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A neo-piagetian perspective on student teachers’ representations of the real life teaching problem: adapting… Newman, Lorna J. 1992

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A Neo-Piagetian Perspective on Student Teachers'Representations of the Real Life Teaching Problem:Adapting Instruction to Individual DifferencesAmong LearnersbyLORNA JANE NEWMANB.A., The University of British Columbia, 1984A THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF ARTSinTHE FACULTY OF GRADUATE STUDIES(Educational Psychology and Special Education)We accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIA14 December 1992©Lorna Jane Newman, 1992In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of Et:Ixt^tRouil^ast44. Spe.oi41 bIlawirew,The University of British ColumbiaVancouver, CanadaDate Dee...km.4re( 2,3"f 1992, DE-6 (2/88)ABSTRACTThis study was an exploratory study of how studentteachers represent the real life teaching problem ofadapting their instruction to individual differencesamong learners and how their representation changes overthe course of the practicum experience. The extent towhich Cases' (1985, 1991) neo-Piagetian conceptualframework may describe the development of these studentteachers' ability to represent this real life teachingproblem was also examined.The non-random sample consisted of 39 intermediatelevel student teachers who completed three sets ofquestionnaires prior to and during the fourth and ninthweeks of the practicum experience. Twelve facultysupervisors also completed rating forms and observationson the student teachers they supervised during the sameweeks.Student teachers' responses to two questionsregarding aspects of individual differences problematicfor teaching prior to and during the practicum experiencewere rated according to the levels of problemrepresentation derived from Case's neo-Piagetian theoryiiof intellectual development. Faculty supervisors' ratingforms and observations provided a means of assessingwhether student teachers translated their representationsinto action. An additional variable of interest to thestudy included the nature of the individual differencesnoted by student teachers.The results suggested that student teachers' levelof problem representation and description of the problemincreased in complexity over the course of the practicumexperience. Also, that Case's neo-Piagetian conceptualframework may provide a useful theoretical tool fordescribing the development of student teachers' abilityto represent the individual differences teaching problem.Implications for teacher education and studies ofteacher thinking were discussed. The need for clinicalinterviews augmented by classroom observations made bysupervisors trained in a neo-Piagetian developmentalperspective was emphasized for future studies. Severalresearch questions, related to the use and furtherdevelopment of Case's neo-Piagetian conceptual frameworkin the domain of teaching, were generated.iiiTABLE OF CONTENTSAbstract ^  iiList of Tables ^  viList of Figures  viiiAcknowledgement ^  ixDedication Chapter I. INTRODUCTION ^  1A. BACKGROUND OF THE PROBLEM ^ 4B. STATEMENT OF THE PROBLEM  5C. SIGNIFICANCE OF THE STUDY ^ 6D. DEFINITION OF THE TERMS  7E. SUMMARY OF THE PROBLEM  10Chapter II. LITERATURE REVIEW ^  12A.B.C.D.THE ENDURING PROBLEM OF TEACHERPREPARATION FOR REAL LIFE TEACHINGPROBLEMS  13IMPLICATIONS FOR TEACHER EDUCATIONOF RESEARCH ON TEACHERS' THOUGHTPROCESSES ^  19IMPLICATIONS FOR TEACHER EDUCATIONOF RESEARCH ON REFLECTIVE PRACTICE 23A NEO-PIAGETIAN FRAMEWORK FOREXPLORING STUDENT TEACHERS'REPRESENTATION OF REAL LIFETEACHING PROBLEMS ^ 36E. SUMMARY ^ 50Chapter III. METHODOLOGY 52A. DESCRIPTION OF THE SAMPLE ^ 53B. PROCEDURES ^ 551.^Questionnaire Rationale^ 562.^Questionnaire Description ^ 573. Questionnaire Administration ^ 594. Rating Criteria and Examplesof Student Teachers' Responsesi.^Level of Problem59Representation ^ 61ivii. Description of ProblemRepresentation ^ 685. Rating Criteria and Examplesof Faculty Supervisors' RatingForms and Observations ^ 686. General Nature of IndividualDifferences Noted by StudentTeachers ^ 71C. SUMMARY ^ 72Chapter IV. RESULTS ^ 74A. MAIN ANALYSIS ^ 791.^Student Teachers' Levels ofProblem Representation ^ 802.^Student Teachers' Descriptionof the Problem Representation3.^Faculty Supervisors' Ratingsand Observations ^ 91B. SECONDARY ANALYSIS 99Chapter V. DISCUSSION ^  108A. DISCUSSION OF THE RESULTS ^ 1091. Student Teachers' Levels ofProblem Representation ^ 1092. Student Teachers' Descriptionof the Problem. Representation 1123. Case's Neo-Piagetian Perspectiveas a Conceptual Framework forThinking About Student Teachers'Representation of Real LifeTeaching Problems ^ 115B. LIMITATIONS OF THE STUDY ^ 117C. IMPLICATIONS FOR RESEARCH ONTEACHING ^ 122D. DIRECTIONS FOR FUTURE RESEARCH ^ 124REFERENCES 127APPENDIX A  137APPENDIX B  143APPENDIX C  158LIST OF TABLESTable 2.1: Models of Reflection ^  31Table 2.2: Levels of Student Teachers' Representationof the Problem of Adapting Instruction toIndividual Differences Among Learners .. 45Table 3.1: Levels of Student Teachers' ProblemRepresentation: Scoring Categories andExamples ^  61Table 3.2: Rating Criteria and Examples for FacultySupervisors' Rating Forms and Observations^  69Table 4.1: Student Teachers' Level of ProblemRepresentation (PR) Prior to, and at the4th and 9th weeks of the PracticumExperience ^  77Table 4.2: Student Teachers' Description of theProblem Representation During the PracticumExperience ^  78Table 4.3: Frequency Table for Levels of ProblemRepresentation (PR) Prior to the Practicum^  81Table 4.4: Frequency Table for Levels of ProblemRepresentation (PR) During the First Half(4th Week) of the Practicum ^ 85Table 4.5: Frequency Table for Levels of ProblemRepresentation (PR) During the Second Half(9th Week) of the Practicum ^ 88Table 4.6: Frequency Table for the Student Teachers'Description of the Problem RepresentationDuring the 4th Week of the Practicum ... 93Table 4.7: Frequency Table for the Student Teachers'Description of the Problem RepresentationDuring the 9th Week of the Practicum ... 96viTable 4.8: Frequency Table for the FacultySupervisors' Ratings of Student Teachers'Accommodations of Individual DifferencesDuring the First Half (4th Week) of thePracticum ^  98Table 4.9: Frequency Table for the FacultySupervisors' Ratings of Student Teachers'Accommodations of Individual DifferencesDuring the Second Half (9th Week) of thePracticum ^  99Table 4.10: Frequency Table of Aspects of IndividualDifferences Noted by Student Teachers inDefinition (Question 7a) and Most DifficultProblem (Question 4a, 9a) During thePracticum ^  101Table 4.11: Frequency Table for Aspects of IndividualDifferences Noted by Student Teachers inQuestions 7b, 4b, 9b, During the Practicum^  103Table 4.12: Frequency Table for Aspects of IndividualDifferences Noted by Faculty Supervisors inTheir Observations of Student TeachersDuring the 4th and 9th Weeks of thePracticum ^  105viiLIST OF FIGURESFigure 2.1: Cases' Hypothesized Structure of Stages andSubstages from Birth to Adulthood ^ 42Figure 4.1: Graphic Summary of the FrequencyDistributions Associated with the StudentTeachers' Levels of Problem RepresentationPrior to, During the First and SecondHalves of the Practicum ^ 92Figure 4.2: A Summary of the Types of IndividualDifferences Noted by Student Teachers100viiiACKNOWLEDGEMENTIt is with pleasure that I extend my appreciation tothe following individuals for their contributions towardsthe completion of this thesis:Words alone cannot describe the gratitude andrespect I have for Dr. Patricia K. Arlin, whoseexpertise, support and encouragement throughout thepreparation of this thesis helped to make it a reality.Much appreciation is extended to Dr. Billie Housegoand to Dr. Marion Porath for sharing their expertise inthe areas of teacher education and neo-Piagetian theory,and for the many hours spent providing insightfulsuggestions and comments on the drafts of this thesis.Many thanks to the student teachers and facultysupervisors of the two year UBC Teacher Education programwho took the time and interest to reveal their thoughtsabout teaching.Special thanks are extended to Ms. Lori Levitt, Mr.Ross Barbour, and my graduate student peers whose supportand encouragement during this lonely process were verymuch appreciated.ixTo my Dad,Walmis Newman Jr.(1925-1991)1CHAPTER 1: INTRODUCTIONThis study is an attempt to describe the ways inwhich student teachers represent real life teachingproblems and the ways in which their representationschange over the course of the practicum experience.Real life teaching problems include those ill-structuredproblems that are complex, uncertain, and laden withdilemmas because they involve on-the-spot decisions about"what students know, what effects teaching has had andwill have, what content they should be trying to teach,what instructional authority they have, and how they canimprove their teaching" (Floden & Clark, 1988 p.506).Ill-structured problems refer to situations where theindividual finds himself faced with a problem for whichthere is no immediate or known solution.^Kitchener(1983) describes the nature of an ill-structured problem:There is not a single, unequivocal solutionwhich can be effectively determined at thepresent moment by employing a particulardecision-making procedure...Evidence, expertopinion, reason, and argument can be broughtto bear on the issues, but no effectiveprocedure is available which can give acorrect or absolute solution. A solution mustbe constructed by integrating or synthesizingdiverse data and opinion. (pp.224-225)2The problem the student teacher faces in adaptinginstruction to individual differences among learners inthe following example is ill-structured in that thestudent teacher must juggle the cognitive, affective andmotivational needs of a sub-group of students with theneeds of a larger group while taking into account therange of individual ability within both groups and theresources (space, time, materials) available as well asthe wider context of parent, supervising teacher,principal, and school board expectations.Differences in reading ability, mainly due toESL problems poses a difficult problem. Thishas been especially problematic in math, wherelack of reading ability severly hampers thestudent's ability to solve problems. To adaptto this, I have been using simpler problemsfor the ESL student that required the samestrategy as those being solved by the non-ESLstudents (See Appendix A, 7a, See Table 4.1,Subject #001).Clark and Lampert (1986) characterize the complexity ofthe teacher's task:The teacher encounters a host of interrelatedand competing decision situations both whileplanning and during teaching. There are noperfect or optimal solutions to thesedecisions. A gain for one student or in onesubject matter may mean a foregone opportunityfor others. A motivationally andintellectually profitable digression mayreduce time devoted to mandated curriculum.Such conflicts among teachers' multiplecommitments lead to practical dilemmas which3must be managed in interaction with students.(p.28)Indeed, the ability of the professional to integrateexperience with theory and research in the formulation ofon-the-spot solutions to unique, complex problems of theday to day task of teaching is what Schon (1983, 1987,1991) termed "reflective practice". The development ofa complex representation of and a reflective stancetoward real life teaching problems is the challenge allstudent teachers are faced with as they begin theirjourney toward expertise.It will be argued in this study that in order toexamine how student teachers begin to think about thecomplexity and conflict inherent in real life teachingproblems, researchers need to explore how the studentteacher represents the problem of teaching and how thatrepresentation develops over the course of experience.The purposes of this study were:(1) To investigate the ways in which student teachersrepresent the problem of adapting instruction toindividual differences among learners.(2) To investigate the ways in which theirrepresentation of this problem changes over the course ofthe practicum experience.(3)^To investigate whether or not the structure and4processes of Case's (1985, 1987, 1991) neo-Piagetianperspective provide an adequate theoretical means todescribe the development of student teachers' ability torepresent real life teaching problems.A. BACKGROUND TO THE PROBLEM:American surveys have found that Teacher Educationprograms focus their preparation of student teacherslargely upon curriculum content, methods and lesson planpreparation with little attention given to thedevelopment of flexibility and problem solving skillsdeemed necessary to deal with real life teaching problems(Emundson, 1990; Goodlad, 1990a). Much has been writtenabout teacher's thought processes when they confront aproblem yet these accounts are often either too specificand superficial or too global and, therefore, lacking insufficient detail to be useful to teacher educators andsupervising teachers who wish to foster the developmentof flexibility and reflection in student teachers (Howey& Zimpher, 1989; Goodlad, 1990b).A neo-Piagetian perspective may provide thetheoretical tools of structure and processes necessary toanalyze the nature of student teachers' representationof real life problems and to model the development ofthat ability over the course of experience.5B. STATEMENT OF THE PROBLEM:How do student teachers represent the real life teachingproblem of adapting their instruction to the individualdifferences among learners?How do student teachers' representations of real lifeteaching problems change over the course of theirpracticum experience?Are the structure and processes of Case's(1985,1987,1991) neo-Piagetian perspective usefultheoretical tools to address the development of studentteachers' abilities to represent real life teachingproblems?In order to examine these questions, studentteachers participating in a thirteen week practicum wereasked prior to their practicum experience what theirdefinition of individual differences among pupils was andwhich aspects of individual differences would likely havethe most impact on the way that they would teach duringthe practicum. They were also asked what aspects ofindividual differences they thought were likely to beproblematic for teaching and why. During the fourth andninth weeks of their practicum the student teachers were6asked to describe the most difficult problem they hadadapting their teaching to individual differences amongstudents. Similarily, student teacher facultysupervisors were asked how student teachers accommodatedindividual differences among learners during the firstand second halves of the practicum. The facultysupervisors were also asked to rank the student teacherson a seven point Likert scale designed to indicate howwell the student teachers were able to accommodateindividual differences among learners during the twoperiods outlined.It was expected that:(1) Student teachers who have a more complexrepresentation of the problem of adapting theirinstruction to individual differences among learners willpropose solutions that are more flexible in theiraccommodation of individual student differences.(2) Student teachers' representation of the problem willbecome more complex over the course of the practicumexperience as would be predicted by Case's neo-Piagetiantheory of intellectual development.(3) The structure and processes of Case's neo-Piagetiantheoretical perspective will provide an adequatetheoretical framework from which to conceptualize thedevelopment of a student teacher's ability to representthe problem of adapting their instruction to theindividual differences among learners.C. SIGNIFICANCE OF THE STUDY:The educational importance of this study is focused7in its potential to provide a means for understanding howstudent teachers represent real life teaching problems,in particular, the problem of adapting their instructionto the individual differences among learners and how thisability develops during the practicum experience. It ishoped that this study will provide a useful theoreticalframework to guide further inquiry and a developmentalperspective on how student teachers represent real lifeteaching problems and ultimately develop the flexibilityand reflective skills necessary to meet the challenges ofthese teaching problems more effectively. Adevelopmental perspective on how student teachersrepresent real life teaching problems and how thatrepresentation changes over the course of theirexperience is particularly relevant to the study ofstudent teachers, their teaching, and the development ofteacher education programs.D. DEFINITION OF THE TERMSThis is an exploratory study of the ways in whichstudent teachers represent real life teaching problemsand the ways in which their representations change overthe course of the practicum experience. Several terms8are important for this study. They are defined below:1. Representation refers to how student teachers thinkabout the real life teaching problems which confrontthem. In particular, what is known and the way inwhich that knowledge is organized or structuredcomprises a view of representation that is adeparture from the more traditional and familiarusage of representation as the use of symbols (xstands for y in the external world) (Mandler, 1983).The student teacher's internal schema or frames ofreference are used in his interaction with theexternal world, in this context, the classroom.2. Real life teaching problems refer to those complex,uncertain, ill-structured problems encountered ineveryday teaching which require the student teacherto make on-the-spot decisions which balance learnerknowledge, ability, understanding, and motivation,task demands, instructional effect--past, present,and future, available resources, and widerexpectations of parents, sponsor teacher, facultysupervisor, principal and school board.3. Developmental perspective refers to a perspective ongrowth or change which charts the unfolding story ofincrements in structural organization. Specifically,cognitive development refers to the intercoordinationof abilities at many ages. In Case's (1985, 1991)neo-Piagetian theory of intellectual development, theconceptual framework adopted in the present study,objects, actions, behaviors, and mental events areconsolidated, coordinated, and integrated in aprocess of hierarchical integration. Thisintegration results in operations of a higher levelof abstraction in many domains or specific skillareas, that its, ie. spatial, motor, social,emotional, logical-mathematical.4. Constructivist perspective refers to learners' activeconstruction of their own understandings rather thanpassive copying of the understandings of others. Theconstruction of new understandings is stimulated whena situation is encountered that challenges theindividual's current organization of knowledge.95^Structures of development refer to the objects,actions, behaviors, or mental events which arecoordinated or hierarchically integrated in thesequence of development. In Case's (1985, 1991)neo-Piagetian theory, the structure is atripartite control structure which consists ofthree components: (1) a representation of thecurrent problem situation, (2) a representation ofthe desired objective, and (3) a representation ofthe strategy--a sequence for going from the currentproblem situation to the desired situation asefficiently as possible. These control structuresare independently assembled for each specificdomain of interest or experience. As the persongrows older, the complexity of the problem situation,objective, and strategy increases but the basiccontrol structures remain the same.6. Processes of development refer to the operationswhich occur to move student teachers from onedevelopmental level (stage or substage) to the next.In particular, Case (1985, 1991) has specified fourinformation processes: schematic search, evaluation,retagging and consolidation which activate twoschemas (objects, actions, behaviors, or mentalevents) either at the same time or in succession.7 Mechanisms of development differ from processes inthat mechanisms set the limit on the number ofobjects, actions or mental events that can behierarchically integrated. For Case (1985; 1991),attentional capacity or short term storage spacewhich increases with age provides the meansfor movement within a stage. The person's growingability to chunk more information together allows forincreased operational efficiency. This operationalefficiency is in turn dependent upon bothmaturational factors and, at the upper reachesof development, upon instruction and amount ofpractice.8. Individual differences among learners refers to thecharacteristics or qualities such as learning rate,ability, prior knowledge, specific interests,motivation level, attentional capacity, maturity1 0level, ethnic background, learning styles, activitylevel, social skills, personality, self-esteem,etc. which make one learner unique or different fromanother learner. In order to take individualdifferences among learners into account when planningor adapting instruction in the classroom, the studentteacher must direct their instruction to the uniqueand specific needs of the learner. Student teachersin the present study defined individual differencesamong learners as: "variations in pupils' cognitive,psychomotor, and affective abilities. As each childis unique, individual differences will always existwithin any given classroom" (Subject #001)."Individual differences are what makes a classroomwhole" (Subject #133). "Every student learns in adifferent way depending on their particular set ofcircumstances and life background. They fit newknowledge into their existing knowledge depending ontheir past experiences and what they relate the newknowledge to" (Subject #115).E. SUMMARY OF THE PROBLEMThis study is an attempt to explore the ways inwhich student teachers represent the real life teachingproblem of adapting their instruction to individualdifferences among learners and the way in which theirrepresentations change over the course of the practicumexperience. The student teacher's representation isthought to be informed by a cognitive-developmental neo-Piagetian framework. This framework may provide aninsight into how student teachers represent real lifeteaching problems and ultimately develop the flexibilityand reflective skills necessary to meet the challenges of1 1these teaching problems more effectively.Chapter Two contains a review of the literaturepertaining to these research questions.12CHAPTER II: LITERATURE REVIEWThe present study was designed to explore (a) theways in which student teachers represent real lifeteaching problems and (b) the ways in which theirrepresentations change over the course of the practicumexperience.The present study draws heavily on the literature ofthree research areas (teachers' knowledge and thoughtprocesses, the notions of reflective practice, and Case'sneo-Piagetian conceptual framework) to address theenduring and often complex problem of how to prepareprospective teachers to deal with the complexities ofreal-life teaching problems. It represents a uniquecombination of these research areas by redefiningclassroom problems as multi-faceted, ill-defined problemsand the student teacher's task of teaching as one fraughtwith uncertainties. To understand how student teachersthink about the ill-defined and uncertain nature of reallife teaching problems, research studies related toteachers' thought processes, and reflective practice areintroduced.