UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Conditional syllogistic reasoning and working memory capacity Instance, Stewart T. 1984

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
[if-you-see-this-DO-NOT-CLICK]
UBC_1984_A8 I57.pdf [ 1.79MB ]
Metadata
JSON: 1.0054511.json
JSON-LD: 1.0054511+ld.json
RDF/XML (Pretty): 1.0054511.xml
RDF/JSON: 1.0054511+rdf.json
Turtle: 1.0054511+rdf-turtle.txt
N-Triples: 1.0054511+rdf-ntriples.txt
Original Record: 1.0054511 +original-record.json
Full Text
1.0054511.txt
Citation
1.0054511.ris

Full Text

CONDITIONAL SYLLOGISTIC REASONING AND WORKING MEMORY CAPACITY by STEWART T. INSTANCE B.S., Cornell University, 1970 M. Arch., State University of New York at Buffalo, 1974 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n THE FACULTY OF GRADUATE STUDIES (Human Learning, Development and Instruction Program, Department of Educational Psychology and Special Education) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1984 <g) Stewart Instance, 1984 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of EDUCATION The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 13th. OCTOBER. 1984 DE-6 (3/81) ABSTRACT i i . A relationship between working memory capacity and propositional reasoning a b i l i t i e s i s examined within the framework of Marcus & Rips (1979) v e r i f i c a t i o n model of conditional syllogisms and the mental operator model of cognitive development proposed by Pascual-Leone (1970). Using the four-stage v e r i f i c a t i o n model to explain required cognitive processes, i t i s argued that development i n the a b i l i t y to solve conditional syllogisms can be attributed, i n part, to an epigenetically determined increase i n working memory capacity. With a sample composed of 77 pre-adolescent and university students, micro-computers presented individual subjects with two 40-item conditional s y l l o g i s t i c reasoning (CSR) tasks and a backward d i g i t span (BDS) task, i n two sessions. The results are not as predicted. Indexing memory capacity by BDS, analyses of covariance and polynomial regression analysis, f a i l to identify a relationship with correct CSR responses. While grade i s shown to explain a major percentage of variance i n CSR scores, knowledge of the .conditional rule i s also i d e n t i f i e d as an important factor. Arguments are grouped according to order of d i f f i c u l t y and validating response time, and the results of subjects i d e n t i f i e d as knowing the conditional rule f a i l to agree with the groupings predicted by the Marcus & Rips model while supporting development of a single operative scheme for conditional s y l l o g i s t i c reasoning. i i i . TABLE OF CONTENTS Page I. STATEMENTS OF PROBLEMS AND HYPOTHESES 1 Introduction 1 Conditional S y l l o g i s t i c Reasoning 1 Developmental Trends i n Conditional Reasoning 2 V e r i f i c a t i o n Model of Conditional Syllogisms 4 Theoretic Role of Working Memory 6 Investigations into Development i n Working Memory Capacity 6 Working Memory Capacity and the Verf i f i c a t i o n Model 11 Summary of Hypothesis 11 I I . METHOD 14 Subjects and Design 14 Equipment and Materials 15 Procedure 16 I I I . RESULTS 19 Analysis of CSR Test Responses 19 Analysis of Performance on Eight Types of Argument by Mastery Level.. 21 Comparison of Present Data with the Reported Data 22 IV. DISCUSSIONS AND CONCLUSIONS 24 REFERENCES 27 FOOTNOTES 28 TABLES 1 (a & b) - Mean Backward Di g i t Spans and Mean Number of Correct Responses for Each Conditional Argument Type by Grade 29 2 - Analyses of Covariance of the Number of Correct Responses for Each CSR Argument Type of Set 2 by Grade 31 3 - Mean Number of Correct Responses, Mean Validation Time, and Rank Order for Each Argument Type of CSR Set 2 Items by Mastery Level 32 4 - Percent of Correct Responses for Each of Eight Conditional S y l l o g i s t i c Arguments by Grade; Comparison with Previous Studies 33 i v . TABLE OF CONTENTS (Cont'd) Page FIGURES 1 - Marcus & Rips Four-Stage Model for V e r i f i c a t i o n of Conditional Syllogisms 34 APPENDICES A. Eight Conditional S y l l o g i s t i c Arguments 35 B. Selected Spans for Backward D i g i t Span Task 36 C. I n i t i a l Instructions to Subjects 37 D. Instructions for Backward D i g i t Span Task 38 E. Instructions for the Conditional S y l l o g i s t i c Reasoning Task 39 1. I. STATEMENTS OF PROBLEMS AND HYPOTHESES Introduction The purpose of the study was to investigate a relationship between pre-adolescent and college students' propositional reasoning a b i l i t i e s and working memory capacity. S p e c i f i c a l l y , the present study explored the p o s s i b i l i t y of explaining developmental findings i n conditional s y l l o g i s t i c reasoning, indicated i n studies by Paris (1973), Taplin, Staudenmayer & Taddonio (1974), and Sternberg (1979), i n terms of epigenetic growth i n the capacity of working memory. Pascual-Leone's (1970) Mental Operator model of cognitive development, which had previously been demonstrated as having a relationship between working memory capacity and Piagetian cognitive substages, provided a theoretical framework. A theoretical basis for the processing of conditional syllogisms was found i n the four-stage model proposed by Marcus & Rips (1979). Conditional S y l l o g i s t i c Reasoning In a propositional statement, an antecedent premise such as " I f you eat your dinner", i s combined with a consequent premise, such as "then you may have dessert", to imply a unidire c t i o n a l causal relationship between the two. To act i n a rati o n a l manner, according to what i s implied i n the propositional statement, a c h i l d must understand the meaning of the co n d i t i o n a l i t y , and deduce an appropriate conclusion from the premises. An empirical investigation of a conditional s y l l o g i s t i c deductive reasoning problem f i r s t present an " i f , then" premise, expressed symbolically as P->Q. A second premise i s subsequently presented that affirms or denies either the antecedent or the consequent. Thus, four arguments can be defined, as follows: 2. 