported  of  courses, and  Attitudes  previous  mathematics  student  (on  the  scale)  accounted variance  and  stepwise  in  detail  The  and  for  school,  males  mathematics  by  no  interaction  had  been  of  reported  the  4.7%,  and  proportion  role  and  in  variables,  variance  Attitude  on  achievement  in  minimally;  sex  8.2%  pattern  course spatial  (19.5%)  of  coursework, orientation  Towards 17.1%,  of  Feminists  respectively,  marks.  Sherman  spatial/visualization. the  the  ability  performed  despite  and  relationship  spatial/visualization  with  mathematics-related  on  18.1%,  course  of  student,  MMPI  independent  largest  coursework,  reported  reported  46.4%  the  the  scales) The  of  orientation  from  the  coursework,  gender  contributed  for  investigated  role  scale  for  toward  MMPI  in  sex  course.  student  accounted  (1980)  Feminists  accounted  .  finding  not  between  mathematics-related  mathematics  variance.  the  to  Vasu  towards  statistics  together,  mark.  of  and  attitudes  introductory  taken  ranged  course  as  Masculinity-Femininity  several an  predict  unsuccessful  spatial/visualization (on  majority  authors.  Finally,  number  the  is  between somewhat  (1980).  He  This  earlier  may  towards (by  that  better  differences  finding  attitudes  obscured  found  significantly  significant  achievement  Fox  have  sex  by  than on  been  role  (1976))  by  a  and recent  late  high  females  in  measures  of  influenced  by  behaviors, to  which  influence  7  achievement  in  mathematics.  Statement As that  revealed  research  into  in  particular,  in  the  That  social  is,  coherent  the  the  correlates  In  no  is  has  (1979),  motivational in  in  addition, to  of  among  an  early  cannot the  reported  variables overall of  motivational  variables  achievement  in  previous the  the  to  may  cognitive  account  achievement, variables.  as  statistics  would  may or  be  a  the  power  of  findings.  shown  and be  in  Hakstian  much a s  over  a  in  achievement  as  correlates  into  reported  have  It  courses  organized  literature.  for  and,  development.  predictive  regard in  of  investigations  of  appears  achievement  be  investigators,  academic  contribution  easily  it  statistics  stage  replicate  with  other  statistics  introductory  investigation  been  summarized above,  in  results  variables,  statistics,  Problem  results  performance  seldom attempt  motivational  variance  the  published  Further,  the  by  sciences,  whole.  literature  Gale  of  of  and that  20% o f  the  above  the  that  study  predictors fruitful  of of  area  of  investigation.  what  Thus,  the  are  the  question  investigated  relative  in  the  contributions  of  attitudinal,  experential  and  variance  achievement  in  education?  in  present  selected  motivational introductory  thesis  cognitive,  variables  statistics  was:  to  classes  the in  8  A  solution  "causal  (1980).  relationships of  is  model  sample  is  to  variable,  are  data.  of  is  used  to  explain  measured  or  manifest  smaller The  "goodness  the  twelve, in  of  twelve three  of  the  suggested the  variables  of  central  problem of  of  fit"  is  not  were  considered  by  observed  number  "fit"  was  together  Table of  1  each  latent  of  in  underlying  a  the  proposed  acceptable,  to  be  also  then  the  single  was  dependent  were  independent  a  short  suggested  that  manifestations  - cognitive,  independent  independent  contains  It  variables  variables  as  the  variable.  twelfth  thought  with  which  independent  The  affective,  variable,  of  the  three  or past  proposed  constructs.  Specification particular,  variables,  the  past  process.  of  a  experience The  state  theory-building  These  models, in  terms  model  of  the  and  of  described  a more  arrows  of  in  the  explanatory  the  achievement  was  coefficients were  area.  Chapter  difficult  linking  path  difficulties  within  their  was  statistics  specification  difficult.  alternative  single  placement  equally  evaluated  use  approach  a  variables  listed  the  underlying  of  the If  definition  experience,  clear  of  the  variables"  variables.  estimate  motivational.  In  set  incorporating  The  substantive  one  a  manifest  variables.  of  latent  in  rejected.  Twelve  eleven  sought  latent  procedure to  p r o b l e m was  procedure  among  or  Model  with This  a model  constructs  model  the  modeling  Bentler  terms  to  A Plausible  II, power  due  to  the  Therefore, were  task. latent not  proved early three  specified  with  a  regard  and to  9 Table 1 L a t e n t and M a n i f e s t V a r i a b l e s and T h e i r B r i e f S u b s t a n t i v e Latent  Variable  Manifest  Definition  Variable  Facility  Logical  Reasoning  Spatial  Visualization  Concept  Learning  Att itudinal Attitude Toward Statistics Attitude Toward Research Academic  o r i e n t a t i o n toward s t u d y i n g and performing introductory statistics o r i e n t a t i o n toward s t u d y i n g and a p p l y i n g p r i n c i p l e s of research d e s i g n and e v a l u a t i n g research p e r c e p t i o n o f own c o g n i t i v e abilities  Self-Concept  Mot i v a t i o n a l Achievement Perceived Specific  tendency to undertake successoriented activities p e r c e p t i o n of s t r e n g t h and n a t u r e of u s e f u l n e s s of s t a t i s t i c s course p e r c e p t i o n of s t r e n g t h and n a t u r e of r e a s o n f o r s t u d y i n g statistics  Motivation Utility  Motivation  Experience  totality of p r e v i o u s experience with mathematics, s t a t i s t i c s and research  Statistics  statistics Like  Variable  a b i l i t y to understand the E n g l i s h language a b i l i t y to perform basic arithmetic operations with speed and a c c u r a c y a b i l i t y to reason from premise to c o n c l u s i o n a b i l i t y t o t r a n s f o r m an image of a s p a t i a l pattern a b i l i t y to abstract a concept from e x p l a n a t i o n and examples  Comprehension  Number  of  Manifest  Cognitive Verbal  Investigated Definitions  Achievement  o v e r a l l knowledge of introductory d e s c r i p t i v e and inferential statistics  achievement. the  and H a l p e r i n investigation  studies  (1978) was  and  of  Hartley  Elmore  exploratory  and in  and H a r t l e y Vasu  nature.  (1976),  (1980),  the  Feinberg present  10  Research Because model Two  was  of  the  examined.  specific  research  any  one  acceptably  of  of  would  be  the  the  among t h e  proposed that,  none  if  three  the  statistics  can  latent  experience  and  models  were  study, were  a  single  assessed.  addressed.  models  the  observed  analysis was  variance be  and  in  of  The  first  investigated  the  tenable,  in  matrix  data  the  of  causal  relevant  are  by  the  preparation  the  sampling of  data  for  by  of  revealed  following  and  of  that  question  and  a in  plan,  is a  the  three and  variable,  past  Thesis organized  discussion  Chapter of  II.  the  data  analysis,  of  statistics?  delineation  measures  elementary  attitudinal  the  thesis  in  each  manifest  literature,  presented of  for  (cognitive,  this  modeling,  descriptions  variables,  of  achievement  accounted  mathematics  remainder  investigated of  models  three  Organization  review  the  variables?  the  variables  motivational)  A  of  addressed:  How m u c h o f  The  three  questions  reproduce  correlations was  Instead,  nature  was:  Does  It  exploratory  not  question  Questions  and  in of  of  independent  the  chapters.  path  analysis  the  Chapter  collection  five  models III and  be  consists dependent  procedures  preliminary  to  and  analysis  11  plan. Included  in  analysis.  As  recast  light  the  analysis  Chapter in  in  Chapter  conclusions  discussed  was  IV.  The  V.  Chapter  of  drawn  from  the  VI the  the  results,  These  results  Chapter  are  there,  these  made.  IV  of  these  final  a  of  research  and a  changes  is  results  the  preliminary  questions  were  c o r r e s p o n d i n g change are  also  described  revised  analyses  are  report  of  summary  results.  the  in in  reported and  Chapter Review  This  chapter  literature  is  related  statistics  is  motivational in  description  of  this path  variables"  section,  the  correlates  three  the  is  of  not  prediction in  this  I.  The  direct  is,  Harper  situation of  the  comprehensively addition,  relevant  to  the  of  the  of  by  a  (1978)  and  with  to  much o f present  of  the  Singh  in  of  (1979)  no  In  a  with  the  final  to  Because study  given  two  the  achievement  area.  examples  of  of  much the  is  reviewed  in  Chapter  recent  reviews  (1976). to  the  large  by  literature  study.  In  literature  correlates is  rather  number  variables, and  contains  academic  mathematics a  also  modeling  present  referred  contains  the  part  is  investigations  this  the  regard  plethora  of  presented.  of  in  achievement,  is  Begle  are  general  interest  reader  relationship  "causal  literature  achievement  of  the  the in  achievement second  models  First,  achievement  (Bentler,1980).  relevance  literature  investigations  In  and  beyond mention  the  possible  The  approach  statistics  report,  determinants That  analysis  level  sections. of  statistics  determinants  of  by  The  to  in  three  prediction  exploratory  high  Rather,  prepared  the  into  section.  reports  and  reflect  to  reviewed.  latent  T h e many  Literature  organized  variables  discussed  of  II.  of  and  similar.  reports  of  and  has  been  reviewed  Fennema  and  Behr  (1980).  appears  not  consequence,  to the  be  directly literature  13  of  mathematics  examples this  achievement  mentioned  thesis  prediction  is of  in  Chapter  confined  to  achievement  Prediction Seven  studies  achievement  in  literature. of  achievement  contribution variance  in  mathematics in  classes  (n=58,85 items  measured  and and  examination.  In  statistical  reasoning  computation obtained high of  to  was  the  allow  achievement Roberts  use in and  (1969) the  the  The  to  the  determinants  of  the  in  the  relationship  investigated to  the  remaining  and a f f e c t i v e  first  graduate  students  in  items.  untimed,  and  a  the  explained  three  were  correlates  test  session  respectively).  required.  of  of  administered  examination,  correlations  in  as  achievement.  41  an  literature  identified  variables  cognitive  15 a l g e b r a i c  using  were  studies  achievement.  to  the  relevance  and  reports  cognitive  during  statistics  arithmetic was  skills  for  Achievement  statistics  Two  and M i c h a e l  of  immediate  correlates  variable.  statistics  except  statistics.  were  both  review  of  two  statistics  of  The  the  several  of  I.  discussed,  Statistics  seven,  one  of  Michael  course  the  to  investigations predictors  of  introductory Of  not  reports in  of  is  of  The The  heavy  The  (0.45,0.53 mathematics  and  elementary  included  criterion  multiple-choice was  concluded  0.57)  skills  35  variable  placed  understanding;  authors  basic  psychology  test  emphasis  concept  an  three  open-book, a  of  were  test  as  on  little  that  the  sufficiently a  predictor  statistics. Bilderback  (1980)  reported  the  development  and  14  partial The  validation  final  jargon", scale.  consisted  of  each  of  was  The  scale  point  in  class  was  was  The  the  minimally  to  29% o f  Roberts scale  and  high  0.95  on any Giambra  (1972)  average  that,  mathematics, calculus  was  was  the  to  the  five-point  the  the  measure  does  of  does  not set  either or  at  only  which  point  each  in  the  correlations  classes)  scale.  course  whether  obtained  were  This  high  conclusion  accounted  concluded statistics  by  the  than  0.90).  in a  graduate  for  11%  use  of  in  the  achievement.  also  level  of  Likert  statistics  relative the  statistical  classes  three  (greater  anxiety high  itself  high  that  internal  While  the  provide  theoretical  high  evidence maximum o f  coefficient. information courses of  science  mathematics  related  that  statistics.  in  administered same  (1980)  classes  advanced  a  state  of  mathematics  from  not  use  validity  behavioral of  did  statistics  collected  previous  introductory found  value  empirical  three  justified  coefficients  it  to  the  of  the  was  validity,  of  in  diagnose  consistency  for  at  since  Bilderback  student  .consistency  scale  predictive  variance  to  individual  for  justified,  the  They  measure  "couched  introductory  each  justify  internal  an  the  towards  endorsed using  0.54  enough  attitudes  items  concluded  and  is  34  authors  (0.33,0.45 to  in  course  given  of  administered  respectively). the  course.  point  which  enrolled  (n=92,8l,65  number  a measure  scale  students  the  of  about  taken  and  sophomores statistics  courses  the  type  overall  enrolled course  taken  elementary  statistics  achievement.  algebra), In  gradein  an  (n=l66).  (calculus,  algebra,  and  He  finite only  addition,  a  15  strong  positive  relationship  point  average  and  that  overall  statistics  evaluated  grade-point  his by  results  means  Hartley  of  only  students  and  design  and  four  Abstract  Reading  measures  of  probability  of  served  the  as  variable total  was  points  regression The  other  overall  regression. entered.  Together,  variance  in  variance  (49%)  other  psychology  -  of  social  variables  of  (Verbal  57  from  Reasoning  Aptitude the  Davis  Test; Reading  self-concept, and  possible  the  The  as  course.  five  subjective  course  variables.  the  of  variables  achievement,  was set  accounted  order  from each  independent  23  four  a  free  of  23  achievement.  In  distributions,  statistics  psychology,  statistics  accounted  correlations,  psychological  academic  23 v a r i a b l e s  was  data  Speed  the  variables  variance.  entire  of  grades  dependent  measured  Results  from  by two  reported.  procedure  The  of  during  were  any  Differential  statistics  procedures  a  19 i n d e p e n d e n t  accumulated  first  in  the  each  concluded  predictor  frequency  collected  towards  attaining  grade-  statistics.  and Reading  attitude  Giambra  report  of  The  10 a s p e c t s  overall  possible  not  cognitive  from  a  terms  (1976)  of  Reasoning  of  in  course.  measures  Measures  did  enrolled  Comprehension  Test).  was  chi-square  undergraduate  included  He  between  achievement.  average  and H a r t l e y  research  obtained  statistics  achievement.  presenting  was  for  for a  by  welfare;  independent  accounted More Verbal  further  entry,  stepwise  they  subjective  for  than  variables  was  86.3% of  the  one-half  Reasoning  32% were:  of  multiple  of  this  alone.  Ten  the attitude  probability  of  explained towards attaining  16  an  "A";  rating  psychology  for  probability  The which  the  attaining  the  of  independent  variables,  blocks  inflation  in  be  beginning  278  They  of  a  correlations  between  concepts  (r=+0.35);  success  in  courses  -  skills;  subjective  probability  of  were e n t e r e d entry,  R due  to  a  blocks.  that  that  the  subject  of the  risk  to  the  with potential  The  5.9%  concluded  low  The  grade.  and  despite  in  cognitive,  course  10.5%  recommended students  in  approach  were  of  authors  (1978)  administered  variables and  71  during  graduate  course.  Eight  achievement  (r=+0.40); expected  of  variable  regression problems  perceptions  first  class  of  at  of  16  grade  (r=+0.34);  the  anxiety  mathematics  an  variable (r=-0.22);  quantitative  (r=+0.33); number  in  zero-order  independent  towards  16  session  enrolled  attitude  of  measures  students  state  course  courses  the  and each  significant:  mathematics  (r=+0.3l);  a priori  course.  statistics  -skills  an  successful,  detect  and H a l p e r i n  statistically  was  18.5%,  The  also  undergraduate  mathematics  psychology  read;  subjective  of  51.3%,  been  and a f f e c t i v e  introductory  were  towards  essay-writing  and p r e d i c t i o n s  multiple  used to  Feinberg  to  order  for  had  the  (57:23).  cognitive  and,  variables  respectively.  process  the  "B";  toward  material  procedure  in  accounted  predictive  equation  retain a  self-rating  variance  ratio  attitude  attitude  "C".  attitudinal, four  presentations;  experiments;  to  second regression  all  blocks  oral  responsibility;  ability  of  a  at  laboratory  speed;  attaining  skill  - social  preference mental  of  of  ability  rating  of  mathematics relative  1 7  to  the  class  relative  to  The first, the  other  that  an  of  the  attempt  independent  attributed  this  independent  variables  4.8%  and  variables  16%  of  the  judgement  "success"  the  Halperin  four  attitudes ability; from in  of  Vasu  tests  of  observed about  cannot  (1980)  who  correlated  degree be  and  of  made,  three  obtained  any  very  in  only  the  of  the  high.  accounting  administered (attitudes  for  The between  achievement. commonality  since  An  and  the  Feinberg  biographic)  were  enrolled Of  with  and  the  overall towards  "child  visualization  29 m e a s u r e s towards  sex-roles;  or  attitudes  r=+0.25,  spatial  0.40,  variance the  statistics.  measuring  reproduction",  and  inter-  significant  of  themselves,  among  possible  achievement, none  from  authors  commonality  achievement  by  The  statistically  However,  -0.22  of  revealed,  statistics  thirty-six  statistics  were,  and demographic  inferential  the  in  successful.  degree  eight  feminism and  11 d i s c i p l i n e s  scales  Of  variables  towards  significantly  high  not  matrix  ability  and  neither.  and  types  achievement  statistics  regression  reported  Elmore  the  and  between  independent of  to  area  mathematics  correlation  was  (p>0.05).  between  ranged  (r=+0.25).  predict  the  non-significant  values  major  variables.  among  independent  of  variables  correlations  correlations  in  perceptions  resulting  to  result  independent  were  and  students  analysis  16  the  (r=+0.33);  in  29  (Paper  variables, mark.  feminism  care",  students  introductory  course  course 15  were  Two  were  (i.e.,  r=-0.3l).  Folding,  of  visualization  188 g r a d u a t e  an  one  mathematics;  spatial  to  of  "human  Three  r=+0.45,  were  Surface  18  Development,  r=+0.35,  remaining  eight  mathematics  (the  Two  of  the  and  tests range  were  of  Comparisons,  measures  correlations  biographic  statistically  significantly  of  r=+0.26;  student,  Cube  or  attitudes  being  +0.23  demographic.  correlated  and  of  r=+0.24).  with  previous  to  The  towards +0.31).  variables  achievement  statistics  were (gender  courses  taken,  r=+0.22). A stepwise variance  in  set  29  of  subset  of  (spatial  multiple  statistics  achievement  variables.  variables  at  a  predictors  to  enlarge  of  other A  the  of  the  of  of  noncognitive  variables  greater  were  statistics 0.21  to  0.70  correlation  the  0.032  to  the  and  the  full  objects  They  one  subsets sex-role explained  respectively).  feminists  testing  the  three  variance  0.082  achievement.  by  of  eliminating  feminists  visualize  m o d e l by  for  that  towards  zero-order  statistics  Table included  2.  Only  in  Table  absolute  between  and  a  investigated  achievement in  ability  the  in  in  towards  by  46.4%  and in  sexspace,  outlined  the  plans  contributions  variables.  achievement  presented  revealed  attitudes  statistics  scope  cognitive summary  to  model  and  concluded that  addition  the  = 0.051,  The  were  R-square  that  accounted  to  in  in  was  significantly  (reductions  roles,  time  attitudes  contributed  authors  revealed  Reducing  visualization,  measures)  regression  and  number in  of  these  correlations  the  value.  verbal  correlations  2.  The  various With  reasoning  and  the  cognitive  and  studies  is  seven which  were  correlations predictors the  between  or  between  ranged  exception  statistics  |0.20|  of  from the  achievement  Correlations Variables  19 Table 2 of C o g n i t i v e and N o n c o g n i t i v e with S t a t i s t i c s Achievement  Variable Basic  Mathematics  Correlation Skills:  Verbal Reasoning: Abstract Reasoning: Reading Comprehension: Reading Speed: Spatial Visualization: Cube C o m p a r i s o n s S u r f a c e Development Paper F o l d i n g A t t i t u d e Toward Statistics: A t t i t u d e Toward Quantitative Concepts: A t t i t u d e Towards M a t h e m a t i c s : M a t h e m a t i c s As M a l e D o m a i n : U s e f u l n e s s of M a t h e m a t i c s : Mother's Attitude: Father's Attitude: A t t i t u d e Toward S u c c e s s in Mathematics: Effectence Motivation: Teacher's Attitude: Self-Confidence: State Anxiety: . A t t i t u d e s Toward P s y c h o l o g y : Value of Psychology: Preference for Laboratory Experiments A t t i t u d e s Toward F e m i n i s t s : Human R e p r o d u c t i o n : Child Care: MMPI S c a l e (Femininity): Self-Ratings: Arithmetic: Relative to C l a s s : R e l a t i v e to Majors: Mathematics Coursework: Number o f C o u r s e s : Success in Courses: S t a t i s t i c s Course Taken: Gender of Subject: Expected Course Grade: Subjective Probabilities:  0.45 0.40 0.70 0.42 0.47 0.58  to  0 . 57  0.24 0.35 0.45 0.33  Authors M&M* F&H H&H . H&H H&H H&H E&V E&V E&V  to  0 . 54  R&B  0.35  F&H  0.23 0.23 0.25 0.27  E&V E&V E&V E&V  0.27 0.29 0.29 0.31  E&V E&V E&V E&V  -0.22  F&H  0.32  H&H  -0.21  H&H  -0.25 -0.31 0.25  E&V E&V E&V  0.26 0.33 0.25  H&H F&H F&H  0.34 0.31 0.22 0.26 0.33 -0.24  F&H F&H E&V E&V F&H H&H  to  0 . 42  * M&M=Michael and M i c h a e l ( 1 9 6 9 ) ; R & B = R o b e r t s and B i l d e r b a c k (1980); F&H=Feinberg and Halperin (1978); H&H=Hartley and Hartley ( 1 9 7 6 ) ; E&V=Elmore and V a s u (1980).  20  reported  by  Hartley  | 0 . 6 0 | was  correlations  variables between  were,  in  mathematics 1980). 49%  the  typical  for  the  with  for  investigated  typical  variance constructs frequently to  above  4%  to  the  were  in  the  Aiken,  body  for or  in  would  be  variance  of  Kulm, 6%  to  arithmetic  approximately  range  overall  1976;  accounted  variables  those  16%.  A  about  9%  accounted  29%.  of  of  of  the  the  1979),  discussed investigated academic  may,  an  Of  the  literature,  has  been  the  account  for  achievement of  the  motivational  perhaps  relationship  (Atkinson, been  in  fact,  the  the  variance  academic  in  has  considered the  in  who  "effectance  unknown p e r c e n t a g e  achievement.  achievement  motive  to  overall  and  (1980),  called  variables  in  Vasu  reviewed  Motivation,  statistics  Achievement  studies  variance  Gale,  and  attitude  motivational  20% o f and  Elmore  of  achievement.  in  of  cognitive  This  mathematics  noncognitive  measure none  contribution  (Hakstian  (e.g.,  value  with  than  consensus  in  and  variables.  variables  variance  the  higher  literature  exception  a  motivation",  much a s  correlation  Variables the  statistics  general  cognitive  approximately  With  motive  a  slightly  the  observed variance,  Motivational  as  with  observed  value  being  no  achievement  noncognitive  achievement  achievement,  of  accord  and  Specifically,  of  between  generally,  achievement is  (1976),  reported.  The  result  and H a r t l e y  of  the  most  achievement  1978).  defined  as  "a  pattern  of  21  planning achieve is  of some  toward  it  actions  has  obtained  achievement  itself" that  interpretation  opinion  achievement of  can  is  is  difference  less  between to  given  a  than  an  From  25% o f  the  direct  This  theoretical  of  this for  a  achievement.  the  finding  ability  account  academic  20% a n d  variables.  empirical  be  hypothesized to in  Further, in  1978).  to  attitude  justification  (Atkinson,  attributable  the  no  be  striving  261).  c o n d i t i o n s may  variance  that  motivational  with  with  the  1977, p.  measured  interpretation  p r o p o r t i o n of  Atkinson's  a  with  e x c e l l e n c e . . . the  (Vidler,  achievement-oriented  motivation  connected  of  under  measurable  accord  standard  stated  perspective,  in  feelings  been  ability-oriented  effects  of  internalized  motivational  in  and  variance  and  indirect stance  Hakstian  and  is  Gale  (1979).  the For  However,  the  variance  in  example,  research  in  achievement  10%  exists.  (Vidler,  that of  of  the  achievement reported  has  been  Further, motivation to  1977).  