^Finally, Case's neo-Piagetian theory ofintellectual development is introduced as a means to13frame an investigation into how student teachers thinkabout the complex nature of real life teaching problemsand how their thinking develops.A. THE ENDURING PROBLEM OF TEACHER PREPARATION FOR REALLIFE TEACHING PROBLEMSThe enduring problem facing teacher education is howto prepare prospective teachers for the uncertainties ofthe classroom. This dilemma is manifested in the theory/practice dichotomy that powers the debate which occurs ineducational circles when educators are faced with thetask of developing teacher preparation programs thatcannot wait until all the data are in on what constitutesthe most enlightened way to educate prospective teachers(See Rowell, Pope, & Sherman, 1992 for a comprehensivereview). The theory/ practice dichotomy refers to theattempt to set theory and practice up in opposition toone another as exemplified by remarks such as "all rightin theory but it won't work in practice." Such astatement suggests that something must have been wrongwith the theory that said it would work. The theory/practice dichotomy is maintained especially in the mindsof teachers precisely because so much of educational14theory has been poor (Barrow, 1990). This dichotomy isreflected in views of teaching which range from a genericset of technical skills or pre-specified responses to besupplied at decision points (Gliessman, Pugh, Brown,Archer, & Snyder, 1989; Gliessman, Pugh, Dowden, &Hutchins, 1988; Leinhardt and Greeno, 1986) to teachingas artistry in which the "epistemology of practice isimplicit in the artistic, intuitive processes which somepractitioners do bring to situations of uncertainty,instability, uniqueness, and value conflict" (Schon,1983, p.49) The nature of the theory/ practice dichotomyis invariably reinforced by student teachers' experiencesin our teacher education programs. When asked to reflecton their teacher training, first year teachers invariablypoint to the practicum experience as the single mostimportant factor in their preparation to teach(Calderhead, 1988; Doyle, 1990; Sirotnik, 1990) yet,Feiman-Nemser & Buchmann (1985) point to the pitfalls ofteacher classroom preparation that await programs thatplace too heavy an emphasis on the value of the practicumexperience. Prospective teachers' previous experience asstudents, little connection between field experiences andeducational theory courses, and the fact that classrooms15are not designed as laboratories for learning to teachare pitfalls because they "arrest thought or misleadprospective teachers into believing that central aspectsof teaching have been mastered and understood" (Feiman-Nemser & Buchmann, 1985, p.63). Indeed, evaluations ofteacher education programs in the United States point tothe fact that a generic collection of teaching skillsthat offer "quick instructional fixes" will not suffice(Goodlad, 1990a, 1990b; Goodlad, Soder, & Sirotnik, 1990;Howey & Zimpher, 1989; Kennedy, 1991; Sirotnik, 1990).Goodlad (1990b) explains:The problem is not that generic principles ofteaching are irrelevant. The problem lies inoverlooking the layers of complexity involvedin teaching young people. (p.700)A host of teaching strategies and methodologies havegrown up in the attempt to fill the theory/ practice gap.Micro-teaching (Simbo, 1989), teaching laboratories,(Kowalski, Glover, & Krug, 1988) and case methodology(Shulman, 1992) provide theory which is grounded in thepractical context of teaching, yet they lack anunderlying conceptual framework, and they view thestudent teacher as a passive rather than activeconstructor of his or her own teaching experiences.16Reflective techniques such as reflective writing,autobiography and ethnography, questioning and dialogue,inquiry activities, and faculty modelling (Adler, 1991;Ross, 1987) and the program approaches to reflectivepractice such as Practice Centered Inquiry (PCI),(Sanders & McCutcheon, 1986) and Reflective InquiryTeacher Education (RITE) (Freiberg & Waxman, 1987) allowthe student teacher a voice in the process of becoming ateacher, but they have yet to be grounded in a cohesiveconceptual framework. Barrow (1990) asserts that:The only antidote to poor theory is goodtheory. Either we accept the challenge andseek out a stronger theoretical base, or elseby definition, we act intuitively or inresponse to external command. (p.309)The developmental perspective which guides theDevelopmental Teacher Education program (Amarel, 1989;Ammon & Hutcheson, 1989; Black, 1989) developed by Blackand Ammon at Berkeley views the student teacher as anactive constructor of his or her developing pedagogicalconceptions. At present, the underlying conceptualframework is loosely described as a "structural-developmental coherent perspective" (Black, 1989, p.2)rather than a developmental theory which includes themajor factors which contribute to development yet is only17somewhat theoretically grounded as it pushes thePiagetian notion of general stages to the background infavor of the domain-specific knowledge of pedagogyassociated with teaching. The loose nature of DTEconceptual framework results in a program that focusesprimarily on how to construct domain-specific pedagogicalconceptions in student teachers. The cost of such afocus is the missed opportunity to understand what thatdevelopment looks like (structures) and why and how itunfolds (processes or mechanisms of development).A well articulated conceptual framework is needed ifwe are to educate student teachers substantively ratherthan just train them technically (Edmundson, 1990;Goodlad, 1990b; Goodman, 1989; Kennedy, 1991; Richardson,1990; Shulman, 1986, 1992; Sirotnik, 1990; Wildman &Niles, 1987). A means of assessing how student teachersthink about real-life classroom problems that is groundedin a developmental conceptual framework which views thestudent teacher as the active constructor of theirexperiences will go a long way in meeting Feiman-Nemserand Buchmann's (1987) criteria of what makes studentteaching teacher education:Student teaching is teacher education whenintending teachers are moved toward a18practical understanding of the central tasksof teaching; when their dispositions andskills to extend and probe student learningare strengthened; when they learn to questionwhat they see, believe and do; when they seethe limits of justifying their decisions andactions in terms of "neat ideas" or classroomcontrol and when they see experience as abeginning rather than a culminating point intheir learning. (p.272)Not only is a conceptual framework needed to rationalizeteacher education programs, but it is also required ifstudent teachers are to begin to develop adequaterepresentations of real life teaching problems. The fewstudies of student teachers' representation of classroomproblems that exist are at best descriptive orimpressionistic. No adequate studies exist on howstudent teachers represent real life teaching problems,let alone how those representations change during thepracticum experience.This investigation into the enduring problem of howto prepare prospective teachers for the uncertainties ofthe classroom contributes in part to the present study'sfocus on student teachers' representations of real lifeteaching problems. It also provides support for thenecessity of an inquiry method based on a conceptualframework. The literature to be reviewed in the19following sections research on teachers' thoughtprocesses and research on reflective practice - will helpto frame more adequately the research questions of thepresent study.B. IMPLICATIONS FOR TEACHER EDUCATION OF RESEARCH ONTEACHERS' THOUGHT PROCESSESResearch on teachers' knowledge and thoughtprocesses has proceeded along the lines of description inan attempt to chip away at the task of describing whatappears to be a complex, cognitively demanding, humanact. Shulman (1986) has established that there are atleast three important sources of knowledge required forthe competent performance of teaching: content knowledge,pedagogical content knowledge, and pedagogical knowledge.Content knowledge refers to teachers' understanding ofthe organization, concepts, and relationships amongconcepts of subject areas such as English or physics.Pedagogical content knowledge is teachers' ability totransform content knowledge into forms that can belearned by ordinary students. It may take the form ofanalogies, applications to everyday life, concrete20examples, and forms of practice which teachers use topromote student learning. Pedagogical knowledge differsfrom pedagogical content knowledge in that it consistsprimarily of a wider knowledge about organization ofclassrooms, classroom management, evaluation,motivational methods, communicative skills, and personalknowledge of the needs of individual students.The description of these sources of knowledge goesbeyond the view of teaching as a collection of genericskills. The sources of knowledge required in the task ofteaching are not only equivalent to the complexityafforded other professions' pedagogical expertise such asmedicine and engineering, but are also firmly embedded inthe context of teaching (Berliner, 1989; 1991; Carter,Sabers, Cushing, Dinnegar, and Berliner, 1987; Chi,Glaser, & Farr, 1988; Elstein, Shulman, & Sprafka, 1990;Sanders & McCutcheon, 1986). Research on the sources ofteachers' knowledge, however, not only requires furtherdescription but also needs to focus on the relationshipsamong teacher knowledge, teachers' interactive thinkingand what actually happens in the classroom within thesocial and practical context in which it occurs.Although the present study does not specifically describe21student teachers' sources of knowledge, it does attemptto chart the development of those sources of knowledge instudent teachers as they think about the real lifeproblem of adapting instruction to individual differencesamong learners.Similarly, research on teachers' thought processeshas focused primarily on descriptions of the planningbehaviours and interactive thoughts and decisions ofexperienced teachers. Progress has been made in thedescription of teachers' planning behaviours, thethinking they do while interacting with students in theclassroom and the models which have been constructed todiagram these processes, yet this research focuses onrelatively discrete, isolated aspects of teachers'thoughts and actions (Calderhead, 1988).The narrow focus of research surrounding theidentification, frequency counts, and antecedents ofteachers' interactive thoughts, and description ofteachers' alternative courses of action has told uslittle about how teachers actually make interactivedecisions (Clark & Peterson, 1986) or about how theybegin to construct and reconstruct more and more adequatepedagogical knowledge. Pedagogical knowledge is22essential to any representation of real life teachingproblems. It is an assumption in this study that changesin pedagogical knowledge will be accomplished by changesin the problem representation of student teachers.At the other end of the spectrum, the accounts ofteacher development which have been inferred from schematheory and comparative studies of the cognitionsunderlying novice and expert teachers' performances(Berliner, 1986; Sabers, Cushing, & Berliner, 1991;Swanson, O'Connor & Cooney, 1990) are too global to beuseful. The general models (Berliner, 1988; Fuller &Brown, 1975; Kagan, 1992) produced by these researchefforts give snapshots of teachers' cognitions at veryloosely defined 'stages' of 'development' with noattention to the specification of actual processes thatmove the teacher from one stage to the next.What is needed is research which: (1) uses"longitudinal designs and cognitive developmentalframework instead of continuing to accumulatedescriptions" (Clark & Peterson, 1986, p.268) (2)emphasizes teachers' active construction of knowledgerather than the passive description of their thoughtprocesses from an information-processing approach23(Calderhead, 1988; Cochran-Smith & Lytle, 1990; Elbaz,1988; Peterson, Clark, & Dickson, 1990). The presentstudy adopts a developmental, constructivist approach tostudent teachers' representations of real life teachingproblems over the course of the practicum experience inthe attempt to understand the development of studentteachers' organizing structures and to test the adequacyof Case's (1985, 1991) neo-Piagetian theory ofintellectual development as a theoretical tool andconceptual framework.C. IMPLICATIONS FOR TEACHER EDUCATION OF RESEARCH ONREFLECTIVE PRACTICEThe notions of reflective practice that areprevalent in the research literature seem to be asnumerous as the practitioners which use them. The terms"reflective practice", "reflective teaching","reflection-in-action", "action oriented research""inquiry oriented research", "reflective practitioner","teacher as researcher", and "teacher as problem solver"all encompass a notion of reflection in the process ofprofessional development which involves away of thinking24about education that places value on making choices andtaking responsibility for those choices (Adler, 1991;Calderhead, 1989; Goodman, 1984; Liston & Zeichner, 1990;Ross, 1989a; Zeichner & Liston, 1987). Such notions ofreflection populate a wide spectrum of variation, yetmost begin with the issues and concerns of the teacher aslearner, honour the complexity of the teacher's own wayof knowing and view the teacher as a 'constructor' ofknowledge involved in a process of development towardexpertise. Ross (1989) aptly summarizes some of theelements of the reflective process:Recognizing an educational dilemma. Respondingto a dilemma by recognizing both thesimilarities to other situations and theunique qualities of the particular situation.Framing and reframing the dilemma.Experimenting with the dilemma to discover theconsequences and implications of varioussolutions. Examining the intended andunintended consequences of an implementedsolution and evaluating the solution bydetermining whether the consequences aredesirable or not. (p.22)Much of the writing on reflective practice evolves fromthe concepts offered by a few key theorists: John Dewey(1933), Donald Schon (1983, 1987), Kenneth Zeichner,(1981) and the Frankfurt School of Social Research in the25work of Habermas (1974). Various interpretations ofthese concepts are manifested in the reflective practiceprograms of Cruickshank (1987), Zeichner and Liston,1987) and the reflective strategies of Adler and Goodman,(1986), Korthagen (1985), Gitlin and Teitlebaum (1983),Grumet (1989), Hill (1986), Lucas (1988), and Symth(1989) and they drive the design of teacher educationprograms.Dewey's (1933) concept of "reflection" defined as:active, persistent and careful considerationof any belief or supposed form of knowledge inthe light of the grounds that support it andthe further conclusions to which it tends(P.9)emphasized a sense of wonder or unrest at the problem,and a purposeful, reasoned search for the solution.Dewey suggested that the development of reflectioninvolved the growth of certain attitudes (for example,openmindedness) and the acquisition of certain skills(for example, reasoning).In many ways, Schon (1983, 1987, 1991) echoedDewey's concept of reflection in his concepts of"knowledge-in action", "tacit knowledge", "knowing inaction" and "reflection in action" which place theteacher at the centre of knowledge about the artistry of26teaching rather than the researcher. Schon defines thereflective practitioner as the professional whointegrates experience with theory and research in theformulation of solutions which are a response to theuncertainty and complexity of the unique problems ofpractice. He argues against the view of professional asapplied scientist who implements the theories of sciencein practical situations. He rejects the view ofteaching as merely a craft that can be mastered solelythrough propositional knowledge or passive observationand embraces the teacher as a professional who bringspractical competence to bear in divergent situations andsearches for "an epistemology of practice implicit in theartistic, intuitive processes which some practitioners dobring to situations of uncertainty, instability,uniqueness, and value conflict" (Schon, 1983, p.49).Schon is more interested in the professional involved inthe process of decision-making in which interactive,interpretative skills are brought into play in theanalysis and solution of complex problems rather than thedecisions themselves as his concept of "reflection-in-action" suggests:^Reflection-in-action^is^a^reflectiveconversation with the materials of a27situation. Each person carries out his ownevolving role...'listens' to the surprisesthat result from earlier moves, and respondsthrough on-line production of new moves thatgive new meanings and directions to thedevelopment of the artifact. (Schon,1987,p.31)Crucial to Schon's process of "reflection-in-action" arethe notions of "problem setting" and problem solving inwhich the practioner must notice the problematic andarticulate its nature and context.In real world practice, problems do notpresent themselves to the practioner asgivens. They must be constructed from thematerials or problematic situations that arepuzzling, troubling and uncertain. When weset the problem, we select what we will treatas the "things" of the situation, we set theboundaries of our attention to it, and weimpose upon it a coherence which allows us tosay what is wrong and in what directions thesituation needs to be changed. Problemsetting is a process in which, interactively,we name the things to which we will attend,and frame the context in which we will attendto them (Schon, 1983, p.40).For the teacher involved in the process of "reflection-in-action" in which he sets a problem in a situation,Schon (1983) posits "fundamental principles" that are"closely connected both to his frames and to hisrepertoire of exemplars" (p.317). By fundamentalprinciples Schon means theory or conceptual apparatus in28use. In a "reflective conversation" with the practicesituation, past experiences of the teacher are brought tobear on the situation, frames are imposed and callattention to certain aspects of the problem, problems areset and actions that entail certain solutions areformulated. How the teacher sees the situation dependson his or her knowledge base, past experience, theuniqueness of the situation and the people involved,social and professional norms of behaviour and theexpectations of others, not to mention the individual wayin which his or her reflection unfolds. Schon'sconception of problem setting is particulary useful inexamining how student teachers represent theuncertainties of real life teaching problems.Kenneth Zeichner's (1981; Zeichner & Liston, 1987)"critical inquiry" offers another perspective onreflective practice. Zeichner goes beyond teaching astechnique and the emphasis on specific situations ofpractice to a level of inquiry that involves questioningwhat is generally taken for granted. He posits threelevels of reflection (Zeichner & Liston, 1987) which getat unarticulated assumptions and root metaphors andinvolve seeing from different perspectives.29Similarly, the work of Habermas (1974) of theFrankfurt School of Social Research also supports acritical conception of reflection. As Calderhead (1989)notes:Reflection is viewed as a process of becomingaware of one's context, of the influence ofsocietal and ideological constraints onpreviously taken-for-granted practices, andgaining control over the direction of theseinfluences. (p.44)The various interpretations of reflective practice whichhave resulted in a proliferation of reflective teachingprograms and strategies (See Adler, 1991 for acomprehensive review) vary in terms of how they view theprocess, content, preconditions, and the product ofreflection. They emphasize to differing extents theroles of problem setting, problem solving, knowledgebases, analytic and interpretative skills, and theattitudes which are brought to bear on the reflectiveprocess.Although many concepts of reflective practice andstrategies of how to educate the 'reflectivepractitioner' have been advanced, operationally definingreflective practice is in itself problematic.Essentially, reflective practice lacks an underlying30conceptual framework from which operational definitionsof reflection, levels of reflection, and the underlyingstructures and processes involved in reflective practicecan flow (Kirby & Teddlie, 1989; Liston & Zeichner, 1990;MacKinnon, 1987;) Empirical evidence to support theeffectiveness of existing reflective strategies utilizedin teacher preparation and professional developmentprograms, even in their present state of operationaldefinition, is lacking (Adler, 1991: Calderhead, 1989).The studies which do examine the use of reflectivepractice by teachers (Korthagen, 1985; MacKinnon, 1986;Oberg & Field, 1986; Russell, 1986) are exploratory innature. The rely primarily on case study and qualitativemethodology as opposed to empirical methods of inquiry.However incomplete the empirical support for theeffectiveness of reflective practice may be, such inquiryhas produced some models of "levels of reflection"(Zeichner & Liston, 1987) or "frameworks for reflectivethinking" (Sparks-Langer, Simmons, Pasch, Colton,Starko, 1990) or "stages in the development of reflectivejudgment" (Ross, 1989b) that are useful in understandinghow student teachers come to represent the problems ofreal life teaching. Table 2.1 provides a description of31these models of reflection.Table 2.1 Models of ReflectionGriffiths and Tann (1992)--Five Levels of Reflection(a) Reflection in action: likely to be personal andprivate.1. Act-react (Rapid Action)-reaction is immediate. ie . child is behaving well, ateacher may automatically give praise, while anotherteacher may equally automatically not.-the teaching action is immediate and routine, but notall teachers have same immediate and automatic reaction.2. React-monitor-react/rework-plan-act (Repair)-although there is a pause for thought, it is "on thespot" and very quick.-untrained observer will miss it.-ie. teacher may see children have unexpected reaction towork and adjust lesson or abandon it. Or see that achild has unexpected interest in work and make decisionto allow child to pursue it rather than carry on withnormal work.(b) Reflection-on-action: likely to be interpersonal andcollegial.3. Act-observe-analyze-and evaluate-plan-act (Review)-thought and reflection are going on after the actionsare completed.-may happen at any time during the normal working day,after school, end of the day or end of the week.-teacher will muse over or talk about the progress ofparticular group or child. May be a result of memory ormaking work.-as a result existing plans for teaching and learning maybe modified.-teacher may reassess how a child is to be managed orthink again about group relations in the class.4.^Act-observe^systematically-analyze^rigorously-evaluate-plan-act. (Research)32-observation becomes systematic and sharply focused.-process of collecting information, analysing it, andevaluating it may be a matter of weeks or months.-tick sheets, video or diary may be used to collectinformation on a particular issue.-teacher will then reflect carefully on the reasons forthe way the issue has arisen in the way it has, and alsoon the information collecting itself (its validity andreliability).5.^Act-observe^systematically-analyze^rigorously-evaluate-retheori ze-plan-act .^(Retheorizing^andreformulating)-level of abstract, rigorous reflection which isformulated and reformulated over a matter of months oryears.-in the process the teachers' own theories will becomechanged and it is possible that accepted theories will bechallenged.