1. Affirming the antecedent (Modus ponens) 2. Denying the antecedent (Modus tollendo tollens) 3. Affirming the consequent 4. Denying the consequent For each s y l l o g i s t i c argument, the conclusion may be either affirmative or negative, resulting i n a t o t a l of eight different argument forms. The subject i s asked to evaluate the v a l i d i t y of the conclusion based on information derived from the f i r s t and second premise. Typically, the syllogisms are of the form''': If there i s a p, then there i s a q There i s a p There i s a q Developmental Trends i n Conditional Reasoning A developmental trend i n comprehension of language connectives has been c l e a r l y established. In his study with grades two, f i v e , eight and eleven, Paris (1973) i d e n t i f i e d two patterns of comprehension evident with age, including the increased d i f f e r e n t i a t i o n of conjunctive from disjunctive propositions, and the causal interpretation of biconditional and conditional sentences. He showed that i n interpreting causality, younger subjects tended to judge a complete proposition as false If any part of the syllogism, antecedent or consequent, was f a l s e . The responses of subjects changed with age, however, suggesting search for a causal relationship between premises and one event's dependence on a second event. 3 . The findings of Taplin, Staudenmayer & Taddonio (1974) supported those of Paris i n suggesting that comprehension of the causal relationship of the conditional connective " i f p, then q", was the most d i f f i c u l t , and involved an intermediary stage of b i c o n d i t i o n a l i t y . In th i s t r a n s i t i o n stage, the c h i l d comprehended a relationship with reversible causality between the two premises, whereby neither were exclusively antecedent nor consequent. As a r e s u l t , P implied Q and Q implied P; t h i s relationship may be symbolically represented as P<->Q. Taplin et al's (1974) investigation of developmental changes i n conditional reasoning, with subjects from grades three, f i v e , seven, nine and eleven, indicated that there was improved performance on a conditional reasoning task with age. Their results also indicated that the degree of improved performance was more evident i n some argument forms than others. Sternberg (1979) studied developmental patterns for l o g i c a l connectives, and examined the r e l a t i v e importance of l o g i c a l and l i n g u i s t i c processes i n this development. Using a form of componential analysis, a technique different from that used by Taplin et a l , he compiled data that generally supported the previous findings. Looking at both l i n g u i s t i c encoding and l o g i c a l combination, he confirmed that the conditional l o g i c a l connective was the most d i f f i c u l t and supported a developmental trend. His data indicated that In encoding tasks, grade two children evidenced conjunctive and disjunctive interpretations of the conditional, while performance of those i n grades four, s i x and eight suggested a biconditional interpretation. With some evidence of the 4. correct conditional interpretation beginning at grade eight, i t was not u n t i l high school and college age that this interpretation was strongly i n evidence. Sternberg inferred from the data that the l o g i c a l combination of premises followed the same general developmental trend as l i n g u i s t i c encoding, but lagged by about two years. V e r i f i c a t i o n Model of Conditional Syllogisms In developing a process model of conditional s y l l o g i s t i c reasoning, Marcus & Rips (1979) appear to have assumed that individuals already knew an underlying conditional 'rule' or scheme. The information processing model developed by these authors consisted of four stages, and r e l i e d on both 'structural' and 'error' assumptions; the former comprising an information processing sequence underlying correct reasoning while the l a t t e r considered explanations of erroneous reasoning. The model makes a number of predictions about response latencies for v a l i d i t y decisions of each of the eight argument forms. These predictions assume that while some s y l l o g i s t i c arguments require two stages of processing, others require three and four. The investigators supported t h e i r prediction that arguments formed three response latency (RT) groups, depending on the number of processing stages required. They noted that RT increased as syllogisms increased i n the number of negations, a result also reported by Lee (1984). 5. According to Marcus & Rips (1979), [p,q] and [p, Not-q] syllogisms are processed through only the f i r s t two stages of the model, 'Encoding Premises and Conclusions' and 'Does Second Premise Equal F i r s t Premise?', and form the f i r s t c luster of arguments. The remaining s i x arguments proceed for further processing i n the t h i r d stage, 'Is Conclusion Consistent with F i r s t and Second Premises?' This stage uniquely i d e n t i f i e s the [Not-q, p] syllogism as requiring a Never True response. Requiring three processing stages, t h i s single argument forms a second 'cluster'. The remaining f i v e syllogisms a l l require the fourth processing stage and thereby form a t h i r d cluster. Identified as Always True at t h i s stage i s the syllogism [Not-q, Not-p], i n which the negating of the conclusion produces a doubly negated proposition inconsistent with the conditional. The remaining syllogisms, despite negated conclusions, are consistent with the premises and are concluded to be Sometimes True. Figure 1, which schematically reproduces the Marcus & Rips model, i d e n t i f i e s the three clusters of syllogisms by the stage i n processing at which a conclusion can be drawn and the appropriate response prepared. INSERT FIGURE 1 ABOUT HERE -see p»-ge 34 In addition to the above structural elements, the model takes into account three potential sources of error. According to Marcus & Rips, the source of most probable error i s the premature termination of processing; hence an inference error could occur