a measure  contribution  of  is  that  relationship  relationship  performance  only  the  achievement  no  reported  (1977)  which  relationship  bear  academic  Vidler  and academic  increase  magnitude  by  observed  most  attention  in  their  motivation  of  that of  no  training  motivation" measure  strong  academic  Vasu  (1980)  accounted of  to  programs  in  and  of  motive  attempts  increases Elmore  finding  achievement  is  to  controversial.  general  results  means  "effectance  variance  the  studied  Finally,  the  highly  between  the  of  for  statistics  achievement. Although  in  the  literature  has  been  focused  22  on  achievement  motive  some a t t e n t i o n . perception striving work  of  for  of  by  achievement  This  to  a  are  undertaking the  a  task,  and  who  as  analysis  the  testing  from  theory.  latent the  and  is  are  derived,  being  more  perceived  a  received  task  Both  is  and  may  drawn  b)  underlie from  the  contingent  and  paths  are  those  consistent  with  future  paths.  the  These  immediate  variables"  variables"  constructs  stated  present  Both  which  is  an  and  and  reasons future  have for  utility  is  analytic  method  of in  turn  using  this  of  present  be  used  of  which  extension  are  then the  values•obtained  from  the  two  of  derived "causal"  test  the  modeling also  models  allow  chapter,  models  to  "Causal  constructs  which  facilitates  strength  approach  an  which  "causal"  the  procedures  model  of  1980).  hypothetical models  Modeling  Variables  testing  approach  the  the  can  (Wolfle,  theoretical section  Causal  formulation  (LVM)  latter  into  Latent  estimates  formulation  The  and  quantitative  model  incorporates  1980).  task.  Contingent  the  explicit  formulated  theory.  a  Numerical  explicit  which  in  have  task.  Path  the  succeed  a  as  with  of  aspects  investigated  goal.  Path A n a l y s i s  effects  to  of  noncontingent  operationalized  other  interpretation  individual  than  motive  (1978),  paths the  a)  two  usefulness  Raynor  perceived  Of  the  are  success.  noncontingent  been  They  itself,  of  fit with  .facilitates  derived  from  path  analysis,  called  "latent  tested  (Bentler,  testing sample  of  a  data.  In  approaches  are  23  discussed  with  Like  are  the  and  residuals  of  major  the  other  of  Figures LVM,  child  path  are  empirical 1 and  yield  values  multiple  treated  by  an  The  Both  to  about  user  of  have  both  of  structural  the  of  represent  equal  each  other  equations.  latter,  researcher  as  rather  (Wolfle,  that  techniques  the  the both  of  zero,  LVM  analyze  assumes  in  example  the  information  relationships  2 depict  used  regression  that,  and  regression,  the  relationships  respectively.  are  independent in  is  theoretical  analysis  which  multiple  variables between  examples.  variables.  statistically  results  simple  which  of  approaches  of  statements  and  expected  difference  statements  of  techniques  user  explanatory  computational  an  the  are  two  pair  among t h e  have  and  the  The  and  matrix,  like  variances,  a  regression,  relationships  techniques,  of  statistical  correlation  linear  aid  multiple  approaches a  the  and the  explicit than  as  1980).  a path-analytic models  of  model  achievement  education^ vocabulary  child  IQ Figure 1 P a t h - A n a l y t i c Model of Adult Vocabulary Score  on  vocabulary  the  three  independent  and  IQ  adult,  of  vocabulary  tests  as  score)  in  adults.  variables,  influencing in  The  a  path-analytic  education the  "causal"  of  child,  dependent  way.  Adult  model IQ  of  variable IQ  exerts  treats child (adult  a  direct  24  influence;  the  remaining  two  variables  exert  their  influence  indirectly. The  LVM  variables  shown  as  did  hypothetical  in  Figure  the  2  includes  path-analytic  constructs,  or  the  model.  latent  child  variables  two  have  been  adult f IQ  adult  intelligence  measured  However,  child education  same  intelligence adult vocabulary  Figure 2 LVM M o d e l o f Adult Vocabulary Score postulated. being  The  measured  manifestations  variable,  Child  measures  of  variables,  Adult  The  applied.  of  term  literature  a  plethora  In  this  IQ the  for  Wolfle analytic  a  latent  latent  variable is  Campbell  word  as  of  on  "cause"  have  The  the  Child.  Score Adult  in  as  latent  scores  The  of  on  measured  Adult,  are  Intelligence. encountered  explained,  (1979)  views  in  the  discussed  or  observed,  the  subject  is  meant  of only  there  exist  causality. to  be  a  the  use  of  explanation.  explained  procedures  is  interpreted  variables.  frequently  analysis  are  changes  Education Vocabulary  plausible  (1980)  two  and  philosophical the  variables  "causes"  and  path  thesis,  designation  IQ  Cook and of  the  "cause"  when As  of  Intelligence,  Child  manifestations  path  four  the  follows:  main  advantage  of  25  Probably the g r e a t e s t advantage of path analysis i s t h a t i t p r o v i d e s a means by w h i c h t h e n a t u r e o f the p r o b l e m a d d r e s s e d b y a n e m p i r i c a l s t u d y may be h a n d i l y summarized. It r e q u i r e s the r e s e a r c h e r to t h i n k about cause, p a r t i c u l a r l y systems of i n t e r c a u s a l connections ...and provides an explicit link between a p r i o r i theoretical notions of causal connections and q u a n t i t a t i v e estimates of c a u s a l impact. (p. 184) However,  Bentler  manifest  variables  such  as  those  sampling  (1980) (as  pointed  is  usual  discussed  and measurement  out  with  by  that path  Wolfle)  error.  He  are  models  based  analytic highly  only  on  procedures sensitive  to  stated:  T h u s , of p a r t i c u l a r importance, I believe, is the modeling of a p r o c e s s at the l e v e l of l a t e n t rather than measured v a r i a b l e s (MV), since the MV's only rarely correspond in a one-to-one f a s h i o n with the constructs of interest to the researcher... conclusions about a n MV m o d e l c a n n o t b e r e l i e d u p o n , s i n c e v a r i o u s t h e o r e t i c a l e f f e c t s w i l l o f n e c e s s i t y be estimated in a b i a s e d manner. They also will not replicate in other studies that are i d e n t i c a l except f o r the l e v e l of p r e c i s i o n of e r r o r in the variables. T h u s , t h e m a i n v i r t u e s o f LVMs are t h e i r ability to separate error from meaningful effects and the associated parametric i n v a r i a n c e . . . (p. 434)  LVM's  may  be  exploratory  or  either  examine  to  plausible  to  in  the  the  confirmatory  to in  or  relationships  exploratory area  of  projects  nature.  observed  explanations  hypothetical is  applied  test  (either  context  that  correlates  and  in  a  previously  theory-  the  are  An LVM m o d e l  relationships to  which  or  may  be  used  search  for  formulated  data-based).  LVM a p p r o a c h  determinants  either  of  was  It  applied statistics  achievement.  Three  It  may  be  concluded  Exploratory  from  the  Models  review  of  the  literature  of  26  the  correlates  statistics  and d e t e r m i n a n t s  that  epistemological in  which  abstract other not  any  It  information  decided  hypothetical  area.  It  of  the  by  statistics  achievement.  that  of  grades  found  statistics,  with  statistics  with  general  cognitive  of  In  variables  of  and  indirect  further  to  in  which have  date  have  effects  of  included  the  an  these  some  LVM  over  path  measured  in  contribution  and c o n t r a s t e d  study  a of  with  variables. were  highly  those  with to  obtained  (e.g.,  included  models,  the  the  of  could  compared a c r o s s  hypothesized  because  the  on  c o u l d be  relatively  of  variables  and e x p e r i e n t i a l  were  state  LVM a p p r o a c h  of  examined,  for  the  latent  be  addition, be  "attitude",  alternative  effects  achievement  selected  (e.g.,  motivation)  studies  could  selected  which  but  the  advantages  the  achievement  academic  several  the  correlate or  stage,  achievement  indicated,  First,  effects  attitudinal  to  could  ways.  could  measured v a r i a b l e s  been in  way.  of  young  descriptive  "cognition",  Effects of  a  LVM a p p r o a c h w h i c h  of  above,  variables  cognitive,  The have  Because  error-free  motivational  direct  introductory  statistics.  an  two  indirect  mentioned  relatively  in  that  in  at  been  Further,  about  examination  and  models.  analysis  so  be  in  relatively  achievement  "experience"  do  the  direct  several  and  could  indicate,  have  (e.g.  constructs  "motivation",  to  a  correlates  on a c h i e v e m e n t  was  in  appears  investigated.  little  achievement  is  reasoning)  correlates  been  variable  It  important  logical  potential  yielded  area  state.  some  or  yet  the  of  which  scores  correlate  correlations  motivation).  arithmetic  or  skills  The and  27  numeric  concept  finding).;  learning  verbal  findings  reasoning  of  The  statistics  and  Roberts  and  (1978)),  and  and  on  based  and  Elmore  and Vasu  Three study. the the the be  are  latent  latent noted  to  hypothesized latent  which  the  shown  variables  to  the  be  no  for  Figures  towards of  and  Halperin  of  Hartley  selected  (1978)  and  perceived  for  Raynor  utility  experiential  and  variable  and H a l p e r i n  are  3,  included  listed  in  the  manifested  in  Figure five  (1978)  and  the  the  to  manifestations  be  only  in  of  Figure  4 and  those That  is,  5.  names  of  Only  It  should are  "Cognition"  is  variables.  are  attitudinal  of  3.  variables  measured  "Motivation" three  The  present  5.  Figures  3.  in  4 and  cognitive  and  in  similarly and  three  respectively.  guidance  placement  examination  hypothesized  "Attitude"  motivational  regard  Feinberg  manifestations  to  was  are  manifest  variables  in  are  variables  hypothesized  There  of  an  (1980)  findings  variables  motive, of  on  on and  attitude  findings  Atkinson  inclusion  presented  those to  by  considered  variables that  on  based  Vasu's  Feinberg  motivational  findings  were  11 v a r i a b l e s three  of  (both  (1980).  models  They  identical  The  the  The  and  (based  (based  achievement  motivation. on  and  (1969)  (1976));  included  research  (1980)  research  included  based  variables  The  reasoning  Elmore  self-esteem  were  specific was  academic  and M i c h a e l ' s  Hartley  on  towards  Bilderback  (1976)).  (1978)  and  attitudinal attitude  on M i c h a e l abstract  (based  Hartley  study  and  Hartley  spatial/visualization finding).  (based  of  path  available vectors,  in to  the the  literature weights  to  with be  28 Verbal Comprehension Number Facility L o g i c a l Reasoning Visualization Numeric Concept L e a r n i n g  -Cognition  Attitude to Statistics Self-Concept Attitude to Research  <  Achievement  Attitude  Need Achievement Perceived Utility Specific Motivation  -Motivat ion  ExperienceFigure 3 E x p l o r a t o r y Model "A" of S t a t i s t i c s Achievement assigned effects many  to of  any  any  independent  different  present  models  study,  considered  to  the  be  Formulating has  been  multiple fuller the  particular  ordered and  model  of  of  indirect several  "hunches  and  guesses"  thereby  advancing  Under  selected  direct  these  for  evaluating  Bentler  (1978),  can  it  a  make  or  indirect  circumstances,  tested.  In  the  investigation  were  effects  is  may  into  more  a  possible  to  When t h e  rigorous  the and  this  way  noted  that  attain  nature  a  of  the  formulation  and  incorporation  of  known,  facilitate  of  in  has  little  construction  models who  phenomenon.  models  the  the  complexity.  formulations  and  evaluation  in  to  h y p o t h e s i z e d and  models  by  understanding  direct  be  subsequently  recommended  or  variable.  could  three  path,  accurate  theory  in  the  model, area  of  interest. The  three  elementary. only,  and  no  models  Model indirect  "A"  selected (Figure  effects  of  for 3) any  examination  hypothesizes variable,  are  rather  direct  effects  on  statistics  29  achievement. Model  "C"  Exploratory  is  Model  more  "A"  is  a model  session.  a  under  which  independent  complex  is  circumstances  which  reflects  directly  to  between  pair  the  any  variable  with  of  past  the  data fact  somewhat  more  complex.  representation  were that  collected. the  collected  latent  contribute  is  literal  the  were  three  "B"  s t i l l .  somewhat  variables The  model  and  single  achievement. latent  experience,  of  the  Further,  is,  it 12  same  test  variable  no  or  the  the  manifest  variables,  was  That  measures  during  of  covariance  of  a  latent  hypothesized.  Cognition^ Achievement Motivation Figure 4 E x p l o r a t o r y Model "B" of S t a t i s t i c s Achievement  Models manifest its  "B"  and  variable  temporal  "C",  Experience  position.  Experience  is  11 m a n i f e s t  variables,  influenced  the  Model effect  "B"  measured  three  Attitude  and  is  felt  as  during it  other  defined is, the  reflects  latent  is  the  That  (Figure  on a c h i e v e m e n t  achievement  on  past  place  the  the as  event,  fact  in  that  are  the  other  which  may  have  variables.  that  Motivation.  both  investigation  session  4) h y p o t h e s i z e s  through  this  despite  same a  in  hand,  of  that  the  Experience.  only  The  indirect  effect  the  direct  influences  of  No  other  indirect  effects  on  Cognition, are  30 Experience  >• C o g n i t i o n  >. A c h i e v e m e n t  t  Attitude  .  .t  Motivation Figure 5 E x p l o r a t o r y Model " C " of S t a t i s t i c s Achievement hypothesized. Motivation effect  and  Attitude,  Model  Experience  "B",  exerts  on  to  through  effect  its  directly  influence latent  in  influence  are  model  "C"  (Figure  indirect  of  covary  effect  Attitude an  and  influence  on C o g n i t i o n . alone,  of  a  direct  also  hypothesizes  on A c h i e v e m e n t Motivation. directly  in  the  direct  to  model  literature  (Atkinson,  have  themselves.  Motivation  the  Cognition,  among  5)  both  shift  from  motivational  to  consequently  The  complexity  motivation  variables,  hypothesized to  Motivation,  the  latent  not  Achievement.  the in  the  and  on A t t i t u d e  on  speculation the  exert  variable,  increase  an  Cognition,  hypothesized  act  of  on a c h i e v e m e n t ,  Like  effect  Each  is  1978).  through  its  Attitude  is  and  indirectly,  hypothesized  exerting  no  effect  type  which the  to  direct of  the  is  an  reflects  the  nature  of  indirect,  about  that  31  Chapter  III.  Method  The which  procedures  were  presented  chapter.  The  variables  followed  and  the  second  of  subjects  the  is  and  used  dependent the  of  the  chapter  analysis  procedures.  are  is  the  described the  the  12  in  to  in  first.  obtain  the  procedures detail.  description  of  this  independent  described  followed  questions  described  measure  Third,  are  the- r e s e a r c h  are  to  procedure  preparation  II  variable  presented.  section  explore  Chapter  instruments  section,  collection  in  to  In  samples of  data  The  the  final  preliminary  Instruments Measures Of were  of the  the  measures  developed  remaining  Independent  nine  and  together  each,  listed  for  which  measures  the  twelve  independent  pilot-tested  were  variables, are  of  Variables  for  selected  from  with  the  name  3.  The  in  Table  were  developed  this  the of  study,  the  test  used  the  The  12  to  independent  pilot-tested  are  three  while  literature.  three  and  variables,  measure  variables marked  by  asterisks. In  the  presented  in  description  following the of  order the  description, in  which  procedure  the  they  used  to  manifest  are  listed  develop  variables in  and  Table  3.  pilot-test  are The the  32 Table Measures  Latent  Variable  3  of the M a n i f e s t V a r i a b l e s and Underlying Latent Variable  Manifest  Variable  the  Measure  Cognitive  Verbal  Attitudinal  Attitude Toward Attitude Toward Statistics* Statistics A t t i t u d e Toward A t t i t u d e Toward Research* Academic S e l f - C o n c e p t •Self-Concept  Advanced Vocabulary Test L o g i c a l Reasoning Diagramming Relat ions Number Facility M u l t i p l i c a t i o n and Subtraction Spatial V i s u a l i z a t i o n Paper Folding Concept L e a r n i n g * Concept Learning  Motivat ional  —  *  *  Comprehension  *  Achievement M o t i v a t i o n Perceived Utility Specific Motivation  _  *  *  -  *  *  Experience  _  *  *  Research  -**  *Developed and p i l o t - t e s t e d f o r t h i s study. * * T h i s m e a s u r e was n o t g i v e n a t i t l e . * * * T h i s m a n i f e s t v a r i a b l e .was n o t a s s i g n e d t o latent variable.  a  three  "new"  variable  and  the  Verbal  Advanced Vocabulary  Test  Harman  parts  requires a  of  (1976). gradients. is  four  stimulus  choose  included  Comprehension.  difficulty the  is  under  the  respective  name.  Verbal using  instruments  the  correct  The  test  minutes word  most  of  Each  testing  followed  synonymous  choices  by  developed  consists  No e v i d e n c e  presented.  comprehension  for  parts.  parts  parallel  Each  choices, The For  a  measured  Ekstrom,  contains  time.  alternate.  on b o t h  two  the  part  five  of  by  was  item  of  of  items  and  made  from which  score sample  is of  similar  nature  18 is  French  up  of  subjects  the  number  181  college  33  students,  Ekstrom  13.8,  standard  a  coefficient With test  collected  aI.  deviation  to  the  measures  of  data  on  Hartley  this and  correlated  0.70  with  The  is  use  The in  to  administered  Logical  of  Relationships similar  illustrates  objects. time.  to  "over  12.1,  a  500"  naval  of  the  subtest  was  of  severe  of  the  Verbal  Aptitude  Test  achievement.  Advanced not  on  which  literature.  that  Vocabulary  selected on  measures  limit  this  study  the  constraints  number  Test of  the  part  et  15  items  one  of  logical  the  for  available  which time  were  that  test  is  the  total  al.  (1976)  5.2  they and  et  ability al.,  each.  For  Venn  any  takes  four  number  of  administered obtained an  was  which  each  item, which  among a  set  minutes  of  correct this  a mean  internal  a  1976),  diagrams  relationships  the  of  this  five  of  recruits,  deviation  of  (Ekstrom  select  score  When E k s t r o m  standard  coefficient  to  Each The  to  measure  parts  best  responses.  consistency  no  statistics  task  the  The  they  testing  of  take.  asked  three  of  because  imposed a  are  of  mean  between  Differential  measure of  in  observed  the  type  subjects feel  identified  (1976)  study  could  two  was  Aptitude  Reasoning.  Diagramming  internal  achievement,  Specifically,  measure  consists  in  present  time.  single  an  statistics  of  Differential  testing be  and  observed  relationship  their  similar  the  5.2  an  hypothesized  Hartley  subtest  Test.  reported  of  measure  Comprehension  test  (1976)  0.79.  regard  and  However,  of  et  item test  score  of  consistency  0.79.  No p r e v i o u s  investigation  appears  to  have  used  this  measure  34  in  an  attempt  achievement. similar  to  account  However,  measure,  Aptitude  achievement.  Again,  administered  et  Number test  of  consists  taking  two  with  number  a  total  of  administered recruits. of  19.3,  a  a  two  a  found  subtest  0.42  subtest  test  measure  parts  testing  part, row  a  of  was  that from  with  a the  statistics  too  long  to  be  Diagramming  tapping  chosen  of  row 10  similar  of  skills  the  standard  deviation  half  is  test  Ekstrom  of  this  resulting of  has  data  9.1  and  single  to  her  is  two-digit score,  the  colleagues  "over  yielded an  60  subtractions  and  test  part  up o f  a  a  1976),  each  made  of  a  was  al.,  difficulty,  10 t w o - d i g i t  The  ability  et  multiplications  half  of  this  (Ekstrom  Each  responses.  first  for  similar  time.  number.  correct  the  of  statistics  investigation.  be  Analysis  coefficient This  to  one-digit  number  particular  The  of  each  alternated  correlated  in  (1976)  Reasoning  and M u l t i p l i c a t i o n  of  minutes  In  and H a r t l e y  this  Facility.  which  by  this  variance  ,1976).  Subtraction  items.  Test,  appears  al.  the  Abstract  during  Relationships (Ekstrom  Hartley  the  Differential  for  a  500" mean  internal  naval score  consistency  0.86.  measure  explain  the  however,  two  Michael  (1969)  combined  with  observed  variance  Halperin  (1977)  has  not  variance reported  one  been  in  of  that  of  algebraic  in  course  observed  in  any  statistics  results  reported  used  a  achievement. relevance.  measure  skills  marks a  some  in  identified  of  statistics. of  0.40  for  to  There  are,  Michael  and  arithmetic  accounted  correlation  attempt  ability  22.1% of Feinberg  (accounting  the and for  35  16%  of  the  variance)  statistics  Paper  again,  of  contains item a to  two  items  sheet  all  the  fully  mathematics  skills  and  subject's  diagrams  length  that  m e a s u r e d by  which  a  test  consists,  once  and d i f f i c u l t y .  minutes  final  hole  was  1976),  drawings,  The  one  al.,  three  three  ability  of  testing  successive  drawing  is  depicts  to  shows,  how  select the  in  half Each  made  in  addition  layers  the  paper  time.  folds  punched through a l l  task  Each  of  the  correct  might  one  look  when  reopened.  yielded  of  a mean  internal  of  the  Sherman,  13.8,  this  correlate  of  direct  (1980),  who  in  for  a  0.84  has  attracted  was  between  study.  not  The  of  (Ekstrom  mathematics  introductory  46 c o l l e g e  relationship  in  of  0.45  as  high  measure  al.,  an  1976). spatial  achievement  (e.g.,  little  by  attention The  Elmore  between They  0.24  this  as  Vasu  measure  reported  that  measures  and  a  single  and  this  and other  (i.e., of  et  and  between  statistics. achievement  students  4.5  statistics.  reported  correlation  were  from  deviation  achievement  Learning. this  of  a  and  relevance  visualization  developed  of  of  correlations  Concept  standard  ability  obtained  achievement  obtained  a  collected  coefficient  ability  1980),  possible  results  finding  visualization  spatial  test  consistency  Despite  and  or  paper.  The  Analysis  study  two  et  similar takes  folds,  paper.  five  of  and  of  This  (Ekstrom  parts  d e p i c t s , , in  folded of  Visualization.  Folding  10  square  basic  achievement.  Spatial of  between  of  0.35).  variable  was  36  The a  initial  one-half  nine  sigma.  described The task  in  two  Education. learning the  of  is  understanding the  and  number  of  was  not of  to  the  any  of  a  form  (see  first the  the  B).  The  master  but  is  unknown  description  of  the  one The  mentioned  subscript  of  in  instructions  the  to  concept  as  an  plus of  the  the  usual  subscripts  was  the  order for  was  to  was  concept  which in  (should  any  fundamental  to  mean  subjects was  23  mean  correct  correctly pattern  Further,  very  of few  item. was of  simplified, items  summation  entering limited,  task  number had  essential  the  to  the  no c l e a r  items.  number  is  administered  (n=15,8),  the  other  of  make  the  required  students  is  description  most  concept  A)  and  eight  it  to  It  there  concept  above,  the  such a concept  23  any  and  as  algebraic  students  remaining  since,  over  two  of  statistics.  item,  accordingly,  Appendix  for  statistics  4.65,  19 . o f  responded c o r r e c t l y  13  is  (Appendix  was  subjects  revised  and  effort.  Education  to  items  "summation",  selected  it  wasted  response  Consequently,  was  learning  attempted  Although  responded  understanding  one  introductory  fourth-year  1.48.  tested  beginning  the  initial  items  composed  of  substituted  over  First,  most  Second,  When  was  concept  was  "summation"  to  occur)  third-  notation  reasons.  unfamiliar  the  A)  test.  concept  for  (Appendix  which  Summation  the  task  of  items  Unfamiliar  capital  this  description  computational  concept.  is  page  form of  increased was  for  students  task  less  did  not  to  to  retained  students.  however,  the  to The  summation  difficult. mention  any  37  strategies task,  or  beyond  a  description you  can  do  entered  item  their  general  statement  the  that  while  in  any  answers  the  items  to  12 m i n u t e s .  The  for  the  "you  completion  can  answering order in  score  the  you  the was  refer  the  to  the  questions,  wish".  spaces the  of  and  Subjects  provided.  number  of  The  correct  responses.  