-this level cannot occur unless the teacher is readingtheory critically.Ross (1989b)--Stages in the Development of ReflectiveJudgementThe Individual:Stages 1 and 2-Views world as simple-Believes knowledge to be absolute-Views authorities as the source of all knowledgeStage 3-Acknowledges existence of differences of viewpoints-Believes knowledge to be relative-Sees varying positions about issues as equally right orequally wrong-Uses unsupported personal belief as frequently as "hard"evidence in making decisions-Views truth as "knowable" but not yet knownStage 4-Perceives legitimate differences of viewpoint-Develops a beginning ability to interpret evidence33-Uses unsupported personal belief and evidence in makingdecisions but is beginning to be able to differentiatebetween them-Believes that knowledge is uncertain in some areasStages 5 and 6-Views knowledge as contextually based-Develops views that an integrated perspective can beevaluated as more or less likely to be true-Develops initial ability to integrate evidence into acoherent point of viewStage 7-Exhibits all characteristics listed in stages 5 and 6-Possesses ability to make objective judgments based onreasoning and evidence-Is able to modify judgements based on new evidence ifnecessarySparks-Langer et. al. (1989)--Framework of ReflectiveThinkingLevel^Description1 No descriptive language (no descriptionprovided)2^Simple layperson description of theinstructional event. ie . She used groups.3^Events labelled with appropriate terms.ie. she used cooperative groups.4^Explanation with tradition or personalpreference given as the rationale.ie . We always use reading groups.5^Explanation with principle or theory givenas rationale. ie . interdependence in groupwork helps build a desire to help otherslearn: this sink or swim feeling keepsstudents committed to their ownlearning and that of their peers.346^Explanation with principle/theory andconsideration of context factors.ie. student characteristics,subject matter, or community factors.ie. in this class, students' social groupsare generally formed along economic lines.Cooperative learning is esp. useful in suchsituations because it provides repeatedpositive experiences with children fromdifferent backgrounds.7^Explanation with consideration of ethical,moral, political issues. ie . Cooperativelearning is being used here because thereis a split along economic lines in thiscommunity and we want students to acceptand value each other in spite of thesedifferences. Such values may contribute inthe long run to saving this planet.Zeichner and Liston (1987)--Three Levels of Reflection1. Technical-emphasis on the efficient application of professionalknowledge to given ends.-goals and objectives are not a subject for scrutiny, norare long range consequences.-Teachers and prospective teachers need to learn toreflect upon the effectiveness of their teachingstrategies, have the learners achieved the given setobjectives?2.^Teaching is placed within its situational andinstitutional contexts.-Teachers are expected to be able to reflect upon whycertain choices of practice are made.-How are these choices constrained and influenced byinstitutional, social, and historical factors?-What hidden curricula may be embedded in theirpractices, in the norms of the institution?-This level of reflection goes beyond questions ofproficiency at achieving particular ends towards athoughtful examination of how contexts influence teachingand learning, and a consideration of the worth ofcompeting educational goals.353. Moral Ethical Issues-thinking about teaching and learning is guided byconcerns for justice and equity.-teachers must become "transformative intellectuals' whoare capable of examining the ways in which schoolinggenerally,^and one's own teaching specifically,contribute to or fail to contribute to a just and humanesociety.-in reflection, teachers would be able to transcendeveryday experience, to imagine things as they ought tobe, not simply accept things as they are.-such images should shape the teacher's practice andtheir thinking about their practice.Inherent in these levels is a perspective on studentteachers' development of reflection which has at itscentre a view of development which views change asemergent, structural, qualitative, and for the most partconstructive or active. Unfortunately, these models ofreflection describe only surface features of thereflection that structures teachers' thinking or, worse,only static vignettes of teachers' reflection. They stopshort of specifying the underlying processes which are inoperation as teachers actively construct those structuresof reflection as they move from one level of reflectivethinking to another. Reflection is thought to be one ofthe processes student teachers engage in as they attemptto represent real life classroom problems. A neo-Piagetian conceptual framework which is reviewed in thenext section may provide a means for describing the36structures and processes which characterized studentteachers' reflection.D.^A NEO-PIAGETIAN FRAMEWORK FOR EXPLORING STUDENTTEACHERS' REPRESENTATIONS OF REAL LIFE TEACHING PROBLEMSAs one of the dominant figures in the field ofcognitive development, Jean Piaget's structural view ofintelligence provided a universal, monolithic,constructivist view of the human mind. Piaget proposedthat children's cognitive structures go through fourstages: (1) the sensorimotor stage, (2) thepreoperational stage, (3) the concrete operational stage,and (4) the formal operational stage. Each stage ischaracterized by a general thinking structure which isbuilt by differentiating and coordinating existingschemata into a coherent system or psychologicalstructure. The structure enables the child to constructa way of viewing the world. According to Piaget, thesestructures determine cognitive performance acrossdomains, and so constitute a "structure d'ensemble"(structure of the whole). Using Piaget's general stageconstruct to analyze performance in specific domains is3 7fraught with difficulties, however.Evidence against the stages include: (1) difficultiesinherent in the definition and identification of generallogical structures (Flavell, 1963), (2) the unevenness ordiscontinuity in the development of logically equivalentstructures (Beilin, 1971), (3) low correlations for theemergence of same age abilities (Pinard & Laurendeau,1969), (4) successful training of certain abilitiesbefore their age of emergence (Gelman, 1969, 1982), and(5) reinterpretation of developmental shifts as domain-specific conceptual changes (Carey, 1985). Findings suchas these seem to be incongruent with Piaget's assertionthat one general cognitive structure determinesperformance. Although neo-Piagetian theories (Case,1985, 1991; Fischer, 1980; Halford, 1982; Pascual-Leone,1969) have retained the concept of stage, they haveundergone considerable transformation in order to refutethe criticisms levied against classical Piagetian theory.First of all, general logical structures have beenreplaced by domain specific, individually assembledstructures. For example, children's structures forlogico-mathematical thought are assembled independentlyfrom their spatial structures implicit in their art.38Secondly, these neo-Piagetian theories emphasize an upperlimit as an age-related constraint on cognition ratherthan a uniformity across same-age cognitive operations.Thirdly, the variability in the level of cognitiveperformance is explained by individual differences inexperience, processing, and cultural factors. Last ofall, neo-Piagetian theories define the constraints onstage transition in broad terms such as informationprocessing terms such as complexity.The theory of intellectual development which directsthe research program of Robbie Case, (1985; 1987; 1991)a neo-Piagetian theorist, grew out of Piaget's structuralview of intelligence and the neo-nativist and informationprocessing views of intelligence. Case's neo-Piagetiantheory of intellectual development accepts the Piagetianpremise that children actively structure theirexperiences and that the internal processes available forbringing about this restructuring are vastly differentfrom one stage of development to the next. Case departsfrom classical Piagetian theory in his detaileddescription of his four stages of development and theprocesses and mechanisms which allow movement betweenstages. He embraces a sociological perspective in39positing structures which are open to the influence ofcultural factors. His view of the human mind is "one ofa multi-level system, whose structures and processes canvary in their degree of applicability, along a continuumfrom specific thorough intermediate (module-wide) throughgeneral systemic" (Case, 1991, p.374). Accompanying thisview of mind is a view of development in which "changestake place at all levels, in a recursive and interactivefashion, according to a process that depends on bothbiological and cultural/experiential factors" (Case,1991, p.374).Case modeled children's ability to solve problems bypostulating the use of control structures or "internalblueprints" which represent the child's habitual way ofsolving problems. All "tripartite entities" (Case, 1991,p.48) consist of three components: (1) a representationof the current problem situation (2) a representation ofthe desired objective(s) and (3) a representation of thestrategy or sequence of mental steps for progression fromthe initial states of the current problem situation tothe desired outcome situation.Case suggested four distinctly different types ofthought processes which comprise the sequence of stages40of development that are encountered in the movement frombirth to adulthood (see Fig 2.1):(1) In the sensori-motor stage (1-18 months) thinking ismotoric.(2) In the relational stage (1 1/2 - 5 years) childrenthink in terms of global relationships and the mentalevents are objects, people, and actions.(3) In the dimensional stage (5 - 11 years) childrenthink in terms of second order relations, in which theelements are categories of relations or dimensions.(4) In the vectorial stage (11 - 19 years) childrenthink in terms of second order dimensions or categories,in an abstract fashion.^The type of mental eventencountered at each stage of development is representedby the component schemes of the control structure.Case postulates three levels of coordination withineach stage, each one defining a different substage (seeFig. 2.1) and using increasingly more powerful strategiesof problem solving. "Unifocal" co-ordinationscharacterize the first substage of a new stage, when twoschemes assembled gradually during the previous stagebecome hierarchically integrated (ie. one becomessubordinate to the other). This assembled unit becomes41the basic building block of the new stage. At the nextsubstage, two of these unifocal schemes are linked in"bifocal" coordinations, in which two operations ofsimilar complexity become co-ordinated. Finally, duringthe "elaborated bifocal" substage, bifocal co-ordinationsbecome flexible and reversible, in such a way thatchanges in one of the component operations lead easily tocompensatory changes in the other. Continued practiceand streamlining results in consolidation of thesestructures into the units which will be hierarchicallyintegrated at the transition to the next stage.Case's model addresses the problem of continuity bypositing a between stage transition in which the unitscoordinated and consolidated at the previous substagebecome the building blocks of the first substage of thenext level. As the child moves from the last substage ofone level to the first substage of the next level, thereis a qualitative shift in thought. Then as the childprogresses through the remaining three substages of alevel, the strategies used become more quantitativelycomplex. The child is capable of more of the same kindof thinking.A — 2Substage 0(1.4 mos.) A or 8^1Substage 1(4.8 mos.)3rdORDERRELATIONSINTERRELATIONAL STAGESubstage 3(3 1/2.5 yrs.)Substage 2(2-3 1/2 yrs.)Al X— BI W.M.A 2 - B2^4A— 8^1 ^1A 7^2 32ndORDERRELATIONSSENSORIMOTOR STAGESubstage 1(1 1/2-2 yrs.) A2A l —^W.PAAX e l 42^2A^B1 : B 1A 2 ••.;-• 8 2 3Substage 3(12-18 mos.)Substage 2(8-12 mos.)At 0 B1$tORDERRELATIONS42Figure 2.1: Case's Hypothesized Structure of Stages andSubstages from Birth to AdulthoodVECTORIAL STAGE•4 thORDERDIMENSIO NAL STAGESubstage 3(15 1/2-19 yrs.)A — El^W.M.i X^B.A 2 - B 2^4RELATIONS Substage 2(13-15 1/2 yrs.)A — ElI ^B,A 2 -;- B 2 3Substage 1(1143 yrs.)^A^— 8 2Substage 3(9-11^yrs.)Al x—A _-B1 WM.A t °rt8 113 2^4 ^Substage 2 A —1^- B I(7.9 yrs.) A / .- B 2^3Substage 1(5-7 yrs.) A — B^2At or ^18^:• or ABSTRACT DIMENSIONAL STAGE43An accompanying increase in working memory capacitymakes this progression possible and allows the child tofocus on an additional chunk of information and integrateit into the problem solving procedure. To summarize, thechild constructs quantitatively different problem solvingstructures as he progresses through the substages of eachmajor stage, while qualitatively different structuresmark his movement from one major stage to the next.The processes which account for these coordinationsare four information processes described by Case (1987)as: (1) schematic search, in which a second schema issought for activation while a first schema remainsactive, (2) schematic evaluation, in which the usefulnessof the combination of the two schemas is evaluated, (3)retagging, in which two schemes are relabelled into asingle paired, or higher order scheme, so that the twoschemes can be retrieved as a single operation and, (4)schematic consolidation, which involves forming a new,smoothly running unit comprising the two formerlyseparated schemes. These processes of development can beattributed to the larger mechanisms of development suchas attentional capacity.44The mechanisms of development which set limits onthe highest level of intellectual operation which can beachieved are: (1) the amount of working memory available(STSS-short term storage space) and (2) practice andinstruction available in specific problem areas,especially as these problem areas become more culturebound and more abstract.Because Case's model is domain-specific and it allowsfor a fine-grained analysis which specifies thestructures, processes, and mechanisms available tostudent teachers in their growth and development towardexpertise in teaching, it may prove to be a usefulconceptual framework. Case's model can be usedheuristically to generate a series of proposed stages instudent teachers' construction of pedagogical knowledge.Specifically, it can be used to provide one means ofdescribing student teachers' representation of theirpedagogical knowledge of the problem of individualdifferences among learners in the classroom. Table 2.2is one way of portraying these shifts in the studentteachers' representations of the adaption of theirinstruction to individual difference among learners.45Table 2.2: Levels of Student Teachers' Representation ofthe Problem of Adapting Instruction to IndividualDifferences Among Learners.Focus: is on how student teachers represent the problemof adapting their instruction to individual differencesamong learners, how they represent this problem, and howthey pose this problem rather than the solution theyoffer to their most difficult problem encountered thoughthe relation of a problem to a solution is also ofimportance.Substages are a function of the number of mental elementsof a particular sort which can be representedsimultaneously.Sensorimotor Substage 3 Precursory Unit:Sensory orienting response: Student teacher hasability to notice class' reaction to her instruc-tion while she instructs the class.Student teacher does not notice individualdifferences among learners.Interrelational Stage 2nd Order RelationsMental elements are objects, people, actionsSubstage 1 A - B Whole class - Individualof learners^learnerStudent teacher focuses on:Class or learners' reactions to her instructionor^^individual learner's reactions to her instruction.If student teacher's attention is focused on theindividual learner, only the effect of theindividual difference in that learner is noted.Individual differences among learners are notidentified or described.If solution is offered, it is directed at the wholeclass and does not address individual differences46among learners.Substage 2 Al-B1 Whole class - Indiv learnerA2-B2 Effect of Indiv diff of learnerStudent teacher focuses on:class of learners' reaction to her instructionwhile noticing one specific instance of an effect of anindividual difference in an individual learner'sresponse to her instruction.If solution in offered, it is a simplistic or globalsolution directed at either the whole class oflearners or at the specific instance of anindividual difference in one learner.Substage 3 Al-B1 Whole class - Indiv learnerA2-B2 Variable of 1 Indiv diffStudent teacher focuses on:class' reactions to her instruction while noticingand identifying 1 individual difference of anindividual learner's response to her instruction.Simplistic solution is offered which attempts toaddress the individual difference of an identifiedlearner but is directed at the class of learners asa whole.Dimensional Stage 3rd Order RelationsMental elements are categories of relations ordimensionsStudent teacher is able to represent the problem/aspectof individual differences along a dimension of a givenvariable. There is a recognition of the complexity ofthe problem and a notion of balance or tradeoff betweenstudent needs and student teacher's instruction.Substage 1 A - B Index - Range of Indiv DifferenceStudent Teacher focuses on:One index of individual learner difference.Range of the individual difference isidentified.Effect of individual difference in 1 learnerand cause of individual difference is noted.Solution is offered but it may be a simplistic orgeneral solution that meets the needs of the class47or a subgroup of learners but is not tailored to theactual individual difference identified amonglearners.Substage 2 Al-Bl Index - Range of Indiv DifferenceA2-B2 Whole Class - Individual LearnerStudent Teacher focuses on:One index of individual learner difference.Range of the individual difference is identified.Complexity of the problem is acknowledged.Notion of balance between individual or classneeds and student teacher's instruction is indicatedbut not elaborated on.Solution stated is a general solution or standard tobe achieved. It is designed to meet whole classroomneeds or subgroup of learners not individualdifference identified in a learner.Goal may be stated but not integrated intoinstruction or solution.Substage 3 Al-B1 Index - Range of Indiv. DifferenceA2-B2 Whole Class - Individual LearnerStudent teacher focuses on:Detailed description of the index of individualdifference.Range of individual difference is indicated.Complexity of the problem is acknowledged.Notion of balance between learner individualdifference needs and student teacher'sinstruction is described.Solution described is designed to meet individualdifference in learner rather than just the wholeclass or subgroup of learners' needs.Goal to be achieved is integrated into the solutionVectorial or Abstract Dimensional Stage 4th OrderRelationsMental elements are second order categoriesSubstage 1 A - B Std. T's Instrn - Indiv Learner DiffStudent teacher focuses on:One index of individual difference among learners.Range of individual difference is identified.48Complexity of the problem is acknowledged.Notion of balance between learner needs and studentteacher's instruction and needs of whole class aredescribed.Solution involves adjustments in student teacher'sactions, beliefs and expectations to meetindividual learner's actions, beliefs, andexpectations in an interactive way (Oneaffects the other.Substage 2 Al-B1 Std. T's Instrn. - 2 or more IndivLearner DiffsA2-B2 Std. T's Monitoring - Indiv FeedbackStudent teacher focuses on:Two or more indices of individual differences.Range of individual differences are identified.Complexity of problem is acknowledged.Notion of balance between learners' Indiv. diffsand whole group's needs or student teacher'sinstruction is described.Solution involves adjustments on student teacher'spart to meet individual learner needs. Solutionfeatures monitoring learner's actions, assessingtheir reactions and taking learner's feedback intoaccount during solution phase to the problem.Substage 3 Al-B1 Std. T's Instrn - 2 or more Indiv.Learner DiffsA2-B2 Std. T's Monitoring - Indiv FeedbackStudent teacher focuses on:Two or more indices of individual differences.Range of individual difference is identified.Complexity of problem is acknowledged.Notion of balance between Indiv diff of learnerand whole class needs or student teacher'sinstruction is described.Solution involves adjustments in both studentteacher's actions, beliefs and expectations andindividual learner's actions, beliefs andexpectations in an interactive way.Solution proceeds in an integrated fashioninvolving adjustments on both student teacher andlearner's parts to meet individual differences ofthe learner.Student teacher is able to view the individualdifference from the learner's point of view.49Acknowledgement that there is no systematic,effective, single, identifiable solution butrather multiple solutions ordered across time.Although it is difficult to specify the content oraspects of student teachers' representations as theythink about problem situations, goals, and strategiesassociated with adapting their instruction to individualdifferences among learners, Case's conceptual frameworkgets beyond the what and specifically addresses the how.Debate in the literature over what beginning teachersreflect upon, that is, classroom management routines andissues, ethical, social, and moral issues (Gore &Zeichner, 1991; Grossman, 1992), becomes less significantin the face of the question concerning just how it isthat student teachers construct their representation ofthe individual difference problem. This adaptation ofCase's theory of intellectual development provides themachinery for an inquiry into the development of thestructures and processes utilized by student teachers intheir representation of real teaching problems. BecauseCase's neo-Piagetian conceptual framework focuses on thestructures and processes of intellectual development,50may prove to be a useful tool in uncovering studentteachers' representations of real life teaching problemsand their restructuring of these representations over thecourse of the practicum as it allows for a much morespecific, detailed, fine-grained analysis of theirdevelopmental process in the domain of teaching.In the present study, a longitudinal sampling ofstudent teachers' representations of the problem ofadapting instruction to individual differences amongtheir learners will be examined using Case's (1985, 1991)theory to conceptualize and predict developmental change.The levels of student teachers' representation of theproblem of individual differences described in Table 2.2will be developed further in Chapter 3.E. SUMMARYThe nature of the present study is to explore theways in which student teachers represent real lifeteaching problems and the ways in which theserepresentations change over the course of the practicumexperience. The major purpose of this study is togenerate hypotheses about this research question. Theemphasis is on the description of phenomena and on the51development of hypotheses from a data base as opposed tothe formal setting, testing, and confirmation ofhypotheses. Such an inquiry is supported by the reviewof the literature which has incorporated the perspectivesof the theory-practice dilemma in teacher education, theresearch on- teachers' thought processes and thecontributions of the growing movement of reflectivepractice in an attempt to build the research questions ofthis study, namely:(1) How do student teachers represent the real lifeteaching problem of adapting their instruction tothe individual differences among learners?(2) How do student teachers' representations of reallife teaching problems change over the course oftheir practicum experience?