with termination of 6. processing after any of the f i r s t three stages indicated above. As pointed out by Marcus & Rips, the model considers the psychological meaning of l o g i c a l connectives which does not correspond e n t i r e l y to the propositional l o g i c . Errors may also result from the processing of negative premises or conclusions during stages three and four, or from the reversal of the P-Q sequence. Theoretic Role of Working Memory Impl i c i t i n the Marcus & Rips model i s the assumption that the cognitive processes involved i n comprehending, analyzing and reaching a conclusion about a problem i n conditional reasoning occur i n working memory. Viewed i n the information processing paradigm, the cognitive processes involved i n attaining a l o g i c a l l y v a l i d conclusion for a conditional proposition necessitate a minimum capacity In working memory, a capacity that appears to undergo developmental change (Pascual-Leone, 1970). From t h i s implication, a potential explanation of the developmental trend noted i n s y l l o g i s t i c reasoning may be advanced: that the a b i l i t y to successfully solve a s y l l o g i s t i c reasoning problem i s contingent on the working memory requirements of the problem and the available working memory capacity In the in d i v i d u a l . Investigations into Development i n Working Memory Capacity The development of working memory capacity was explored by Pascual-Leone (1970) who proposed a neo-Piagetian model. This model postulated a quantitative parameter to account for Piaget's q u a l i t a t i v e 7. description of i n t e l l e c t u a l development. According to Piaget (cf. 1958), the integration of information occurs i n a ' f i e l d of centration' or ' f i e l d of equilibrium and that t h i s f i e l d increases i n size with age. Pascual-Leone attempted to quantify the increasing size of th i s ' f i e l d ' and to relate i t to the Piagetian construct of i n t e l l e c t u a l development. In his subsequent investigation, Case (1972) demonstrated that the Pascual-Leone model could be validated by a different measure, and added support to the Mental Operator as the set measure of ' f i e l d of centration' or 'M-space'. In validating the neo-Piagetian construct, Case (1972) used a d i g i t i n s e r t i o n technique by which subjects were required to locate a target d i g i t within a previously presented series of d i g i t s . He noted, however, that the Backward Di g i t Span (BDS) task yielded i d e n t i c a l norms to those obtained with the d i g i t i nsertion technique. I t was suggested that the transformation of d i g i t order required by the BDS task interfered with rehearsal and 'chunking' strategies, and thereby equated i t with the cognitive processing requirements of the d i g i t i n s e r t i o n task. According to Case (1972, p. 287), what was measured i n the d i g i t i n s e r t i o n task, and by implication i n the BDS task, was the "maximum number of activated schemes which (could) be coordinated at any one time." I t can be inferred from t h i s d e f i n i t i o n that Piaget's ' f i e l d of centration' and Pascual-Leone's 'M-space' are functionally synonymous with working memory and similar to the Short Term Store of Atkinson and Shiffren (1968). 8. As indicated by Pascual-Leone (1970), the growth i n M-space, or working memory, i s considered to be li n e a r , and determined primarily by epigenetic factors. Occurring generally between the ages of three and sixteen years, the modal value of M-space increases from a + 1 to a + 7, and can be related to Piagetian substages. In the notation used to indicate working memory capacity, lc represents the number of activated schemes that can be attended to and manipulated at a given developmental stage, while a_ represents the working memory capacity requirements of the schemes that direct and coordinate the manipulation. By 'scheme' i s meant an " o r i g i n a l set of reactions ... susceptible to being transferred from one situ a t i o n to another by assimilation of the second to the f i r s t , " (Pascual-Leone, 1970, p. 306). They share common features, such as being recursive, definable by thei r content ( i . e . , perceptual, cognitive, e t c . ) , and form three general groups, i d e n t i f i e d as superordinate, f i g u r a t i v e and operative. Superordinate schemes are the ov e r a l l plans activated to consider a sp e c i f i c problem situation. Similar to a computer program that uses subroutines, these 'executive' schemes are in t e r n a l representations of procedures appropriate for attaining p a r t i c u l a r objectives. The second type, fi g u r a t i v e schemes, are capable of releasing responses of superordinate schemes; that i s , they are internal representations of known or recognizable elements of information and correspond to 'chunks' ( M i l l e r , 1956). F i n a l l y , there are operative schemes which are in t e r n a l representations of functions or rules applied to figurative schemes to generate transformations. 9. According to these d e f i n i t i o n s , a includes the working memory requirement for the superordinate and operative schemes, and k includes the working memory requirement of the figurative schemes to be manipulated. In view of the additive relationship between a and k i n deriving memory capacity, and the maximum representational capacity of working memory or Jc, at a given age, these factors appear to be important i n establishing the l e v e l of i n t e l l e c t u a l functioning. Underlying the Pascual-Leone construct Is the notion that a_ remains constant across age groups for a s p e c i f i c , well-learned task. Here, superordinate and operative schemes associated with a given task tend to become well-established i n the in d i v i d u a l . At the point at which the task i s thoroughly, or 'overly' learned, the working memory requirement of these schemes, a, attains a task-related minimum that remains constant i n any subsequent performance of the same task. I t should be noted, however, that the value of across different tasks can vary