support  support, the  this  claims in  measure of  terms  reported  a  Feinberg  Michael  of  and  mathematical  validity  of  Halperin  for  can  Michael  0.47 of  between  found  correlated  0.40  study,  data some  be m a r s h a l l e d for  statistics  achievement Further,  a measure  course  from  example,  concepts.  that  with  no  However,  (1969),  algebraic  (1978)  this  existed.  validity,  and  learning  skills  developed  construct  correlation  a measure  was  empirical  of  literature.  and  concept  aids  questions  was  Because to  cognitive  of the  time-limit  other  of  basic  achievement  in  statistics.  Attitude was of  developed 32  items  subject's of  for  was  The  this  of  statistics/research the  An  agreement or of  about  design  from p e r s o n a l  on a  seven-point  a  items areas  scale,  by  about was  this  inquired about  about  some  C) the  facet  statistics.  concern The  of  variable  (Appendix  constructed  of  Extent  of pool  statement  faculty  with  item item  students.  experience.  Likert  Each  thinking  most  measure  initial  with  literature,  and  The  constructed.  pool  statements  in  study.  calculating  initial  identified  Statistics.  first  degree  studying,  included  Toward  and  to  were  graduate  1  that  it  introductory  areas  agreement  point  so  was  being  those  students, measured "strongly  38  disagree" was  and  provided,  the  items  score  point labelled  were  was.equal  items  of  to  the  The  the  randomly  section.  The  65  items  students  The  of  of  the  selection  and  of  beginning  Item a n a l y s i s  of  33  items  0.50  or  greater  the  positive  with  the  selected  with  and  total  and p o s i t i v e are  left-hand  the  the  or  design  inclusion  naive  total  of  toward  initial in  to  next  120 t h i r d -  and  courses.  were  design. was  items  the  Psychology  solicited  The  exclusion  intended  subjects  but  for  which  to  allow  (corresponding  which in  Table  the 4  final the  items  a  to  scale  left-hand  item  of  into  the  contains  a  of  each or  of  of  higher  pool,  items  column  in  reflected  (Appendix  groups  27  correlated  0.50  group,  original  were merged  also  ten  correlated as  that  statistics  The  which  the  for  revealed  towards  s t i l l ,  in the  data  score.  poles  statistics  polarity,  column  33  subjects,  it  statistics.  described  courses  attitudes  included  reported  the  research  after  attitude  administered  which  The  Therefore,  towards  Educational  of  negatively.  reversed.  with  Half  responses,  measuring  pilot-study  negative  score,  concern for  from  half  point  statistics).  concerning  Descriptive  scale  research  in  of  in  statistics  students  been  attitude  then  enrolled  disagree'.  and  Research,  were  A neutral  numeric  combined  statistically  the  areas  had  agree".  nor  the  items  courses  emphasize  statistics  of  Toward  fourth-year content  of  positive  was  Attitude  not  of  pool  measuring  did  total  polarity  degree  agree  positively,  32-item  statistics  "strongly  "neither  worded  negative  reflected  7 being  all were  B). of  negative  final  20-item  Table  4.  description  The of  39 Table 4 Item and S c a l e S t a t i s t i c s the A t t i t u d e Scales (n=120)  for  Statistics Item s t a t i s t i c s : Positive items: No. of Items Mean Mean s . d . Mean i t e m / t o t a l Negative items: No. of Items Mean Mean s . d . Mean i t e m / t o t a l Scale  for  the  indicate  calculated 20  items  that  items  display  sufficient  persons.  Responses  neutral item  point.  scale  Further,  The  total  theoretical  below.  corr.  10 4.01 1 .78 0.64  1 0 4.52 1 .64 0.62  20 74.02 22.42 5.60 0.93  20 84.69 21 . 7 5 5.50 0.93  were of  in  the t o t a l  selected of  for  both  variance are,  on  that  scores  of  randomly Attitude  vary  a  final  negative to  Toward  the  form.  120  presented  enough The  with  to  for  (Appendix  B),  to the  the  items  described  20-  possible  close In  twenty  the  the  consistent.  allow is  among  about  scale.  the  Research,  internally  mean  140-point  polarity  discrimination  statistics highly  statistics  positive  clustered  is  subjects,  The  average,  investigation  combined  of  and  allow  people  70 o n  this  it  scores  the  the  descriptive  among  value  administered  measure  10 3.79 1 .65 0.63  from  indicate  discrimination  items  corr.  10 3.50 1 .59 0.61  statistics: No. of Items Mean s.d. Stan, error H o y t ' s ANOVA  statistics  Research  the form  twenty of  the  immediately  40  This  measure  empirically validity  students of  the  for  of  of  the  univocal concern  Roberts  a  and  received  pool  of  items  which  items  item  c o m p a r i s o n was  of  the  form of  the  latter  be  their  did  each As  attitude  the of  scale  a  about  was  graduate  item,  and  group,  the  broad  and  each  major  34-item the  scale  measure  was  investigation, with  for  indeed  content  students.  this  developed  of  not  pool  sufficiently  A copy in  for  fellow  whole.  was  made w i t h  on  measure  a  statistics  used  scale  as  was  item  members a n d  pool  (1980).  items  the  initial  assessed  introductory  to  evidence  unidimensionality  the  time  the  faculty  that  to  final  that  the  Bilderback  in  comparison  of  of  statistics  some  First,  series  review  Second,  the  a  indicated  included area  to  towards  However,  gathered.  content  panel  attitude  validated.  was  submitted  of  those  this tap  the  not but  included  study  of  in  revealed  same  areas  of  concern. With  regard  investigations for  a  have  reliable  achievement.  Further, of  0.43  broader  of  issues  indicated  proportion Roberts  correlations toward  to  0.33  statistics  to and  that of  obtained  and Vasu  (1980)  between  measures  of  achievement  in  Attitude  of  variance  Bilderback  between  Elmore  construct  measures  the  and 0.54  of  their  course  reported  attitude  attitude in  measure in  observed  towards  other account  statistics  (1980)  mark an  validity,  observed  of  attitude  statistics. correlation  mathematics  and  statistics.  Toward  Research.  A  measure  of  this  variable  was  41  developed 34  for  items  was  agreement  about  most  design.  in  The  of  the  Item  of been  positive The  f o r m was  0.50 items  described  the  of  of or  of  "research". statements research  identified  graduate  of  studying,  introductory  those  C)  degree  include  "strongly  A  neutral disagree".  half  negatively. responses, The  toward  33  were  items  Attitude  each  of  the  about with of  the the  the  in  in  the  students,  and  a  was  items  of  research  combined  with  the  same  described  total  or  scale  positive  degree  resulting  of  research  design Again,  negative  items 65-item  above.  revealed  and  polarity  32  data  score.  the  design.  The  research  worded to  negative the  being  labelled  were  Statistics.  pilot-study  7  equal  reflected  subjects  Likert  and p o i n t  was  items  and  description  provided,  the  therefore  the  utilized  seven-point  score  after  were  Statistics-scale.  disagree"  The  randomly  to  on  Half  research  Toward  administered  greater  score  concern  Toward  point  nor  numeric  of  above,  Attitude  1 being  attitude  in  to  areas  point  enquiring or  about  facet design  fellow  measured  Item a n a l y s i s items  and of  that of  reversed.  measuring  by  again,  and  the  as  were  was,  agree  positively,  some  students  members,  to  agree".  "neither  to  so  (Appendix  enquired  research  concern  statements  similar  with  item  pool  experience. of  response  "strongly  had  of  item  about  devised  concern  development  scale,  total  of  faculty  personal  Each  about  was  areas  by  a manner  initial  statement  pool  areas  Sources  An  thinking  item  literature, from  a  or  initial  study.  constructed.  with  evaluating, The  this  that  28  correlated the  poles  ten which  42  correlated as  a  0.50  group,  original scale  item  column  contains items is  and  for  total of  score,  concern  selected  groups  final  Table  included  Toward  areas  were  the  statistics  somewhat  the  for  but  which  included  inclusion  in  s t i l l , in  the  the final  B).  the  of  with  all  pool,  (Appendix  polarity,  higher  reflected  Statistics  hand  or  20-item  4.  The  the  final  than  Statistics  that  scale,  items  scale  of  are  right-hand  calculated  in  higher  of  from  of  total  Except  observed the  reported  column  the  scale.  negative  for  in  positive  the  Table  scores, that  the  statistics  and  4  for  the  also the  mean  20-item  closely  right-  20  score  Attitude  resemble  each  other. This it.  scale  However,  members  and  has  a panel  valid  in  the  major  areas  statistics  Academic  items. and  terms  and  were  (Appendix  B)  The  of  of  the  to  the  the were  (1976),  with  the  and Worthen  included  list  of  because  competence  they in  indicated  No  scales  measure subject's those  that the  of  with faculty  the  scale  items  tapped  students  in  measuring  addition  The  five  appeared  statistics.  of  this  responses  investigated  research-related  (1970).  comments  introductory  The  sum o f  the  associated  this  literature.  rated  by  of  in  data  Specifically,  design.  Self-Concept•  from a  feelings  concern  identified  abstracted  were  students)  content.  research  was  validity  (utilizing  abilities  Hartley  Sanders  review  fellow-graduate  was  variable  no e m p i r i c a l  to Each  of  five  variable to  fourteen  by  Hartley  which  competencies additional be  highly  item  were  compiled abilities  relevant  requested  to the  43  subject some of  to  ability  the  The yield  the  Likert  A neutral  no  endorse,  single  was  data  are  the  relationship  10.5%  of  These  the  the  of  the  measure  dimensions  used  in  six  The  score  "tasks on  used  in  scales) I  this  his  to  subjects,  can  be to  presented  for  achievement  (1976)  study  used  no  in  reported  accounted  for  achievement.  in  this  thesis.  reported  that  self-ratings  ability  in  mathematics,  own  accounted this  for  10.1% of  perception,  achievement  too,  is  part  investigation. The the by  Shye  which  format, each  is  measure  sum o f  motive  undertake", measure  measure  summed  suitable  statistics  (1978)  ability.  and c o n s e q u e n t l y  their  in  the  of  was  form,  of  Hartley  in  end-points  were  self-concept  measuring  B)  items  lack  and  of  provided.  some e v i d e n c e  of  this  a  7="very  measure,  variance  developed  differential  seven-point  prefer",  this  Motivation.  This  of  Hartley  achievement  businessmen. semantic  for  students, item  was  fourteen  academic  An  items of  the  and H a l p e r i n  (Appendix  eighteen  "average",  perception  Achievement motivation  high"  part  other  statistics.  and  abilities  are  subject's to  low"  Because  explained  in  to  of  Feinberg  relative  1="very  example,  ratings  ratings  Further, of  For  amount  The  However, of  the  possessed.  done  available.  scale,  they  for  score.  Likert  felt  labelled  pilot-testing  the  were  endorsements  statistics.  seven-point  subjects  scale  point,  a  that  on a  and the  in  achievement  subject's  responses  (1978).  He  investigated  a  of  success-oriented  was  sample  constructed  asks of  the  of  the  the  "tasks sum o f  to  subject  three at the  resemble to  numeric  I  the  rate  concepts,  which  the  (on  "tasks  I  succeed". endorsements  44  of  each  item.  achievement Shye  for  measure  higher  motivation.  this  of  A  measure.  achievement  score  It  because  was  motive  classes  of  theory  of  by  this  contingent  summing t h e  enquired during  Utility.  his  utility  course  perceived  of  utility  no  that  questions.  of  the  statistics  to  the the  drawn  by  the  only  that  was  because  had  been  Motivation,  based  paths.  two  was  of  available.  was  to  regard  it  Specific  B)  while  be  were  of  reported  pilot-tested  would  subjects  were  degree  literature  not  noncontingent  studies, with  the  was  (Appendix  and  responses  about  It  Like  variable  in  subjects  consequently,  Perceived measure  which  selected  found  all  and  greater  data  individually-administered.  canvassed  a  No p s y c h o m e t r i c  not  from  reflects  It  The  second  on  Raynor's  was  measured  first  course  to  item  subject's  the  question  the  subject  asked  about  intended  career  path. Each scale,  item  with  nonutility. use", of  was  the  utility  was  by  the  endpoints  indicating  A neutral  point,  The  when  the  measure  by  the  was  extreme  on  the  response The  a  degrees  of  measure each  utility  useful  was  nor  simply  item  represented  five-point  of the  of  the  and no sum  negative degree  of  subject.  developed  variable  because  of  this  Because  no  subjects  were  data  calculated.  were  on  "neither  to  sum  measure  psychometric  subject  labelled  score  reversed.  perceived  This  endorsed  provided.  items,  polarity  was  was  no  identified  available  for  group-administered in  the  literature.  pilot-testing,  no  45  Specific (Appendix  B)  Motivation. consisted  from d e s c r i p t i o n s and  of  noncontingent  motivation. statistics  They  The  of  of  two  items,  both  Raynor's  (1978)  theorizing  paths  and  enquired  course  measure  and  the  their  about  which  of  reason desire  to  variable  were  about  relationship  the  strength  of  this  drawn  contingent  to  achievement  for  taking  take  the  the  course,  respectively. Each of  item  which  affect. was  wi.sh  to  indicated  take the  because  no  it"  two  testing  of  and  group  this  or  response statistics  same  as  (1978), 80%  to  that and  of  statistics  course,  the  of  Finally,  of  had  both  take  it  This  and because  nor  scale  not  was  were  variable the  to  I  take  developed  identified.in no  pilot-  The  first  and H a l p e r i n  course  found  that  measure and  the  Halperin  marks  reported  statistics  the  was  that in  a  post-algebra  (1978)  marks  is  found  class  one  B)  mathematics  (1972)  least  or  of  Feinberg  Giambra  at  (Appendix  number  (1972),  mathematics  (1980)  negative  out.  obtained  with  endpoints  items.  required  completed.  taken  Feinberg  and Vasu  is  the  extremely  variable  about  later  0.31  for  to  this  Giambra  previous  correlated Elmore  carried  inquiry  who  and  This  this  scale,  s u b j e c t s .were a v a i l a b l e ,  measure  by  subjects,  course.  completed  was  of  and V a s u d 9 8 0 ) .  mathematics number  wanted  previously  used  Elmore  his  no  single  courses  it  respectively.  measure The  positive  provided  "neither  Because  a  five-point  because  measures  Experience. the  was  "equally  items,  literature.  on a  extremely  point  labelled  for  the  endorsed  A neutral  point  it"  was  in  that  courses  statistics.  number  of  courses  46  completed  in  statistics  The  of  final  examination statistics course  test  mark  was  as  form  were of  were  items,  one  is  the  the  normal  mean,  the  standard  curve,  areas  0.22  correlational  requiring  use  Because  concepts,  it  closed-book  could  format.  and by  and  tables the  of  on  with  the the  All  been  four  variable, each  examination.  The  items the  developed  University  completed,  and  of the  thesis. items. the  Twenty-three four  statistical three graph an  open-ended  conclusion  items  in  required  depicting  the  understanding  areas  of  the  percentile. test  included  emphasized  administered  instructors  descriptive  statistics.  statistical  examination have  was  inferential of  at  Of  a  one-hour  by  of  27  a  combined with  statistics,  pool  this of  common  incorporated  format.  based  examined  included.  a  a  dependent  final  remaining  deviation  of  to  composed  The  the  testing  in  on  statistics  statement  form.  under  own  appended  was  of was  from  pilot  calculations  The  his  fixed-choice  substantive  test  selected  not  student  measure  This  No  required  elementary  the  the  introductory  examination  items  by  into  Columbia.  examination  format.  correlated  Variable  achieved  used  items  learning  The  statistics  Dependent  instructor  British  a  the  achievement.  examination to  or  achievement.  Measure The  mathematics  No  significance  items were  understanding either  chose  the  in  open-  of or  open-book  47  Subjects Target was  the  Population.  population  statistics  courses  Accessible introductory Session British  of  of  in  target  persons  statistics at  Columbia  registered  Students  course  the  and  in  the  population  for  introductory  the  University  of  British  this  and  statistics  and  elementary  research  served  as  requested  during  purpose  the  would was  of take  were  requested  The  Data were  collected  during  the  Universities  of  courses  the  Summer  as  courses  560  combined  of the  included  (Education  course  an  University  Education  design  in  served  The  six-week  and  a  sampled  482 at  at the  introductory  (Education  The  of  once  classes  potential during  brief  explanation  to  class  the  following  Collection  the  the  time,  immediately  Collection.  study  introductory  the  Victoria  and  cooperation  described  Data  one  from  class  study  this  502  Alberta).  Volunteers  subjects.  of  Columbia  Victoria),  Sample.  Alberta,  statistics  of  of  in  during  research.  University  University  of  University  three-week  the  for  registered  education  University  two  at  population  education.  Population.  1981  accessible  The  and  measures first  British  the  listed subjects  was  course.  The  each of  members,  above  the and  time  it  cooperation  explanation.  Preparation  of  class  Columbia  each period  independent of  each  and V i c t o r i a .  variable  course  at  Because  of  48  unexpected  problems  administered  to  approximately The  approximately of  containing a  copy  one  a  the  of  of  course  quarter  session,  each  the  service,  administered  and a  brief  mail  University  were  the  of  the  one-third  tests  beginning  with  each  test,  Alberta sessions  in  hours  of  a in  student  description  the  all  had  given  stapled  together  instructions  (Appendix  after  taken  place.  session  instances.  study,  were  subjects  single  was  the  tests  a  a  At  test  the  the  packet,  consent  in  of  form  order  and of  administration. Administration across the  classes.  class.  Second,  completed  the  participate measures The  First,  left  administrator tests  those  consent the  begin.  The  the  students form.  room.  timed  were  perceived  motivation, minutes),  academic attitudes  minutes),  Folding The attempt  (6  order to  motivational  of  then  did  were  read  in  (8  and  the  perceived  to  participate  did  aloud  not  for  wish  to  of - the  each  test.  sequence:  (containing  past  the  (4 Task  the  performance  measures  achievement  (5  Relationships  (12  Paper  minutes).  first,  as  attitudinal on  (10  minutes),  minutes),  selected, of  the  experience)  Diagramming  Learning  was  read  administration  and M u l t i p l i c a t i o n  contamination by  who  following  and  minutes),  Concept  was  to  statistics/research  administration  minimize  study  motivation,  self-esteem,  Test  the  standardized  stopwatch.  the  specific  toward  measures  a  were  wished  questionnaire  Subtraction  minutes)  who  using  administered  utility,  Advanced Vocabulary (8  Only  each,  of  Students  Instructions  experiential/motivational of  explanation  D)  the  an and  cognitive  49  tests.  Second,  administered  the  from  anxiety  highly  after  a  fatigue.  (the  Concept  speeded  short  break,  Finally, Learning  cognitive  the  Task)  to  allow  test  was  task  most  was  minimal likely  to  last  in  placed  sequence. The  final  dependent class  were  examination  variable)  instructors Data  Columbia. for  individual  Each  In  addition,  data  The  against  forms  (for  onto  the  final  for  Centre,  each  record  on  the  forms  (for  the  answer  fields  it  examination).  was  onto  of  the  a  British of  a  the  test  being  entered.  The  was  coded  responses by  and were  identification the  pre-tests)  No d a t a  pre-tests  sheet  checking  the  the the  identifying  examination  by  by  consisting  identifying  accompanied  verified  of  University  as  of  examinations.  number  final  file,  measure  subjects  each  investigator.  was  original  the  original  digit  disk  keypunching the  the  the  course  two-digit  the a  final  single  to  by  to  identification  response  verified  from  a a  added  keypunched  fields.  and  (i.e.,  responses  Computing  class,  item  coding  then  the  were  the  Item  at  subject  keypunched,  of  directly  each  forms  administered  part  Preparation.  stored  code  were  as  keypunched  file  the  only  immediately  interference arouse  the  or  entry  entered the  errors  coded were  tolerated. Two from each  kinds  the  of  data  measure  was  the  data  of  any  or  the  final  incomplete pool.  First,  identified subject  record  who  examination,  any  were  sought  subject  and  his/her  had  completed  but  not  who  record  out had  not  deleted.  either  both,  and  were  the  deleted attempted Second, pre-tests  eliminated  from  50  further consideration. Scoring Procedures. cognitive  measures  The  of  Verbal  S p a t i a l V i s u a l i z a t i o n and weight  "0"  of  was  chosen f o r a given assigned  the  weights  scores  item. "1".  i f an  incorrect of  The  were  "1",  correct  total  total  The  score being  of  t h e sum  responses  omitted  "4"  of the  was  were  scales  polarity,  items of n e g a t i v e The  scored  scale.  responses  i n c o r r e c t or  of  the  "0"  correct,  file,  on  the  the  measures  A t t i t u d e Toward R e s e a r c h scored.  Because  were  very  few  the s u b j e c t s , the n e u t r a l weight The  total  score  sum  of the w e i g h t s  p l u s the  sum  of the r e v e r s e d w e i g h t s  of  Academic  of the  Utility  Self-Concept,  and  Specific  summing t h e n u m e r i c r e s p o n s e  Once  again,  because  i n the data p o o l ,  a s s i g n e d to each o m i t t e d The  were  hand-scored  the  Perceived  s i m p l y by  been  of for  items of  of the  polarity.  measures  Motivation,  t h e sum  i n t o the data  a s s i g n e d t o each m i s s i n g response.  positive  had  weights.  were  by  e a c h a t t i t u d e m e a s u r e was  the  were e n t e r e d  A t t i t u d e Toward S t a t i s t i c s and the  A  responses  items of n e g a t i v e p o l a r i t y  reversed before  Facility,  weighted.  s c o r e was  t o t h a t i t e m was  weights  Responses to the  four  measure.  i f the response  respectively.  the  response  E a c h i t e m o f t h e C o n c e p t L e a r n i n g T a s k was or  of  C o m p r e h e n s i o n , Number  Choices  for a particular  each  L o g i c a l Reasoning  assigned  weight  on  the  Achievement  Motivation to  each  t h e r e were v e r y  mid-scale  value  few of  were  item  of  missing "4"  was  response.  measure of the v a r i a b l e , E x p e r i e n c e ,  was  a single  item.  51  Thus,  the  There  were The  response  to  no m i s s i n g measure  this  responses  of  the score  Achievement,  was  the  examination.  Each  item  before data  the  marks  file.  The  The  total  preliminary The  first  collected  from  the  Following  this  step,  order  to  was  score  observed  was  the  the  step  was  the  data  the  the  was  item  Columbia and  data  from  the  whether  they  could  Statistics  one-hour  two  entered item  be  into  the  marks.  completed of  Alberta  samples  final  investigator  analysis  the  score.  measure.  the  were  sum o f  analysis  the by  item  Analysis  of  this  on  hand-scored each  "total"  variable,  attained  for  the  for  Preliminary  British  determine  constituted  dependent  attained  stages.  in  item  two  the  data  samples.  were  pooled  in  for  compared the  final  analysis. The  results  revealed  that  significant rephrasing and  the  Item  of  the  these  analyses,  reported  two  samples  could  differences  between  the  the  research  consequent  questions  reformulation  of  not  be  samples  (discussed the  final  in  Chapter  merged.  4, The  necessitated  the  in  4),  Chapter  analysis  plan.  Analysis Item  analyses  dependent  and  (Nelson,  measure,  the  and  were  independent  LERTAP  error  of  mean a Hoyt  computed variables  1974). score,  The the  internal  for  each  using  program  standard consistency  the  measure computer  calculated,  deviation,  in  the  program for  the  coefficient,  of  each  standard addition  52  to the  the  other  data  samples.  