(3) Are the structures and processes of Case's (1985,1987, 1991) neo-Piagetian perspective usefultheoretical tools to address the development ofstudent teachers' ability to represent real lifeteaching problems?In order to explore how student teachers represent thereal life teaching problem of adapting their instructionto individual differences among learners, a means foroperationally defining the terms associated with each ofthe four questions posed will be provided. Chapter Threewill describe these procedures and methods.52CHAPTER III: METHODOLOGYIn order to describe how student teachers representthe real life teaching problem of adapting theirinstruction to individual differences among learners,student teachers' responses over the course of a thirteenweek practicum to the following three sets of twoquestions will be explored (See Appendix A):Prior to the Practicum Experience:1. What is your definition of individual differencesamong pupils?2. What aspects of individual differences do you thinkare likely to be problematic for teaching. Why?During the Fourth and Ninth Weeks of the PracticumExperience:1. Describe the most difficult problem you have had inadapting your teaching to individual differencesamong your pupils during these first weeks (thesepast four weeks).What steps did you take to resolve this problem?2. What have been the most important individualdifferences to take into account when teaching thisparticular group of pupils. Give an example of anattempt to meet these differences that you were mostsatisfied with.Similarly, student teacher faculty supervisors wereasked to rank the student teachers on a seven pointLikert scale in response to the following question andprovide examples of the student teachers accommodation ofindividual differences among learners at the fourth and53ninth weeks of the practicum:1. How well has the student teacher been able toaccommodate individual differences among learners?2. Give one or more examples of how the student teacheraccommodated individual differences among learners.A. DESCRIPTION OF THE SAMPLEThe sample consisted of 39 student teachersparticipating in their extended thirteen week practicumand 12 faculty supervisors (4 males and 8 females)responsible for the students. Participants were 19 maleand 20 female students in the two year IntermediateTeacher Education Program and they were assigned tointermediate level teaching situations ranging fromgrades 4-7 during the extended thirteen week practicumexperience. They had completed most of their coursework, including most of their methodology courses and hadparticipated in a two week practicum experience earlierin the teacher education program. This practicumexperience consisted primarily of student and teacherobservation with limited classroom assistance in the formof small group instruction, tutoring, and individualstudent assistance on in-class assignments. The 39student teachers were student teachers for which a54complete data set was available.Elementary student teachers were selected for studyover secondary student teachers because if was felt thatthey had more opportunity to interact with a fixed numberof students across the school day. It was also felt thatby remaining with a smaller number of pupils, studentteachers had more opportunity to monitor the individualdifferences among learners and adapt their instructionaccordingly. Secondary schools available for studytypically had class periods of fixed time lengths, andoften with different students in each time period.Intermediate student teachers were selected forstudy over primary student teachers because opportunitiesfor observing how student teachers deal with theindividual differences problem were more available.Although the emphasis in primary classrooms was onindividualized learning with only brief thirty second toseveral minutes of group instruction such asintroductions or directions on how to do an activity, theintermediate level included both informational lessonsand individualized teaching and learning situations. Itwas felt that the intermediate classroom provided aninstructional context which contained both types of55instruction and constituted a teaching environment thatwas more representative of the real world of teaching andthe dilemmas inherent in the complex task of everydayteaching.Four male and eight female Faculty supervisorsobserved subsets of the intermediate student teachersranging in number from two to six. Over the course ofthe thirteen week practicum, faculty supervisors observedstudent teachers on approximately seven separateoccasions for at least one hour.B. PROCEDURESThree student teacher and two faculty supervisorquestionnaires were used to explore "how" studentteachers represent the real life teaching problem ofadapting their instruction to individual differencesamong learners over the course of the practicumexperience. The description of the questionnaires isdivided into five sections: (1) Questionnaire Rationale,(2) Questionnaire Description, (3) QuestionnaireAdministration, (4) Rating Criteria and Example ofStudent Teachers' Responses, and (5) Rating Criteria andExamples of Faculty Supervisors' Observations and RatingForms. Section (6) will include a discussion of the56general nature of the individual differences whichstudent teachers noted.(1) Questionnaire RationaleThe rationale for the development of thequestionnaire was three fold. First of all, it providedan opportunity to evaluate the intermediate teachereducation program. Second, it allowed for an opportunityto track student teachers' development in the areas ofclassroom management, pacing, curriculum, and lessonplanning, as well as individual differences in theirmovement toward expertise. Third, its format includedboth open-ended responses from student teachers andrating forms and observations from their facultysupervisors. The triangulation employed in this studyallowed for a blend of process tracing and ethnographicmethods of inquiry. Such a method of inquiry issupported by research which advocates that research ofthis nature should be based on natural rather thanexperimental methods (Elbaz, 1988; Goodman, 1988;Mitchell & Marland, 1989). Such a method of inquirypermitted a close examination of the subtleties of thedevelopment of student teachers' problem representation57over the course of the practicum experience. In thepresent study, the questions of adapting instruction toindividual differences among learners were used to elicitwritten responses from student teachers in order toprovide a way of exploring the structures and processesthey might have available for representing the individualdifference problem.(2) Questionnaire DescriptionThe three sets of two questions about individualdifferences among learners which student teachersreceived were part of a larger questionnaire which alsoaddressed the topic areas of: (1) classroom management,(2) pacing, (3) curriculum, (4) lesson planning. Eachpage of the questionnaire was devoted to one topic andtypically contained two questions about that topicfollowed by a paragraph-length blank space for responseelaboration. Students were able to use additional spacefor longer answers. The questionnaire given to thestudent teachers immediately prior to the practicumexperience ( " Pre-Practicum Questionnaire " ) focused on theproblems and issues which student teachers anticipated inthe five topic areas. The other two questionnaires58("Practicum - First Half" and "Practicum - Second Half")completed during the practicum asked student teachers toreflect on the topics as they actually experienced themin their practice teaching.The two sets of questionnaires given to the facultysupervisors consisted of observation and rating formsaddressing each of the five topic areas. Again, eachpage of the questionnaire was devoted to one topic andtypically contained a seven point rating scale (a linewith seven points marked on it with the end points ofminimal accommodation (1) to considerable accommodation(7) identified) and a question which elicited facultysupervisors' observations of the student teacher in thatarea followed by a paragraph-length blank space forresponse elaboration. Most faculty supervisors workedwith twelve student teachers in both intermediate andprimary levels of the elementary teaching program yetonly completed questionnaires on their intermediate levelstudent teachers. As supervision of student teachersconstituted the faculty supervisors entire teaching loadfor the term, all of their time could be devoted toobservation of student teachers.59(3) Questionnaire AdministrationImmediately prior to their practicum experience,consenting student teachers were asked to complete the"Pre - Practicum Questionnaire" in one sitting. Completionof the "Practicum: First Half Questionnaire" by studentteachers began in week three of the practicum after anopportunity for introduction to and immersion inclassroom learning during weeks one and two. Each topicarea was scheduled for completion on a single week.After completion of the five topics for the first half ofthe practicum (weeks 1-7), student teachers returnedtheir questionnaires in sealed envelopes to their facultysupervisors. A similar procedure was followed for thesecond half (weeks 8-12) of the practicum in whichstudent teachers returned their "Practicum: Second HalfQuestionnaire" in week thirteen. The individual learnerdifferences topic questions were scheduled for week fourand week nine. Supervisors completed their twoquestionnaires (rating and observation forms) during thesame weeks as the student teachers.(4) Rating Criteria and Example of Student Teachers'ResponsesThe student teachers' responses to the two questions60answered prior to the practicum experience and during thefourth and ninth weeks were a probe as to how studentteachers represent the real life teaching problem ofadapting their instruction to individual differencesamong learners. Each of the two questions prior to andover the course of the practicum experience were ratedaccording to the criteria specified in the followingdiscussion. Each contains examples of student teachers'responses as they relate to the rating criteria. Aspectsof the two questions include: (1) an assessment of whatstudent teachers believe are the most importantindividual differences to take into account when teachingand, (2) a description of the student teachers' mostdifficult problem in adapting their teaching toindividual differences among learners and the steps theytook to resolve this problem.1. Level of Problem Representation:Pre-Practicum: What aspects of individualdifferences do you think are likely to beproblematic for teaching?4th/9th Weeks: What have been the most importantindividual differences to take into account whenteaching this particular group of students? Givean example of an attempt to meet these differencesthat you were most satisfied with.Student teachers' responses to the pre-practiumformat of this question provided a baseline of their61level of problem representation while their responsesduring the fourth and ninth weeks gave a measure of theirgrowth in level of problem representation over the courseof the practicum. Student teachers' responses to thisquestion were scored according to the Levels of StudentTeachers' Representation of the Problem of AdaptingInstruction to Individual Differences Among Learnersbased on Case's (1985, 1991) neo-Piagetian conceptualframework (see Table 3.1).Table 3.1 Levels of Student Teachers' ProblemRepresentation: Scoring Categoriesand ExamplesNote:^Substages are characterized by the number ofmental elements of a particular sort which can berepresented simultaneously.Case's Neo-Piagetian^Application to StudentTheory of Intellectual Teacher's RepresentationDevelopment^ of Real Life TeachingProblemsSensorimotor Substage 3 Precursory Unit:Sensory orienting response: Student teacher hasability to notice class' reaction to her instruc-tion while she instructs the class.Student teacher does not notice individualdifferences among learners.Interrelational Stage 2nd Order RelationsMental elements are objects, people, actions62Substage 1 A - B Whole class - Individualof learners^learnerStudent teacher focuses on:Class or learners' reactions to her instructionor^individual learner's reactions to her instruction.If student teacher's attention is focused on theindividual learner, only the effect of theindividual difference in that learner is noted.Individual differences among learners are notidentified or described.If solution is offered, it is directed at the wholeclass and does not address individual differencesamong learners.Example: "The slower students need extra help and it isimperative that they get it. I would offer help at lunchor after school."Substage 2 Al-B1 Whole class - Individual learnerA2-B2 Effect of indiv diff of learnerStudent teacher focuses on:class of learners' reaction to her instructionwhile noticing one specific instance of an effect of anindividual difference in an individual learner'sresponse to her instruction.If solution in offered, it is a simplistic or globalsolution directed at either the whole class oflearners or at the specific instance of anindividual difference in one learner.Example: "I'm noticing only one problem and that is witha boy who seems to be challenging me. He continues toshout out inappropriate answers and I continually movehim to the back."Substage 3 Al-B1 Whole class - Individual learnerA2-B2 Variable of 1 indiv diffStudent teacher focuses on:class' reactions to her instruction while noticingand identifying 1 individual difference of anindividual learner's response to her instruction.Simplistic solution is offered which attempts toaddress the individual difference of an identifiedlearner but is directed at the class of learners asa whole.Example: "behavioral problems...While teaching lessons,constantly it has been the same group of individuals whoare off task. Setting rules and expectations for off task63behavior has reduced the number of interruptions duringlessons."Dimensional Stage 3rd Order RelationsMental elements are categories of relations ordimensionsStudent teacher is able to represent the problem/aspectof individual differences along a dimension of a givenvariable. There is a recognition of the complexity ofthe problem and a notion of balance or tradeoff betweenstudent needs and student teacher's instruction.Substage 1 A - B Index - Range of Indiv Diff.Student Teacher focuses on:One index of individual learner difference.Range of the individual difference isidentified.Effect of individual difference in 1 learnerand cause of individual difference is noted.Solution is offered but it may be a simplistic orgeneral solution that meets the needs of the classor a subgroup of learners but is not tailored to theactual individual difference identified amonglearners.Example: "Some are more willing to try new ideas andchallenges while others are afraid of being wrong. It isimportant to reassure the students and offerencouragement and reinforcement. They need to beencouraged as much as possible since most of them sufferfrom low self-esteem to begin with."Substage 2 Al -Bi Index - Range of Indiv DifferenceA2-B2 Whole Class - Individual LearnerStudent Teacher focuses on:One index of individual learner difference.Range of the individual difference is identified.Complexity of the problem is acknowledged.Notion of balance between individual or classneeds and student teacher's instruction is indicatedbut not elaborated on.Solution stated is a general solution or standard tobe achieved. It is designed to meet whole classroomneeds or subgroup of learners not individualdifference identified in a learner.64Goal may be stated but not integrated intoinstruction or solution.Example: "They are all at various writing stages. Somemay write complete sentences while some are not even surewhat a sentence is. Those requiring extra help I let the'better' sentence writers partner up and help. I alsocirculated to help."Substage 3 Al-B1 Index - Range of Indiv DifferenceA2-B2 Whole Class - Individual LearnerStudent teacher focuses on:Detailed description of the index of individualdifference.Range of individual difference is indicated.Complexity of the problem is acknowledged.Notion of balance between learner individualdifference needs and student teacher'sinstruction is described.Solution described is designed to meet individualdifference in learner rather than just the wholeclass or subgroup of learners' needs.Goal to be achieved is integrated into the solutionExample: "The various skill levels of the students atgrasping and understanding new concepts, such as how touse "scale of distance" , was something that I constantlyhad to deal with. The only way I dealt with the high tolow skill levels was to reteach the whole group at times,provide very simplistic steps as to how to apply theconcept, and monitor and individualize instruction forthose having difficulty."Vectorial or Abstract Dimensional Stage 4th OrderRelationsMental elements are second order categoriesSubstage 1 A - B Std. T's Instrn - Indiv Learner DiffStudent teacher focuses on:One index of individual difference among learners.Range of individual difference is identified.Complexity of the problem is acknowledged.Notion of balance between learner needs and studentteacher's instruction and needs of whole class aredescribed.Solution involves adjustments in student teacher's65actions, beliefs and expectations to meetindividual learner's actions, beliefs, andexpectations in an interactive way (Oneaffects the other.Example: "The different levels within the groups ofstudents within creative writing. It is not the sameproblem with students in their writing. It is eitherpunctuation, spelling, capitals or omissions. That makesit hard for me as a student teacher to handle all thesedifferent concerns and problems with a class of 30different individuals. I find that when the student aredoing creative writing, I talk to each individual orgroup of individuals who are having problems with thesame element of writing. By giving each individual athing to look at and to be aware of in their ownwriting."Substage 2 Al-B1 Std. T's Instrn. - 2 or more IndivLearner DiffsA2-B2 Std. T's Monitoring - Indiv FeedbackStudent teacher focuses on:Two or more indices of individual differences.Range of individual differences are identified.Complexity of problem is acknowledged.Notion of balance between learners' Indiv. diffsand whole group's needs or student teacher'sinstruction is described.Solution involves adjustments on student teacher'spart to meet individual learner needs. Solutionfeatures monitoring learner's actions, assessingtheir reactions and taking learner's feedback intoaccount during solution phase to the problem.Example: None present in the data set.Substage 3 Al-B1 Std. T's Instrn - 2 or more Indiv.Learner DiffsA2-B2 Std. T's Monitoring - Indiv FeedbackStudent teacher focuses on:Two or more indices of individual differences.Range of individual difference is identified.Complexity of problem is acknowledged.Notion of balance between Indiv diff of learnerand whole class needs or student teacher'sinstruction is described.Solution involves adjustments in both studentteacher's actions, beliefs and expectations and66individual learner's actions, beliefs andexpectations in an interactive way.Solution proceeds in an integrated fashioninvolving adjustments on both student teacher andlearner's parts to meet individual differences ofthe learner.Student teacher is able to view the individualdifference from the learner's point of view.Acknowledgement that there is no systematic,effective, single, identifiable solution butrather multiple solutions ordered across time.Example: None present in the data set.The example of a student teacher's response used toillustrate the Dimensional Stage, Substage 3 in Table 3.1supplies an instance of the differing levels of studentproblem representation. The identification of thevariable of individual difference: "understanding of newconcepts such as how to use scale of distance" and theillusion to "various skill levels" and "high and lowskill levels" suggest the student teacher is able torepresent the variable of individual difference and thedimension of the problem as the range of skill level fromhigh to low. The notion of balance between meeting highand low level student needs is communicated on hersolution to the problem. Although she starts out byreteaching the whole group, she offers other solutions:"provide very simplistic steps as to how to apply theconcept", "monitor and individualize instruction for67those having difficulty" which suggest she understandsthat there is a relationship between how she instructsand how students learn.In contrast, the example of the student teacher'sresponse at the Interrelational Stage, Substage 3 inTable 3.1 illustrates the qualitative difference betweenthese levels. While the student is able to state whatthe index of individual difference is, he states it interms of the actions of a group of learners: "behavioralproblems...it has been the same group of individuals whohave been off task." No range of high to low incidenceof this individual difference is indicated in the studentteacher's response. The student teacher's representationremains focused on the group rather than on theindividual. The solution: "setting rules andexpectations for off task behavior" is rather general andsimplistic in that it is a blanket solution directed atthe behavior of the whole group rather than the needs ofthe individuals which are causing them to act out or thespecific individual differences among the learners of thegroup. There is no acknowledgement in the studentteacher's representation of the relationship between thestudent teacher's instruction and the effect it has on68the individual students in the class or their reactionsto that instruction.2. Description of Problem Representation:Pre-Practicum: What is your definition of individualDifferences among pupils?4th/9th Weeks: Describe the most difficult problemyou have had adapting your teaching to individualdifferences among your pupils? What steps did youtake to resolve this problem?Student Teachers' responses to this question wereanalyzed for the presence of the three components whichconstitute Case's (1985) higher-order unit or controlstructure:(1) a representation of the problemsituation, that is, a representation of theconditions for which the plan is appropriate;(2) a representation of their most commonobjectives in such a situation, that is, theconditions which they desire, and toward whoseachievement their plan is directed;(3)^a representation of the strategy theyemploy, that is, the set of mental steps thatthey develop for going from the problemsituation to the desired situation in asefficient a manner as possible. (p.68-69)The number of aspects of each of these components wascounted in the student teachers' responses.