and w i l l depend upon the complexity and amount of transformation and coordination required. I m p l i c i t i n the Pascual-Leone proposal i s that the working memory th e o r e t i c a l l y available to retain the fi g u r a t i v e schemes i s the capacity remaining i n the epigenetically determined M-space after the executive and operative schemes have been accommodated. This suggests that working memory assigned to a or k i s interchangeable, and i s governed by the demands of the task and o v e r a l l capacity. The BDS task can be used to i l l u s t r a t e t h i s interchangeability and the task-related constancy of j i . B r i e f l y , i n a BDS task the subject i s sequentially shown a series of two-to-nine d i g i t s . With no external memory a i d , the i r task i s to r e c a l l the d i g i t series i n the reverse order of presentation. To accomplish t h i s , the 10. subject must retain the individual d i g i t s i n memory, and then manipulate them into the required reverse order and recite this sequence back to the experimenter. This manipulation and coordination function, that i s , the backward transformation, i s assumed to be governed by task appropriate superordinate and operative schemes which require a portion of working memory; thi s working memory requirement i s equivalent to _a, and assumed to be constant once the BDS task i s well-learned. It i s also assumed (Case, 1972) that the nature of the BDS task keeps the subjects from 'chunking' d i g i t s together and thereby implies that each d i g i t i s equivalent to a single figurative scheme. The span of d i g i t s that a subject i s capable of r e c a l l i n g i n a reverse order therefore indexes the number of fi g u r a t i v e schemes that they can manipulate for the BDS task; this span i s considered to be an indirect measure of k. It becomes apparent that for any given overlearned task then, ja and It should have unique values, but i n no case may «i + lc exceed the epigenetically determined maximum capacity of working memory. This suggests that, where a task requires more capacity than an indiv i d u a l has available, that task should not be successfully performed. As summarized by Case (1972), i t should be noted that a_ and _k do not account f o r a l l variables of cognitive performance i n terms of va r i a t i o n i n working memory. Also important i s the proportion of working memory devoted to a p a r t i c u l a r task and the repertoire of schemes available to the i n d i v i d u a l , p a r t i c u l a r l y as influenced by learning factors and f i e l d factors that govern what schemes are to be activated. 11. Working Memory Capacity and the V e r i f i c a t i o n Model The notion of figurative and operative schemes may be applied to the model of Marcus & Rips, where different working memory requirements may be inferred. As indicated by the author's model, the number of processing stages through which each argument passes d i r e c t l y affects the amount of processing time required. The processing stages may be considered equivalent to three operative schemes, implying three working memory levels (_a,jf,_a). Each l e v e l represents one of the three argument groupings as defined by the model and supported by RT observed by Marcus & Rips (1979). These researchers also suggested that processing stages were not the only determinant of response latency. They also incorporated into t h e i r model factors for the negation of premises, and the reversal of premises i n four of the arguments (Types: [q,p], [q, Not-p], [Not-q,p], [Not-q, Not-p]). Summary and Hypothesis There i s evidence to suggest that working memory capacity i s not fix e d , but increases as the c h i l d develops (Pascual-Leone, 1970; Case, 1972, 1974). Hence, i t i s proposed that the a b i l i t y of a subject to successfully solve a s y l l o g i s t i c reasoning problem should be affected by the working memory capacity available at a part i c u l a r point i n development. S p e c i f i c a l l y , i t was hypothesized that the a b i l i t y of subjects to solve each of the eight s y l l o g i s t i c arguments, according to the conditional truth function, w i l l depend on th e i r working memory capacity as defined by backward d i g i t span. The present study attempted to Identify r e l a t i v e working memory capacity, as inferred from BDS scores, required to successfully solve s y l l o g i s t i c arguments, giving consideration to the a l l o c a t i o n of memory between operative 12. and fi g u r a t i v e schemes. Subjects were presented with a series of concrete and abstract syllogisms, and their working memory capacity determined using a BDS task. In the present study, the premises involved i n a s y l l o g i s t i c proposition were considered to be equivalent to figurative schemes. This view supplemented that of Marcus & Rips (1979) and provided additional explanation for the response latencies predicted. By th i s view, each p o s i t i v e l y stated premise, or more s p e c i f i c a l l y , the subject of that premise, was assumed to represent one figu r a t i v e scheme and correspond to a k value of one. In the most common of arguments, [p,q], two p o s i t i v e l y stated premises are involved and represented the least number of fi g u r a t i v e schemes to be manipulated i n solving a s y l l o g i s t i c problem. In t h i s case, i t was reasoned that k took on a value of two. Negation or reversal of premises required additional manipulation of figurative schemes, and resulted i n additional processing time. It must be noted that the v e r i f i c a t i o n model i d e n t i f i e d the encoding of premises and conclusions as a separate stage from processing arguments. However, the experimental methodology of Marcus & Rips did not make th i s d i s t i n c t i o n ; RT was measured from onset of the complete syllogism to validating response. Implicit i n th i s methodology and the resulting analysis, i s that encoding should be constant across argument types. Such an assumption i s open to question. There exists strong support for encoding being the source of different levels of d i f f i c u l t y i n solving each of the eight syllogisms (Sternberg, 1979; Taplin et a l , 1974). To emphasize the evaluating process, the current study measured validating time (VT) from onset of the conclusion to validating response; t h i s procedure reduced, but did not eliminate measurement of encoding time, r e s t r i c t i n g i t to the encoding of the conclusion. 