Chapter  were  the  results  and  all  carried  Computing Centre  Equivalence The  together measures  of  the  samples  order  to as of  Hotelling's the  The  analysis,  facilities,  in  from  The  procedures  were  British  Columbia  of  analyses  these  identical and  are  from  for the  reported  in  4.  This  the  statistics.  collected  Alberta  at  item  a  out at  the  test  using  the  OWMAR  (Hakstian,  whether  (Timm,  (Timm,  multivariate Note  or The  used  computer  CPU  installed  470 V / 7 of  not  British  they  mean  variables  1975).  matrices 1975).  analysis 1).  Amdahl  which  was Both  of  were  could  vectors were  A test  of  be  compared analyzed  of  the  compared  the  performed statistics  variance  Columbia.  Samples.  C o l u m b i a and A l b e r t a  sample.  variance-covariance  Bartlett-Box  the  University  independent  T-square  analyses  C o l u m b i a and A l b e r t a  British  determine single  on  the  British  from  other  12  using  homogeneity  of  using  the  were  computed  computer  program  53  Chapter Preliminary  The  results  Chapter  III  As  be  will  are  pooled.  Instead,  final  analysis.  of  questions  research  modified research the  these  smaller  sample  The were  taught  place  at  Columbia of  four  one (two  Alberta.  sections  duration,  and  of  the  were  of  two the  the  were  II.  the  not  be for  exploration  Consequently,  phases  present  that  retained  analysis  analyses)  chapter.  could  prevented  the  Preliminary  this  in  procedures  (recasting are  the  presented  in  chapter.  Analysis  Sample  the  classes  Summer  three  classes), The  last  of  sample  Chapter and  described  revealed  size  sizes  recast  These  statistics  of  in  and m o d i f y i n g  third  during  smaller  posed  were  section  Alberta  The  questions  the  the  Procedures  analyses  findings  of  Results  of  initial  samples  questions  Description  first  two  accordingly.  second and  the  and  initially  Analytic  preliminary in  sample  -  and F i n a l  the  discussed,  Columbia  the  of  presented  British  the  Results  IV.  first  from which  Session  of  universities  University three  introductory  of  courses  subjects  1981.  The  were courses  - University  Victoria, listed  statistics  at  and  were a  drawn  of  of  took  British  University three-week  magistral  or  54  higher in  level  graduate  to  programs  the  University  of  was  designed  to  statistics, class,  but  again,  All  inferential of  binomial  and  for in  the  Almost agreed  to  consent  and  forms  (out  17,  exception one  16,  of  of  to  the  12 this  two  members the  high  classes  34 rate from  Two  class of  analysis  the members the  in  of  measures  of  theory,  of  the  t-test  contained, variance.  the  four  by  signing  of  set  this  statistical  classes the  pre-tests.  courses  the  University  of  during  University  members,  levels  introductory  of  set  participation  the  on  use  same  relationship  courses  three  completed  on  and  the  This  first.  probability  investigation  Columbia,  Alberta  and  and  in  taught  taught  research  one-way  32 c l a s s  British of  of  and  the  of  Lessons  of  period  Education.  were  lessons  at  skills.  histograms,  topics  completing  11 a n d  University  of  in  and  University the  class  in  held  introductory  design  measures  samples. to  in  lessons  and  distributions,  participate  Specifically, the  the  only  approximately  The  the  registered  six-week  students  and  formulation  introduction  all  not  regression).  and dependent  an  a  included  included  part class,  over  statistics  followed.  sampling  independent  fourth  contained  simple  most  research  graduate  variability,  course  The  distributions  distribution,  addition,  at  course  statistics  hypotheses,  elementary  the  and  the  place  Descriptive  frequency  (correlation  section  in  courses  tendency  took  for  proficiency  aimed  of  were  Education.  give  content.  measurement,  who  Alberta,  was  section  central  in  also  four  statistical This  students  of  offered of  at  Victoria pre-tests  respectively).  The  (92%  was  of  to  94%)  British,Columbia,  55  in  which  only  consent  12 o f  forms  the  and  26  registrants  pre-tests.  (46%)  completed  The  reason  for  this  The  preliminary  the  anomaly  is  examination  of  unknown. Integrity the  data  The  pool  first  sub-test. who  had  test  the  Data  had  two  objectives,  was The  to  were  pre-tests final  5 contains  the  numbers  post-tests,  possible  to  and  match  -  discussed  each  subject  Table  Chapter  III.  attempted  each  that  final  only  subjects  examination  subjects numbers and  who c o m p l e t e d  of  subjects  post-tests.  for  whom  With  the  Sample  Sizes PostTests  Preand PostTests  University: ~~ British ColumbiaO) B r i t i s h Columbia(2) Victoria Alberta  12 16 11 32  26 17 12 34  11 13 9 32  Total  71  89  65  of  one  to  leave  the  no  subject  subject  from  pre-testing  failed  battery.  Of  the  available,  but  not  to six  !  the  session  attempt subjects  post-test  the  5  PreTests  exception  post-  pool.  of  the  in had  ensure  the  data  pre-  Obtained  to  and  the  the  as  was  in  pre-tests, was  that  objective  both  included  Pool.  ensure  second  completed  Table  it  of  University to all for  scores,  keep  of  Victoria  a medical  subtests  in  whom p r e - t e s t all  had  failed  who  had  appointment, the  pretest  results to  were  complete  56  the  respective  courses. Item  The standard  British  Columbia  deviation,  Sample.  standard  (British  Analysis  error  Table and Hoyt  Table 6 Scale Statistics C o l u m b i a S a m p l e (n Mean  Dependent V a r i a b l e : Examination Score  2.Cognitive Measures: Advanced Vocabulary Test Paper F o l d i n g Test M u l t i p l i c a t i o n and Subtract ion Diagramming R e l a t i o n s Concept L e a r n i n g Task 3.Attitudinal Measures: Attitude Toward Statistics A t t i t u d e Toward Research Academic Self-Concept 4.Motivational Measures: Achievement Motivation Perceived Utility Specific Motivation *This  measure  coefficient dependent  for  contained  each  variables  of  the  for  the  a  contains internal  =  7.67  2.36  1 .34  26.55 1 1 .88  3.58 3.84  the  mean,  consistency  33))  Standard Deviation  32.61  Independent Variables: 1. Experience  6  Standard Error 3.63  Hoyt Coeff. 0.77  -*  —  2.16 1 .58  0.63 0.82  73.70 20.73 5.55  20.31 5.88 2.85  3.70 2.12 1.27  0.97 0.87 0.78  87.76  18.92  5.60  0.91  95.76 67.42  17.25 14.07  5.52 2.99  0.89 0.95  93.70 8.58 5.30  10.24 1 .54 1 .98  4.03 0.72 1 .09  0.84 0.78 0.72  single  item.  measures British  of  the  Columbia  independent  sample.  and  Additional  57'  item  analysis  information  is  presented  and  discussed  in  the  text. The  internal  consistency  acceptable.  This  obtained  coefficient  value  Hoyt  for  0.70  possible  by  1970).  correlations  on  be  found this  value to  (59.3%)  of  of  post-secondary  was  2.36. Of  the  five  characterized above  0.80).  Paper  coefficients cognitive  measure,  acceptably The  speeded  It  of  because  the  retest  or  of  these  were  of  (Hoyt  and  an  group basis mean  score  that,  fact  on  is of  between  -0.17  item-total  often  The  statistics  of  internal  0.87,  and  coefficient  noted  that  with the  average  speeded nature  of  the  neither  and  completed  to  be  (i.e.,  One  revealed  Hoyt other to  Subtraction,  be  may  would the  be  somewhat  An e s t i m a t e be  more  results  was  coefficient  coefficient  test.  from  with were  had  associated  Hoyt  reliability  the  number  observed  was  a  =0.78).  an  Subtraction  of  0.72,  consistency  Task,  at  Item-total  respectively.  Learning  out  average.,  courses  were  the  set  coefficients  -0.09).  two  that  32.6  the  was  acceptable  medium d i f f i c u l t y .  or  consistent,  form  the  0.77,  Multiplication  and  examination  and Diagramming R e l a t i o n s  Concept  obtainable  a  measures,  and  test,  parallel  to  ranged  levels  0.82  s h o u l d be  on  The  Four  Folding  the  based  (mean v a l u e ,  high  Multiplication of  on  mathematics  internally  0.97.  test  0.33.  homogeneous  extremely of  of  be  measure  cognitive  by  final  indicates to  negative  the  equal  Cronbach,  was  observed  was  scores  55 m a r k s  mean  is  scale  examination  a  judgement  using  (e.g.,  of  for  the  inflated of  test-  valid, reported  but by  58  Ekstrom  et  However, timed  the  as  it to  measures  from  the  a  length,  the  sample,  divided  of  the  two  form  the  was  halves  parts  reliability.  coefficient  two  separately  between  no a t t e m p t  in  discussion.  into  parallel  this  that  consistency Test, may  of  26.55  (73.8%)  measure.  in  the  the  part  scores  be  was  33  fifth  somewhat  Further,  Of  obtained  for  was  value  skewed.  20  under  was  0.89.  made b y  Ekstrom  of  of  any  the  Kit.  cognitive  markedly  set  correlation  sample,  low  mean m a r k  other  the  noted  Advanced Vocabulary This  is  parallelism  internal  (0.63).  data  rough estimate  s h o u l d be  the  the  measure  Columbia  achieve  in  The  was  nor  equal  British  al.  the  of  serve  However, et  ,  because  parts  could For  al.  to  higher  a  than  than  29  in  or  the  measure,  the  ceiling the  for  of  British  above  others effect;  mean  distribution  subjects of  lower  due  the  cognitive  any  scores Columbia  (i.e.  80%  or  greater). These  results  (1976),  who  Test  13.8  of  collected obtained  reported and  from from  and d i s p l a y e d P<0.001). British reported results measures  may  the a  For  an  based (the  compared w i t h  obtained  a  standard  a  sample British  the  test  of  46  Columbia  of  differ  et  al.  .  of  student  the  of  mean  Ekstrom  Advanced  students.  score  al.  Vocabulary  based  were  et  less  on  data  The  data  variable,  (t=13.5,  df=2l2,  results  based  significantly  from  those  not  report  Ekstrom data  of  5.2,  Folding,  not  on c o l l e g e  on  sample  higher Paper  those  college  did  Ekstrom  tests  mean  deviation  significantly  Columbia data by  be  et  for  Diagramming R e l a t i o n s  on  al.  did  the  remaining  and  the  two  Multiplication  59 and  Subtraction). Examination  response/total  of  measures  revealed  that,  33  subjects.  choice 3.3%  (all  with  Vocabulary  frequency  of  and  The  the  0.0%,  Relations  Test,  no  for  the  measures  statistically  significant  results  that  inappropriate The  for  the  the  internal  and m o t i v a t i o n  Specific  Motivation and  respectively) during  the  not  respectively).  for  0.78  (0.72).  instrument  coefficients  was  Attitude were  Folding,  or  Toward  Examination  the  negatively  correlated  with  the  total  correlation  coefficients  0.55  and  respective The  statistics  ranges mean  being  scores  0.32 of  and to the  item  on  these  have  been  (87.76 than  those  and  measures  the  of  to  obtained 84.69,  correlation measure  was  item/total  measures  respectively, 0.29  95.76  and  Mean  for  -  Toward  and  (74.02  score.  of  exception  Attitude  either  0.52  research, 0.78  the  measures  item-total  no  toward  10.0%,  Like  may  one  for  higher  that  attitude  to  Diagramming  the  with  scores  revealed  were  of  process  of  highest  above,  Test  Research  development  all  sample.  higher,  significantly  by  response  compared  reported  each  T h e mean  the  the  respectively).  Columbia  four  from  correct  Paper  Advanced Vocabulary  consistency  items  as  Learning,  the  correctly  the  the  Subtraction)  13.8%,  difference  British  attitude  Statistics  of  of  displayed  between  or  each  seven  also  and  and  answered  measure  (5,  Concept  of  was  correlations  and Numeric  suggest  item  score  for  Multiplication  exception  last-named  total  distributions  coefficients  but  the  negative  and  response  point-biserial  cognitive  Advanced  the  with  of the  0.74.  Self-Concept  and  60  Achievement Columbia fairly  Motivation  sample, highly of  93.70  a  the  members  utility out  a  of  None  0.68  of  However,  the  were  standard  errors  scores  on  items  on  the  Self-Concept  measures  from  T h e mean  with  67.42  to out  be of  a  (mean  On t h e  average,  being  of  Utility the  much l o w e r  high  of  8.58  measure  of  (5.3  of  the  of  of  out  Hoyt  results  and  on  with  their  correlations  to  the  were  and  Achievement  0.89  and  the  two  Motivation  0.19  items  and  to on  Perceived  respectively.  The  Alberta  0.60  between  Specific  0.56,  negatively  Self-Concept  ranges  of  measure  item-total  correlations  Sample. and  correlated  measures  The  and  additional  means,  internal data  are  from the  standard  deviations,  consistency  coefficients  presented  in  analyses  are  item  Table  7.  reported  in  text. The  was  Perceived  average,  the  0.64  Alberta  the  of  as  the  measures  The  Again,  126).  on  score.  for  the  calculated  of  course  their  British  achievement-oriented  the  measure  the  themselves  were,  respectively,  Utility  the  of  Self-Concept,  maximum s c o r e  10).  total  0.43  of  on  saw  members  perceived  relatively  on  respectively.  each  the  10).  respective  Motive  and  score  motivational  and  (mean  sample  Motivation  possible  0.75  the  possible  three  98),  that  average,  possible  (mean  Specific a  of  the  skilled  maximum s c o r e out  on  indicate  within  indicates  internal  consistency  acceptable  limits.  that,  the  on  (0.73) The  average,  mean the  of  the  final  score  of  test  was  examination  34.8  (63.2%)  found to  be  of  61 Table 7 Scale Statistics ( A l b e r t a S a m p l e (n = Mean  Dependent V a r i a b l e : Examination Score Independent 1.  32))  Standard Deviation  Standard Error  Hoyt Coeff.  34.78  6.98  3.60  0.73  2.00  1.14  -  -*  23.97 10.72  5.61 2.82  2.15 1.61  0.85 0.66  68.38 17.19 7.31  19.17 6.31 2.88  3.49 2.24 1 .42  0.97 0.87 0.74  Variables:  Experience  2.Cognitive Measures: Advanced Vocabulary Test Paper F o l d i n g Test M u l t i p l i c a t i o n and Subtraction Diagramming R e l a t i o n s Concept L e a r n i n g Task 3.Attitudinal Measures: A t t i t u d e Toward Statistics A t t i t u d e Toward Research Academic S e l f - C o n c e p t  77.09  23.45  5.32  0.95  85.97 67.66  23.97 8.24  5.36 3.02  0.95 0.86  4.Motivational Measures: Achievement Motivation Perceived Utility Specific Motivation  93.66 7.72 5.00  10.64 1 .67 2.55  3.63 0.60 1 .37  0.88 0.87 0.71  *This  measure  contained  medium d i f f i c u l t y . value  of  -0.25  coefficients -0.09.  The  statistics Three consistent.  to  were  one  the  single  item-total of  observed  average  courses of  The  a  0.61, to  number  be of  cognitive  Advanced Vocabulary,  and Diagramming R e l a t i o n s  correlations  with  c o m p l e t e d was five  item. ranged  a mean v a l u e  negative,  with  a  post-secondary  of  from  0.22.  mean  a  Five  value  mathematics  of or  2.0. measures  were  highly  Multiplication  had a s s o c i a t e d  Hoyt  and  internally Subtraction  coefficients  of  62  0.85,  0.97  observed  to  discussed speeded an  and show  an  above,  the  test,  inflated  form  of  estimate  of  of  Folding,  was  0.66.  This  may  be  0.93.  by  of  due  to  was  Examination  of  et  the  for  five  on  on  the  by  all  measure 32  with  motivation (internal measures  was  of  instrument negatively  one  total  or  development correlated  the  yielded  the  more  two  accurate  test. for  the  fifth  lower  than  relatively The  cognitive for  low  value  the  measure,  other  variability  obtained  is  four -  lower  distributions  coefficients Vocabulary no  item  revealed test  item  (on  of  each  was  Paper  and  and that,  a  -  the than  the except  single  answered Folding)  from  the  correlation  for  The  those  total was  No  item  correctly correlated  research  on  for for  that each  for  the  were  not  during  either  and  Motivation  scores  and  item  attitude  Specific  obtained  score 0.67  of  mean  statistics  procedure.  with  measure  except  0.71).  toward  different  item-total  a  higher,  of  attitude  for  parallel-  value  be  was  have  approximate  may  As  score.  consistency 0.86  The  may  This  Folding,  Only  consistency  significantly  mean  the  internal  Advanced  Paper  subjects.  negatively The  of  Subtraction,  response  point-biserial the  consistency  was  al.  response/total items  internal  0.74.  between  2.82.  Ekstrom  of  Learning  correlation  the  the  Concept  the  somewhat  deviation  reported  and  on  consistency was  of  reliability.  reliability  Paper  Numeric  coefficient  coefficient  based  test,  internal  standard  internal  estimate  the  The  respectively.  Multiplication  coefficient,  halves  that  0.87  scale  scale. measure,  the was The with  63  respective The  ranges  0.11  o b s e r v e d means  Achievement Alberta  of  Self-Concept  felt 67.7  The  utility  on  out  of  specific  out  a possible  of No  item  correlated mean  with  on  and  0.56  a  was,  with  correlations  The  for  in  to  two  Utility  and  comparability  assess  ways,  and  of  and  of  as  of  their  was out  of  (mean  98)  and  total  of  rather  a  on were  score  of  fairly  high  possible  10).  low  (mean  Achievement  respective two  of  5.0  0.08  Motivation  total  measures  score.  were  0.74  and  0.29  between  the  two  items  Specific  Motivation  The  0.53  to  the  and  to  0.67  on  were  the 0.77  the  respectively) variable.  on  the The  12  in  the  Chapter  two  samples  III. of  Both  the  were were  Hotelling's  statistics.  test  British  Samples  calculation  Bartlett-Box T-square  the  equivalence,  described  involved  the  Hotelling's  dependent  of  the  respectively.  T-square  32  able  possible  7.7  or  the  correlations  Perceived  statistical,  and  a  however,  corresponding ranges  order  compared  of  their  Equivalence In  of  and  average,  score  course  Utility  the  relatively  out  the  Self-Concept  on  possible  93.7  0.84.  of  that,  Self-Concept  negatively  of  to  measures  were  that  0.47  10).  either  respectively. measures  felt  motivation  item-total  0.52,  (mean  Perceived  Their  and  indicate they  subjects  (mean  the  that  achievement-oriented 126).  0.86  on  Motivation  sample  to  was  performed  Columbia and A l b e r t a independent  value  of  to  samples  variables  T-square  examine  (3.008,  and  (n=33 the  df=12,52,  64  p=0.0029) was  was  statistically  performed  covariance  to  matrices.  significant  that  represented  two  Because  the Of  of  the  when  samples  of  univariate  thirteen  of  tests  Timm  were  were  (1975) five  higher  df=63,  p=0.031)  Diagramming  The  the  Learning  the  Concept  British  Alberta  positively  about  of  higher  utility  the  statistically  Statistics (t=2.15, The  df=63,  variance-  statistically was  concluded,  comparable  and  did  on  stated  the  Alberta  df=63,  This  and  statistical  each  of  procedure  Hummell  and  British  on  Sligo  different subjects  Vocabulary  (t=2.2l,  (t=2.34,  df=63,  the  average,  higher  p=0.0l6). average,  that  the  sample,  p=0.048)  (1971).  Columbia  the  differences  the  followed  significantly  df=63,  and  significant  on  Relations  scored,  sample,  achieved  Advanced  (t=2.49,  statistics  (t=2.02,  for and  Finally, felt  class as  on  more  would  inferred  Attitude Perceived  be from  Toward Utility  p=0.035).  statistically  surprising,  given  the  Columbia  and A l b e r t a  variable  ratios,  Columbia  Task  than  on  sample  Columbia  It  performed  performed.  significantly  p=0.022).  the  was  not  had  were  scored  and  were  variables.  mean v a l u e s , tests  value  T-square  independent  univariate  of  test  populations.  value  recommendations  Bartlett-Box  comparability  resulting  two  different  the  The  df=78,12507.8, p=.026).  the  the  significance,,  the  The  (F=1.33,  therefore,  measures  test  significant.  classes  significant logical  samples.  statistical were  not  differences  differences  Because  of  comparisons possible.  were  between  the among  low the  However,  the  not  British  subject-tothree  British  the  samples  65  collected  from  comparable. same  The  and  was  order  of  lessons  in  and  Stanley  (1970).  Alberta and  Some  fact  On  the  six  weeks  of  this  reason  that the  the  of  material on  hand,  duration is  found  were,  was  in  and the  the  and  logically  classes  others  based  other  class,  the  in  receipt p.  two  Alberta  47,  Alberta  of  of  the  in  the  terms  of  contents  text  by  Glass  University  the  too,  of  the  combined  of  statistics  fact  based  that  the  on G l a s s  did  at  way  Although  not.  consequently,  training  in  by  a point  might  statistics.  equivalent,  the  and  been  as  the  the  the  were  the  three  first  day  two-week of  the  The  results  therefore, were  the  not  by two  of  delay course  administered  contaminated  they  pre-tests  approximately  course.  Logically,  just  was  differences  of  instructor  which  have  on  of  pre-tests  the  of  each  pre-tests Because  these  through  significant  administration  received  III),  pretests,  not  of  pre-tests  Chapter  the  observed  samples.  class  subjects  the  times  Columbia classes  were  three  the  were  course  for  British  thirds  to  courses  for  the  the  presentation  differed  (see  of  appeared  • •  the  the  each  comparability  lessons  A plausible is  of  Columbia  similar  three  was  research.  statistical  of  all  class  Stanley.  British  Specifically,  duration,  content.  within  to  twoof  the  prior samples  statistically  equivalent. The reported in use  time and  univariate above, of  may  significant have  been  administration.  apply  the  idea  of  difference  caused,  This  task  "summation",  in  in  part,  required with  an  Concept by the  the  Learning, difference  subjects  altered  system  to of  66  symbols  and  concept  before  have  been  test,  for  group time  testing  Alberta  toward  also  be be  useful,  tentatively  the  Alberta  samples  variable  ratios  n's  would  either to it  of  the  answer became  the  to  spirit  the  inappropriate  they they  data  analytic  The  recast  a)  What  recast  the  to  that  not  remain  too  the  latter at  of  issue.  the  sample  stable  in  and  size  The  to  small  estimates  coefficients  of  necessary  Chapter  I.  Thus,  questions. had  imply within  insofar  as the  to  fulfill  the  use  the  of  two an  possible  allowing  application  were: between  LVM  exploratory  techniques.  relationship  the  Columbia  small.  requiring  questions  the  sample,  difficult  cases,  research  questions,  that  Columbia  British  questions  without  research is  had  a  the  path  could  feeling  statistics  presented  the  positive  Questions  were  the  questions  original the  or  attainment  more  fact  may  sample.  calculation  research  First,  the  raised  32:12  the  research  of  Research  structure  Second,  exploration  the  both  procedure. of  Alberta  33:12 and  British  with  the  in  the  this  Learning  a concept  greater  to  meant  rephrased  conditions.  the  of  necessary  The  in  exposed to  Concept  than  the  results  allow  latent  and  that,  been  Finally,  non-equivalence  of  not  rather  attributed  unlike  have  Thus,  no e x p e r i e n c e  preliminary  Specifically,  test,  observed  Recasting The  session.  statistics  responding,  would  subjects.  had had v i r t u a l l y of  sample  achievement  the  would  may  Alberta  the  an  attitudes class  the  achievement  in  of  67  elementary  statistics  and  each  of  the  twelve  manifest  variables? b)  What  are  revealed  by  the  characteristics  subjective  intercorrelations  of  the  clusters  examination  among t h e  independent  of and  the  dependent  variables? c)  How  much  introductory twelve  of  the  variance  statistics  manifest  can  variables,  in  be  taken  achievement  accounted both  as  a  for  in  by  the  group  and  cumulatively?  The  rephrased  outlined  above.  in  questions.  the  allows  and  demanding  some o f  the  decided  to  of  the  select  analysis,  but  Stanley,  That  1970)  likely In  Columbia  of  the  would is,  when  manifest  the in  of  than would  take  small to the  the  make  not  of  sizes  level  these  sample  Alberta  the  study of  to  of  is  I).  the  Finally, allow  retained. it  was  significance level.  more the  as  This  speculative small  (e.g.,  effects  in  questions  0.05  said  questions  study,  statistical  are  considered  reported  be  the  allow  conditions  three  Chapter  consideration  investigating and  the  of  rephrased  only  detection  0.05  the  the are  those  conventional  into  sample  with  nature  level  set  1 (see  analysis,  0.10  the  Table  nature  f u l l f i l l  variables  results  exploratory  rather  criterion  questions  addition,  subjective  relaxed  less  In  summarized  criterion,  sizes.  