(5) Rating Criteria and Examples of Faculty Supervisors'Observations and Rating FormsFaculty supervisors rating forms and observations69provided a means of triangulation to check on how wellstudent teachers were able translate their representationof the problem of individual differences into action.Responses were scored along a 7 point Likert scale whichrepresents a continuum from low to high levels ofaccommodation of individual differences. Table 3.2provides a description and examples of facultysupervisors' observations of student teachers'accommodation of individual differences at each of theseven points.Table 3.2 Rating Criteria and Examples For FacultySupervisors' Rating Forms and ObservationsRating Forms^Observations1 MinimalAccommodation2Relatively little note taken by thestudent teacher of the possibility ofindividual differences among learners."Indifferent to individual differences""Not very involved with this aspect ofteaching yet""No evidence of adjusting work toindividual student needs"Instruction is uni-directional fromstudent teacher to learner.Instruction is geared to meet theneeds of the whole group or subgroupswithout much attention given to theneeds of the learners within thesegroups."Used what's in place before arrival"70"Treat subgroup of individualdifferences ie. ESL, the same, sameinstruction given"Instruction is uni-directional fromstudent teacher to learner.Limited personal interest taken inlearners."Although writing activities may bedivergent in nature, students aregiven the same workload""Class is taught as a whole"Some individualized instruction isgiven to students.One area or one way of accommodatingindividual differences is mentioned."Individual tutoring""Group or buddy teaching is used topull in students who participateminimally in activities""Use of visual aids for motivation andillustration of concepts"Student teacher is able to receive somefeedback from the learners.Two areas of individual differencesor two ways in which individualdifferences are accommodated are noted."Accommodation according to interestand ability""Assessment used to determine levels ofability""Exemptions and different goals fordifferent individual needs""Challenging students to think on theirown""Given both written and verbalinstructions when required"Individual needs shape the activitiesand curriculum choices.Monitoring and feedback are meansidentified to assess individual diffs."Each child creates their own spelling71lists from words with which they areunfamiliar""Individualized learning programs"7 ConsiderableAccommodationTwo way, bi-directional nature tostudent teacher and learnerinteractions.Student teacher attempts to takethe child's point of view in allinteractions.Student is an equal partner indetermining what they will learn."Open-ended assignments, studentchoice""Expectations for work produced bydiffers from individual toindividual""Students are held responsible fortheir own learning and achievement"(6) General Analysis of the Nature of the IndividualDifferences Noted By Student Teachers and FacultySupervisorsWhile student teachers' representation of theindividual difference problem and the use of Case's neo-Piagetian conceptual framework as a theoretical tool forits elucidation form the main analysis, it is of someinterest to note the nature of individual differenceproblems which student teachers and faculty supervisorsidentified. The information gleaned from such ananalysis of the student teachers' responses may influencetheir representation of the problem of individualdifferences and its impact on their instruction over the72course of the practicum experience. The nature ofindividual differences noted by faculty supervisors mayindicate the individual differences which areparticularly salient to them in their evaluation ofstudent teachers' instruction and ability to accommodateindividual differences during the practicum experience.C. SUMMARYThe data that the questionnaires yield will providea basis for addressing the research questions and theirrelated hypotheses of:(1) Student teachers who have a more complexrepresentation of the problem of adaptinginstruction to individual differences amongstudents will propose solutions that are moreflexible in their accommodation of individualstudent differences.(2) Student teachers' representations of the problemwill become more complex over the course of thepracticum experience as would be predicted byCase's neo-Piagetian theory of intellectualdevelopment.(3) The structure and processes of Case's neo-Piagetian theoretical perspective will providean adequate theoretical framework from which toconceptualize the development of student teachers'ability to represent the problem of adaptingtheir instruction to the individual differencesamong students.73Chapter Four will provide an indepth discussion ofthe results as they relate to research questions andfindings.74CHAPTER IV: RESULTSThis chapter will provide an exploratory discussionof student teachers' responses to each of the three setsof two questions about individual differences amonglearners posed to them as part of a larger questionnaireand the faculty supervisors' two sets of ratings andobservations. The quantitative analysis will consist ofan examination of the raw data obtained from participantsfor each variable and a discussion of the frequencytables pertaining to overall group responses. Also, ananalysis of the nature of individual differences whichstudent teachers and faculty supervisors identified mayprovide additional information of interest to the presentstudy. Comparisons between student teachers rated highand student teachers rated low on the variables of leveland description of problem representation may providefurther insight into the similarities and differenceswith respect to how student teachers represent the reallife teaching problem of adapting instruction toindividual differences among learners. Questions raisedas a result of the discussion will be presented with andelaborated upon in Chapter Five.75Student teachers were presented with three sets oftwo questions about individual differences amonglearners. The two questions asked before the thirteenweek practicum experience were designed to access studentteachers' definition of individual differences amonglearners and predict their impact on their teaching. Thetwo questions asked in the fourth and in the ninth weekswere designed to elicit student teachers' level ofproblem representation, and their description of thesituation, objectives, and strategies employed in anindividual differences problem. An examination ofresponses may provide an interesting insight into theresearch questions: How do student teachers representthe real life teaching problem of adapting instruction toindividual differences among learners? and How do theserepresentations change over the course of a thirteen weekpracticum experience?Identification of Student Teachers' and FacultySupervisors' RatingsTable 4.1 provides the levels of problemrepresentation coded for the student teachers over thecourse of the practicum experience (01 = sensorimotorstage, substage 3 to 07 = vectorial stage, substage 1;76see Appendix C for a description of the codes for levelsof problem representation). Table 4.1 also provides thefaculty supervisors' seven point Likert scale ratings onhow well student teachers accommodated individualdifferences among learners during the practicumexperience (01 = minimal accommodation to 07 =considerable accommodation). Table 4.2 provides thedescription of the problem representation coded for thestudent teachers during the course of the practicumexperience (see Appendix C for a description of codes fordescription of the problem representation). Each studentteacher retains the identification number originallyassigned to him or her as part of the larger teachereducation program evaluation study. The three sets oftwo questions can be found in Appendix A. Within thepresent chapter, each example used to describe theresults will be labelled as follows: (See Appendix A,question #00; see Table 4.1 or 4.2, Subject #000). Thiswill provide the reader with a relatively efficientmethod of identifying student teachers' ratings on thethree sets of two questions used in the present studyfrom the larger questionnaire.77Table 4.1:^Student Teachers' Level of ProblemRepresentation (PR) Prior to, and at the 4th and 9thWeeks of the Practicum ExperienceSubject(n=39)PriorPR4th WeekPRSupRating9th WeekPRSupRating001 05 06 05 07 06003 01 03 07 01 06004 05 05 05 04 06006 05 04 04 04 06011 03 02 02 02 04014 04 03 03 03 05015 03 04 06 03 03016 04 04 04 05 04017 02 05 05 03 07018 05 03 05 05 06021 02 05 05 05 06026 00 04 04 04 04041 03 04 04 03 03042 04 01 01 03 03043 05 06 04 06 04044 05 03 02 05 02045 03 04 01 03 02082 07 05 06 07 07083 02 01 06 03 06111 01 03 02 07 03113 02 04 07 04 06114 00 01 02 03 02115 03 04 05 05 06125 01 01 05 03 06131 03 04 05 04 05132 00 02 04 04 03133 02 02 05 04 05134 00 03 04 04 05142 02 03 07 04 04143 01 03 02 04 02144 03 04 07 05 05152 04 03 04 03 04156 02 03 06 05 05157 06 05 03 05 04158 02 04 05 04 06163 04 02 06 04 06164 00 01 04 03 04171 05 04 05 04 06172 06 06 06 07 0678Table 4.2 Student Teachers' Description of the ProblemRepresentation During the Practicum ExperienceSubject(n=39)ProbSitn.4th WeekProb^ProbObj.^StrategyProbSitn.9th WeekProb^ProbObj. Strategy001 04 01 02 03 01 03003 03 00 03 02 00 02004 04 01 02 02 00 00006 03 01 02 02 00 01011 02 00 01 02 00 02014 02 00 03 01 00 02015 03 01 04 03 00 00016 02 00 01 02 01 02017 02 00 01 02 00 01018 03 01 03 04 01 03021 04 00 00 04 01 03026 02 00 02 02 01 02041 02 01 03 02 00 03042 01 01 01 02 00 01043 04 01 01 04 01 01044 01 01 02 02 01 01045 03 01 02 03 00 01082 05 01 04 03 01 04083 02 01 00 02 01 02111 02 01 01 06 01 04113 03 01 02 02 01 03114 01 00 01 02 00 01115 03 01 02 04 01 02125 02 00 01 04 01 05131 02 01 03 03 01 03132 02 00 01 03 01 01133 02 00 01 03 01 01134 02 01 02 01 00 02142 03 01 00 03 01 02143 02 00 02 03 01 02144 03 01 02 03 01 01152 02 01 02 02 00 01156 02 00 01 03 01 03157 02 01 03 03 01 04158 04 01 02 03 01 03163 02 01 02 05 01 05164 02 00 01 03 00 01171 04 01 03 04 01 03172 03 02 03 05 02 0379Interrater ReliabilityA random selection of twenty of the sets ofresponses were coded by a second rater using thecategorical descriptions outlined in chapter 3. Theinitial percentage of agreement between the two raterswas: 88% for levels of problem representation, 85% forthe description of the problem representation, and 90%for the general analysis of individual differences notedby student teachers and faculty supervisors. In allinstances, disagreement differed by only one category inthe initial independent coding. After discussion,consensus was reached on cases of disagreement and 100%agreement between the two raters was obtained.A. MAIN ANALYSISThe results will be presented and discussed in thefollowing three sections:1. Student Teachers' Levels of Problem Representation2. Student Teachers' Description of the ProblemRepresentation3. Faculty Supervisors' Ratings and ObservationsIn addition, the nature of the individual differencesnoted by student teachers and faculty supervisors will beexamined as other variables of interest to the present80study.1. Student Teachers' Levels of Problem RepresentationThe question: "What aspects of individualdifferences do you think are likely to be problematic forteaching?" asked of student teachers prior to thepracticum experience provided a baseline of their levelof problem representation. The parallel question: "Whathave been the most important individual differences totake into account when teaching this particular group ofstudents?" asked of student teachers during the fourthand ninth weeks gave a measure of their levels of problemrepresentation during the practicum experience. Studentteachers' responses to these questions will be examinedin terms of levels of representation of the problem ofadapting instruction to individual differences amonglearners as adapted from Case's (1985, 1991) neo-Piagetian theory of intellectual development.Responses were rated according to the complexity ofthe student teachers' thinking about the problem ofindividual differences and assigned a stage and substagewhich matched the complexity of their problemrepresentation (See Chapter 3 for a description of the81Levels of Student Teachers' Problem Representation).Tables 4.3, 4.4, 4.5 provide a distribution of theratings for level of problem representation over thecourse of the practicum experience.Table 4.3:^Frequency Table for Levels of ProblemRepresentation (PR) Prior to the PracticumSensorimotorPRLevel*Frequency(n=39)Percent3 0 5 12.8Interrelational 1 4 10.32 2 8 20.53 3 7 17.9Dimensional 4 5 12.82 5 7 17.93 6 2 5.1Vectorial 7 1 2.6*Lowest to Highest Levels of Problem RepresentationPrior to the practicum experience, student teachers'levels of problem representation were distributed throughout the levels of problem representation with clusteringsat the sensorimotor stage, substage 3, theinterrelational stage, substage 2, and the dimensionalstage, substage 2. Although the largest group of studentteachers had a lower level of problem representation(interrelational stage, substage 2), there was also a82group of student teachers at the lowest level of problemrepresentation (sensorimotor stage, substage 3) and agroup of student teachers at a higher level of problemrepresentation (dimensional stage, substage 2).Of the total number of student teachers (n=39), 5 or12.8% of student teachers gave sensorimotor stage,substage 3 level of problem representation responses.The following is an example of a sensorimotor stage,substage 3 responses:I'm not sure that any individual differenceswill be particularly problematic. I hope allmy students get some enjoyment and meaning outof the activities I plan for them (SeeAppendix A, Question 7b; See Table 4.1,Subject #026).The student teacher is focused on orienting himself tothe learners as a class and the learning activitiesunfolding before him. He does not notice individualdifference among learners.Of the total number of student teachers (n=39), 8 or20.5% of student teachers representation of the problemof individual differences was characteristic of theinterrelational stage, substage 2. The following is anexample of an interrelational stage, substage 2 response:When one student deviates from the otherstudents in academic ways it can causeproblems for teaching a classroom of students83(and the student, teacher, or remainder of theclass). (See Appendix A, Question 7b; SeeTable 4.1, Subject #142)Responses rated at the interrelational stage, substage 2of the levels of problem representation suggest that thestudent teacher is able to focus on the classes' reactionto her instruction while noticing one effect of anindividual difference in an individual learner's responseto her instruction.^Seven or 17.9% of the studentteachers'^responses were also situated at theinterrelational stage in the substage 3 level of problemrepresentation suggesting an ability to identify oneindividual difference of a learner's response to classinstruction while noticing the whole classes' reaction toinstruction.By contrast, 7 or 17.9% of student teachers'responses reflected a higher level of problemrepresentation, that its, at the dimensional stage,substage 2. The following is an example of a dimensionalstage, substage 2 response:Differences in cognitive abilities-especiallythe ability to speak English, but also justgenerally make it difficult form me to caterto all these different levels without feelingthat either the needs of those at the veryhigh and low ends are being ignored. Also,84differences in maturity level in grade sevenappear to make classroom discipline ratherproblematic (See Appendix A, Question 7b; SeeTable 4.1, Subject #001).At this stage, the student teacher is able to identify anindex of individual difference, describe the range ofability levels, note the complexity of the problem, andindicate a notion of balance or tradeoff involved inmeeting the range of ability levels.Only one student teacher's response showed avectorial stage, substage 1 level of problemrepresentation. Such a response indicates an awarenessof not only the elements noted at the dimensional stage,substage 2 but also the idea that meeting individualneeds involves an interaction between instructor andlearner in which monitoring and feedback help shapeadjustments in student teacher's instruction.Table 4.4 provides a distribution of the ratings forlevel of problem representation during the first half ofthe practicum experience (Week 4).By the fourth week of the practicum, all of thestudent teachers had moved beyond a sensorimotor stage,substage 3 level of problem representation. The realityof adapting real instruction to real individualdifferences among real learners in the real classroom85clustered student teachers' responses in theinterrelational and dimensional stages of problemrepresentation.Table 4.4:^Frequency Table for Levels of ProblemRepresentation (PR) During the First Half (4th Week) ofthe PracticumSensorimotorPRLevel*Frequency(n=39)Percent3 0 0 00.0Interrelational 1 5 12.82 2 4 10.33 3 10 25.6Dimensional 4 12 30.82 5 5 12.83 6 3 7.7Vectorial 7 0 00.0*Lowest to Highest Levels of Problem RepresentationOf the total number of student teachers (n=39), 5 or12.8% of student teachers' responses were at a lowerlevel, interrelational stage, substage 1 of problemrepresentation. The following is an example of thislower level of problem representation at theinterrelational stage, substage 1:The class'^responsiveness to answeringquestions. I picked on certain nonresponsivestudents with questions I knew they couldanswer (See Appendix A, Question 4b; SeeTable 4.1, Subject #125).86In this response, the student teacher focuses exclusivelyon the class' reaction to her instruction. She is unableto identify or describe individual differences amonglearners and her solution is a global one directed atclass members rather than the individual differencesamong learners in that class.Of the total number of student teachers (n=39), thelargest number of the group of student teachers wasclustered around the transition point betweeninterrelational stage and dimensional stages. Ten or25.6% of the student teachers' responses were at theinterrelational stage, substage 3. The following is anexample of an interrelational stage, substage 3 response:With this particular group of pupils,behavioral problems have been the mostimportant individual difference to take intoaccount. While teaching lessons, constantlyit has been the same individual who is offtask. Setting rules and expectations for offtask behavior has reduced the number ofinterruptions during lessons (See Appendix A,Question 4b; See Table 4.1, Subject #003).The student teacher is able to identify the index ofindividual difference: behavioral problems, yet he doesnot describe the range of the behavioral problem or itscomplexity. The student teachers' solution of settingrules and expectations for off task behavior attempts to87address the individual difference of the learner, but itis directed at all the learners in the class rather thanone learner in particular.By contrast, of the total number of student teachers(n=39), 12 or 30.8% were at the dimensional stage,substage 1, a stage in which student teachers are able torepresent individual differences among learners as acategory or dimension. The following is an example ofthe qualitatively different dimensional stage, substage1 response:Some are more willing than others to try newideas and challenges while others are afraidof being wrong. It is important to reassurethe students and offer encouragement andreinforcement. They need to be encouraged asmuch as possible since most of them sufferfrom low self-esteem to begin with (SeeAppendix A, Question 4b; See Table 4.1,Subject #045).At this higher level of problem representation, thestudent teacher is able to coordinate an identificationof an individual difference: self-esteem with the rangeof individual difference: some are more willing to trynew ideas while others are afraid of being wrong. Thesolution is a general one directed at the low self-esteemgroup rather than tailored to the self-esteem needs ofeach individual learner.88Faced with the realities of the classroom, thestudent teacher who was identified at the vectorialstage, substage 1 level of problem representationretreated down a stage to the dimensional stage, substage3. None of the student teachers' responses reflect avectorial stage, substage 1, high level of problemrepresentation during the first half of the practicumexperience.Table 4.5 provides a distribution of the studentteachers' levels of problem representation during thesecond half of the practicum experience.Table 4.5:^Frequency Table for Levels of ProblemRepresentation (PR) During the Second Half (9th Week) ofthe PracticumSensorimotorPRLevel*Frequency(n=39)Percent3 0 0 00.0Interrelational 1 1 2.62 2 1 2.63 3 11 28.2Dimensional 4 13 33.32 5 8 20.53 6 1 2.6Vectorial 7 4 10.3*Lowest to Highest Levels of Problem RepresentationBy the ninth week of the practicum experience, none89of the student teachers' level of problem representationwas at the lowest sensorimotor stage, substage 3, andonly two student teachers' were rated at the lowerinterrelational stage, substages 1 and 2 levels ofproblem representation. Of the total number of studentteachers (n=39), 11 or 28.2% of the student teachers'responses were at the interrelational stage, substage 3while 13 or 33.3% were at the dimensional stage, substage1. This finding suggests that the majority of studentteachers in the sample were wrestling with the movementfrom a representation of the problem as one concernedwith people and actions to one concerned with categoriesof relations or dimensions by the ninth week of thepracticum. They were able to identify an index ofindividual difference in one learner while focusing onthe class of learners, yet only some were able tocoordinate this with a description of the range ordimension of that individual difference.Of the total number of student teachers (n=39), 8 or20.5% of the student teachers' responses were at thedimensional stage, substage 2 level of problemrepresentation. The following is an example of adimensional stage, substage 2 level response:90Our class has students who have very poor workhabits and language skills as well as somesuperachievers. Addressing individual needshas been a challenge. One attempt was toprovide underachievers with moreresponsibility in areas of school they enjoy(ie. PE or Science) and try to have thesestudents use these experiences andresponsibilities for written work or math SeeAppendix A, Question 4b; See Table 4.1,Subject 018).At this higher level of problem representation, thestudent teacher focuses on the range and complexity ofthe index of individual difference while still addressingthe needs of the class as a whole. The solution offeredhere is directed at a subgroup of learners, in this caseunderachievers rather than individual underachievers, yetthe solution does take into account areas which are ofinterest to these underachievers.Four or 10.3% of the student teachers' responseswere at the vectorial stage, substage 1 level of problemrepresentation. The following is an example of avectorial stage, substage 1 response:The different levels within the groups ofstudent within creative writing. It is notthe same problem with students in theirwriting. It is either punctuation, spelling,capitals, or omissions. That makes it hardfor me as a student teacher to handle allthese difficult concerns and problems with aclass of 30 different individuals. I findthat when the students are doing creativewriting I talk to each individual or group of91individuals who are having problems with thesame element of writing. By giving eachindividual a thing to look at and to be awareof in their own writing.. See Appendix A,Question 4b; see Table 4.1, Subject #111).At this highest level of problem representation found inthe sample, the student teacher is able to adapt herinstruction to the needs of the individual learner. Hersolution is arrived at through adjustments in heractions, expectations due to monitoring of and feedbackfrom the individual learner.Figure 4.1 provides a graphic summary of thefrequency distributions associated with the shifts inlevels of problem representation over the course of thepracticum experience.2. Student Teachers' Description of the ProblemRepresentationIn order to explore the nature of student teachers'problem representation, student teachers were asked to:"Describe the most difficult problem you had adaptingyour teaching to individual differences among yourpupils. What steps did you take to resolve thisproblem?" at the fourth and ninth weeks of the practicumexperience. Student Teachers' responses to this question92will be examined in terms of presence of the threecomponents which constitute Case's (1985, 1991) controlstructure:Figure 4.1: Graphic Summary of the FrequencyDistributions Associated with the Student Teachers'Levels of Problem Representation Prior