13. With the exception of RT measurement, the current study replicated Experiment 2 of Marcus & Rips (1979), and attempted to determine i f the v e r i f i c a t i o n model i s consistent with the performance of subjects c l a s s i f i e d as knowing the conditional rule. If the model were to be supported, VT of subjects with a mastery of the conditional rule should increase according to the complexity of processing required. In addition, the l e v e l of d i f f i c u l t y , as measured by the number of o v e r a l l correct responses, should also increase with the number of processing stages proposed by the model. Both VT and number of correct responses should separate arguments into three similar groups corresponding to the three levels of operative scheme memory capacity, a_y _a', and at least for those subjects who can be regarded as knowing the log i c rule. 14. I I . METHOD Subjects and Design I n i t i a l l y , a t o t a l of 92 subjects was i d e n t i f i e d , of whom 31 were drawn from each of grades f i v e and seven, and 30 from paid undergraduate and graduate university students. Elementary students were selected from a school i n the Lower Mainland of B r i t i s h Columbia; the university subjects were drawn from students at the University of B r i t i s h Columbia. Upon obtaining the participants' consents through the school and university instructors, a t o t a l of 77 subjects remained i n the sample for the present experiment. The sample consisted of three groups, 25 grade f i v e , 27 grade seven and 27 college students. As results of previous studies (Taplin, Staudenmayer & Taddonio, 1974; Sternberg, 1979) had i d e n t i f i e d l i t t l e evidence of conditional s y l l o g i s t i c reasoning below grade f i v e , the youngest subjects for the current study were selected from t h i s grade l e v e l . Based on the investigation of Pascual-Leone (1970), i t was determined that these younger subjects could be expected to have a modal M-space value of a + 4 to a + 5. To provide subjects with a range i n modal M-space values to a + 7, the maximum i d e n t i f i e d by Pascual-Leone, grade seven and university students were also selected. With testing occurring at the end of the school year, grades f i v e and seven subjects were assumed to correspond to the Late Concrete and Early-Middle FormalPiagetian substages, respectively; college subjects were assumed to correspond to Late Formal and beyond. 15. Equipment and Materials The two tasks, Backward Digit Span and Conditional S y l l o g i s t i c Reasoning, were both presented i n d i v i d u a l l y to subjects using a micro-computer; t h i s equipment automatically recorded item responses and validating response latency. Six systems were used, each consisting of an Apple HE micro-computer, a 12-inch monochrome monitor, and two disk drives; one drive was used to run the program and the second to record the data. Each system was so arranged as to prevent subjects from seeing a screen other than the i r own. In the BDS task, eight d i g i t spans were evaluated twice; spans tested were from two through nine d i g i t s . The sequences and order of d i g i t span length were determined randomly from Random Number Tables (Edwards, 1968); consecutive duplicate and sequentially ordered d i g i t s i n any span were eliminated. The selected spans are presented i n Appendix B. A random presentation of target spans was selected to avoid a response set, t h e o r e t i c a l l y consistent with the established BDS testing paradigm. The conditional syllogism reasoning (CSR) task consisted of the same eighty items used by Lee (1984). B r i e f l y stated, these syllogisms were the result of ten semantic situations, two abstract and eight concrete, i n a f a c t o r i a l combination with the eight argument forms previously described and summarized i n Appendix A. The syllogisms comprised three statements or propositions, including a major premise, a minor premise, and a conclusion. 16. Procedure Subjects were tested i n groups of s i x , i n two 30-45 minute periods. The same experimenter administered a l l sessions for grades f i v e and seven subjects, assisted by a female graduate student; this assistant tested a l l university subjects. During the f i r s t test sessions, subjects received f o r t y CSR problems; during the second session, they received the BDS task and the second set of forty CSR problems. Each subject's f i r s t test session began with a brief introduction to acquaint participants with the experiment and to confirm that participants were s u f f i c i e n t l y f a m i l i a r with the computer keyboard to accomplish the proposed tasks (Appendix C). The tasks were self-timed, with presentation of a l l materials computer-controlled according to duplicate programs copied from a common master. Each task was preceded by s p e c i f i c instructions presented on the computer screen pertaining to the task. Presented f i r s t was the BDS task (Appendix D) Following the instructions, the f i r s t practice d i g i t span sequence began, starting with the word 'READY', shown for 1.2 seconds. The screen then went blank for 1.2 seconds before the f i r s t d i g i t appeared; each d i g i t was presented i n d i v i d u a l l y i n the centre of the screen for 1.2 seconds. At the end of the f i r s t practice series only, the subject was reminded of s p e c i f i c instructions. ... F i r s t practice series ... Now, please indicate the d i g i t s you have just seen i n backwards order. Remember, i f you cannot think of a d i g i t , put an '-' i n i t s place. 