only  exploratory  Because  the  First,  some c o m p a r i s o n  literature by  research  by  sample  Glass  and  of  small  magnitude  questions,  the  British  retained.  three sample  were  analyzed  separately,  68  thereby  providing,  in  part,  Methodology Included used are  to then  in  data  reported  Chapter  British  calculation among  the  and  the  12  and  analysis  of  -  -  of  the  questions.  procedures The  results  analysis  completed the  matrix  by  correlations variables,  a  of  the  sample  steps:  of  in  two  of  intercorrelations  stepwise  between  and  was  the  0.10  Table  I,  correlations  was  the  regression  and  determined  by  i.e.  p.536).  The  then  possible each  were  examined,  level,  was  each  between  Achievement,  significant for  The  -  coefficient  1970,  significant  research  followed  Statistics  statistically  Stanley,  description  Sample. was  zero-order  value  a  Analysis  V.  Columbia  —-  correlation  tabled  Columbia  independent  variable  recast  variables,  procedure. The  is  Final  Analyses  British  from  the  section the  in  replication.  of  investigate  Correlational  The  this  a  pair  independent  calculated. whether comparing  |0.292|  pattern  examined  of  Each  it it  was to  (Glass  of  the and  statistically  and  described  subjectively. The  subjective  process  description  of  independent  variables  followed  by  an  the  included,  significant and  attempt  an---examination  relationships  statistics to  first,  between  achievement.  "cluster"  the  This  and the was  statistically  69  significant meaningful of  inter-independent way.  intercorrelations  was  made  to  The  relate  data  regression,  cluster was  it  were  for  the  Social  determine  the  level  variable's the  variance  in  the  Sciences. of  sample  matrix  coefficient for  independent stepwise  level and  first  regression  regression independent  was  variable  characteristics  SPSS  was  of  was the  data  the  examined. the  data the  as  set  zero-order  described  the  critical  sample  Table  I,  p.  and  of  by  the  to  analyze  outcome the  32  536).  Two  the  results  entry of  at  of the  sample  above.  procedure,  might  of  REGRESSION.  order  enter  for  correlation  a  described  to  collected  for  computed  stepwise  allowed  to  is  used  forward  contributions  of  subprogram  as  of  This  dictated  independent nature  criterion.  the  examined  exploratory  a  significance  stepwise  were  using  were  matrix  Statistical  given  examined  of  the  the  sample,  1970,  a  attempt  forward  First,  the  Stanley,  the  and an  F-tests  also  as  procedure  free  and  Columbia  Columbia, a  the  three-part.  procedure,  variables  free  any  analysis  procedures  using  British  of  were  calculated  British  0.10  again the  was  was  regression  In  The  |0.296|  (Glass  reported,  from  of  the  subjects stepwise  the  a  of  variable  Alberta  value  significance  dependent  from the  from  to  Partial  Because  from  in  statistics.  nonsignificant  Sample.  data  in  however,  Alberta  the  isolated  s u b p r o g r a m REGRESSION of  The  correlation  coefficients  described,  subjected  contribution.  analysis,  was  achievement  then  the  which  subjectively  to  using  Package to  Each  variable  The in  whichever dictate.  the free  of  data  second  which  any  point  the  Third,  the  70  results  of  the  analyses  of  the A l b e r t a  British  C o l u m b i a sample were c o m p a r e d .  sample of  data  and  the  71  Chapter Results  In  this  chapter,  zero-order  correlation  regression  procedure  are  presented  analyses  of  Columbia  and  results for  of  both  the  Final  findings  matrix to  Second,  Alberta  Alberta  the  the  used  first. the  of  the  are  Columbia  the  results  British of  compared  the  forward  Columbia  the  reported,  regression  of  parsimonious  the  are  examination  data  correlational and  briefly.  procedures  the  British  Finally, are  the  presented  intercorrelations variables  and  Of  variables,  the  the 66  23 w e r e  0.10  level.  with  the  the  lower measures  dependent  statistically  Of  All  The  the  27  standard  triangular of  variable  intercorrelations  independent  significant.  and  among  of  Analyses  Sample  Intercorrelat ions.  *Means  the  samples.  British  8*.  from  analyze  Correlational  The  Analysis  and  data  samples  exploratory  V.  variables,  deviations  are  of  or  were  presented  Table  beyond  the  achievement statistically  were  in  in  independent  statistics  four  of  independent  the  at  correlations  are  12  presented  among  significant  12 c o r r e l a t i o n s  significant  the  matrix  positive.  Table  6.  72 Table  8  Inter-correlations Among Variables ( B r i t i s h Columbia 1  2  3  4  5  Measure 6  the Sample)-  Number* 7 8  9  10  1 1 1 2  Measure:*** Experience: 1. Cognitive 2. 3. 4. 5. 6.  0.41 0 . 37 0 . 02 0 . 46 0 . 64  Measures: 0.63** 0 . 18 0 . 8 2 0 . 01 0 . 2 4 0 . 15 0 . 7 3 0 . 29 0 . 6 6  Affective 7. 8. 9.  ~  0 . 89 0 . 35 0 . 24  0 . 87 0 . 59  0.78  Measures:  0.32 0.03 0.15-0.08 0.32 0.17  Motivational  0.47 0.13 0.04-0.10 0.05 0.12  0.45 0.18 0 . 9 1 0.05-0.19 0.66 0.03 0.24-0.01  0.89 0.13  0.95  Measures:  1 0 . - 0 . 0 3 0.30-0.28-0.12-0.09-0.14 0.08 0.33 0.13 0.84 1 1 . 0 . 3 3 0.21 0 . 1 4 0 . 1 7 0 . 1 4 0 . 1 0 0 . 3 2 0 . 5 3 0 . 3 7 0 . 2 5 0 . 7 8 1 2 . 0 . 2 6 0.21 0 . 0 6 0 . 1 5 0 . 0 3 0 . 1 2 0 . 3 3 0 . 3 8 0 . 4 0 0 . 1 5 0 . 4 0 0.72 Statistics 13.  0.53  Achievement:  0.38  0.40-0.06  0.26  0.46  0.20  0.03  0.01  0.09  0.01  0.16  * 1 , = E x p e r i e n c e ; 2.=Advanced Vocabulary Test; 3.=Paper Folding Test; 4.=Multiplication and Subtraction; 5.=Diagramming R e l a t i o n s ; 6 . = C o n c e p t L e a r n i n g ; 7. A t t i t u d e Toward Statistics; 8.=Attitude Toward Research; 9.=Academic Self-Concept; 10.=Achievement M o t i v a t i o n ; 11.=Perceived U t i l i t y ; 12.=Specific Motivation; 13,=Statistics Achievement. **Reliability c o e f f i c i e n t s e n t e r e d on t h e m a i n d i a g o n a l . * * * U n d e r l i n e d v a l u e s were s t a t i s t i c a l l y significant (p<0.l0).  Three  of  significant cognitive and  the  independent  correlations  - Advanced  Concept  with  was  observed  (r=0.53),  variable  (r=0.38),  (r=0.46). between  which  can  variables  Statistics  Vocabulary  Learning  correlation a  four  be  Achievement said  to  be  achieved  Achievement  Paper  The  which  Folding  fourth and  Past  closely  were (r=0.40)  significant Experience related  to  73  cognitive  abilities.  Achievement usual  and  finding  the  Toward  Statistics  times.  Lack  Columbia Of  the  cluster.  Diagramming  (r = 0 . 6 4 ) ,  and  relationships, significant  Concept,  of  the  interpreted  of  Past  "past  strong  Attitude  in  British  the  12 f o r m e d  correlations was  (r=0.46),  significantly Paper  positive  Folding Learning  (r = 0 . 5 3 ) . with with  (r=0.32),  Utility  an  included  Concept  together  These the  three  noncognitive Academic  (r=0.33)  achievement"  ability,  a  several  (r=0.4l),  Statistics  not  reported  group of  Experience  Perceived  a  a  Achievement.  Toward  and  as  experience,  Vocabulary  is  result.  12  considered  - Attitude (r=0.32),  this  between  between  been  Experience  Statistics  correlations  variables  matter  correlations,  Relations  when  has  subject  influenced  Advanced  relationship  A correlation  the  Five  (r=0.37),  variables  of  a  motivational  Specifically, with  of  achievement  may h a v e  Experience. correlated  and  significant  interpretable  or  literature.  knowledge  sample  absence  attitudinal  in  of  The  -  may  subcluster attitude,  Selfbe  relating and  high  achievement. A between  further pairs  correlated  Learning ability"  of  significant  cognitive  and Paper  the  was  reflected  abilities,  Paper  0.66.  and  This  logical  observed Relations  Folding  correlation  combined with  were  Diagramming  (r=0.35)  observed  Folding  subcluster  visualization  with  and S u b t r a c t i o n  while  correlations  variables.  significantly  Multiplication (r=0.59),  four  Concept  Learning  between "higher  reasoning  numeric  (r=0.73),  Concept cognitive  and  skills.  spatial  74  The  last  Attitude  three  Toward  Statistics  Toward  Statistics  Concept  Learning  subclusters merged  to  it  and the  Statistics  motivational  that  and  was  Perceived  Utility  Specific  with  correlations  Statistics  and  Specific  cluster  to  the  but  were  Attitude  (r=0.45),  and  The  two  correlations  may  cluster  which,  in  Statistics,  indirectly  of  was  not  be  Number  related  to  research this  and  cluster  subjects'  lack  Specific  Toward  Motivation Self-Esteem  (r=0.40).  were Utility  (r=0.32)  Attitude Attitude  Toward Toward  (r=0.33). and  achievement  orientation".  typical  correlated Statistically  and  attitudinal to  (r=0.38), (r=0.37).  were  o b s e r v e d between  of  subjects  abilities  and  statistics.  The  and Achievement of  Attitude  other  related  own  included  variables.  Motivation  be  correlations  Utility  "academic  might  their  significant  Perceived  combined  represented  cluster  between  only  12  (r=0.46).  Toward  and Academic  each  Perceived  towards  are  with  and  and  opinion  Attitude  six  (r=0.53),  Statistics  this  Achievement three  the  (r=0.47),  Relations  these  attitudinal  Motivation  significant  of  correlated  significantly  may h a v e  Folding  achievement"  Reasoning  cluster  Research  variables,  of  of  Achievement.  second  The  Paper  Diagramming  "statistics  Logical  correlations  and  addition  appears  and  Statistics A  with  and  become a  however, Facility  significant  experience  a  with  in  statistics.  A  high  positive of  again, the  score  who p o s s e s s  absence  may,  motivational  a  on high  orientation relationship  have  subject  a  It  been matter.  due  75  Parsimonious 12  independent  forward  Forward  variables  regression  Experience Achievement  (F=11.90,  accounted  27.7% of  statistics The  were  When  entered  procedure,  contributed  for  Regression.  df=l,31, the  in  only  significantly  the the  the to  the  variance  all  forward of  variance This  in  of  free  measure  p=.00l6).  observed  measures  Past in  variable  achievement  in  (R=0.577). partial  variables  with  associated  for  correlations statistics  with  them,  are  of  the  remaining  achievement, presented  in  and  Table  9.  11  independent  the  F-ratios  A s may  be  seen  Table 9 P a r t i a l C o r r e l a t i o n s and F - R a t i o s the Non-Contributory Independent Variables ( B r i t i s h Columbia Sample)  Independent  Variable  Partia1  F-Ratio  Correlation Advanced Vocabulary Paper F o l d i n g M u l t i p l i c a t i o n and Subtraction Diagramming R e l a t i o n s Concept Learning Attitude Statistic Attitude Research Academic  s  0.208 0.257  Toward Toward  Self-Concept  Achievement M o t i v a t i o n Specific Motivation Perceived U t i l i t y  in  the  Paper at  the  table, Folding 0.10  the  highest  partial  and Achievement level.  When  -0.089 0.013 0.184  0.24 0.01 1.05  0.039  0.05  0.050 -0.195  0.08 1.18  0.120 0.023 -0.183  0.44 0.02 1.04  correlation  (0.257) the  1 .36 2.11  - a  was  value  cognitive  and  that not  between  significant noncognitive  76  variables made  were  equally  However, from  The  examined,  the  this  low  it  effects  variables  and the  variables,  A  total  number  of  number  (27)  British of  the  be  judged  achievement correlations correlations matrix  of  (r = 0..48).  cognitive  The  and A t t i t u d e  the  standard  and  Achievement  and  at  in  Table  independent or  an  beyond  independent  were  statistically  were  positive.  (25)  the  is  The  similar  to  the  calculated  data.  Multiplication  pattern  the  correlations  Achievement  with  in  the  of  of  independent  presented  between  Statistics  (r=0.44)  and  correlations  matrix  the  significant  variables  Statistics  observed  in  is  pairs  independent  Learning  of  five  Columbia  with  correlations  *Means  cannot  of  variable  between  significant  (r=0.36),  Concept  not  variables  achievement.  triangular  measures  dependent  significant  observed  correlated  12  statistics All  lower  statistically  further  significant.  Folding  the  were  and  Three  the  66 c o r r e l a t i o n s  level.  the  11  statistics  suppression  The  among  of  20  variable  from  of  all  Sample  intercorrelations  0.10  to  that  table.  Intercorrelations.  Of  evident  contributions  possible  Alberta  10*.  became  deviations  were  were  Subtraction remaining  Toward  are  Paper  (r=0.37)  and  significant  Attitude  zero-order  presented  -  two  Research  Columbia data.  significantly  cognitive  involved  attitudinal  British  which  It  in  Toward  (r=0.32).  This  correlations is  more  Table  7.  was  typical  77 T a b l e 10 Inter-correlations among t h e Variables (Alberta Sample) 1  2  3  4  Measure 6 7  5  Number* 8 9 1 0  11  12  Measure:*** Experience: 1. Cognitive  Measures:  2. - o . 1 1 0 . 8 5 * * 3. - o . 1 30 . 4 6 0 . 66 4 . 0 . 09 0 . 5 2 0 . 26 0 . 93 5. 0 . 09 0 . 3 5 0 . 29 0 . 08 6. 0 . 3 3 0 . 2 3 0 . 2 3 0.31 Affective 7. 8. 9.  0.87 0.43  0.74  0.14 0.06 0.14-0.11 0.24 0.03 0 . 0 2 - 0 . 0 6 0.10-0.03-0.01-0.14  0.31 0.22 0.17  0.95 0.81 0.95 0.35 0.18  0.15 0.09 0.27  0.46 0.03 0.03  0.25 0.46 0.55  0.34 0.49 0.56  0.16 0.04 0.33  0.88 0.11 0.87 0.03 0.62  0.71  0.18  0.48  0.44  0.32  0.07  0.08  0.26  Measures:  0.29 0.28 0.19  Motivational 10. • 12. 1 1  0.28  0.10 0.12 0.04  0.02 0.14  Statistics 13.  Measures:  0.19 0 . 3 3  0-32 0.19  0.86  0.41 0.18 0.19  Achievement: 0.21  0.36  0.37  0.25  * 1 . = E x p e r i e n c e ; 2.=Advanced V o c a b u l a r y Test; 3.=Paper Folding Test; 4.=Multiplication and Subtraction; 5.=Diagramming Relations; 6 . = C o n c e p t L e a r n i n g ; 7. A t t i t u d e Toward Statistics; 8.=Attitude Toward Research; 9.=Academic Self-Concept; 10.=Achievement M o t i v a t i o n ; 11.=Perceived U t i l i t y ; 12.=Specific Motivation; 13.=Statistics Achievement. **Reliability c o e f f i c i e n t s a r e e n t e r e d on t h e m a i n d i a g o n a l . * * * U n d e r l i n e d v a l u e s were s t a t i s t i c a l l y significant (p<0.10). of  the  Vasu,  patterns  reported  in  the  literature  (e.g.,  Elmore  and  1980).. Of  the  25  obtained  between  (r=0.33)  and  significantly  statistically Past  Experience  Perceived with  significant  Past  and  Utility  Experience  each  correlations, of  (r=0.32). in  the  Concept Both  British  two  were  Learning correlated  Columbia  data.  78  However, of  other  cognitive  which  evidence  and  was in  the  this  difference  Alberta  pre-tests Of  of  three  Paper  (r=0.52) significant Relations  and  logical  (r=0.33).  proficiency  in  is  both  the  the  of  the  analysis  and  each  may  equated  also  of  and with  "achievement  of  a a  visualization ability".  of  the  the  British  latter  were  was  data  and  variable  degree  motivation"  not in  and  of the  and  Advanced  interpreted  variables  third  observed  Multiplication  consisting  high  The  correlations  (r=0.46)  be  two  subcluster  Learning.  Learning  set  fourth  Diagramming  correlations  subcluster,  but  four of  and Concept  Concept  component,  often  one  A  this  "general  analysis  significant  motivation"  integral  spatial  the  only  This  motivation,  facility, represent  Motivation  (r=0.4l),  Since  and  Subtraction  (r=0.35).  (r=0.43).  of  cognitive  and  between  in  Relations  Achievement  that  fact,  significant  "achievement  fact  In  statistically  Vocabulary  an  observed  Diagramming  Subtraction  is  not  may  times  variables.  the  observed  not for  Advanced Vocabulary  Relations  number it  among  between  was  explanation  among t h e  Multiplication  Learning  ability,  data.  achievement  correlations  was  Experience  administration  relationships  observed  to  cluster  Columbia data  possible  different  (r=0.46),  Concept  was  Three between  were  reasoning,  statistically between  the  correlation  verbal  Columbia  the  achievement"  related  British One  Diagramming  and  subcluster  that  Folding  and  included  is  the  set.  significant  variables, each  data  "statistics  variables  from  influenced  the  the  noncognitive  abstracted  found  the  for  as  an  only  of  which in  success.  speed which The  "statistics"  79  subclusters further is,  include  the  interpretation  it  may  influence  be  same  of  that  the  directly  through  related  Motive  was  Subtraction,  and  Concept  correlated A  with  and  cluster  Motivation.  Attitude  of  (r=0.35)  Self-Concept  are  Multiplication  and  of  which  were  Achievement, was  Statistics  and A t t i t u d e between  Self-Concept and  (r=0.44)  0.46  and  with  possible Motivation,  Research  and A t t i t u d e  Specific  and  six  Specific Toward  Attitude  significantly  All  Utility,  significant  achieved  0.81).  Last,  Toward  Statistics  Motivation  (r=0.33)  the  were  significant. The  "attitude-motivational"  representing the  the  attitudinal  noncognitive  other,  Statistics  and  the  two  Achievement.  Columbia  data,  related  except to  attitude  to  in  the No  be  was  very  observed Alberta such  interpreted  achievement,  correlated similar  as  since  significantly  measures  cluster  cluster  achievement.  may  intercorrelated  This  that,  cluster  contribution  measures  attitudinal-motivational  was  indirect  case,  both  (r=0.32).  (r's  between  each  That  which  In  a  this  Achievement  Toward  Statistics  correlations  all  an  statistically  Statistics  Perceived  significance  and  link  Research  among  Toward  statistical  both  eight  Attitude  Toward  correlations  exerts  variables  to  Learning,  Statistics  with  Attitude  cluster.  achievement.  related  coefficients  correlated  motivation  allows  Achievement.  second  correlation  variables  ability"  cognitive  to  Achievement  to  cognitive  "general  achievement  on A c h i e v e m e n t  themselves  three  to  with with the  in  the  British  sample,  the  cluster  was  observed  relationship  80  in  the  British  Columbia  Parsimonious procedures  were  Experience R  as  was  was  second  in  which  Forward  entered, in  statistical  The  did  the  regression the  Regression.  computed.  observed  The  sample.  not  independent  properties  of  yield  the  of  was  variables the  data  Table for  first  analysis  procedure  Two  procedure,  the the  a  forward  same  free  were set  in  order  British  regression which of  free  would  to  multiple  Columbia  forward  only  data.  regression,  enter  where  the  dictate.  11  P a r t i a l C o r r e l a t i o n s and F - R a t i o s Non-Contributory Independent Variables (Alberta Sample)  Independent  Variable  Partial  F-Ratio  Correlation ~  Advanced Vocabulary Paper F o l d i n g Multiplication and Subtraction Diagramming R e l a t i o n s Concept Learning Attitude Toward Statistics Attitude Toward Research Academic S e l f Concept Achievement Motive Specific Motivation Perceived Utility  0.262 0.422  2.14 6.28*  0.356 0.162 0.431  4.20* 0.76 6.62*  0.387  5.11*  0.266 0.020  2.20 0.12  0.024 0.218 0 . 170  0.02 1 .44 0.86  *p<0.05  When E x p e r i e n c e only  8.11%  accounted value  was  of  for. 0.11  the The  was  entered  variance level  - higher  of than  into in  the  statistics  significance the  regression  chosen  equation,  achievement  associated criterion  of  with 0.10.  was this The  81  partial with the  correlations  statistics coefficients,  the  table,  are  presented  in  of  11  - Paper  Attitude  and  variables be  Experience no  When  to  independent explanation  (23.4%  The  three  The  12.  of  variables, in  9.1%  partial  will  of  be  explained  the  the  Columbia  sample  indicated  were  Concept  total  of  the  by  the  Learning  Attitude  Toward  df=2,29)  F=3.159,  were three  to  as  F=3.918,  a  with  variable.  significantly  for  data,  procedure,  variance;  accounted  attitudinal.  variance,  df=1,30),  and  r=0.387).  Alberta  variance;  of  (partial  independent  variables  and  df=3,28).  39.3% of  the  corresponding F-ratios  for  achievement. and  independent noted  the  variables  that  the  between  Achievement  and Achievement  was  significant  at  not  British  Achievement,  of  one,  in made  that  Learning  regression  the  correlations  nine  the  seen  variables  (partial  other  F=9.146,  6.8%  then,  statistics  the  from  three  variance;  (further  on  be  with  Multiplication  remaining  contributed in  may  beyond  Concept  based  forward-  The  As  r=0.422),  from any  variance  (further  remaining It  the  11.  variables  associated  independent  the  collected  free  F-ratios  Statistics  27.7% of  variables  Folding  variance  the  a  the  Statistics Paper  data  F-ratios. of  that,  contribution  the  subjected  Toward  for  independent  Table  (partial  cognitive,  accounted  the  r=0.356),  recalled  significant  partial  were  11  contributions  Folding  r=0.43O  will  the  significant  (partial  It  remaining and  Subtraction  Three  the  achievement,  four  statistically Experience  of  or  beyond  the  are  highest  presented partial  Motivation 0.10  correlation,  (partial  level.  in^- T a b l e  r=0.257)  Inspection  of  82 T a b l e 12 P a r t i a l C o r r e l a t i o n s and F - R a t i o s 9 Non-Contributory Independent Variables (Alberta Sample)  for  Independent  Variable  Partial Correlation  Advanced Vocabulary M u l t i p l i c a t i o n and Subtraction Diagramming R e l a t i o n s  -0.035  0.03  0.214 -0.006  1 .29 0.001  Attitude Research Academic  -0.030 -0.116  0.028 0.367  -0.257 0 . 1 02 - 0 . 157  1 .92 0.284 0.379  Toward Self  Concept  Achievement Motivation Specific Motivation Perceived Utility the  table  equally  reveals  that  taken  highly  as  than  Exploratory forward  a  the  for  were  allowed  was  very  close  not it  is  statistics almost beta  weights  at  variables From may  be  to  0.0  the  results  significant  in  of  12  variables  long  as  presented  by  based  for  dissimilar on  the  were  independent contributed  after and  Experience which  from 12  the  independent  partial  Table  free  13.  F-ratio From  the  the  total  variance  in  each  set  of  variables  is  orders  of  each in  British  variables  all  the in  contributions, step,  results  which  although  last  the  variable)  as  explained  totally  that  equation  are  that,  the  almost  regression  set  The  samples  enter  relative  are  seen  the  the c o g n i t i v e  both  achievement the  of  Regression.  to  apparent  equal,  noncognitive variables  noncognitive.  Forward  regressions  but,  whole,  variables  table  c o g n i t i v e and  non-contributory,  variables more  F-Ratio  of  the  the  two  (the  contribute  are  independent  sample,  entered  only more  and  samples.  Columbia  which  entry,  into  it the  statistically than  1%  to  the  83 T a b l e 13 of E n t r y , R-Square Change and for E x p l o r a t o r y Forward Regressions  Order Weights  Beta  British 0 r d e r Advanced Vocabulary Paper Folding M u l t i p l i c a t i o n and Subtraction Diagramming R e l a t i o n s Concept Learning  RSquare Change  Alberta  B  0 r d e r  RSquare Change  B  .6 2  0. 075 0 . 047  0,. 3 3 5 0,. 5 9 8  1 1 3  0 . 002 0 . 068  - o . 073 0 . 261  9 3 10  0 . 002 0,. 0 3 2 0 . 0 3 4 -•o,. 4 6 5 0 . 001 0 ,. 0 4 7  -*  5  0 . 060  0 . 408  1  0 . 234  0 . 346  A t t i t u d e Toward Statistics A t t i t u d e Toward Research Academic S e l f - C o n c e p t  *  Columbia  -  -  -*  -  -  2  0 . 091  0 . 146  -*  -  -  7  0 . 0 2 2 -•0., 1 6 9  10 8  0 . 003 0 . 008  0 . 167 - 0 . 093  Achievement Motivation 4 Perceived Utility 5 Specific Motivation 8  0 . 040 0 ., 4 0 4 0 . 0 5 6 -•0., 2 5 3 0 . 001 - 0 . , 0 4 9  4 9 6  0 . 040 0 . 007 0 . 021  - o . 353 - o . 147 0 . 235  Experience  0 . 277  7  0 . 014  0 . 161  F<0.001  increase  1  for in  the  cognitive, The  only  this  percentage  attitudinal a  contribute  more  global than  Vocabulary,  both  significantly  with  did  not  Of  more  of  variance  explained  motivational,  and  variable  entered  to  rating. 1%  be The  include  of  which  Achievement  contribute.  contributed Perceived  sample.  second,  Concept,  0 . ,531  The  than  1%  Paper  and  were  been  Self-  variables  which  found  motivational Achievement  again.  Academic  Folding  Diagramming  first,  cognitive  is  cognitive  had  two  third,  are  and to  Advanced correlate  Relations,  which  variables  which  Motivation  and  Utility. the  above-listed  variables,  only  two  (Paper  Folding  and  84  Achievement in  variance  which in  Motivation) explained  contributed  the  British  Subtraction, Specific Attitude  Alberta  more  Concept  Toward  sample  in  to  the  than  Columbia  Motivation.  