to, During theFirst and Second Halves of the Practicum93representation of the problem situation, representationof objectives, and representation of strategy orstrategies employed. The number of aspects of each ofthese three components will be noted. Responses wererated according to the presence of components and thenumber of aspects of these components of problemrepresentation (See Chapter 3 for a description of therepresentation of the problem). Table 4.6 provides adistribution of the ratings for the description ofproblem representation during the first half of thepracticum experience.Table 4.6: Frequency Table for the StudentTeachers' Description of the Problem RepresentationDuring the 4th Week of the Practicum# of^Problem^Problem^ProblemAspects*^Situation^Objective^StrategyF^% F^% F^%0^0^00.0^14^35.9^3^7.71 3 7.7 24^61.5^12^30.82^19^48.7^1^2.6^14^35.93 10^25.6 0^00.0 8^20.54 6^15.4^0^00.0^2^5.15^1 2.6 0^00.0 0^00.0*Least to Largest number of aspects notedDuring the first half of the practicum experience,the two components: representation of the problem94situation and representation of the problem strategy werepresent in all student teachers' descriptions of theirrepresentation of the individual differences problem. Ofthe total number of student teachers (n=39), 14 or 35.9%did not explicitly state a representation of the problemobjective in their description. Twenty-four or 61.5% ofthe student teachers were only able to give a descriptionof one objective in their representation of the problem.As indicated in Table 4.7 above, the majority ofstudent teachers' representations of the problemsituation component of the individual difference problemfeatured two aspects whereas their representations of theproblem strategies component consisted of one or twoaspects. The following is an example of a lower leveldescription of the components of problem representation:I haven't had to adapt on the whole, I justmake sure that the students I feel to beslower get ample time to answer the questions(See Appendix A, Question 4a; See Table 4.2,Subject #114).In the student teacher's representation of his mostdifficult problem during the first half of the practicum,his representation of the problem situation contains onlyone aspect; no problem objective is represented, and hisrepresentation of the problem strategy contains only one95aspect.By contrast, the following example of a higher levelof description of components of problem representationsuggests a more detailed representation of problemsituation, objective(s), and strategy:We have a number of ESL (Iranian) students inthe class. Some don't understand a word ofEnglish (or very few words) and can't write.Others are "dying" to learn and pretend tounderstand the directions when they reallycan't. Therefore, I had to make sure that allmy lessons were directed at everyone, butespecially more so to them (See Appendix A,Question 4a; See Table 4.2, Subject #158).This student teacher's representation of his mostdifficult problem contains a detailed description of atleast four aspects of the problem situation. Hedescribes an objective for his instruction: to make sureall lessons were directed at everyone. His strategy forimplementing this objective involves two aspects:planning instruction to accommodate all levels of priorknowledge especially the varying levels of ESL studentsin his class.Table 4.7 provides a distribution of studentteacher's description of the problem representationduring the second half of the practicum experience.96Table 4.7: Frequency Table for the StudentTeachers' Description of the Problem RepresentationDuring the 9th Week of the Practicum# of^Problem^Problem^ProblemAspects*^Situation^Objective^StrategyF^% F^% F0 0 00.0 14 35.9 2 5.11 2 5.1 24 61.5 12 30.82 14 35.9 1 2.6 10 25.63 15 38.5 0 00.0 10 25.64 6 15.4 0 00.0 3 7.75 2 5.1 0 00.0 2 5.1*Least to Highest Number of Aspects Noted.By the second half or ninth week of the practicum,the majority of student teachers' representations of theproblem situation component increased to three aspects.Their representations of the strategy employed to movefrom the problem situation to the desired situationranged from one to three aspects. No change wasreflected in the student teachers' representations oftheir objectives when faced with a problem situation. Ofthe total number of student teachers (n=39), 24 or 61.5%still represented only one aspect in their description ofthe representation of the problem objective. This resultsuggests that student teachers may still have difficultyrepresenting the problem objective component of a97difficult problem even by the second half of thepracticum experience.3. Faculty Supervisors' Ratings and ObservationsThe faculty supervisors' ratings and observationswere designed to provide a means of triangulation tocheck on how well student teachers were able to translatetheir representations of the problem of individualdifferences into action during the practicum experience.Faculty supervisors' ratings were scored along a 7 pointLikert scale which represented a continuum from low tohigh levels of accommodation of individual differences(See Chapter 3, Table 3.2 for a detailed description ofratings and observations). The following Table 4.8provides a distribution of the supervisors' ratings ofhow well student teachers accommodated individualdifferences during the first half or fourth week of thepracticum experience.The majority of student teachers (n=28), 8 or 20.5% wererated as a four and 12 or 30.8% were rated as a fiverepresenting a mid level of accommodation.98Table 4.8: Frequency Table for Supervisors' Ratings ofStudent Teachers' Accommodation of Individual DifferencesDuring the First Half (4th week) of the PracticumMinimalRating Frequency(n=39)PercentAccommodation 1 2 5.12 5 12.83 3 7.7Mid 4 8 20.5Accommodation 5 12 30.86 5 12.8Considerable 7 4 10.3AccommodationTypically, such accommodation of individual differencesincluded recognition of at least one index of individualdifference among learners and at least one strategy whichinvolved some individualization of instruction toaccommodate individual learner's or subgroup's oflearners needs.Table 4.9 provides a distribution of thesupervisors' ratings of student teachers' accommodationof individual differences during the second half or ninthweek of the practicum experience. By the second half ofthe practicum, all student teachers were observed toprogress beyond the lowest level of minimal accommodationof individual differences.99Table 4.9: Frequency Table for Supervisors' Ratings ofStudent Teachers' Accommodation of Individual DifferencesDuring the Second Half (9th Week) of the PracticumMinimalRating Frequency(n=39)PercentAccommodation 1 0 00.02 4 10.33 4 10.3Mid 4 8 20.5Accommodation 5 7 17.96 14 35.9Considerable 7 2 5.1AccommodationThe majority of student teachers, 14 or 35.9% of^thetotal number of student teachers (n=39) were rated as asix, a higher level of accommodation. At this level,faculty supervisors reported that individual needs shapedthe learning activities and student teachers usedmonitoring and feedback as a means to identify and meetindividual differences among learners.B. SECONDARY ANALYSISThe nature of individual differences noted bystudent teachers and faculty supervisors in all of theirresponses to the questionnaires represents their100perspectives on what constitutes an individual differenceand the types or aspects of individual differences whichmust be adapted to during instruction. A fulldescription of the codes for the types of individualdifferences is included in Appendix C. A brief summaryof these types of individual differences appears inFigure 4.2.Figure 4.2:^A Summary of The Types of IndividualDifferences Noted by Student Teachers0 = unable to identify a type of individual difference1 = learning rates2 = general intellectual and academic ability3 = specific skill or aptitude or ability4 = prior knowledge ie. ESL5 = specific interest areas6 = general motivational levels7 = ethnic or cultural background8 = behavioral differences9 = learning styles10 = attentional differences11 = maturity levels12 = social skills13 = socio economic status, social background14 = personality characteristics, self-esteem15 = general category/ all individual differences16 = physical or motor differencesTable 4.10 provides a distribution of the ratings ofindividual differences noted by student teachers in theirdefinitions of individual differences and theirdescriptions of their most difficult problems encountered1 01during the fourth and ninth weeks of the practicum.Table 4.10:^Frequency Table for Aspects of IndividualDifferences Noted by Student Teachers in Definition(Question 7a) and Most Difficult Problem (Question 4a,9a) During the PracticumTypes of Prior 4th Week 9th WeekIndividual Defn Difficult DifficultDifferences* Problem ProblemF^% F^% F^%0 2^5.1 0^00.0 1^2.61 9^23.1 10^25.6 9^23.12 7^17.9 15^38.5 21^53.83 2^5.1 2^5.1 1^2.64 3^7.7 5^12.8 4^10.36 2^5.1 0^00.0 1^2.67 1^2.6 0^00.0 0^00.08 1^2.6 6^15.4 2^5.19 4^10.3 0^00.0 0^00.010 0^00.0 1^2.6 0^00.011 1^2.6 0^00.0 0^00.012 2^5.1 0^00.0 0^00.013 3^7.7 0^00.0 0^00.015 1^2.6 0^00.0 0^00.016 1^2.6 0^00.0 0^00.0As a group, student teachers alluded to a widevariety of individual difference types (16). Learningrates were mentioned most often in student teachersdefinition of individual differences followed by generalintellectual and academic ability and learning styles.When asked to describe a difficult individualdifferences problem they were experiencing during the102first half of the practicum, the variety of individualdifferences in student teachers' responses narrowed tosix types. General intellectual and academic ability wasthe area of individual difference in which studentteachers experienced their most difficult problemfollowed by learning rates and behavioral differences.By the second half of the practicum, the variety ofindividual difference types increased to seven. Generalintellectual and academic ability was still theindividual difference type cited most often by studentteachers followed by learning rates. By the ninth week,however, the individual difference of prior knowledge wasof more concern than behavioral differences. This resultmay indicate that by the second half of the practicum,student teachers' focus has shifted away from behavioraldifferences and classroom management issues and on to theaspects of individual differences which the learnerbrings to the learning enterprise. Table 4.11 providesa distribution of the ratings of individual differencesnoted by student teachers in their response to "Whataspects of differences are most likely to be problematicfor teaching" (Question 7b) and "What have been the mostimportant individual differences to take into account103when teaching this group of pupils?" (Questions 4b,9b)Table 4.11: Frequency Table for Aspects of IndividualDifferences Noted by Student Teachers in Questions 7b,4b, 9b During the PracticumTypes ofIndividualDifferences*PriorDefnF^%4th WeekDifficultProblemF^%9th WeekDifficultProblemF0 8 20.5 2 5.1 2 5.11 5 12.8 2 5.1 5 12.82 7 17.9 12 30.8 10 25.63 3 7.7 8 20.5 10 25.64 0 00.0 4 10.3 2 5.15 1 2.6 0 00.0 0 00.06 2 5.1 2 5.1 2 5.18 4 10.3 1 2.6 3 7.79 5 12.8 1 2.6 3 7.710 0 00.0 1 2.6 0 00.012 1 2.6 2 5.1 0 00.013 2 5.1 2 5.1 0 00.014 1 2.6 1 2.6 4 10.315 0 00.0 1 2.6 0 00.0The variety of individual difference types noted bystudent teachers in their definition of individualdifferences narrowed to ten when student teachers wereasked what aspects of individual differences would likelybe problematic for teaching prior to the practicum.General intellectual and academic ability were mentionedmost often by student teachers followed by equal mentionof both learning rates and learning styles, then priorknowledge. During the first half of the practicum,104general intellectual and academic ability continued to bealluded to most often by student teachers followed byspecific aptitudes and skills and then prior knowledge.By the second half of the practicum, the patterncontinued in that student teachers still showed the mostconcern for general intellectual and academic abilities,yet specific aptitude and skill became of equal concernto student teachers. General motivational level becamethe second area of individual differences most noted bystudent teachers edging out learning rates which wereallocated to a third position. This pattern may reflectthe student teachers' growing ability to adapt theirinstruction to individual differences. The learners'motivation levels become more important as the practicumenters its ninth week and the novelty of a differentteacher wears off among learners. A parallel pattern oftypes of individual difference emerged in the facultysupervisors' observations of the student teachers duringthe practicum experience. Table 4.12 provides adistribution of the ratings of individual differencesnoted by faculty supervisors in their observations ofstudent teachers' accommodation of individual differencesduring the fourth and ninth weeks of the practicum.105Table 4.12: Frequency Table for Aspects of IndividualDifferences Noted by Faculty Supervisors in TheirObservations of Student Teachers During the 4th and 9thWeeks of the PracticumAspects of^4th Week^9th WeekIndividualDifferences*Frequency Percent Frequency Percent0 8 20.5 7 17.91 2 5.1 4 10.32 8 20.5 8 20.54 4 10.3 3 7.75 6 15.4 1 2.66 2 5.1 6 15.48 1 2.6 3 7.79 2 5.1 3 7.714 4 10.3 4 10.316 1 2.6 0 00.0Similar to the student teachers, faculty supervisorsmentioned general intellectual and academic ability mostoften at both the fourth and ninth weeks of thepracticum. During the first half of the practicum,faculty supervisors' observations noted student teachers'attempts to accommodate individual differences in thearea of learners' specific interest areas followed byprior knowledge. This finding indicates studentteachers' concern with the individual difference of priorknowledge during the first half of the practicum.By the ninth week of the practicum, faculty106supervisors' observations noted student teachers'attempts to meet general motivational levels in theirlearners. Both learning rates and personalitycharacteristics were the types of individual differencementioned third most often by faculty supervisors. Thisfinding shows that student teachers were observed toadapt their instruction to types of individual differencewhich were affective in nature not just cognitivelyoriented. This suggests that student teachers werebeginning to address the individual differences of thewhole child, not just the academic component.In summary, the types of individual difference notedmost often by student teachers and faculty supervisorswere general intellectual and academic ability andlearning rates. Prior to the practicum experience,student teachers noted a wide variety of individualdifferences. Over the course of the practicumexperience, student teachers' focus on individualdifference types broadened from a cognitive emphasis toone which included affective components. This change offocus was also reflected in the types of individualdifference noted by faculty supervisors' observations of107how student teachers accommodated individual differencesin their instruction.These data were used to explore and to generatequestions about student teachers' representations of reallife teaching problems and the ways in which thoserepresentations change during the practicum experiencebased on the results discussed in this chapter. Furtherdiscussion of the results as they apply to theformulation of questions, the evaluation of Case's neo-Piagetian conceptual framework as a theoretical tool, andthe implications of these questions and theoreticalperspective for research on teacher education, studentteacher thinking, and reflective practice will bepresented in Chapter Five. In addition, the limitationsof the study and directions for future research will bediscussed.108CHAPTER V: DISCUSSIONThis study was designed to explore how studentteachers represent the problem of adapting instruction toindividual differences among learners and how thisability develops over the course of the practicumexperience. The extent to which Case's (1985, 1991) neo-Piagetian theory of intellectual development may providea theoretical framework for conceptualizing studentteachers' representations of the problem of individualdifferences was also investigated. These questions wereformulated from research on teacher education, teachers'thought processes, and reflective practice.The major purpose of the study was to provide aconceptual framework from which questions designed toelucidate student teachers' representation of the problemof adapting instruction to individual differences amonglearners, could be delineated and further analyzed. Theresults and limitations of the study contribute to theimplications of and generation of future researchquestions on teacher education, student teacher thinking,and reflective practice.109A. DISCUSSION OF THE RESULTS1. Student Teachers' Level of Problem RepresentationStudent teachers' responses to the question: "Whataspects of individual differences are likely to beproblematic for your teaching?" prior to the practicumprovided a means to explore their representations of theindividual differences problem. Results from the presentstudy indicate that prior to the practicum studentteachers' levels of problem representation ranged fromthe lowest sensorimotor stage, substage 3 to the highervectorial stage, substage 1. This finding suggests thatstudent teachers begin at the point at which they are intheir thinking about the individual difference problem,not all at the same starting point or where researchersand teacher educators think they "ought" to begin.Although 5 or 12.8% of student teachers did begin at thesensorimotor stage, substage 3, the majority of studentteachers (19 or 48.7%) started at the low interrelationalstage in their level of problem representation. Thisfinding suggests that these student teachers had somesense of what a class of learners was like and howinstruction unfolds, but their attention was focused ongroups of people and their actions rather than categories110of relations or dimensions of individual differencetypical of the dimensional stage. Another group ofstudent teachers, 14 or 35.8% were able to identify therange and complexity associated with the individualdifferences problem and showed levels of problemrepresentation at the dimensional stage.By the fourth week of the practicum, all of thestudent teachers had moved beyond a sensorimotor stage,substage 3 level of problem representation. Faced withthe realities of adapting instruction to real learners'individual differences, the majority of student teachers'levels of problem representation were clustered in theinterrelational (19 or 48.7%) or dimensional (20 or51.3%) stages. The student teacher who showed avectorial stage, substage 1 level of problemrepresentation prior to the practicum, succumbed to thetime pressures of the practicum experience and retreatedto the dimensional stage. Typically, this pattern ofretreating to a previous substage of problemrepresentation when faced with the uncertainties of realteaching situations affected 12 or 30.7% of studentteachers.By the ninth week of the practicum, of the majority111of student teachers 22 or 56.4% showed a dimensionalstage level of problem representation. This findingsuggested a qualitative shift in student teachers'representation of the individual differences problem fromone concerned with people and actions to one concernedwith categories of relations or dimensions. Of 13 or33.4% of student teachers at the interrelational stage,11 or 28.2% were at substage 3. Such a finding indicatesthat these student teachers were able to identify anindividual difference while instructing the class, butwere unable to coordinate this with a description of therange or dimension of that individual difference. Fouror 10.3% of student teachers were able to represent theproblem of individual differences at the higher vectorialstage, substage 1 level. This suggests an ability toadapt instruction to the needs of the learner whichinvolved adjustments in the student teachers' actions andexpectations arrived at through monitoring and feedback.By the ninth week of the practicum, 6 or 50% of thesubgroup of 12 student teachers whose levels of problemrepresentation retreated a substage, actually recoveredreflecting a U shaped pattern very similar to the patternTuriel (1969) found in the results he used to support his112idea of stage 4.5 "transitions".Faculty supervisor ratings and observations on howwell student teachers accommodated individual differencesamong learners paralleled student teachers' growingabilities to represent the problem of individualdifferences in more complex ways. At the fourth week ofthe practicum, the majority of student teachers (12 or30.8%) were given a rating of 5 on a 7 point Likertscale. By the ninth week, the majority (14 or 35.9%)were given a rating of 6. All student teachers wereobserved to progress beyond the lowest levels of minimalaccommodation of individual differences by the secondhalf of the practicum.These results taken together with the studentteachers' description of the components of problemrepresentation which will be discussed next, provide arich and detailed picture of how student teachers abilityto think about the real teaching problem of adaptinginstruction to individual differences among learnersdevelops during the practicum.2. Student Teachers' Description of ProblemRepresentationWhen asked to describe the most difficult problem113they had adapting their teaching to individualdifferences among learners at the fourth and ninth weeksof the practicum, the majority of student teachers'responses reflected the presence of all three componentsof problem representation. The complexity of studentteachers' descriptions of problem situation and problemstrategy components increased during the practicum from1 or 2 aspects to 2 or 3. Student teachers' descriptionsof the problem objective component remained unchangedover the practicum. In fact, 14 or 35.9% of the studentteachers' responses did not include an explicit statementof problem objective. The majority of student teachers(24 or 61.5%) were able to describe one aspect of theproblem objective. These findings suggest that studentteachers may still have difficulty representing theproblem objectives component of a difficulty problem evenby the second half of the practicum experience.An additional analysis of the types of individualdifferences noted by student teachers and facultysupervisors in their questionnaire responses reflectedthat general intellectual and academic ability as well aslearning rates were the individual differences most oftennoted. Over the course of the practicum experience,114student teachers' focus on individual difference typesbroadened from a cognitive emphasis to one which includedaffective components. This change of focus was alsoreflected in the types of individual differences noted byfaculty supervisors in their observations of studentteachers. It parallels to some extent student teachers'growing ability to identify and meet the needs ofindividual differences among their learnersStudent teachers' ability to note individualdifferences which describe the whole child, their abilityto describe more aspects of the problem situation andstrategy components of problem representation, and theirprogression beyond a sensorimotor stage, substage 3 levelof problem representation to levels of problemrepresentation primarily at the interrelational substage3 and dimensional substages suggest a growth in theirability to represent the problem of individualdifferences. These findings are expected given Case'sview of development in which experience plays animportant role in the hierarchical integration ofcognitive structures. Evidence of the increasingcomplexity of student teachers' level and description ofproblem representation during the practicum indicates the115importance of the role of experience and reflection onexperience in student teacher development. In addition,this evidence suggests that Case's model with itsemphasis on the role of experience is an appropriateconceptual framework to describe the development of thestudent teachers' ability to represent real life teachingproblems.3. Case's Neo-Piagetian Perspective as a ConceptualFramework for Thinking About Student Teachers'Representation of Real Life Teaching ProblemsOne of the purposes of the present study was toinvestigate whether or not the structures and processesof Case's (1985, 1987, 1991) neo-Piagetian theory ofintellectual development could provide an adequatetheoretical means to describe the development of studentteachers' ability to represent real life teachingproblems. Case's model has provided a rich set ofcategories to describe the shifts occurring across thelevels of student teachers' problem representation duringthe practicum. The findings were consistent with basicprinciples of Case's theory and his emphasis on thecontribution of environmental factors and experience.The finding that student teachers' initial levels of116problem representation ranged from lowest sensorimotorstage, substage 3 to higher vectorial stage, substage 1levels further supports the use of a perspective whichembraces a constructivist approach. Case's neo-Piagetiantheory provides a means of assessing where the student isin their representation of real life teaching problemsrather than where researchers and teacher educators thinkthe student teacher "ought to be".The findings of the present study are consistentwith findings reported by Ammon and Hutcheson (1989) inthe use of their five levels to represent the structuralstages in the domain of developmental pedagogy. Theyfound that the majority of student teachers attainedmedian levels of pedagogical conception while fewteachers aspired to the higher levels. Although Ammonand Hutcheson (1989) do not specify the structures andprocesses which account for the student teachers'movement from level to level, their findings arecompatible with the results of the present study. Sucha parallel suggests that Case's neo-Piagetian perspectivemay be an appropriate theoretical tool to conceptualizestudent teachers' representations of real life teachingproblems.117As an exploratory, first step, the present studyprovided a useful set of categories from which studentteachers' levels and complexity of representation of theindividual differences problem could be described. Therefinement of these categories together with thedevelopment of a set of scenarios which address otherreal life teaching problems to test student teachers'levels of problem representation represent the next stepsin research which uses Case's neo-Piagetian conceptualframework. The present study provides support for aconceptual framework which does have the potential toprovide a theoretical basis for research in teachereducation, teacher thinking, and reflective practicewhich investigates the process of becoming a teacher.B. LIMITATIONS OF THE STUDYSeveral methodological issues including thegeneralizability of the results, the verbal protocols asa measure of student teacher thinking, and theconclusions which can be drawn from the results requirecareful consideration.The present study was exploratory only.