17. These instructions remained on the screen for f i v e seconds. The subject had a maximum time l i m i t for responding of f i f t e e n seconds; responses were not displayed on the screen. At the end of each d i g i t span sequence, the screen became blank for f i v e seconds and then the next sequence began with the word, 'READY.' After the four pertaining problems, subjects were told they had completed the four practice problems and to proceed to the actual task. The experimental task was i d e n t i c a l to the practice session, but excluded a l l i nstructions. At the conclusion of the BDS task, the screen became blank for f i f t e e n seconds while the computer loaded the CSR program; the instructions for the next task were then displayed (Appendix E). Following the instructions, the f i r s t argument appeared on the screen, beginning with the f i r s t proposition which appeared on the screen for f i v e seconds: The screen then went blank for 1.2 seconds, u n t i l the second proposition was shown: and (second proposition) This proposition was also displayed for f i v e seconds, when the screen again went blank for 1.2 seconds and the conclusion was displayed! Then would t h i s be true? (Conclusion) After f i v e seconds, the multiple choice answers appeared: Item 1: Suppose that you know that, ( f i r s t proposition), Always true: Sometimes true: Never true: A S N 18. Once answered, corrective feedback was presented. At the end of each problem sequence, the screen went blank while the computer recorded the subject's response and va l i d a t i o n response time (VT) recorded up to one millisecond on the diskette. Subjects were presented with the same instructions before the second set of forty CSR problems when tested a few days l a t e r . 19. I I I . RESULTS I n i t i a l processing of data from indi v i d u a l subjects resulted i n a set of three measurements, including backward d i g i t span and two conditional s y l l o g i s t i c reasoning scores, number of correct responses, and associated val i d a t i n g time for ind i v i d u a l requirements. BDS was established as the longest span answered correctly by subjects i n both span re p l i c a t i o n s . Five subjects f a i l e d to a t t a i n the c r i t e r i o n ; BDS was estimated for these subjects based on the ove r a l l number of d i g i t s i n the correct r e l a t i v e position. The raw number of correct CSR responses for each of the eight arguments was determined for each of the two presentations of the task. Each task consisted of eight arguments i n d i v i d u a l l y presented f i v e times, permitting a maximum score per task of f i v e for each argument. These data are summarized i n Table 1. A further CSR datum, VT, was measured from onset of the argument's conclusion to making the correct response. INSERT TABLE 1 ABOUT HERE A • S e e p a g e 2? Analysis of CSR Test Responses To determine the effect of knowledge of the conditional rule on CSR performance, subjects were c l a s s i f i e d into one of two groups, mastery and non-mastery. Mastery-level subjects were determined from results of the f i r s t CSR task, according to a method o r i g i n a l l y proposed by Lee (1984), i n which a score of four or greater was required on at least s i x of each eight arguments. Sixteen of the 77 subjects met t h i s c r i t e r i o n , including two i n Grade 5, two i n Grade 7, and twelve at college l e v e l . 20. Under the premise that conditional s y l l o g i s t i c reasoning resembled the v e r i f i c a t i o n model proposed by Marcus & Rips (1979), the analysis had two purposes: to determine (1) the effect of working memory capacity on CSR problems, and (2) the extent to which predictive performance of the model could be explained by knowledge of the conditional rule i m p l i c i t l y assumed by Marcus & Rips (1979). To determine the Influence of working memory capacity on conditional s y l l o g i s t i c problems, a series of analyses of covariance were performed on the number of correct responses and VT of indiv i d u a l arguments. BDS and mastery were used as covariants, with grade the grouping factor. The results were not as predicted. In no argument did BDS exceed the chance l e v e l , while mastery was a s i g n i f i c a n t factor i n a l l arguments, and grade i n s i x . BDS was also tested i n a polynomial regression analysis, which also f a i l e d to i d e n t i f y any effect of working memory capacity. INSERT TABLE 2 ABOUT HERE See page 3' To examine further the findings of the analysis of covariance, a determination was made of the percent of variance of correct argument responses accounted for by each of three predictors: grade l e v e l , BDS, and mastery of the conditional rule. In a l l but one argument, [Not-p, Not-q], the majority of variance attributed to the three factors was explained by grade l e v e l , accounting for between 3.3% and 29.8% of variance, with a mean of 15%. While grade l e v e l explained only 5.4% of the variance on argument [Not-p, Not-q], mastery l e v e l accounted for 12.1%, the most variance explained for by th i s factor on any of the arguments; with a mean of 6.8%, mastery accounted 21. for 2.1% to 12.1% of variance. By contrast, BDS, with a range of 0% to 2.2% and a mean of 0.9%, explained l i t t l e . The analysis was repeated on the t o t a l score of a l l eight arguments from the second CSR task, to determine the effect of the three factors on the overall response pattern. The analysis supported the findings for individual arguments by identifying grade as explaining the majority of variance at 32.1%, and mastery as the second factor, explaining 17.8% of variance. As i n the previous analysis, BDS accounted for only 1.1% of variance. Clearly, the results f a i l e d to support the hypothesis by identifying no argument i n which BDS accounted i n any si g n i f i c a n t way for performance on the CSR task. This finding suggests that development i n working memory capacity has l i t t l e effect on cognitive a b i l i t i e s , as defined by the conditional reasoning problem. In view of the importance of grade l e v e l to CSR performance, i t must be inferred that other developmental factors contributing to improved performance on this task with age, remain to be Ide n t i f i e d . In addition, factors other than grade and master l e v e l appear to be involved, as the majority of variance on a l l arguments remains unexplained. • Analysis of Performance on Eight Types of Arguments by Mastery Level To examine whether the order of argument d i f f i c u l t y was consistent with that predicted by apparent working memory requirements of the Marcus & Rips (1979) model, repeated measures analyses of variance were performed on combined results of the two CSR presentations. As mastery of the conditional rule was i m p l i c i t l y assumed i n the v e r i f i c a t i o n model, data for mastery and non-mastery subjects were analyzed separately. 