significantly  contributed  1%  (as  in  the  sample  will  Statistics the  Alberta  Learning, It  reported  be  than  1%  sample.  Alberta  included  recalled  that  variance  above).  in  the  Other but  change variables did  Multiplication  Toward  Concept  to  sample  Attitude  and  explained  more  Statistics, Paper  Learning  not and and  Folding,  contributed  achievement  for  the  85  Chapter Summary  In  this  chapter,  presented  first,  described  in  delineated. investigation  a  V.  some  is  and  achievement few  in  both  some  investigations  statistics the  the  limitations  of  have  for  been  general subjects  reported  the  among s t u d e n t s  sciences.  This  by  the  the the  results study  conclusions  future  is  are  of  the  research.  Investigation  has  of  investigation of  the  specific  achievement  social  of  the  discussion  terminated  much a t t e n t i o n  determinants  of  a  implications  Summary Although  by  Then,  chapter  and  Conclusions  summary  followed  Chapter The  and  VI.  thesis  focused  on  the  correlates  academic  achievement  (e.g.,  mathematics),  study  of  the  enrolled  in  is  a  and  of  very  correlates  of  programs  in  report  of  such  an  investigation. Measures basis  of  the  volunteer classes  of  twelve  at  the Among  Facility  Michael  Halperin,  independent  literature  subjects  Victoria. Number  of  during  a  the  the  of  cognitive  and Numeric  Alberta,  or  of  Learning  the  collected  from  each  four  of  Columbia  investigated (based  reasoning  logical  on  British  variables  verbal  selected  were  session  Concept  1969),  abstract  area,  class  Universities  and M i c h a e l , 1978),  in  variables,  on  were  findings  (Feinberg  reasoning  and  (Hartley  and and  86  Hartley,  1976)  1980).  Noncognitive  to  correlate  1980),  and  In  relationships motivation,  academic  of  statistics investigated.  The  research  based  (1976),  who  psychology in  to  on  as  a  hypothesized  theoretical  and  variance  in  The  instructor  variables  may  as  part  the  Gale  Hartley  of  for  could  to  and  toward Hartley toward  achievement  account  was  Atkinson who much  an  variance  in  (1978),  as  it  for  based  have  the were  variables,  explained  as  of  attitude  motivational  the  achievement  attitude  related  (1979),  account  the  dependent  score  measure of  was  the  statistics  speculation  findings  mathematics  on  Raynor  stated 25%  the  of  that the  achievement. of  This  of  This  and  was  endeavour  proportion  Hakstian  measure  examination.  of  empirical  academic  achievement,  measure  motivation  achievement.  motivational  that  that  statistics  and  by  the  and  Hartley,  utility  of  reported  a  were  variables,  in  measure  to  unknown,  with  perceived  regard  additional,  (1978)  a  found  and  research,  findings  scientific With  of  been  (Roberts  (Hartley  achievement  inclusion  Vasu,  1978).  toward and  and  which  statistics  above-mentioned  motivation,  reported  statistics.  was  the  and  experience  and H a r p e r i n ,  course  was  self-esteem  attitude  specific  had p r e v i o u s l y  toward  post-secondary  to  (Elmore  achievement  attitude  (Feinberg  addition  which  statistics  previous  statistics  visualization  variables  included  Bilderback, 1976),  spatial  with  investigated  or  and  the  obtained was  final  variable, on  a  administered  examination.  statistics  one-hour by  each  common course  87  The  original  statistics  "causal  latent  structure  for  the  observed  two  studies  both  in  of  study  the  rather  social than  In  appear  of  information  and  Further,  the  it  was  the  was  a  underlie three  partial  concerning  the  A  the  set  exploratory account  their  procedures  of  contributions  of  1976;  chosen  science  as  to  performed Elmore  on  of  in  manifest 1980),  education,  because  among  the  statistics  accessible  students  on  and V a s u ,  models  the  common  statistics  conclusions  Students  more  replication  variables  variables.  be  approach.  speculated,  test  hoped  a  set  variance  in  statistics been  of  that  utility.  of  one  population difficulties  populations  investigation is,  future  could  rather  the  That  problems  investigation  of  had  as  based  directions  treatment  adequacy  It  to  practical  about  diagnosis  or  and  Bentler's  of  students.  addition,  degree  it  to  proposed to  were  mathematics  science  specified,  Hartley,  latent  sciences,  statistics  social  a  using  plausibly  planned  regression  present  of  of  matrix.  studies  and  determinants  variables"  attitudinal  (Hartley  the  was  literature  Both  achievement  with  the  stepwise  variables  thought  the  application  model m i g h t ,  was  and  achievement.  whereas  Each  the  latent  correlation  ability  results  was  investigation  investigate  with  variables  delineated.  The  of  which  to  through  modeling  independent  models  was  achievement  (1980)  of  intent  could  research  with  shed  models  have  into  statistics  have  simple  it  some to  would  yielded  the  could light  have  early take. on  explain  the the  achievement.  intended  initially  to  investigate  the  latent  88  structure  and  each  introductory Unforseen  model  by  statistics  delays  independent  in  students  at  statistically  significant  Columbia  Alberta  total  sample  Columbia too  of  and  small  to  structure  and  65  into  permit the  order  to  exclude  "latent  then, to  limited  the  analyzed Because  The  the  than  The  revised of  achievement,^subjective  the  total  of  and  of  of  the  sample the  was  latent  clusters  in  12 v a r i a b l e s .  the  models was,  correlations  and  forward  regression  samples  each  as  were  compared.  the  the  0.10  criterion  level. enquired  variable of  matrix,  statistics Each  about  to  variables  correlation  variance  in  analysis  investigation,  adopted  of  of  Alberta  questions  independent  redeveloped  of  from  the  0.05  observed  of  British  consideration  forward  conventional  the  were  zero-order  was  of  of  method  results  nature  research  set  of  the  all  The  significance  the  split  each  in  British  (from  that  the  resulted  exploration  Columbia  and  about  to  plan  and a n a l y s i s  each  32  estimates  and  examination  examination  contribution by  more  33 a n d  of  the  resulting  questions  analysis  exploratory  the  relationship  research  British  statistical  Alberta  between  meant  in  variables.  separately, of  of  rather  the  of  of  universities.  measures of  The  samples  approach  computation  procedures.  level  to  pools.  samples  coefficients.  from the  latent  three  the  University  stability  variable"  incorporating  from a l l  respectively)  the  combined  differences  two  path  Consequently,  the  data  Alberta,  of  the  administering  variables  and  using  the  statistics revealed  and  by  about  the  achievement  made  question  was  answered  89  independently  of  the  Correlational revealed  that  visualization correlated  other analysis  past  and a t t i t u d e  with  achievement.  Application  55.5% of Similar  The the  forward  analysis  of  and  of  a  to  forward  achievement variables. and of  be  attitude  spatial entry  British  was  in  related  for  taken  to  to  were  statistics  revealed a  that  statistically in  statistics  together  accounted  Columbia  sample.  and A l b e r t a  clusters  Cognitive-motivational  of  independent matrix.  achievement.  the  set  12  contributed  to  that  sets  attitude  toward  significantly.  observed  regression were  of  in  the  in  results  variance  of  order  in  independent statistics The  results  analyses  computed  clusters  The  for  learning,  variables  Both  the  by  attitude  significantly  54.9% of  forward data  research  achievement.  spatial  learning,  that  visualization) similar  toward  that  revealed  (concept  not  revealed  concept  statistics  accounted  Three  data  correlation  regression  Non-parsimonious Columbia  the  related  was  intercorrelations  variance  facility,  statistics  identified  appeared  the  Alberta  and a t t i t u d i n a l - m o t i v a t i o n a l were  of  significantly  regression  12 v a r i a b l e s  the  number  with  was  accounted  of of  were  spatial  variance.  statistics  correlated  set  sample  reasoning,  statistics  cluster  coursework  visualization, toward  of  verbal  Columbia  attitudinal-motivational)  first  proportion  achievement. for  the  British  Two c l u s t e r s  and  Only  previous  the  toward  achievement.  identified.  significant  of  experience,  (cognitive-experiential  only  two.  the to  order  for  the  British yield  90  "hints the  and  clues"  variables  independent the  in  (Bentler,  the  two  data  variables  relative  motivational  1980)  was  sets.  not  contributions variables  were  discussion  psychometric data of  sets,  the  followed  two  recast  With the  of  of  Folding). displayed Folding The  In a  Vocabulary of  0.85  Folding).  In  both  low,  the  variance  responsible British of  for  Columbia  scores  (19  to  British  the  and  have  obtained the  (Advanced  also  the  low  data,  the of  data,  internal in  more  compared in  the  each  one  which  of  total  Alberta  the  three  of  0.63,  similar.  Alberta  and  Paper  Vocabulary while  consistency  of  of  coefficients  Advanced  Paper  of  0.82.  data,  with  consistent  (Hoyt  0.66  Paper  fact in  analyses  Vocabulary  for  consistency may  both  distribution of  item  internal  This  reliability  a  the  internally  to  low.  skewed  the  non-equivalence  consistency  coefficient an  on  presented.  Columbia Hoyt  and  comment  Columbia  of  discussing  internal  situations  36 o u t  general  were m a r k e d l y  being  was  a  discussion  measures  and  Results  samples  the  the  attitudinal  Alberta  to  as  .  of  samples,  of  low  situation  coefficient  the  then  two  results  British  observed  the  entry  the  involved  relatively  reverse  Advanced  and  cognitive the  was  are  for  first,  Sections  Columbia  the  brief  exceptions,  exceptions  two  a  questions  two  British  These  by  of  among  dissimilar.  the  includes,  samples.  research  of  of  relationships  cognitive,  equally  characteristics  the  Order  similar  of  Discussion The  about  have  cases.  and  36- p o s s i b l e  was been  In  limited marks)  the range may  91  also  on  have  contributed  The  similarity  the  psychometric  either  to  the  other.  described  samples  significant  administration Performance  class  by  of the  The  by  the  IV  (p.64),  the  significantly statistical either  could  the  that level  the of  could  result  of  populations. time the  of  Utility)  would  the  result  due two  to  Still  a  and,  in  weeks  could  of  to  the  sample. have  operator measures  been during  (Attitude been  matter.  Advanced Vocabulary to  As  in  was  justify  students It  is  British  sampling being  third  in  and  being Chapter  performed  unlikely  that  performance Columbia  fluctuation  or  possible  their  the  on and  they  representative  influenced  addition,  as  reported  decreased  the  samples  each  univariate  prior  subject  measures.  administration  students  on  from  . c o u l d . have  Columbia  between  be  the  difficult  both  two  task  to  variance-  Alberta  noncognitive  British  on  the  "summation"  experience.  of  five  the  Learning  more  Differences  samples  different  is  of  extend  difference  the  occurred  to  exposure  the  different  of  which  the  to  samples  not  multivariate  result  performance  instruction  Alberta  the  Perceived  in-class sample  the  three  the  subjects'  better  test.  be  of  and  Diagramming R e l a t i o n s by  be  about  differential  influenced  IV,  Alberta did  or  significantly  Concept  both  measures values,  pre-tests  instruction and  the  least  may  C o l u m b i a and  mean  Chapter  the  Statistics  influenced  of  were  at  reliability.  British  statistics  on  time,  Toward  in  and  in  lower  of  which  differences  instruction  affected  the  profiles  matrices  between  of  the  properties  covariance As  to  explanation  of is  motivational  attitudes  toward  92  participating sample  were  irrelevant  in  not  and  each  of as  analysis independent  the  reported  with  five  Chapter  and  V,  statistics  were  achieved  a  the  did  not  British  Achievment  In  British  the  Although  results,  drawing  when  since  significant  seven  (or  and  not)  the or  12  both  Selfand  sample,  Past  significantly  and  in  were  not  Subtraction,  Research the  with  were  Alberta  data  set. due  samples  to  sets.  sampling  such  as  can  zero-order data  Academic  Toward  some c o n f i d e n c e  the  sets,  correlations  Achievement  Concept  data  Columbia  Attitude  small  in  of  Motivation  Multiplication  conclusions  ones, of  the  and  Alberta  correlated  Columbia data false  and A l b e r t a  from  significant  Folding  significant  with  analyzing  this  No p a r t i a l  statistically  British  data.  Statistics  but  in  the  these  correlated  to  each  achievement.  Specific  Alberta  achievement  answer  between  Motivation,  significantly  Columbia  seemingly  question  developed  Relations,  Achievement;  Toward  The  (Diagramming  Statistics  the  was  Columbia and  and Advanced V o c a b u l a r y  danger  on  research  (Paper  Experience  a  well  Alberta  considered.  Utility).  not  the  statistics  correlations  Achievement  both  in  first  variables.  Perceived  Attitude  that  perform  between  manifest  in  variables  in  observed  likely  to  The  zero-order  correlation  Concept,  seems  motivated  One.  twelve  variables  Learning)  It  relationship  correlations  Two  while  the  of  multiple  highly  Question  about  question,  as  study.  tasks.  Research enquired  the  be  error  the  British  placed  in  correlations In  addition,  is  the  the were two  93  significant  coefficients  literature  (see  Four  of  significant  Table the  conflict direct  of  Finally,  observed Columbia.  the  The  exposure  to  discrepant  of  on  more  in the  subject  the first  is  intense  and  the  that  day  of in  be  exposure  clearly  Columbia  the  to  the  that a  in the  1977). between  Method task  findings. relationships A  Achievement,  Achievement  as  from  was British  function  of  explanation  for  had  developed  not  sample  whereas  Alberta  in  specific  and  in  explained One  is  interpretable.  and  not  finding  Achievement  these  Statistics  attitude  to  of  were  with  explain.  significant  but  class), the  as  a  variance  between  such  matter.  British  crystallized  relatively  may  the  relationships  Research  data  regard  (Vidler,  to  Toward  and  agreement  explanation  Toward  to  difficult  less  Attitude  Alberta  findings  sufficiently  are  with  literature  statistically  discrepancy the  in  Relations,  partial  Attitude  in  the  variables a  results  is  achieve  This  speculations,  significant  exceptions  between  between  become  from  provide  two  relationship  in  Self-Concept,  sample-specific  with  measured  of  and Diagramming  may  the  achievement  variables  but  reported  absence  required,  and  motivational  achievement,  arising  in  to  motivational.  Gale's  variance,  are  were  and  the  Academic  The  variables  of  failed  statistics  Hakstian  opinion  Achievement  with  Raynor's  academic  reported  which  and  with  consensus  variables  Atkinson's  contribution  general  and  five  Three  against  those  2).  correlation  noncognitive. argues  replicated  attitude  sample,  subject  (in  after  matter.  these  whom i t might two  was have  weeks  94  The  remaining  interpretable.  The  observed  sample  was  not  (1976),  and,  the  and  Experience,  in  the  Alberta  British  fluctuation subject In  some case  extent of  the  results  one  literature  by  explanation  variables the  much  analysis  of  the  by  not  in  Hartley  of  this  serve  to  in  present  analysis  Achievement was  observed  Alberta.  Sampling  discrepancy; explain  the  cognitive were  to  In  the  investigation. "fit" those  other  them.  literature  the and  Hartley  the  (1980),  between the  investigation  of  and  Columbia  and  between  the  less  Vocabulary  British  results  variables,  Two.  The of  in  second  variables  correlation  reported No  the  relationships  clusters  the  the  are  between  reported  the  in  the  worse.  Question  about  correlations.  could  in  present  of  and Vasu  but  replicated  enquired  as  Elmore  sample  Advanced  relationship  reported  the  Research  in  achievement  was  question,  The  findings  reported  absent  noncognitive  of  that  set.  Columbia  course  and  was  between  analysis  as  reported  summary,  variables  the  large  data  is  and  in  further,  of  discrepant  relationship  Achievement  as  three  partial  or  revealed  matrix.  Chapter  V,  research  The was  multiple  question  by  subjective  answer  based  upon  to  this  zero-order  correlations  were  examined. Two matrix clusters found  to  clusters  were  abstracted  calculated  from  the  were be  interpreted  related  to  as  from  British  the  data.  These  a-cognitive-experiential  cluster,  achievement,  and  Columbia  intercorrelation  an  attitude-motivational  95  cluster, from  which  the  ability  of  to  the  suggest  cognitive The  may  absence  suggests  students  the are  sample,  combined  to  achievement  the  related as  an  to  general  attitudinal-  a by  Experience  some  exposure  of  small  the  the  noncognitive  the may  in  or  contribute  of  a  course, (through  Achievement. in.which  Alberta  sample  relationship British  of  several  a  cognitive  suggests to  variables  However,  subject  results  course-time  the  contribution  and c o g n i t i o n .  as  from  passes  matter.  occurrance  tentatively  The  outset  the  zero-order  one,  dropped  correlations  disappears  the  tentatively  indirectly  in  subject  in  intercorrelation  Statistics  significant  a  and sizes.  the and  in  Experience  the  attitude  at  variables  of  be  Columbia  directly  variance  II  sample  British  the  can  Chapter  either  course  to  in  identified  sets  and achievement  with  between  data  effect  lack  motivation  both  subjects,  clusters  both  the  direct  noncognitive of  the  when m e a s u r e d  of  the  or  beginning  the  exposed to  attitude  a  was  abstracted  were  interpreted  second  statistically  one  that  because  that,  of  Further,  and  was  matrix  The  delineated  contribute  is  correlations  cluster  Alberta  of  abilities)  Experience  and  models  analysis  Experience  variables  correlation  between  and  examination  matrix  of  cluster.  differences  final the  first  Columbia  related  clusters  motivation.  motivational  British  Both  sample's  The  and  The  not.  Alberta  achievement.  the  was  the is  when  between Columbia  significant variable  that  at  variance  indirect  students  as  did  the  directly  and  indirectly  in  through  have  matter,  the  had  Alberta to  the  96  variance  in  achievement.  The  influence  of  motivation  may  remain  indirect. When c o n s i d e r i n g subject,  a model  and c o g n i t i v e II,  which  the  motivation  with  indirect  may  matrix.  above  The  described of  indirect  influence  that  correlation Bentler's might  Model  the  effects  "A",  effect  both  on b o t h  of  suggests  that  II,  achievement  already  of  may  motivation  results  of  do not  about  the  of  when  yield  possible  as  values  the  as  to  addition It  and  and  Model  of  of  guesses"  path  an the  should  examination  "hunches  and  correlation  plausible  the  subjective any  Chapter  attitude  such  on c o g n i t i o n ) .  the  in  some e x p o s u r e  (with  naive  experience  a model more  the  Experience  observed  be  occurred  of  described  direct  analysis Chapter  effect  in  an be the (in  coefficients  take.  Question  enquired about variables the  the  direct  the  matrices  sense)  of  Achievement  explain  has  the  Research  to  such as  statistics  matter  the  of  plausibly  in  subject  noted  retains  replacement  cognition)  explanation  prediction  variables,  (with  "C",  the  to  the  the  Three.  The  contribution  variance  in  question,  as  reported  application  of  both  of  third  the  set  research of  12  independent  statistics  achievement.  in  V,  Chapter  parsimonious  and  was  question  The  developed  exploratory  answer through  regression  procedures. Only in  Experience  statistics  three  variables  significantly  achievement (Paper  in  the  Folding,  contributed British  Attitude  to  the  Columbia Toward  variance  sample,  Statistics  while and  97  Concept  Learning)  exploratory the  analysis  variance  were  very  for  those  yielded  of  the  the by  In  Toward  in  reported found  Both  that  that  attitude  fourth  Vasu  to  was  observed  stronger  than  contributions were The  not  to  that of  both  of  and  those  to  Vasu and  to  variables  had  of  the  variable,  samples  than  the  Vasu and  Attitude  variance  Elmore  and  in  Vasu  The  with  reported  former  statistics  a  significant  Visualization. found  by  This  Columbia  Elmore  and  However,  and mathematics was  extremely  by  was the  skills small.  Self-Concept,  reported  and  relationship  sample,  authors.  Academic  that  and  and  Achievement.  attitude  resemble  Elmore  to  and  been  the  visualization  Achievement.  these  sample,  not  variables,  visualization that  of  spatial  Spatial  British by  do  correlated  and  Statistics  spatial  significant,  for  skill  reported  addition,  contributions  Alberta  contributed  related  the  the  sample  or  both  Experience  in  of  Hartley  Achievement  only  contribution  lower  was  In  contributing  cognitive  and  Elmore  variable,  related  (1976),  the  sample.  relative  Columbia  sample,  mathematical  between  the  analysis  British  Hartley  relationship  Alberta  samples.  significantly  while  be  of  among  achievement,  A  two  Alberta  Statistics,  Achievement.  the  the  skills  the that  and H a r t l e y  the  mathematical  in  nonsignificantly  results  Hartley  (1980).  so  revealed  different  Unlike results  did  Hartley  was and  Hartley. Both yield  the  parsimonious  some e v i d e n c e  variables  on  about  and the  Achievement.  exploratory direct The  regression  effects  results  of  of the  the  procedures independent  analyses  of  the  98  British a  Columbia  direct  of  sample  reveal  influence  on A c h i e v e m e n t .  the  next  variables  were  cognitive.  entry,  Achievement Research  Question  hypothesized  to  Two,  be  direct.  variable  indicate  that  motivation  several  observed  withstand  sample  sizes  Just effects  as  some  of  discussion  of  data,  so  direct  above,  were  of  the  results  reflected  in  and to  the  most  result  of  the  was  the not  results the  and  of  entered  variables  was the  finding  in  may the  achievement  given  the  small  below. the  direct in  the  British  Columbia  attitude,  discussed  exploratory data.  and  Spatial  made  significant  achievement.  next,  was  reflected  the  Alberta  in  of  concerning  the  in  discussion  Whether  discussed  of  order  variance  This  certain,  were  the  entry  variance  learning  variance  the  exert  Once  contributing  again,  4.04%  to  R-square.  serious the  Alberta  samples.  that  samples  the  is  in  effect.  cognition  of  Limitations The  to  concept  Motivation in  the  indeed  the  next  direct  analysis of  in  to  Motivation.  cognition  of  effects  visualization  change  a  did  cognitive  speculation  and  analyses  the  the  limitations  the  parsimonious  Achievement  However,  exerts  Experience  contributions  of  Achievement  other  noted  influence  contributions  the  contribute  was  cross-validation  and  Experience  When c o n s i d e r e d  to  As  the  motivational  would  that  of  limitation  nonequivalence This could  not  the of of  statistical be  pooled,  Study this  investigation  the  British  and and  logical  arose  Columbia finding  consequently  two  as and  meant small  99  samples  rather  analysis.  than  The  necessary,  and  the  not  be  into  the  latent  being cast  was  entire  set  Education, in  students  were  high.  evaluating  the  on  and  testing  Summer  up  was  of  so as  course  than  the  Achievement  to  one  ask class  range  of  are  even  the  manifest  sample  target who  due  to  that  sizes, chance,  of  the  were  It in  students  Further,  courses  four  low  students  sciences  were  taken  of  population.  courses.  