^Itsintention was to generate questions based on the118development of a framework for student teacher thinkingwhich combines several research traditions. Thetraditions are cognitive development, teachers' thoughtprocesses and reflective thinking. The sample for thepresent study was made up of a total of 39 studentteachers completing the final thirteen week practicum ofthe two year teacher education program and 12 facultysupervisors. Participants were not randomly selected,therefore, generalizations to other student teachers andto other teacher education programs must be consideredwith caution. Although the size of the sample wasadequate for the exploratory nature of the study, thenumber of student teachers within each substage of thelevels of problem representation varied. Only sixstudent teachers were rated at the sensorimotor level ofproblem representation. Similarly, only five studentteachers were rated at the vectorial level of problemrepresentation. Therefore, the effect of studentteachers' experience over the course of the practicum onlevel of problem representation should be interpretedwith caution.The use of questionnaires to stimulate studentteachers' thinking about the nature of individual119differences and the adaption of their teaching toindividual differences among learners gives rise toseveral methodological concerns. The three sets of twoquestions asked prior to, and at the fourth and ninthweeks of the practicum experience represented a way ofstimulating thought processes associated with therepresentation of the individual differences problem andprovided opportunities for student teachers to revealtheir own thinking about this real life teaching problem.Anomalies in the student teachers' responses may be dueto the time pressures experienced over the course of thepracticum experience. Prior to the practicum, studentteachers gave well articulated, lengthy responses to thequestions asked of them. At the fourth week of thepracticum, responses ranged from a few words to a coupleof hurried sentences. By the ninth week, responsesincreased in length to a couple of sentences to detailedparagraphs. The amount of time spent on thequestionnaires appeared to vary for this reason and mayaccount in part for the U shaped pattern of responsedescribed above. Although the use of questionnaires doesnot achieve the quality of responses and explanationsthat are elicited in a clinical method within an120interview setting, factors such as cost, time, economy ofadministration and the exploratory nature of the studyinfluenced the method employed.Task scenarios rather than questionnaires coupledwith clinical interviews which probe for informationbased on teacher's immediate reactions to questions mayprovide a standardized way for controlling variationswhich seem to arise due to the flexibility of time givento complete the questionnaires. More importantly, theopportunity for the interviewer to elicit continuousresponses from each student teacher will help todetermine how the student teacher is interpreting thequestion posed as well as how he/she is thinking aboutthe task. In this situation, the interviewer is able toask as many questions deemed necessary in order to elicitthe student teacher's representation of the problem.Although the methodology of the present study usedtriangulation in a blend of process tracing andethnographic methods of inquiry, anomalies in the facultysupervisors' ratings and the observations they gave onhow well student teachers accommodated individualdifferences among learners in their instruction wereapparent. For example, some faculty supervisors rated121student teachers as a 6 or 7 (considerable accommodation)on the 7 point Likert scale while citing examples ofaccommodation which reflected only moderate accommodationand median level of problem representation. A questionin the faculty supervisor's questionnaire which assessedthe faculty supervisor's definition of individualdifferences and the aspects of individual differenceswhich they deem to be problematic for teaching may haveshed some light on these anomalies. The extent to whichthe student teacher reflects on his own construction ofthe problem of adapting instruction to individualdifferences, formulates his own strategies for dealingwith the problem based on his representation, and thenuses this representation in the classroom setting couldbetter be established through classroom observation whichemploys observers versed in Case's neo-Piagetianconceptual framework.In the present study, the suggestion is that studentteachers who have a higher level of problemrepresentation and a more detailed description of theproblem may have the thought processes and pedagogicalknowledge available to them for organizing andreflecting-in-action on their own problem representations122within the practice setting. The extent to which studentteachers reflect on their "knowledge-in-action" maydepend on the representations they have available tothem. Evidence for this may best be established throughclinical interview techniques augmented by carefulclassroom observation.Despite these limitations, several implications andquestions for future research student teachers' thoughtprocesses emerged from the findings. These will now bediscussed.C. IMPLICATIONS FOR RESEARCH ON TEACHINGStudies of teachers' thought processes have focusedon identification, frequency counts, and antecedents ofteachers' interactive thoughts (see Clark & Peterson,1986 for a review). Such a narrow focus of research hasyielded little about how teachers actually makeinteractive decisions or how they begin to construct andreconstruct more adequate conceptions of pedagogicalknowledge. What these researchers neglect to considerare the implications of a developmental perspective forstudies of teacher thinking. Within a constructivistframework of growth in knowledge, researchers have theopportunity to examine how student teachers think about123teaching and learning. The student teacher's ownexperiences and actions, and the cognitive developmentalprocesses which may be associated with his ability tothink about teaching from a developmental perspective,may provide researchers with insight into the studentteacher's own "reflection-in-action". The use of a neo-Piagetian conceptual framework may provide a richtheoretical tool for further research on teacher thinkingand for the development of teacher education programs forstudent teachers.If researchers begin to study the student teacher'srepresentations of real life teaching problems from atheoretical perspective which can yield a fine grainedanalysis of the underlying structures and processesavailable to student teachers as they construct their ownrepresentations of the problems they confront in theclassroom, then they may begin to understand "how" and"why" student teachers develop the ability to teach. Ifresearchers ask questions about the student teacher's ownlevel of problem representation, then they may begin tomatch teacher education curriculum to the needs of thestudent teachers. If they begin to observe studentteachers in the act of teaching, then they may be in a124better position to describe the growth of problemrepresentation, pedagogical knowledge, and reflection-in-action which occurs as student teachers engage in theteaching process. They may also be in a better positionto address the theory/ practice dichotomy whichcharacterizes the curricula of our present teachereducation programs. In this view, teacher education willbegin where the student teacher is rather than on whereresearchers and teacher educators think the studentteacher "ought to be". What the present study may offerthe researcher and teacher educator is a developmentalperspective and a conceptual framework for identifyingthe underlying structures and processes whichcharacterize the student teacher's level and complexityof problem representation when he is faced with real lifeclassroom problems which may be defined as ill-definedproblems.D. DIRECTIONS FOR FUTURE RESEARCHThe intent of the present study was to generatequestions based on an exploration of the ways in whichstudent teachers represent the problem of adaptinginstruction to individual differences and the ways in125which their representations change over the course of thepracticum. As a result of the findings, severalquestions were generated to stimulate further researchon, student teachers' representations of real lifeteaching problems from a neo-Piagetian perspective.These questions are:1. To what extent do the level and complexity of studentteachers' problem representations predict success indealing with the uncertainties of the classroom?2. To what extent do cross-domain parallels existbetween student teachers' level of problemrepresentation in the domain of teaching and inthe scientific, social, and spatial domains?3. When faced with classroom situations which may bedescribed as ill-defined problems to what extent dostudent teachers:a. select information from their pedagogicalknowledge base, repertoire of experiences andand actions to formulate representations ofthe problem?b. formulate alternative representations of theproblem?c. formulate representations of the problem based ontheir hypotheses about how the students arethinking?d. formulate their own theories of teaching andlearning as they formulate representations of theproblem?4. 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Whichaspects of individual differences will likely have the most impact on theway that you teach during the practicum?7b. What aspects of individual differences do you think are likely to beproblematic for teaching. Why?_ Check here if you continue on the other side, to make sure we read it.^Pre-7Practicum First Half^ 139Week 4 Name^4a. Describe the most difficult problem you have had in adapting yourteaching to individual differences among your pupils during these firstweeks. What steps did you take to resolve this problem?4b. What have been the most important individual differences to take intoaccount when teaching this particular group of pupils? Give an example ofan attempt to meet these differences that you were most satisfied with.Check at left if continuing on back so we will make sure to read it. Practicum -4Practicum Second Half^ 140Week 9 Name^9a. Describe the most difficult problem you have had in adapting yourteaching to individual differences among your pupils during these past fiveweeks. What steps did you take to resolve this problem?9b. What have been the most important individual differences to take intoaccount when teaching this particular group of pupils? Give an example ofan attempt to meet these differences that you were most satisfied with.Check at left if continuing on back so we will make sure to read it. Practicum -9141UBC Supervisor First Half Practicum Weeks 1-7^(Student teacher's first name, initial of last)6a. How well has the student teacher been able to accommodate individualdifferences among learners?1^2^3^4^5^6^7Minimal mid ConsiderableAccommodation Accommodation6b. Give one or more examples of how the student teacher accommodatedindividual difference among learners. Please do not use the sameexample(s) as for adjusting for fast and slow learners. Please mention thebasis of the student teacher's accommodation (ability, motivation, interest,learning style, etc.).Please check if continuing on back, so we will make sure to read it.^Supervis-6142UBC Supervisor Form Second Half, Weeks 8-12^(Student teacher's first name, initial of last)6a. How well has the student teacher been able to accommodate individualdifferences among learners?1^2^3^4^5^6^7Minimal mid ConsiderableAccommodation Accommodation6b. Give one or more examples of how the student teacher accommodatedindividual difference among learners. Please do not use the sameexample(s) as for adjusting for fast and slow learners. Please mention thebasis of the student teacher's accommodation (ability, motivation, interest,learning style, etc.). If you wish, you may note improvement (or lack ofimprovement) by comparison to the first seven weeks._Please check if continuing on back, so we will make sure to read it^Supervis-18143APPENDIX BDescription of the Two Year UBC Teacher Education Program144MAJOR FEATURES OF INITIAL TEACHER EDUCATION PROGRAMS AT UBCThe revised programs of Initial Teacher Education were first offered in September,1987. Since then, some further modifications have been made each year. What follows is asirrnmAry of the major features of the programs as they are offered during 1991-92.A. Overall program featuresThe minimum post-secondary preparation for beginning teachers, bothelementary and secondary, is five years.In order to provide adequate time for candidates to achieve an educationwith both breadth and depth, the pedagogical phase of initial teachereducation presupposes the completion of a minimum of three years of post-secondary general education and subject studies. For secondary teachers adegree in the selected teaching field(s) is required.In order to provide adequate time for candidates to acquire and assimilatethe knowledge, skills, and attitudes necessary to begin a teaching career andto become accustomed to the standards and practices of the teachingprofession, the pedagogical phase of initial teacher education extends over aminimum of 12 months.B. General and subject-matter studiesIn order to prepare for the general nature of their future teachingresponsibilities, all prospective teachers complete introductory or surveycourses in English and in as many as possible of the major fields of humaninquiry. Some studies should have a significantly Canadian content orapproach. Where possible, the preparatory program includes both someintroductory study of educational theory and practice (preferably includingclassroom contact) and also a second-level course in English composition orwriting.Each prospective elementary teacher completes at least a one-term courserelated to each of the core subjects in the B.C. elementary school curriculum(mathematics, a laboratory science course, and courses in history and/orgeography in addition to the English requirement noted above). In order forindividual teachers to be an academic resource to their schools and^-communities, each teacher develops subject-matter strength in one selectedelementary school subject. This consists of 18 credits (3 full courses) at thethird or fourth year level in addition to introductory or survey courses in thatsubject.Secondary teacher candidates achieve depth of knowledge and understandingin at least one, and preferably two, secondary teaching subjects.145C.^Pedagogical studiesa^Initial teacher education includes a blend of pedagogical courses andexperiences of a general character with others more focussed on the gradesand subjects to be taught. Teaching methods courses encompass bothgeneral and subject-specific studies.• Special attention is to be paid to the prospective teacher's communicationskills, both oral and written and both verbal and non-verbal.• The selected program of studies is tightly structured and sequenced withopportunity for some electives during the final term.D.^School experience• In order to give candidates adequate opportunity to perfect their classroomskills, to establish and consolidate appropriate attitudes and behaviourpatterns, and to enhance their professional confidence, the final practicumextends for a full term of 13 weeks.• Prior to the extended practicum, school experience of different sorts isintegrated with courses.a^Admission to any teaching practicum requires the completion of all liberaleducation and subject-matter requirements of the program. Admission tothe extended practicum requires, in addition, the completion of all generaland subject-specific teaching methods courses as well as other prescribedintroductory pedagogy courses. Oral and written English screening testsmust also be completed before the extended practicum.Year 1, Term 2This term includes an intensive two-weekschool placement in which candidatesconsolidate their understanding ofinstructional principles and approaches.This classroom experience provides a basisfor further studies of ways of organizingknowledge for instruction and of methodsand strategies for teaching. Elementarycandidates will prepare to teach all subjectsat specific grade levels.Education 321 {Orientation School Experience: Elementary)^0 creditsCurriculum and Instruction CoursesArt Education 320^ 1 creditsEducation 320 (Physical Education) ^ '' creditsEnglish Education 320 ' creditsMathematics Education 320^ ' creditsMusic Education 320 ' creditsReading Education 320 ^2 creditsScience Education 320  ^ 2 creditsSocial Studies Education 320  ^ 2 creditsYear 2, Term 2Following completion of the extended,practicum, candidates undertakeprofessional studies to put their teachingcompetence in a more comprehensiveframework of knowledge andunderstanding. The term includes electiveor prescribed studies appropriate to eachcandidate's personal academic andprofessional interests.Education 420 (School Organization in its Social Context).^2 creditsEducational Psychology and Special Education 423^ 3 credits(Learning. Measurement, and Teaching)Educational Studies elective: one of:- Educational Studies 425 (Educational Anthropology 1..^3 credits- Educational Studies 426 (History of Education) 3 credits- Educational Studies 427 (Philosophy of Education)^.....^3 credits- Educational Studies 323 (The Social Foundations of Educations^3 credits- Educational Studies 429 (Educational Sociology) 3 creditsAcademic. Curriculum, and Professional Electives^ 9 - 12 credits(Courses selected in consultation with an advisor; candidates who wishto complete a teaching concentration in an elementary school fieldshould select 12 credits of courses related to their pm-admissionsubject specializationYear 2, Term 1Candidates spend this term in selected B.C.elementary schools. Each candidate worksclosely with a team of experienced teacherswho have been specially prepared for thissupervisory and instructional responsibility.Faculty support, advice, and assessment areprovided on a regular basis.Education 418 i Extended Practicum: Elementary) ^ :3 zrethtsYear 1, Term 1Prospective teachers are introduced to thetheoretical bases of modern educationalpractice. Studies include analysis of thenature and objectives of education and ofthe developmental characteristics oflearners. Attention is given to candidates'own interpersonal and communication skillsand to strategies and methods of teaching.Structured classroom observations andteaching experiences (such as tutoring, peerteaching, and microteaching) are provided.Education 310 (Principles of Teaching: Elementary)^6 creditsReading Education 310^ 3 credits(Introduction to Elementary Reading and Language Arts Instruction)Education 315 (Pre-PracticumExigl-glience)^ 0 creditsEducation 316 (Communication Skala in Teaching)^3 creditsEducational Psychology and Special Education 313 3 credits(Educational Application of Developmental Theories)Educational Psychology and Special Education elective: one of:- Educational Psychology and Special Education 322^" credits(Education during the Early Childhood Years)- Educational Psychology and Special Education 323 2 credits(Education during the Middle Childhood Years)Educational Studies 314 (Analysis of Education)^ 3 credits146The Elementary Teaching Program (2 years)The basic program sequenceTotal program requirements: 71 - 74 credits147PRACTICUM EXPERIENCESThe Elementary Teacher Education Programs are sequentially ordered and includethree practica. Each practicum plays an important part in the professional education ofprospective teachers and is a prelude to the next practicum. The Faculty regardsEducation 418 (9) as the culmination of a sequence of practica: Education 315 (0) Pre-Practiczan School Experience, and Education 321 (0) Orientation School Experience:Elementary. In recognition that Education 418 (9) is the culminating experience, all of theunits for the practica are associated with that course.Education 315:■^During the first term, teaching candidates will make eight half-day visits toschools located throughout the Lower Mainland. Tasks will relate toReading Education 310, an on-campus course, and will include instructional on a one-to-one or smai^1 group basis.Education 321:Candidates then undertake a two-week practicum designed as an orientationto the school, the classrooms, and the teachers of the extended practicum.Teaching candidates will undertake a variety of instructional tasks.Education 418:■^The culminating school experience is a thirteen-week extended practicumduring which teaching candidates will experience a range of teachingassignments, including a sustained block of teaching with a teaching load of80%.Both the two-week school orientation and the thirteen-week extended practicumwill be in the same school.PLACEMENT FOR PRACTICAThe Faculty attempts to place candidates in the locations of their choosing. For thisreason, we ask students to specify no fewer than four preferred locations for their two-weekand extended practica. It may not be possible to accommodate all student requests.Teaching candidates must therefore be prepared to accept placement in schools anywherewithin 125 km of the UBC Campus, arranging for and bearing the cost of their owntransportation and accommodation.Placements for the two-week and extended practica can usually be arranged incentres outside the Lower Mainland region of the province. These locations vary from yearto year and are dependent upon student response.148EDUC. 315. Pre practicum Experience.