22. I n i t i a l analyses across a l l eight arguments, for each group, found that arguments varied i n d i f f i c u l t y , according to the number of correct responses and i n VT. Further analysis, with repeated measures analyses of variance across pairs of arguments, i d e n t i f i e d the rank order of arguments indicated i n Table 3. INSERT TABLE 3 ABOUT HERE _S_li_P.mJL?: The analyses revealed different orders of argument d i f f i c u l t y for each mastery l e v e l on each CSR datum. Further, and as predicted by the Marcus & Rips (1979) model, arguments could be grouped into clusters of si m i l a r d i f f i c u l t y . However, the order of d i f f i c u l t y i n neither mastery l e v e l group was as expected from the model. Those subjects c l a s s i f i e d as possessing the conditional rule evidenced fewer argument clusters than non-mastery subjects In both correct responses and VT. This reduction i n the number of c l u s t e r s , from four to two, with improved performance where one of the clusters for mastery subjects represented seven of the eight arguments, suggests a developmental trend towards a single VT cluster. Comparison of Present Data with the Reported Data To test external v a l i d i t y , an analysis was conducted on data from the conditional s y l l o g i s t i c reasoning task to permit comparison with findings reported by Taplin & Staudenmayer (1973) and Taplin, Staudenmayer & Taddonio (1974). Results of a l l three experiments are summarized i n Table 4. While some differences are noted on s p e c i f i c arguments, p a r t i c u l a r l y for grade 5 subjects, there appears a si m i l a r o v e r a l l grade-related trend. INSERT TABLE 4 ABOUT HERE __5ee_pa£e__"5j A further comparison was made with results reported by Sternberg (1979) on the percent of correct conditional sets; that i s , the number of sets of eight consecutive arguments i n a single series as a percentage of the t o t a l number of sets. The results are very s i m i l a r . In the current study, the percent of correct sets was 3.2%, 3.6%, and 12.6% for grades f i v e , seven and college, respectively, compared to 3% for grade s i x and 19.0% for college subjects reported by Sternberg. 24. IV. DISCUSSION AND CONCLUSION The study found l i t t l e support for the central hypothesis, nor for the model of conditional s y l l o g i s t i c reasoning, as proposed by Marcus & Rips (1979). However, support was found for v a r i a t i o n i n argument d i f f i c u l t y somewhat different from that predicted by the v e r i f i c a t i o n model. While i t was argued that development i n working memory capacity could contribute to the age-related improvement i n CSR performance noted by previous investigators such as Paris (1973), t h i s was not the case. In the current study, grade l e v e l was i d e n t i f i e d as a major factor In CSR performance with l i t t l e relationship to BDS. As discussed by Lee (1984), the conditional truth function i s frequently i m p l i c i t l y assumed i n studies of conditional s y l l o g i s t i c reasoning. In the current study, those subjects appearing to know the conditional rule were e x p l i c i t l y i d e n t i f i e d by their results on one of the two CSR tasks. Performance on the CSR task by mastery and non-mastery groups varied very s i g n i f i c a n t l y , (F(l,75) = 124.5, £ < 0.01). Once available to the subject, the conditional rule appears to be stable and a good predicter of performance on the second CSR task. I t can be inferred, then, that knowledge of the conditional truth function, or the a b i l i t y to activate the appropriate operative schemes, may be a better explanation of success i n answering syllogisms than working memory capacity. Before dismissing the working memory capacity hypothesis, the v a l i d i t y of the Backward Di g i t Span task, as used i n the current study, must be questioned. The computerized task varied from standard testing approach i n presenting a l l subjects with a random order of span lengths. In the t y p i c a l 25. BDS task, subjects are in d i v i d u a l l y presented with spans of increasing length u n t i l they f a i l to correctly respond to a span of s p e c i f i c length. In the computerized task, subjects could a t t a i n a high BDS, such as s i x , while f a i l i n g shorter spans; this s i t u a t i o n i s not possible with the standard testing paradigm. Viewed from the information processing paradigm, the VT data of the mastery subjects suggests that a single operative scheme may be involved i n the CSR task. This operative scheme appears to develop i n stages and may result from the gradual integration of at least one other scheme; a review of data from non-mastery subjects indicates that arguments may be separated Into four VT clusters, while only two clusters were evident for mastery subjects. The a v a i l a b i l i t y of a functional conditional rule, or conditional operative scheme, may help to account for the lack of agreement between the current data and the Marcus & Rips (1979) model. The three argument clusters predicted from the model f a i l e d to appear through either the number of correct responses or VT, suggesting that argument d i f f i c u l t y may not be explained by processing f a i l u r e at selected stages within the model, as i t s authors proposed. Rather, the explanation may be a lack of a single, integrated process or conditional truth function, with the Marcus & Rips (1979) findings resulting from a c o l l e c t i v e developmental trend i n the acq u i s i t i o n of the conditional rule present i n t h e i r college-age subjects. Caution must be used i n interpreting the VT data for some non-mastery subjects where very low VT and high r i s k error rates on three arguments suggests that these individuals may have been guessing. As these three arguments, [q,p], [not-q, p], and [not-q, not-p], were also found to be the most d i f f i c u l t by non-mastery subjects, guessing may have resulted from minimal development of appropriate processing a b i l i t y for these syllogisms. 