Session  be  rather  being  than  tested,  courses  into  the  was  account  very when  investigation. limited  to  take  of  in The  up t o o  short  abilities  range  much c l a s s  the  limited.  The  relate main  In  courses  Consequently, which  abilities placed  time  lengths,  tested.  of  of  restrictions  test  variables  instructors  period.  more  postulated  twelve  was  social  properties.  range  study  the  all  three  were  not  of  became  investigation  small  Volunteers  necessitated  restricted  to  of  must  the  tests  time  impossible  more  about  results  this  Summer  from  set  subjects,  classes.  psychometric  School  relatively it  session  no  fluctuation  statistics in  questions  for  doubt.  of  representative  the  in  into  the  considerations  Finally, tested  that  participation  These  greater  sample  introductory  winter  although  the  available  originally  reason,  Finally,  the  enrolled  research  the  to  were  were  same  limitation  certain  the  which  the  results  from  were  enrolled  regular  of  of  one  underlying  out.  serious  no means  For  subject  generalizability by  larger  models  structure  carried  A second  is  three  evaluated.  generally the  single  reformulation  could  variables  a  any to  in  and  a a  addition, to  give  conclusions Statistics  alternative,  that  1  of  testing  less  outside  of  representative  class  time,  small  results  sample  Further, rather  the  than  However, drawn  this  sizes  Statistics this  be  and  sample.  literature.  is  in  subject  has  the  models  achievement  in  This  be  Statistics,  intercorrelation  of  the  even  related had  might the  students  external  validity.  is  has  not  based  been  achievement  of  suggests yield  the that  in  to  upon t h e  fact  the  literature.  in  the  the  in  subject  the  may  "fit"  only  matter. of  the of  explanations exposed  the  Attitude  investigation  and  less  statistics  examination the  spatial with  variable,  plausible  inexperienced  Statistics  reported  in  be  correlate  only  noncognitive  may  variables, do  related  usage)  of  reported  some e x p o s u r e  results  matrices  were  to  two  skills,  results  the  School  correlates the  The  investigation.  Bentler's  conclusion  finding  that  Summer  (in  concluded that  This  may  who  the  mathematical  Toward  different  to  Achievement  It  Second,  guesses"  replicates  experienced  the  and  Achievement.  and  power  restricts  may  Experience  an  inconclusive.  students  regard  finding  the  are  session  results.  visualization  investigation  were  from the  it  in  Implications  subjects  "hunches  Achievement,  resulted  the  some  with  and  restrict  that  winter  First,  that  of  fact  c o u l d have  sample.  Conclusions The  00  two of  subject,  respectively. Figure from  the  6 portrays  a  inexperienced  model which subject.  As  data  discussed  collected above,  the  101  Figure 6 Model of Achievement (Less Experienced Student) indirect some the  role  direct dotted  this  taken  as  motivational  effect.  line  issue,  weights,  of  in  and  The  Figure  test  or  calculated a  However,  guide the  extremely  variables  possible Only  6.  refine  the  from the  for  sample  is  direct  so  be  supplemented  effect  is  further  research  model.  The  British  specification  may  the  small  that  indicated can  sample,  path the  by  clarify  standardized  Columbia  of  by  beta  could  be  coefficients. weights  may  be  inaccurate.  Experience  >• C o g n i t i o n - ^ _ _ _ ^ Attitude  /  Achievement  t  Motivation-'' Figure 7 Model of Achievement (More E x p e r i e n c e d S t u d e n t )  The "C"  model  delineated  observed  depicted in  in  Chapter  relationships  Figure II,  students,  who  statistics.  Again,  model  the  is  a n d may  among  experienced  7,  have was  very  plausibly  variables been  similar  exposed  to  account  model for  collected to  discussed above.  the from  instruction Although  in the  1  beta  weights  the  path  subject  reported  coefficients,  to  extreme  Finally,  it  investigated  in  achievement  in  contributions the been  amount  above  this  be  on  concluded  study,  the  serve  as  specifications  statistics  estimates  as  these  of  may  be  cross-validation. that,  is  several  initial such  with  approximately  statistics of  of  could  fluctuation  may  02  the  set  of  55% o f  the  variance  explained.  independent  instruction  to  However,  variables  which  measures  the  in the  varies  with  subjects  have  exposed. Several  the  implications  results  investigations correlates  analysis, Finally, variables  appear  to  into  the  from  should the  which  be  the  be  were  should  a  may  of  to  and more  explanatory  of  source  to  further on  stringent power  were  regression  investigation. of  determined.  the are  which  exploratory  possible  from  achievement  achievement,  mathematics of  drawn  statistics  from c o n s i d e r a t i o n  empirically  be  First,  statistics  analysis  determinants fruitful  research  exposure  models  excluded be  of of  subject  potential  and  effect  subjective  future  investigation.  determinants  Second,  investigation correlates  this  and  desirable. developed  of  for  independent in  The  the area  achievement  predictors.  present of  the  would  1 03  Notes Hakstian, variance.  R. OWMAR: Unpublished  One-way multivariate memorandum. Undated.  analysis 5 pp.  of  1 04  References A i k e n , L.R. U p d a t e on a t t i t u d e s in learning mathematics. 1976, 46, 293-311.  and o t h e r Review of  affective Educational  variables Research,  Atkinson, J.W. The mainsprings of achievement oriented activity. In J.W. Atkinson and J.O. Raynor (eds.), P e r s o n a l i t y , M o t i v a t i o n and Achievement. New York: H a l s t e a d P r e s s , 1978. Austin-Martin, G. C o r r e l a t e s of mathematics a n x i e t y in female c o l l e g e freshmen. Paper p r e s e n t e d at the Annual C o n f e r e n c e of the Rocky Mountain Educational Research Association ( 1 1 t h , H o l y C r o s s R e t r e a t , L a s C r u c e s , New M e x i c o , O c t o b e r , 1980). Begle, E.G. C r i t i c a l V a r i a b l e s in Mathmatics E d u c a t i o n . W a s h i n g t o n , D . C . : M a t h e m a t i c a l A s s o c i a t i o n of America and the N a t i o n a l C o u n c i l of T e a c h e r s of M a t h e m a t i c s , 1979. Bentler, P.M. Multivariate causal modeling. Annual 419-456.  analysis Review of  with latent Psychology,  variables: 1980, 31,  Bentler, P.M. Interdependence of theory, methodology, and empirical data. In D.B. Kandel (ed.), Longitudinal R e s e a r c h on D r u g U s e . . N e w Y o r k : H a l s t e a d P r e s s , 1978. Cook,  T.D. and Campbell, D.T. and A n a l y s i s Issues for F i e l d Mifflin, 1979.  Cronbach, York:  L. J. Essentials H a r p e r a n d Row, 1 9 7 0 .  of  Quasi-Experimentation: Design Settings. Boston: HoughtonPsychological  Testing.  New  Davis, E.C. and Risser, J.J. Study of V a r i a b l e s A s s o c i a t e d with F i n a l Grade in Mathematics C o u r s e s . Publication l o c a t i o n unknown, 1965. (ED 0 1 1 7 6 0 ) . E k s t r o m , R., F r e n c h , F. and Harman, H. Factor-Referenced Cognitive Tests. Testing Service, 1976.  Manual f o r the K i t of New J e r s e y : Educational  Elmore, P.B. and Vasu, E.S. R e l a t i o n s h i p between selected v a r i a b l e s and s t a t i s i c s achievement: b u i l d i n g a t h e o r e t i c a l model. J o u r n a l of E d u c a t i o n a l P s y c h o l o g y , 1980, 12, 457467. Fennema, E. and Behr, M. Individual differences l e a r n i n g of m a t h m a t i c s . In R . J . Shumway (ed.), in Mathematics Education. Reston, Virginia: C o u n c i l of T e a c h e r s of M a t h e m a t i c s , 1980.  and the Research National  1 05  Fennema, E. and Sherman, J. mathematics achievement, affective factors. American 1977, j_4, 51-71. Feinberg, L.B. correlates statistics. 11-18. Fox,  Sex-related differences in spatial visualization and Educational Research Journal,  and Halperin, S. Affective and cognitive of course performance in introductory J o u r n a l of E x p e r i m e n t a l E d u c a t i o n , 1978, 46,  L.H. T h e E f f e c t s o f Sex R o l e S o c i a l i z a t i o n on M a t h e m a t i c s P a r t i c i p a t i o n and A c h i e v e m e n t . Intellectually Gifted Child Study G r o u p , 1976. (ED 1 4 2 8 6 7 )  Giambra, L.M. M a t h e m a t i c a l b a c k g r o u n d and g r a d e - p o i n t average as predictors of course grades in an undergraduate statistics course: a replication. T e a c h i n g of Psychology, 1972, 3, 184-185. G l a s s , G. V. and Stanley, E d u c a t i o n and P s y c h o l o g y , Prentice-Hall, 1970.  J. C. Englewood  Statistical Methods in Cliffs, New Jersey;  Hackman, J.D. and Taber, T.D. Patterns of undergraduate performance related to success in college. American Education Research Journal, 1 9 7 9 , J_6, 117-138. H a k s t i a n , R. and G a l e , C. V a l i d i t y S t u d i e s w i t h t h e CAB E d u c a t i o n a l and P s y c h o l o g i c a l Measurement, 1979, 3_9, 400. Harper, J.K. The C u r r i c u l a and Other Community C o l l e g e . C o l u m b i a , 1978.  III. 389-  R e l a t i o n of High School Achievement and F a c t o r s to Academic Achievement at a M.A. Thesis. U n i v e r s i t y of British  Hartley, A.A. and H a r t l e y , J . T . P r e d i c t i n g performance in the basic research methods c o u r s e i n p s y c h o l o g y . Educational and P s y c h o l o g i c a l Measurement, 1976, 36, 449-452. H e n s o n , R. Expectancy beliefs, ability and personality in predicting academic achievement. J o u r n a l of Educational Research, 1976, 70, 41-44. Huberty, C.J. and S m i t h , D.U. M e a s u r e s o f d i s c r i m i n a t i o n among achievement l e v e l s in s t a t i s t i c s . Paper p r e s e n t e d at the Annual Meeting of the American Educational Research A s s o c i a t i o n (Washington, D . C . , 1975). (ED 1 0 9 2 5 4 ) Hummel, T.J. and Sligo, J.R. Empirical comparison of univariate and multivariate analysis of variance procedures. Psychological Bulletin, 1971, 76, 49-57. Kulm,  G.  Research  on m a t h e m a t i c s  attitude.  In  R.J.  Shumway  106  (ed.) Research in Mathematics Education. Reston, V i r g i n i a : N a t i o n a l C o u n c i l of T e a c h e r s of M a t h e m a t i c s , 1980. Mathematics, 1980. M a t h i s , H.R. The V a l i d i t y of the A m e r i c a n C o l l e g e Test in P r e d i c t i n g Academic Achievement in Community C o l l e g e s of A p p a l a c h i a n K e n t u c k y . Doctoral Dissertation. Raleigh, N.C.: North Carolina State University, 1972. Michael, J.J. and Michael, W.B. The validity of a prestatistics s u r v e y of b a s i c m a t h e m a t i c a l s k i l l s in relation to achievement in the first course in psychological statistics. E d u c a t i o n a l and P s y c h o l o g i c a l Measurement, 1969, 2 9 , 915-919. N e l s o n , L.R. LERTAP M a n u a l . Dunedin, New D e p a r t m e n t , U n i v e r s i t y of O t a g o , 1974.  Zealand:  Education  Raynor, J.O. Future o r i e n t a t i o n in achievement m o t i v a t i o n : a more g e n e r a l t h e o r y of a c h i e v e m e n t motivation. In J.W. Atkinson and J.O. Raynor ( e d s . ) , P e r s o n a l i t y , Motivation and A c h i e v e m e n t . New Y o r k : H a l s t e a d P r e s s , 1978. R o b e r t s , D.M. a n d B i l d e r b a c k , E.W. R e l i a b i l i t y and v a l i d i t y of a statistics attitude survey. E d u c a t i o n a l and P s y c h o l o g i c a l M e a s u r e m e n t , 1 9 8 0 , 4_0, 2 3 5 - 2 3 8 . Robitaille, D.F. A s s e s s m e n t Summary Printer, 1981.  T h e 1981 B r i t i s h C o l u m b i a Report. Victoria, B.C.:  Mathematics Queen's  Sanders, J.R. and Worthen, B.R.• An A n a l y s i s o f E m p l o y e r s ' P e r c e p t i o n s of the R e l a t i v e Importance of S e l e c t e d Research and R e s e a r c h - R e l a t e d Competencies and S h o r t a g e s of Personnel with such Competencies. U n i v e r s i t y of Colorado, 1970. Sepie, A.C. a n d K e e l i n g , B. The r e l a t i o n s h i p between t y p e s a n x i e t y and under-achievement in mathematics. Journal Educational Research, 1 9 7 8 , 7_2, 1 5 - 1 9 . Sherman, J. Mathematics, spatial visualization and f a c t o r s : changes in g i r l s and b o y s , g r a d e s 8-11. of E d u c a t i o n a l P s y c h o l o g y , 1980, 72, 476-482. Shye,  S. Achievement structural analysis. 1 9 7 8 , J_3, 3 2 7 - 4 6 .  Singh, B.K. Achievement. 1976. Timm,  N.H.  of of  related Journal  motive: a faceted definition and Multivariate Behavioral Research,  Non-Intellective C o r r e l a t e s of Academic Allahbad: Indian International Publications,  Multivariate  Analysis.  Belmont,  Cal.:  Wadsworth  107  Co.,  1975.  Troutman, J . G . C o g n i t i v e p r e d i c t o r s of f i n a l grades in finite mathematics. E d u c a t i o n a l and P s y c h o l o g i c a l Measurement, 1978, 3 8 , 401-404. Vidler, D.C. Motivation  Achievement motivation. In E d u c a t i o n . New Y o r k :  in S.Ball Academic P r e s s ,  (ed.), 1977.  White, K.R. The r e l a t i o n s h i p between s o c i o e c o n o m i c s t a t u s and academic achievement. Paper presented at the Annual Meeting of the American E d u c a t i o n a l Research A s s o c i a t i o n (San F r a n c i s c o , C a l i f o r n i a , A p r i l 12, 1979) W o l f l e , L. M. S t r a t e g i e s of path a n a l y s i s . Research Journal, 1 9 8 0 , _T7, 1 8 3 - 2 0 9 .  American  Education  108  Appendix  A  I n i t i a l Form of Concept Learning Task  Instructions This  learn  an  form  is  a measure  unfamiliar  described  and  ability  use  to  descriptions questions  in  minutes. have  the Task  I  nine  concept.  while any  how  mathematical  second, the  of  will  you  tell  concept.  You can the  wish.  you  when  and  are  refer  time  four  the  asked  back  questions  The  well  First,  questions  answering  order  quickly  to  and  limit  minutes  you concept  to  test  the  is  your  concept  you can is  can  do  twelve  and e i g h t  the (12)  minutes  passed. First,  please  Do y o u  know  If  answered  you  what  answer  the  this  symbol  "Yes",  please  question. { i = 1 }*{5} write  X,j  what  means?  you  think  it  means  tell  you  "turn  here:  Please begin  now".  turn  the  page  and  begin  when  I  to  and  109  Concept  A.  Description.  Subscript  "elements", matrix. such  Notation. we  If  can we  If  refer  have  a  to  we any  matrix  have  a  element  by  with  "matrix" its  containing  position  12 e l e m e n t s  (i.e.,  in  the  numbers),  as: olumn  we  can  number  X  1 2  =  Row  2  Row  3  any  of  the  the ,  1  call  COLUMN o f in  Row  3,  of  its  ROW  first  row z  3  4  2  3  1  5  0 - 1  6  2  7  0  -6  numbers of  matrix.  X i  2  4  the  and  1  and = 0,  the  For  or  elements  matrix  example,  the etc.  second  and X , 42  "j"  Xjj  .  " i "  is  the  number  refers  column,  or  to  the  the number  is of  the the  element 3.  So,  110  B.  Addition  Notation.  "addition". together.  When The  which  numbers  where  to  you  diagram are  begin  In  to  be  this  see given added  this  to  will  add  you  tell  where  •  {n}  on  might  be:  {i = U  •  {2}  the  Xjj  over  diagram  X,-  3  = X  1 3  and  + X  Z 3  are you  "•"  means  to  ADD  numbers  how  to  decide  the  to  stop  adding  sign  the  1st  subscript  (ROW)  the  2nd  subscript  (COLUMN)  -the  Based  symbol  together.  adding  {i=m}  the  symbol,  below  -addition  subscript  task,  matrix  = 1 + 6  element  given  = 7  to  above,  add  an  example  111  Test  Questions.  Please following work.  the  •  X  ±2,  your  item.  Use  calculate  1  write  the  your  answer  Use  any  matrix  blank  from  each  space  the  item  you  wish  "Concept  =  { j = 1 } • { 4}  3.  {i = 2 } » { 3 }  K  4.  {i = 2 } « { 3 }  X  5.  {i = 2 } » { 2 }  Xj^  6.  {j = 2 } « { 4 }  Xj  7.  if  c = 3,  {j = 2 } » { 4 }  c  X j  =  8.  if  c = 2,  {J=1}«{3}  (  Xij  -c)  X  X  does  X^j it  i 3  A  =  = X ,  =  ia  = XZJ  X j  =  3  {k=1}•{3} [{k=l}»{3}  4  f e t  X  k l  k f c  ]  = equal [{k=l}«{3}  X , k t  in  the  space  for  your  rough  Description"  answers.  2.  9.  for  ]  ?  to  1 1 2  Appendix  Non-Copyright  Introductory  B.  Test  Materials  Statement.  "My name i s S h e e n a S e l k i r k a n d I am a g r a d u a t e student in Measurement and Research Methodology at the University of B r i t i s h Columbia. This study is an investigation into the extent to which abilities and attitudes are r e l a t e d to the performance in introductory s t a t i s t i c s . Your participation is voluntary, but I would c e r t a i n l y a p p r e c i a t e your c o - o p e r a t i o n . T h e m o r e c o m p l e t e my d a t a a r e , t h e b e t t e r I c a n t a l k about how w e l l the measures p r e d i c t marks i n the c l a s s . The complete set of measures will be a d m i n i s t e r e d in t o d a y ' s c l a s s and w i l l take about one and one-quarter hours, with a short break half-way through. The q u e s t i o n n a i r e s will i n c l u d e s e l f - r a t i n g s , an a t t i t u d e m e a s u r e , a n d s e v e r a l cognitive measures. In a d d i t i o n , I w o u l d l i k e y o u t o g i v e me permission to receive your mark i n t h e f i n a l exam f r o m y o u r instructor. A l l r e p o r t i n g o f r e s u l t s w i l l be d o n e o n l y on a group basis. All information will be treated a s c o n f i d e n t i a l a n d w i l l be shared with no-one. If y o u w o u l d l i k e t o know a b o u t t h e p l e a s e c o n t a c t me i n t h e f a l l a n d I w i l l If you are w i l l i n g letter of consent, questionnaire."  to p a r t i c i p a t e , and we will  r e s u l t s of t h i s study, t e l l you about them. please begin  r e a d and s i g n the with the first  1 13  Letter  I  of  Consent.  give  , ,  to  give  my  she  will  that  the  if  mark  not  reveal  marks  will  Further, withdraw  final  in  I  to  will  Sheena  Selkirk,  be  reported that at  a  no way  instructor  am c u r r e n t l y  mark  study in  I  the  understand  from the  taken,  which  the  to  any  I later  may date  influence  on  the  and  permission  I  to  that  final  that  understand  statistics  refuse  course,  condition  person.  group  my  the  registered,  other  as  of  only.  participate either  standing  or  action, in  this  course.  Signed,  11 4  Concept  Learning  Task.  T h i s f o r m i s a m e a s u r e o f how quickly and well you can l e a r n an u n f a m i l i a r m a t h e m a t i c a l c o n c e p t . F i r s t , the concept is described and second, 13 questions are asked to test your a b i l i t y to use the c o n c e p t . Y o u may r e f e r b a c k t o the concept description while answering the q u e s t i o n s a n d y o u may d o t h e q u e s t i o n s i n any o r d e r you w i s h . T H E R E A R E NO T R I C K Q U E S T I O N S . A L L T H E I N F O R M A T I O N YOU NEED TO ANSWER T H E Q U E S T I O N S I S C O N T A I N E D IN T H E C O N C E P T D E S C R I P T I O N , E X C E P T FOR B A S I C A R I T H M E T I C AND A L G E B R A I C SKILLS. The time l i m i t f o r t h i s t a s k i s twelve (12) minutes. I will t e l l y o u when f o u r m i n u t e s a n d e i g h t m i n u t e s h a v e p a s s e d . P l e a s e t u r n t h e p a g e a n d b e g i n when I s a y , " T u r n and begin now. " CONCEPT  DESCRIPTION  Subscript Notation. If we h a v e a " v e c t o r " c o n t a i n i n g n u m b e r s o r "elements", we may refer t o any element i n the v e c t o r , using subscripts. F o r e x a m p l e , i f we h a v e t h e f o l l o w i n g v e c t o r :  1 - 2 Score:  0  3 5  E l e m e n t Number 4 5 6 7  3  9  1  0  4  8  9 U )  7  0  6  We may c a l l a n y o f i t s e l e m e n t s Xj , where i = 1 , 2 , 3 and to 10. For this e x a m p l e , i f i = 4 , X; = 9 . Similarly, t h e n X; =0 a n d X,, =X =X =0. L  so if  on up i=9,  4  Summation N o t a t i o n . In this task, the symbol "•" means ADDITION. When y o u s e e t h e s y m b o l " • " , y o u a r e t o ADD n u m b e r s together. The f o l l o w i n g d i a g r a m w i l l h e l p you t o l e a r n to know WHICH NUMBERS y o u a r e t o a d d . where  to  begin  adding  ^_^-where  In} the  • {irt t  addition  sign  the  Based on t h e an e x a m p l e o f  v e c t o r of numbers g i v e n a b o v e , the use of t h i s n o t a t i o n might  {2}  = X^  •  {5}  X-,  + X  s  + X^  + X  r  to  stop  element and be:  on  adding  to  the  add diagram,  = 5 + 3 + 9 + 1 = 18  1 15  TEST  QUESTIONS  Please write your answer for each question in the space following the question. Use any b l a n k space you w i s h f o r your rough work. T h e two v e c t o r s t o u s e i n a n s w e r i n g t h e s e q u e s t i o n s are: Vector  Element  Number:  1 2 3 4 5 6 7 8 Vector Vector  X: Y:  5 7  + Y  8 1  1.  X  2.  Xf  3.  4(Y  4.  3(X  5.  2(X*  6.  {1}  •  (8}  Xk  =  7.  {4}  •  {7}  Y  =  8.  {2}  •  {6}  X,-  9.  {7}  •  {7}  Y*  3  Y  )  Z  - Y  9 5  4 8  7 3  =  + X^  z  1 4  =  + 4X  3  2 0  =  +  + 5Y-, ?  3 6  )  )*  5  = + Xj  k  Y;  =  =  10.  {3}  •  {6}  (X  11.  (4}  •  {5}  (Yj  -  12.  {6}  •  {8}  3Xj  =  13.  does  {1} [{1}  =  + 2)  k  •  5)  {3} •  =  (3}  =  X,Xj  Y; ]  equal [{1}  •  {3}  Yj  ]  ?  116  Attitude  Measure.  ATTITUDES  ABOUT  STATISTICS  AND R E S E A R C H  DESIGN  This questionnaire consists of questions about doing research and statistics. Y o u r t a s k i s t o d e c i d e how m u c h y o u a g r e e o r d i s a g r e e w i t h e a c h s t a t e m e n t , a n d t h e n t o mark an "X" t h r o u g h t h e number t h a t i n d i c a t e s y o u r d e g r e e of a g r e e m e n t . The s c a l e t o be u s e d f o r e a c h s t a t e m e n t is: 1- s t r o n g l y d i s a g r e e 2- d i s a g r e e 3- d i s a g r e e a l i t t l e 4- n e i t h e r a g r e e n o r d i s a g r e e 5- a g r e e a little 6- a g r e e 7- s t r o n g l y a g r e e . For  example:  I  like  statistics  If you "disagree a l i t t l e " with this statement, mark an " X " t h r o u g h " 3 " , o r i f y o u "strongly agree" s t a t e m e n t , y o u w o u l d mark an " X " t h r o u g h " 7 " . There are 40 s t a t e m e n t s . Please respond to o n l y mark one " X " f o r e a c h statement. Previous questionnaire h a s shown t h a t m o s t s u b j e c t s f i n i s h minutes.  was  N o t e t h a t on t h e f o r m u s e d f o l l o w e d by t h e n u m b e r s " 1 "  1.  Planning  research  2.  I  that  think research  3.  I  would  would  it  be  would  method might enjoy  talking  by t h e through a  be  be  subject, "7".  rewarding  best  to  about  e a c h o n e , and use of this in about five  each  activity  interesting  to  solve  a  research  you would with the  for  think given  question me.  about  which  problem.  problems  with  my  friends. 4.  Thinking  about  statistics  makes  5.  I  like  to  decide  don't research  6.  Almost  7.  The  8.  I  9.  The  is  find  good  anything  symbols the  have or  is  used  different  feel  about  sick. whether  some p i e c e  of  bad.  more  in  to  me  interesting  statistics ways  in  are  than hard  which  one  most  are  statistics. for  me t o  could  do  understand.  research  very  confusing. assignments  I  will  enjoy  those  which  involve  1 17  statistics. 10.  Statistics  makes  me no m o r e  anxious  than  any  other  subject  does. 11.  Evaluating  12.  I would  13.  I only  14.  I  15.  I  research  never think  it  a  about  am l o o k i n g find  buy  is  statistics doing  forward  easy  to  challenging  to  and  book  research doing  if  the  I didn't  when  my own  understand  stimulating.  I  have  to.  to.  research  different  have  some  ways  day.  of  planning  research. 16.  would  I  enjoy  statistical 17.  Doing  18.  I would  19.  The  like  worst  20.  There to  21.  is  do  about  what  to  conclude  from  calculations.  research  statistics  thinking  would  to  be  read  are  to  the  too  waste  about  exams get  a  how  to  those  time do  in  right  much e m p h a s i s  of  for  me.  research.  which  you  have  to  use  and  how  answers.  in  university  on  research  it.  Working  as  a  research  consultant  is  a  job  I'd  like  to  do  someday. 22.  An  interesting  different 23.  I  enjoy  24.  If  I  Doing  26.  I  ever  than I  28.  The  30.  Even  how  to  do  read  statistics  to  be  compare  to  the  statistical  it  I  do  some  statistics  in  results.  problems.  would  like  it  if  someone  else  out.  make  about was  me f e e l  the  anxious.  conclusions  from  some  research  done.  exciting  which  and  statistical  enjoyable. formulas  are  derived  would  be  understand.  statistics when  about  would  it  might  research  carry  how  in  then  about  to  rather  ways  easy Doing  had  about  find  29.  and  statistics  would  27.  ways  thinking  planned 25.  assignment  how  I  is  almost  am i n t e r e s t e d to  do  research  always in  the  in  it.  boring. subject,  I  rarely  think  1 18  31.  