—Observation in educational settings.EDUC 315 is the initial school experience for students in the elementary program.The purpose of the eight half-days in the schools is to provide student teachers with anintroduction to the school setting and an opportunity to interact with students. Themorning activities should be divided between observation and one-to-one or small groupinstructional activities. Suggestions for these activities are derived from ReadingEducation 310, an on-campus course. Successful completion of Education 315 is requiredbefore students proceed to Education 321.UBC's teacher education programs are based upon the principle of gradualimmersion into the responsibilities of teaching.  Thus, during this practicum studentteachers are not expected to assume full responsibility for an entire class. They areexpected to conduct themselves in a professional manner as described in the Protocol forStudents Undertaking School Experiences and to undertake instructional activities that aredeemed appropriate by the school advisor and faculty advisor.Observation: It is hoped that school advisors will observe most lessons taught by thestudent teacher and that faculty advisors will observe at least one lesson. It is desirable forobservation to be followed by oral and written feedback.Evaluation: School advisors are asked to complete an EDUC 315 School ExperienceFeedback Form. If possible, school advisors should discuss the report with the studentteacher on the last morning of EDUC 315 and give the student teacher a copy. Facultyadvisors are asked to ensure that UBC copies are forwarded to the Teacher EducationOffice.For additional information regarding teaching practica, please see "GeneralRegulations Affecting Teaching Practica," and "Policies and Procedures" in this handbook.149EDUC 321. Orientation and School Experience: Elementary.--A two-week sequence ofobservations and instructional assignments in a selected elementary school which usuallybecomes the setting for Education 418: the Extended Practicum. [0-0: 1-2]EDUC 321 is the second school experience in UBC's elementary teacher educationprogram. During this practicum student teachers are not expected to assume full tearhingresponsibility. They are expected to conduct themselves in a professional manner asdescribed in the Protocol for Students Undertaking School Experiences, and to undertakeinstructional and non-instructional activities that are deemed appropriate by the schooladvisor and faculty advisor. The purposes of the two-week school experience for theelementary program are:1. To provide the student teacher with opportunities to observe the way schoolsorganize for and provide instruction.2. To provide the student teacher with opportunities to apply the knowledgetaught in the first-term university course work.3.^To provide an opportunity for student teachers and school advisors to getacquainted prior to undertaking the thirteen week extended practicum.The following activities are regarded as appropriate for students at this point intheir professional development. Selection and sequencing of activities will be theresponsibility of the school advisor in consultation with the faculty advisor:1.^HousekeepineMczruzgemenr: Prepares a seating plan: registers attendance;reads announcements; conducts pupils from place A to place B; prepares atransparency for overhead projector (initiated by another person); assistswith fire drill; supervises play y ound; supervises lunchroom; operatesfilmstrip projector; operates •^projector; operates ditto or otherduplicating machinery; exhibits pupils' work: keeps records of pupils'achievement1 . Instruction: Reads a story to entire class; prepares tasks, visual aids,chalkboard displays; reviews homework; demonstrates an experiment; helpsindividual pupils with 'seatwork': instructs a small group of pupils (planningby another person); plans and teaches a lesson to a small group; teaches anentire lesson to entire class (planning by another): plans and implementsinstruction for entire class for entire lesson.3.^Evaluation: Collects anecdotal data on an individual child or group ofchildren; administers an oral quiz prepared by another; prepares andadministers an oral quiz; prepares and administers a written test; evaluatesan oral test; evaluates a written test; evaluates homework; returns/discusses'graded work.i c eEDUC 418 (18 credits) Extended Practicum: Elementary. —A developmental program ofteaching practice, normally in one B.C. elementary school. Candidates will teach allsubjects in the elementary curriculum. Prerequisite - all requirements set for Year 1. [0-40-, 0-0]Course OverviewThe thirteen-week ("extended") practicum provides student teachers withopportunities to demonstrate that they are capable of assuming the responsibilitiesexpected of an enrolling teacher. Student teachers who have successfully completed thethirteen week practicum will have demonstrated that they can independently plan,implement, and evaluate instruction over substantial penods of time at a standard expectedof a beginning teacher.In addition to instruction, which includes the preparation, delivery, and evaluationof lessons, other important experiences of the extended practicum include:1. Reflection about tea•^often carried out in groups of student teachers,school advisors, and^ty advisors; may include analytical discussions.2. Observation of the teaching of other student teachers, school advisors andother teachers; observing individual school students or groups of schoolstudents.In order to enable the student teacher to be reflective and to have time to observein classrooms, the student teacher's maximum teaching load will be 80% of the schooladvisor's normal teaching load.1 C152STUDENT TEACHERS' ROLES AND RESPONSIBILITIESPre-Practicnm:■ Familiarizes self with the "Protocol for Student Teachers Undertaking SchoolExperiences" and the "Guide to Professional Practice" in this handbook• Makes telephone contact with school principal and school advisor.• Discusses the subjects and classes to be taught during the thirteen-weekpracticum.■ Inquires about the availability of resources in school district and proceduresfor accessing them.• Explores library and other resource centres in schooL• Begins working on overviews and unit plans after consulting the appropriatecurriculum guides.Weeks One - Three:• Is in attendance on the first day of school.• Begins the thirteen-week practicum at the weekly percentage recommendedby both the school advisor and faculty advisor(s).• Attends and participates in three-way conference arranged to clarify theobjectives of the practicum and the expectations of student teachers, schooladvisors and faculty advisors.• Participates in discussions about the observation forms and procedures.Learns where copies go, the purpose of the forms and how the evaluation willproceed.• Makes available to faculty advisor complete timetable.• Observes teachers at work and notes good approaches and methods.153Throughout Practicum:• Prepares lesson/unit plans in accordance with the advice of both school andfaculty advisor(s) and makes copies available to school advisor at least 24hours in advance of the time when the lesson will be taught and/or facultyadvisor(s) upon request• Maintains binder(s) of unit/lesson plans and makes binder(s) available toschool and faculty advisor.• Re-does lesson or unit plans if advisors so request.■ Attempts to make good use of various kinds of teaching materials andteaching aids. Seeks out school and district resources.• Discusses difficulties with school advisor(s), faculty advisor(s) and suggestspossible solutions.• Makes a contribution to housekeeping in the classroom.• Actively participates in the overall school program.• Maintains records of pupil performance• Keeps faculty advisor apprised of new/interesting developments in classroomprogram as well as any changes, cancellations or alternative arrangements.• Increases teaching time in accordance with recommendations of thishandbook• Engages in self-reflective activities regarding all aspects of teaching methodsand school participation.• Ensures that a good balance of teaching experience occurs over the course ofthe practicum.• Invites observations, comments, criticisms, and suggestions for improvement.• Makes note of and reflects upon successful methods and styles.• Acknowledges and reflects upon areas of difficulty.■ Participates actively in structured pre and postconferences related to formalobservations.154• Seeks to understand comments and checklist items noted by school and/orfaculty advisor(s) and asks for clarification where necessary.• In the case of serious concerns, discusses and seeks to understand fully thefeedback from school and faculty advisor(s). Reads carefully and, ifnecessary, seeks clarification of the content of the Interim Report written byschool or faculty advisor(s), to be submitted to the Teacher Education Office.• At week six or seven takes part in a half-way conference arranged by thefaculty advisor.Weeks Eight - Thirteen:• Increases teaching time consistent with recommendations in this handbook.• Prepares for summative evaluation conducted by school advisor(s) andfaculty advisor(s).• Returns all student work and provides school advisor(s) with student marks.Post-Practicum:Writes thank-you letters to school advisor(s) and to the schooladministration.Returns all curriculum materials and resources.•a155Faculty Advisors' Roles and ResponsibilitiesUBC's faculty advisors are responsible for working with schools to organize theorientation for student teachers. Prior to the students' arrival in the schools, facultyadvisors should contact the schools to which they have been assigned and review thepurposes of the Orientation School Experience and its relationship to Education 418:Extended Practicum (Elementary).The faculty advisor's prime role in this practicum is to assist both the student andschool advisor in establishing a professional working relationshipOnce student teachers arrive in the schools, faculty advisors are expected to makefrequent visits to the schools to assist in adjustments in the placement of the studentteachers, to support school staff in working with student teachers, to respond to staffquestions about the UBC program, and to confer with student teachers. Faculty advisorsshould also orient school advisors to Education 418, providing information about UBC'sTeacher Education program, the philosophy of the extended practicum, expectations ofstudent teachers, school advisors and faculty advisors, observation and feedbackprocedures, and evaluation.As time permits, faculty advisors will observe each student and provide writtenfeedback.For additional information regarding teaching practica, please see ''GeneralRegulations Affecting Teaching Practica," and Policies and Procedures" in this handbook.FACULTY ADVISORS' ROLES AND RESPONSIBILITIESPre-Practicum:■ Makes contact with school principal and school advisor.Provides information about the student's program, availability of tuition feewaivers and availability of EDUC 432.■ Provides information about days scheduled for workshops related to studentteaching.■ Conducts orientation sessions regarding observation and evaluation.■ Consults with teachers about the appropriate workload and grade levels to beassigned to the student teacher.■ Assesses the match between student teacher and school advisor(s).Week One - Three:• Ensures student teachers are familiar with Protocol for student teachers.Resolves any initial difficulties, anxieties, or misconceptions.Arranges three-way conference to clarify the objectives of the practicum andthe expectations of the student teacher, the school advisors and the facultyadvisor.Discusses the evaluation forms and procedures.Monitors the student teacher's initial work in the classroom.Throughout Practicum:• Regularly checks the student teacher's lesson and unit plans forappropriateness and completeness.• Maintains regular contact with each school advisor to ensure that satisfactoryprogress of the student teacher is taking place.• Observes the student teacher as frequently as time permits (recommendedonce per 5 to 7 teaching days).• Gives written feedback after each observation where possible, using thechecklist, a section of the checklist, or the open-ended comment form.Retains a copy and distributes other copies to school advisor and studentteacher.• Conducts pre and postconferences and formal observations with each studentteacher (minimum bi-weekly).• At week six or seven, conducts a half-way conference with school advisor(s)and student present to provide all parties with a picture of strengths andareas which need improvement.• In the case of serious concern regarding the student teacher, consultsGuidelines For Faculty or School Advisors Who Have Serious ConcernsAbout A Student's Performance (p. 43).157Weeks Eight - Thirteen:■ Continues to observe and to assist each student teacher in his/her charge.• Reviews the evaluation procedures with each school advisor and studentteacher.• Completes a set of summative evaluation forms (one checklist and one open-ended evaluation form both marked FINAL) for each student teacher.• Coordinates the process for establishing the final standing (complete/fail)and submits the standings to the Director of Field Placement and Research.Evaluating Student TeachingIt is hoped that students will receive both oral and written feedback from schooladvisors and faculty advisors.To this end UBC Faculty of Education has designed two forms for the evaluation ofstudent teaching. These will be distributed to all school advisors by the faculty advisor andshould be used throughout the practicum.School and faculty advisors are encouraged to provide the student teacher withsome form of written feedback following each classroom observation. Both the checklistand the written comments form can be used in whole or in part. Once completed by eitherschool advisor or faculty advisor, a copy of the evaluation form should be given to thestudent teacher. In keeping with the "triad" notion of communication, school advisors andfaculty advisors are encouraged to share one copy of their completed form with the othertwo persons. Advisors should retain one copy for their records.At the end of Education 418 both the school advisor(s) and faculty advisor write afinal summative evaluation of the student teacher's performance and complete a check listThese final forms should reflect the feedback the student has received throughout thepracticum. One set of forms should be completed by the school advisor and another by thefaculty advisor.APPENDIX CCodes for:A. MAIN ANALYSIS1. Student Teachers' Levels of Problem Representation2. Student Teachers' Description of the ProblemRepresentationB. SECONDARY ANALYSIS1. Types of Individual Differences Noted by StudentTeachers and Faculty Supervisors1581591. Student Teachers' Levels of Problem Representation00 = Sensorimotor Substage 3 Precursory Unit:Sensory orienting response: Student teacher hasability to notice class' reaction to her instruc-tion while she instructs the class.Student teacher does not notice individualdifferences among learners.Interrelational Stage 2nd Order RelationsMental elements are objects, people, actions01 = Substage 1 A - B Whole class - Individualof learners^learnerStudent teacher focuses on:Class or learners' reactions to her instructionor^individual learner's reactions to her instruction.If student teacher's attention is focused on theindividual learner, only the effect of theindividual difference in that learner is noted.Individual differences among learners are notidentified or described.If solution is offered, it is directed at the wholeclass and does not address individual differencesamong learners.02 = Substage 2 Al-B1 Whole class - Indiv learnerA2-B2 Effect of Indiv diff of learnerStudent teacher focuses on:class of learners' reaction to her instructionwhile noticing one specific instance of an effect of anindividual difference in an individual learner'sresponse to her instruction.If solution in offered, it is a simplistic or globalsolution directed at either the whole class oflearners or at the specific instance of anindividual difference in one learner.03 = Substage 3 Al-B1 Whole class - Indiv learnerA2-B2 Variable of 1 Indiv diffStudent teacher focuses on:class' reactions to her instruction while noticing160and identifying 1 individual difference of anindividual learner's response to her instruction.Simplistic solution is offered which attempts toaddress the individual difference of an identifiedlearner but is directed at the class of learners asa whole.Dimensional Stage 3rd Order RelationsMental elements are categories of relations ordimensionsStudent teacher is able to represent the problem/aspectof individual differences along a dimension of a givenvariable. There is a recognition of the complexity ofthe problem and a notion of balance or tradeoff betweenstudent needs and student teacher's instruction.04 = Substage 1 A - B Index - Range of Indiv Diff.Student Teacher focuses on:One index of individual learner difference.Range of the individual difference isidentified.Effect of individual difference in 1 learnerand cause of individual difference is noted.Solution is offered but it may be a simplistic orgeneral solution that meets the needs of the classor a subgroup of learners but is not tailored to theactual individual difference identified amonglearners.05 = Substage 2 Al-B1 Index - Range of Indiv DifferenceA2 -B2 Whole Class - Individual LearnerStudent Teacher focuses on:One index of individual learner difference.Range of the individual difference is identified.Complexity of the problem is acknowledged.Notion of balance between individual or classneeds and student teacher's instruction is indicatedbut not elaborated on.Solution stated is a general solution or standard tobe achieved. It is designed to meet whole classroomneeds or subgroup of learners not individualdifference identified in a learner.Goal may be stated but not integrated into161instruction or solution.06 = Substage 3 Al-B1 Index - Range of Indiv. DifferenceA2-B2 Whole Class - Individual LearnerStudent teacher focuses on:Detailed description of the index of individualdifference.Range of individual difference is indicated.Complexity of the problem is acknowledged.Notion of balance between learner individualdifference needs and student teacher'sinstruction is described.Solution described is designed to meet individualdifference in learner rather than just the wholeclass or subgroup of learners' needs.Goal to be achieved is integrated into the solutionVectorial or Abstract Dimensional Stage 4th OrderRelationsMental elements are second order categories07 = Substage 1 A - B Std. T's Instrn - Indiv LearnerDiffStudent teacher focuses on:One index of individual difference among learners.Range of individual difference is identified.Complexity of the problem is acknowledged.Notion of balance between learner needs and studentteacher's instruction and needs of whole class aredescribed.Solution involves adjustments in student teacher'sactions, beliefs and expectations to meetindividual learner's actions, beliefs, andexpectations in an interactive way (Oneaffects the other.08 = Substage 2 Al-B1 Std. T's Instrn. - 2 or more IndivLearner DiffsA2-B2 Std. T's Monitoring - IndivFeedbackStudent teacher focuses on:162Two or more indices of individual differences.Range of individual differences are identified.Complexity of problem is acknowledged.Notion of balance between learners' indiv. diffsand whole group's needs or student teacher'sinstruction is described.Solution involves adjustments on student teacher'spart to meet individual learner needs. Solutionfeatures monitoring learner's actions, assessingtheir reactions and taking learner's feedback intoaccount during solution phase to the problem.09 = Substage 3 Al-B1 Std. T's Instrn - 2 or moreIndiv. Learner DiffsA2-B2 Std. T's Monitoring - IndivFeedbackStudent teacher focuses on:Two or more indices of individual differences.Range of individual difference is identified.Complexity of problem is acknowledged.Notion of balance between indiv diff of learnerand whole class needs or student teacher'sinstruction is described.Solution involves adjustments in both studentteacher's actions, beliefs and expectations andindividual learner's actions, beliefs andexpectations in an interactive way.Solution proceeds in an integrated fashioninvolving adjustments on both student teacher andlearner's parts to meet individual differences ofthe learner.Student teacher is able to view the individualdifference from the learner's point of view.Acknowledgement that there is no systematic,effective, single, identifiable solution butrather multiple solutions ordered across time.2. Student Teachers' Description of the ProblemRepresentation00 = 0 components, or aspects of the problem situation,problem objective, or problem strategy noted orused.01 = 1 component02 = 2 components03 = 3 components04 = 4 components05 = 5 components163I. Types of Individual Differences Noted by StudentTeachers and Faculty Supervisors01 = Learning rate or time needed to learn. Fast vs.slow learners, quickness to learn.02 = General Intellectual and academic ability, aptitudes03 = Specific skills, abilities, aptitudes, or potentialin a specific subject area (ie. art, reading abilityphysical education)04 = Prior knowledge, information, teaching, academicbackground, ie. ESL student does not have priorknowledge05 = Specific interest areas, differences in whatstudents are interested in is related to a specificsubject area06 = General motivationa levels, task commitment, keenstudents vs. uninterested students.07 = Multicultural differences, ethnic backgrounds,different languages and customs08 = Behavioral differences, discipline, activity levels,how well students cooperate, cause or don't causeproblems09 = Learning styles ie. visual, auditory, left and rightbrain, impulsive, reflective10 = Attentional differences, difficulty focusing, cannotattend, perceptual, daydreaming, different from 08(behavior problem kids)11 = Maturity differences ie. behaviors not appropriateat grade level: whinning, thumbsucking12 = Social Skills, teacher to student and student to164165student interactions. Personality differences whichaffect social interactions (external/observable)13 = Socioeconomic status, social, psychologicalbackground14 = Personality characteristics which are internal andnot directly observable ie. self-concept, self-esteem, introvertedness, extravertedness15 = General category, all individual differences16 = Physical differences ie. motor, deaf, blindbehavior differences as a result of disease relatedconditions ie. cancer, CP, MS.

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