I  sometimes  32.  I  try  33.  It  is  34.  My  favourite  35.  I  36.  I  to  I  38.  I  avoid  boring  am l o o k i n g would doing  37.  do  statistical taking  to  talk  statistics about  assignments forward  always  calculations  to  put  learning off  fun.  classes.  research  involve  for  with  other  people.  evaluating  research.  lots  statistics.  about  doing assignments  which  statistics.  will  find  like  to  statistics read  the  to  be  section  very  logical.  on  methodology  reports. 39.  I  never  40.  I  hate  involved  talk doing  to  others  about  statistical  how  to  do  calculations.  research.  in  research  1 19  Academic  the you  Self-Concept.  Please rate your a b i l i t y on e a c h o f t h e f o l l o w i n g . Mark p o i n t on t h e s c a l e t h a t i n d i c a t e s t h e amount o f e a c h a b i l i t y f e e l you p o s s e s s . T h e s c a l e t o be u s e d f o r e a c h a b i l i t y is:  1 very low  2  3 little below average  4 average  a  low  For example, i f you mental a b i l i t y , relative you would put a mark that ability. a.  General  mental  b.  Retention  c.  Comprehension of  d.  Technical  e.  Skill  f.  Dealing  g.  Explaining  h.  Applying theory  i.  Selecting  at  of  7 very high  high  ability learned  material  writing  with  6  f e l t t h a t you had "very high" general to the p o p u l a t i o n of graduate s t u d e n t s , (a c i r c l e , a n " X " , e t c . ) on t h e " 7 " f o r  material  oral  5 little above average  a  read  ability  presentations complex  things  some  to  at  subject  matter  a  to  level  suit  some p r a c t i c a l  significant  some g i v e n  audience  problem  problem from a  group  of  possible  problems j.  Perceiving  and  dealing  with  k.  General  mathematical  1.  Ability  to  work  m.  Ability  to  r e m e m b e r many  n.  Ability  to  visualize  "human  relations"  ability  swiftly  a  and  accurately  details  problem  of  a  problem  mentally  problems  120  Achievement  Motivation.  For the n e x t t h r e e q u e s t i o n s , p l e a s e c i r c l e t h e n u m b e r on each of the s c a l e s that r e p r e s e n t s your c h o i c e of r e s p o n s e . Use the f o l l o w i n g as a g u i d e : 1 very much prefer opt ion "A"  a. "1" 1. a, b, c. d. e.  a, b, c, d, e,  3. a. b. c. d. e. f.  2 much prefer opt ion "A"  3 prefer option "A"  For example, i f for the first for that item.  4 pe r f e r neither option  5 perfer opt ion "B"  6 much prefer option "B"  7 very much prefer opt ion "B"  you "much p r e f e r " d i f f i c u l t t a s k s in item q u e s t i o n , you would c i r c l e or c r o s s out the  I PREFER TASKS WHICH: involve uncertainty.1 2 . sure outcomes a r e d i f f i c u l t . 1 , 2 . 3.4 . 5 . 6 . 7 . a r e easy I do m y s e l f . 1 2 . 3 . 4 . 5 . 6 . 7 . 1 do a s p a r t o f a g r o u p h a v e some r i s k . 1 , 2 . 3 . 4 . 5 . 6 . 7 . h a v e n o o r e x c e s s i v e risk require problem require merely solving 1 directions f u l f i l l need to f u l f i l l need to succeed... .. avoid failure I AM MOST S A T I S F I E D WITH T A S K S W H I C H : involve uncertainty.1.2, sure outcomes are di f f i c u l t . 1 . 2 3 . 4 . 5 . 6 . 7 . a r e easy I do m y s e l f . 1 . 2 , 3 . 4 . 5 . 6 . 7 . 1 do a s p a r t o f a g r o u p h a v e some r i s k . 1 . 2 , 3 . 4 . 5 . 6 . 7 . h a v e no o r e x c e s s i v e risk require problem require merely solving 1.2, 3 . 4 . 5 . 6 . 7 . . . f o l l o w i n g directions f u l f i l l need to f u l f i l l need to succeed avoid failure I OFTEN UNDERTAKE TASKS WHICH: involve uncertainty. sure outcomes are d i f f i c u l t . 1 . 2 . 3 . 4 . 5 . 6 . 7 . a r e easy I do m y s e l f . 1 . 2 . 3 . 4 . 5 . 6 . 7 . I do as p a r t of a g r o u p h a v e some r i s k . 1 . 2 . 3 . 4 . 5 . 6 . 7 . h a v e no o r e x c e s s i v e risk require problem require merely solving 1 . directions f u l f i l l need to f u l f i l l need to succeed avoid failure  121  Specific 1.  Why  Motivation. are  you t a k i n g t h i s course? a. only because i t is b. more b e c a u s e i t i s I want t o c.  e. How  much d i d  you  a. b. c. d. e. Perceived  because  e q u a l l y because i t i s r e q u i r e d and because I wish to take it more b e c a u s e I w i s h t o t h a n b e c a u s e it is required only because I wish to  d.  2.  required r e q u i r e d than  want  to  take  this  v e r y much some a little I n e i t h e r wanted I definitely did  course?  to take i t nor not to n o t want t o t a k e t h i s  take it course  Utility.  1. How u s e f u l d o y o u t h i n k f u t u r e c o u r s e of studies? a. b. c. d. e.  course  will  be  to  you,  in  your  very useful somewhat u s e f u l slightly useful n e i t h e r u s e f u l nor o f ' n o use d e f i n i t e l y o f n o u s e t o me  2. How u s e f u l d o y o u chosen career path? a. b. c. d. e.  this  think  this  course  will  be  to  you,  in  your  very useful somewhat useful slightly useful n e i t h e r u s e f u l n o r o f no u s e d e f i n i t e l y o f n o u s e t o me  Experience. If you have studied secondary institution courses taken:  with  mathematics or before, please  Note: scored according 1=none a n d 5 = f o u r o r m o r e  to  statistics list and  number  of  in a postd e s c r i b e the  courses  taken  122  Initial  Task  Appendix C. Form of A t t i t u d e  Scales  Instructions.  Attitudes  About  Statistics  and  Research.  This questionnaire consists of statements about doing r e s e a r c h and s t a t i s t i c s . Your t a s k i s to d e c i d e how much you agree or d i s a g r e e w i t h e a c h s t a t e m e n t , a n d t h e n t o mark an " X " t h r o u g h t h e number t h a t i n d i c a t e s y o u r d e g r e e o f a g r e e m e n t . The s c a l e t o be u s e d f o r e a c h s t a t e m e n t is: 1 strongly disagree  For I  2 disagree  3 disagree a little  4  neither agree nor disagree  5 agree a little  6 agree  7 strongly agree  example:  like  statistics  1  2  3  4  5  6  7  If you " d i s a g r e e a l i t t l e " with this statement, an "X" through "3", or if you "strongly s t a t e m e n t , y o u w o u l d mark an " X " t h r o u g h " 7 " . T h e r e a r e 69 mark one " X "  statements. Please for each statement.  respond  to  each  you would mark agree" with the one,  and  only  Note: Only 65 statements are included in t h i s appendix because four a d d i t i o n a l items which e n q u i r e d about both areas were included in the o r i g i n a l form of the measure. They were d e l e t e d from a n a l y s i s f o r t h i s thesis. Statements  about  Statistics.  N o t e : i n t h i s and a p p e n d i x , a l l items within section are listed in o r d e r of observed i t e m - t o t a l c o r r e l a t i o n , calculated from the p i l o t - s t u d y d a t a . The i t e m - t o t a l correlation follows the item, enclosed in parentheses. Each item chosen for i n c l u s i o n in the f i n a l s c a l e i s marked by an asterisk. The order of the item in the i n i t i a l f o r m i s i n d i c a t e d by t h e item number p r e c e e d i n g t h e i t e m itself.  A. *40.  Statements I  find  of  Positive  statistics  Polarity.  exciting  and  enjoyable.  (0.831)  1 23  54.  I am l o o k i n g (0.733)  32.  I  22.  I would enjoy thinking statistical calculations.  12.  The a s s i g n m e n t s I would statistics. (0.628)  47.  I sometimes  44.  T h e ways i n w h i c h s t a t i s t i c a l to understand. (0.596)  27.  An i n t e r e s t i n g d i f f e r e n t ways  64.  I find  14.  Statistics makes does. (0.551)  7. 35. 2.  I  enjoy  forward  thinking  do  about  to  I f i n d i t easy to s t a t i s t i c a l terms.  69.  Notes from reference.  to  of  I  10.  The symbols understand. Almost (0.706)  25.  The worst statistics  68.  I  39.  Doing  hate  exams t o get  doing  conclude  those for  which  are  easy  statistics (0.560)  in  (0.552). than  any  a  rewarding when  for  me.  statistical  of  s h o u l d be  subject  (0.498)  do  I  meaning  other  job  the  saved  various  for  future  Polarity. classes  in  statistics.  statistics  hard  for  interesting  than  statistics.  more  are the  those in which you right answers. (0.668)  me  (0.745)  are  is  makes  (0.608)  derived  understand.  the  from  involve  fun.  to  classes  statistical  statistics  to  are  statistics (0.693)  b e t o d o some the r e s u l t s .  mistakes  used in (0.714)  anything  are  anxious  remember (0.381)  taking  what  logical.  be  about  problems.  formulas  easy  would  Negative  avoid  most  lots  calculations  very  statistics (0.098)  52.  9.  be  I make very few calculations. (0.445)  try  enjoy  proofs  statistician  Statements  about (0.628)  me n o m o r e  29.  ^_  statistical  assignment might and then compare  statistical  Being a (0.460)  learning  statistical  statistics  find  to  calculations. feel  anxious.  have  (0.656) (0.655)  me  to  to  use  124  *45.  Doing  *56.  I would a l w a y s put o f f d o i n g any doing s t a t i s t i c s . (0.651)  *  Thinking (0.639)  6.  statistics  is  about  almost  doing  I never know what calculations. (0.616)  42.  I only think (0.551 )  28.  I can't figure out how statistical calculations.  *17.  I would (0.507)  never  buy  to  doing  a  It is frustrating statistics. (0.469)  36.  When I do statistical mistakes. (0.399)  62.  I would (0.374)  never  save  24.  Thinking (0.363)  about  studying  Statements  A.  about  Statements  *33.  I  *67.  I like reports.  *16.  Evaluating (0.691)  *  Planning (0.627)  5.  would  of  like to  and  read  read (0.718)  research  people (0.527)  when  draw  book  notes  if  feel  sick.  statistical have  I  to.  conclusions  I didn't  to  waste I  from a  statistics  *38.  Working as a r e s e a r c h someday. (0.593)  *11.  I  to  to  be  a  make  to.  studying lots  statistics  makes  from  have  time  me  research.  of  class.  anxious.  about  (0.763)  on m e t h o d o l o g y and  rewarding  d o i n g my own  consultant  talking  do  challenging  would  forward  how  sections is  I  enjoy  statistics  involved  Polarity.  the  *21.  would  me from  calculations,  about  research  am l o o k i n g  makes  which  Research.  Positive to  assignment  pointless  my  (0.654)  conclude  statistics  50.  3.  boring.  statistics  60.  about  always  is  job  research  research  stimulating.  activity  research. a  in  I'd  for  me.  (0.607) like  methods  to  do  w i t h my  1 25  friends. 8.  (0.559)  I f i n d i t i n t e r e s t i n g to m i g h t be b e s t t o s o l v e a  think given  23.  I find it research.  58.  My favourite (0.544)  assignments  48.  T h i n k i n g about (0.537)  research  is  53  I  research  projects  66  I often think i n t e r e s t me.  3. 43  1.  -L  like  to  I like subject  I  easy to understand (0.546)  about which r e s e a r c h problem. (0.558)  plan  about the (0.532)  the  involve one  ways  to think about study. (0.492)  different  of  to  ways  favourite  "in  my h e a d " .  investigate  doing  of  evaluating  my  research  I would rather design a research someone e l s e ' s p l a n . (0.419)  only  of  think  Negative about  activities. (0.533)  problems  which  in  every  almost  project  than  I  31.  Doing  57.  It is (0.713)  46.  I would r a t h e r read about the o f r e s e a r c h t h a n a b o u t how i t  41.  If I ever had e l s e p l a n n e d how  55.  E v e n when a b o u t how  13.  I don't research  61.  I never (0.566)  15.  I find the d i f f e r e n t ways very confusing. (0.545)  is  boring  doing a  to  follow  about  waste talk  research of  time  about  when for  I  have  me.  research  to.  (0.733)  (0.726)  with  other  people.  c o n c l u s i o n s from some was d o n e . (0.680)  t o do r e s e a r c h I to c a r r y i t o u t .  would l i k e (0.668)  it  if  l i k e to have t o i s good or b a d . to  other  decide about (0.579)  people  about  in  whether  how  which  one  to  piece someone  I an i n t e r e s t e d i n t h e s u b j e c t , I rarely you c o u l d do r e s e a r c h i n i t . (0.656)  talk  how  Polarity.  19.  research  planning  research.  Whenever I w r i t e a p a p e r about s o m e t h i n g , I t h i n k I m i g h t do r e s e a r c h i n t h a t s u b j e c t . (0.353) Statements  method  think  some p i e c e  do  of  research.  c o u l d do  research  1 26  *37.  T h e r e i s t o o much e m p h a s i s how t o d o i t . (0.52.9)  university  research  and  r e s e a r c h , I u s u a l l y s k i p the s e c t i o n r e s e a r c h was c a r r i e d o u t . (0.533)  that  63.  When I read d e s c r i b e s how  49.  The worst a s s i g n m e n t s a r e those that a b o u t w h e t h e r some r e s e a r c h i s g o o d o r  18.  Having  4.  to  Thinking stomach.  any the  in  plan  to  do  research  about doing (0.487)  34.  I have trouble r e s e a r c h methods  65.  I would one about  26.  I never (0.374)  research  involve a decision bad. (0.528)  boring. gives  (0.507)  me b u t t e r f l i e s  understanding why people t o s o l v e t h e same p r o b l e m .  rather write the r e s e a r c h  read  is  on  books  or  on  how  to  my  use different (0.456)  a t e r m p a p e r a b o u t what I in a p a r t i c u l a r subject. articles  in  do  think than (0.381) research.  1 27  A p p e n d i x D. Administration Instructions HAND OUT B O O K L E T S ( + / - 2 m i n . ) Introduce t h e s t u d y i n y o u r own w a y . For example, "today there i s a s p e c i a l set of t e s t s which I have been requested to administer. Here i s a statement about the p r o j e c t , which i s a l s o on t h e c o v e r s h e e t o f y o u r t e s t b o o k l e t . " READ ( + / - 2 m i n . ) "My name i s S h e e n a S e l k i r k and I am a graduate student in Measurement and Research Methodology at the U n i v e r s i t y of B r i t i s h Columbia. T h i s s t u d y i s an i n v e s t i g a t i o n i n t o the extent t o which a b i l i t i e s and a t t i t u d e s are r e l a t e d to the performance in i n t r o d u c t o r y s t a t i s t i c s . Your p a r t i c i p a t i o n i s v o l u n t a r y , but I would certainly appreciate your cooperation. T h e m o r e c o m p l e t e my d a t a a r e , t h e b e t t e r I c a n talk about how well the measures p r e d i c t marks i n the class. The complete s e t of measures w i l l be administered in today's class and w i l l t a k e a b o u t one and o n e - q u a r t e r hours, with a short break half-way. through. The questionnaires will include self-ratings, an attitude measure, and s e v e r a l c o g n i t i v e m e a s u r e s . In addition, I would like y o u t o g i v e me p e r m i s s i o n t o r e c e i v e y o u r m a r k i n t h e f i n a l exam f r o m y o u r i n s t r u c t o r . All reporting of results will be done only on a group basis. All i n f o r m a t i o n w i l l be t r e a t e d a s confidential and will be shared with no-one. I f y o u w o u l d l i k e t o know a b o u t t h e r e s u l t s o f t h i s s t u d y , - p l e a s e c o n t a c t me i n t h e f a l l a n d I will tell you about them. If you are willing to p a r t i c i p a t e , p l e a s e read and s i g n the letter of consent, a n d we w i l l b e g i n w i t h t h e f i r s t q u e s t i o n n a i r e . " ALLOW TIME FOR P E O P L E TO L E A V E T H E ROOM I F T H E Y W I S H . (+/- 1 min. ) READ ( + / - 1 m i n . ) " B e s i d e s s i g n i n g y o u r name a n d f i l l i n g i n y o u r name a n d s t u d e n t n u m b e r on t h e l e t t e r of permission, you should also write in the number of the c l a s s (that is )." T E L L T H E S T U D E N T S T H E NUMBER OF T H E C L A S S . READ ( + / - 1 m i n . ) "The f i r s t task i s to f i l l in a q u e s t i o n n a i r e , which c o n s i s t s of t h r e e p a g e s . The first is open-ended q u e s t i o n s a n d r a t i n g s , a n d t h e o t h e r two a r e r a t i n g s . This f o r m t a k e s a b o u t 10 m i n u t e s t o f i l l i n . P l e a s e begin now." TIME TEN MINUTES. READ  (+/3 min.) " P l e a s e go on t o t h e n e x t f o r m now. This is the a t t i t u d e q u e s t i o n n a i r e . I s h a l l read the instructions aloud while you read them s i l e n t l y . This questionnaire c o n s i s t s of q u e s t i o n s about d o i n g r e s e a r c h and s t a t i s t i c s . Y o u r t a s k i s t o d e c i d e how m u c h y o u a g r e e o r d i s a g r e e with each s t a t e m e n t , a n d t h e n t o mark an " X " t h r o u g h t h e number t h a t i n d i c a t e s your degree of agreement. The s c a l e to be -used for each statement is: 1-strongly disagree, 2disagree, 3-disagree a little, 4-neither agree nor d i s a g r e e , 5-agree a l i t t l e , 6-agree, and 7 - s t r o n g l y a g r e e .  128  TIME  For example: I like statistics If you " d i s a g r e e a l i t t l e " w i t h t h i s s t a t e m e n t , y o u w o u l d mark an " X " through "3", or if you " s t r o n g l y a g r e e " with the statement, you w o u l d mark an " X " t h r o u g h " 7 " . There are 40 statements. Please r e s p o n d t o e a c h o n e , a n d o n l y mark one " X " f o r e a c h statement. P r e v i o u s use of t h i s questionnaire has shown that most subjects f i n i s h in about f i v e minutes. Please b e g i n now. F I V E MINUTES.  READ  (+/- 3 m i n . ) P l e a s e t u r n t o the next questionnaire now. For the rest of the questionnaires, I s h a l l read the i n s t r u c t i o n s , a l o u d and then time each part of the test quite closely. The n e x t t e s t , an A d v a n c e d V o c a b u l a r y T e s t , is a measure of your knowledge of word m e a n i n g s . In the e x a m p l e b e l o w , one s t i m u l u s word is printed above five response words. Y o u r t a s k i s t o c i r c l e t h e number o f the r e s p o n s e w o r d t h a t h a s t h e same o r n e a r l y t h e same meaning as the s t i m u l u s word. T r y t h e e x a m p l e now. ALLOW 10 S E C S . FOR T H E E X A M P L E The correct answer is "jolly", so you s h o u l d have c i r c l e d t h e n u m b e r 5. Y o u r s c o r e w i l l be t h e n u m b e r o f i t e m s y o u have answered correctly. T h e r e i s no c o r r e c t i o n f o r g u e s s i n g . You w i l l have 4 m i n u t e s f o r each p a r t of t h i s t e s t . There are two p a r t s , a n d e a c h p a r t h a s 18 i t e m s . When y o u h a v e f i n i s h e d p a r t 1, s t o p a n d d o n o t g o o n t o p a r t 2 u n t i l asked t o do s o . T u r n and b e g i n -- n o w . " T I M E FOUR M I N U T E S . "Turn TIME READ  and  begin  part  2 —  now."  FOUR M I N U T E S . (+/- 3 m i n . ) "Please turn to the next test now. This measure is a Paper F o l d i n g T e s t . In t h i s t e s t y o u a r e to imagine the f o l d i n g and unfolding of square pieces of paper. In each problem, the f i g u r e s at the l e f t of the vertical l i n e r e p r e s e n t a square of paper being folded. The l a s t o f t h e f i g u r e s h a s one o r two s m a l l c i r c l e s drawn o n i t t o show w h e r e t h e p a p e r h a s b e e n p u n c h e d . Each hole has been punched through a l l t h i c k n e s s e s of the paper at that point. The f i v e f i g u r e s t o t h e r i g h t of t h e vertical line show where the holes might be when t h e p a p e r is completely unfolded. You a r e t o d e c i d e w h i c h one of the figures i s c o r r e c t a n d draw an X t h r o u g h t h a t f i g u r e . Try t h i s sample p r o b l e m . ALLOW 15 S E C S . FOR P R O B L E M A T T E M P T . The c o r r e c t answer i s " C " - you s h o u l d have marked " C " with an X. T h e f i g u r e s b e l o w show y o u how t h e p a p e r was f o l d e d a n d why " C " i s c o r r e c t . As you can s e e , the p a p e r i s f o l d e d i n half and a h o l e punched in the l e f t - h a n d a r e a . When i t is u n f o l d e d , t h e r e a r e two holes in the paper. In these problems, all the folds a r e shown i n t h e f i g u r e s t o t h e l e f t of the v e r t i c a l l i n e , and the paper i s not turned or m o v e d i n a n y way e x c e p t t o make t h e f o l d s s h o w n . Remember, the correct a n s w e r i s t h e f i g u r e t h a t s h o w s how t h e p a p e r l o o k s when i t i s c o m p l e t e l y u n f o l d e d . You w i l l have three minutes to complete e a c h o f t h e two p a r t s o f t h i s test.  1 29  Each p a r t has 1 page. Your s c o r e w i l l be the number of correct responses. When y o u h a v e f i n i s h e d p a r t 1, s t o p . Do n o t g o on t o P a r t 2 u n t i l a s k e d to do so. Turn and b e g i n - - now. TIME THREE MINUTES "Turn and b e g i n p a r t 2 — now. TIME READ  THREE MINUTES (+/3 m i n . ) "We a r e now m o r e t h a n h a l f - f i n i s h e d w i t h t h e b a t t e r y of t e s t s . If you wish we will take a short "stretch" b r e a k , b u t p l e a s e d o n ' t l e a v e t h e room s i n c e t h e b r e a k w i l l o n l y be a few m i n u t e s l o n g . ALLOW TWO M I N U T E S FOR B R E A K . READ ( + / - 2 m i n . ) OK c o u l d we g e t s t a r t e d a g a i n ? . . . . The next test i s S u b t r a c t i o n and M u l t i p l i c a t i o n . This is a test to see how quickly and accurately you can subtract and multiply. It i s not e x p e c t e d t h a t you w i l l f i n i s h a l l the problems in the time allotted. You are to write the answers i n the boxes below the p r o b l e m s . Several practice problems are given below with -the first one correctly worked. Practice f o r s p e e d on t h e o t h e r s . This practice may h e l p y o u r s c o r e . ALLOW 20 S E C S . FOR P R O B L E M S . Y o u r s c o r e on t h i s t e s t w i l l be t h e n u m b e r of problems solved correctly. Work a s r a p i d l y a s y o u c a n w i t h o u t sacrificing accuracy. Be s u r e t h a t y o u a r e u s i n g t h e c o r r e c t process; check the s i g n f o r e a c h row. You w i l l have 2 m i n u t e s f o r e a c h o f t h e two p a r t s o f t h e t e s t . E a c h p a r t has one p a g e . When y o u h a v e f i n i s h e d p a r t 1, s t o p . Do n o t b e g i n part 2 u n t i l a s k e d t o do s o . T u r n a n d b e g i n -- now. T I M E TWO M I N U T E S . Turn and b e g i n p a r t 2 — now. T I M E TWO M I N U T E S . READ (+/- 2 m i n . ) The n e x t measure i s a t e s t c a l l e d D i a g r a m m i n g Relations. Sometimes the relationships among groups of things are best explained by diagrams t h a t c o n s i s t of overlapping c i r c l e s . In t h e d i a g r a m s i n t h i s t e s t , we do not care about the relative s i z e s of the c i r c l e s . For example, take the relationships among three groups of different things birds, pets and t r e e s . The d i a g r a m shows t h a t no t r e e s a r e e i t h e r pets or birds, but some birds a r e p e t s a n d some p e t s a r e b i r d s . Each item in this t e s t names t h r e e g r o u p s o f t h i n g s . You a r e t o c h o o s e from the lettered d i a g r a m s a t t h e t o p o f t h e t e s t page t h e one d i a g r a m t h a t shows t h e c o r r e c t r e l a t i o n s h i p among t h e three groups of t h i n g s in each i t e m . Mark the letter of the diagram that you s e l e c t . T r y these sample i t e m s . ALLOW 20 SECONDS FOR S A M P L E I T E M S . You should have marked A f o r e x a m p l e 1 a n d E f o r example 2. Y o u r s c o r e on t h i s t e s t will be the number of correct choices you have made. T h e r e a r e two p a r t s t o t h i s test, and you a r e g i v e n 4 m i n u t e s to c o m p l e t e each part. When you h a v e f i n i s h e d p a r t 1, s t o p . Do n o t b e g i n p a r t 2 u n t i l a s k e d t o do s o . Turn and b e g i n now.  1 30  TIME Turn TIME  $SIG  FOUR M I N U T E S . and b e g i n p a r t FOUR M I N U T E S .  2 —  now.  READ  (+/- 2 m i n . ) The l a s t t e s t i s a concept learning task. This form is a measure o f how q u i c k l y a n d w e l l y o u c a n learn an unfamiliar mathematical concept. First, the concept i s d e s c r i b e d a n d s e c o n d , 13 q u e s t i o n s a r e a s k e d t o t e s t your a b i l i t y to use the c o n c e p t . Y o u may refer back to the concept d e s c r i p t i o n s while answering the q u e s t i o n s a n d y o u may d o t h e q u e s t i o n s i n a n y o r d e r y o u w i s h . There are no trick questions. A l l the i n f o r m a t i o n you need to answer the questions is contained' in the concept description, except for basic arithmetic and a l g e b r a i c skills. The time limit for this task is twelve (12) minutes. I will tell you when four minutes and e i g h t m i n u t e s have p a s s e d . P l e a s e t u r n t h e p a g e a n d b e g i n when I say, "Turn and b e g i n — now."  TIME READ  TWELVE M I N U T E S . ANNOUNCE FOUR AND E I G H T M I N U T E S . (+/- 1 m i n . ) T h a t ' s i t . Ms. Selkirk would like me to thank you again for your cooperation. I f y o u want h e r a d d r e s s , y o u may a s k me f o r i t . P l e a s e hand i n your test b o o k l e t s t o me.  


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items