26. Interestingly, VT's representing clusters 2 and 3 i n data from non-mastery subjects which correspond with two of the easier syllogisms for this group, are somewhat lower than VT on similar arguments by mastery subjects. For syllogism [p,q], i t i s possible that non-mastery subjects viewed the argument conjunctively. Such an interpretation i s consistent with findings reported by such previous authors as Paris (1973), Taplin (1973), and Staudenmayer & Bourne (1977), where frequent exposure to the conjunctive i n early development can be reasoned to result i n a separate operative scheme (Marcus & Rips, 1979). The data suggests that, i n the developmental process, as the CSR operative scheme adapts to respond to more varied syllogisms, i t integrates the conjunctive scheme. While the study did not support working memory as being an important variable i n the development towards conditional s y l l o g i s t i c reasoning, i t did support development towards a single CSR operative scheme. The encoding-evaluation issue investigated by Sternberg (1979), c l e a r l y determined the primacy of encoding i n the o v e r a l l development of CSR processing. The current work as s i s t s i n our understanding of the two year lag i n attainment of the evaluation subprocess noted by Sternberg. Further, i t provides evidence that younger subjects are able to accomplish complex problem solving such as conditional s y l l o g i s t i c reasoning, once the appropriate scheme i s available to them. The challenge for education i s to assist the c h i l d i n building these appropriate schemes. 27. REFERENCES Atkinson, R.C. & Shiffren, R.M. (1968) Human memory: A proposed system and i t s control processes. In K.W. Spence & J.T. Spence (Eds.) Advances i n the psychology of learning and motiviation research and theory. Vol. 2 New York: Academic Press. Case, R. (1972) Validation of a neo-Piagetian mental capacity construct. Journal of Experimental Child Psychology, 14, 287-302. Case, R. (1974) Mental strategies, mental capacity, and ins t r u c t i o n : A neo-Piagetian investigation. Journal of Experimental Child Psychology, 18, 382-397. Edwards, A.L. (1972) Experimental Design i n Psychological Research, New York, Holt, Rinehart and Winston, Inc. Lee, S.S. (1984) Children's acqu i s i t i o n of conditional l o g i c structure: Teachable? Contemporary Educational Psychology, 9, 419-483. Marcus, S.L. & Rips, L.J. (1974) Conditional reasoning. Journal of Verbal Learning and Verbal Behavior, 18, 199-224. M i l l e r , G.A. (1956) The magical number seven, plus or minus two: Some l i m i t s on our capacity for processing information. Psychological Review, 63, 81-97. Paris, S.G. (1973) Comprehension of Language connectives and propositional l o g i c a l relationships. Journal of Experimental Child Psychology, 16, 278-291. Pascual-Leone, J . (1970) A mathematical model for the t r a n s i t i o n rule i n Piaget's development stages. Acta Psychologica, 32, 301-345. Piaget, J . (1958) Assimilation et connaissance. In A. Jonckheere, B. Mandelbrot, & J . Piaget (Eds.), La Lecture de 1'experience. Paris: P.U.F. 42-108. Sternberg, R.J. (1979) Developmental patterns i n the encoding and combination of l o g i c a l connectives. Journal of Experimental Child Psychology, 28, 469-498. Taplin, J.E., Staudenmayer, H. (1973) Interpretation of abstract conditional sentences i n deductive reasoning. Journal of Verbal Learning and Verbal Behavior, 12, 530-542. Taplin, J.E., Staudenmayer, H., & Taddonio, J.L. (1974) Developmental Charge i n conditional reasoning: L i n g u i s t i c or logical? Journal of Experimental Child Psychology, 17, 360-373. FOOTNOTES As th i s paper w i l l refer to each of the eight arguments i n d i v i d u a l l y , i t w i l l be done by placing a square bracket around the second premise and conclusion; a negated premise or conclusion w i l l be indicated by "Not-." As an example, the notation for the modus ponens argument above, i s [p,q]. A l l eight arguments are i l l u s t r a t e d i n Appendix A, which includes the notation used throughout t h i s paper. 29. TABLE 1(a) Mean Backward Di g i t Spans and Mean Number of Correct Responses for Each Conditional Argument Type by Grades (N = 77) Grade 5 (N = 25) Grade 7 (N = 25) College (N = 27) BDS Mean S.D. (Range) 4.40 1.66 (2-8) 4.68 1.28 (2-7) 4.93 1.98 (2-9) CSR Set 1 [p. q] Mean S.D. 3.04 (1.27) 4.00 (1.00) 4.63 (1.01) [p, Not--q] 2.00 (1.58) 2.40 (1.35) 4.48 (1.01) [Not-p, q) 2.68 (1.28) 3.32 (1.18) 3.85 (1.20) [Not-p, Not--q] 3.44 (1.23) 2.48 (1.50) 3.56 (1.34) [q, p] 2.08 (1.44) 1.84 (1.52) 2.81 (1.62) [q, Not--P] 3.00 (1.19) 2.88 (1.42) 3.81 (1.15) [Not-q, P] 1.84 (1.28) 2.24 (1.39) 3.48 (1.34) [Not-q, Not-•p] 1.20 (1.29) 2.24 (1.39) 2.59 (1.37) 30. TABLE 1(b) Mean Backward Digit Spans and Mean Number of Correct Responses for Each Conditional Argument Type by Grades (N = 77) Grade 5 Grade 7 College (N = 25) (N = 25) (N = 27) BDS Mean 4.40 4.68 4.93 S.D. (Range) 1.66 (2-8) 1.28 (2-7) 1.98 (2-9) CSR Set 2 [p, q] Mean 3.00 3.68 4.22 S.D. (1.23) (1.11) (0.85) [p, Not--q] 2.28 3.28 4.11 (1.31) (1.40) (0.85) [Not-p, q] 2.28 2.76 3.37 (1.40) (1.17) (1.33) [Not-p, Not--q] 2.76 2.72 3.41 (1.36) (1.43) (1.31) (q, p] 1.80 1.32 2.59 (1.15) (1.11) (1.42) [q, Not-•P] 2.48 2.20 2.85 (1.42) (1.26) (1.70) [Not-q, P] 1.88 2.48 3.37 (0.88) (1.19) (1.42) [Not-q, Not-p] 1.08 (1.22) 1.60 (1.32) 2.41 (1.55) 31. TABLE 2 Analyses of Covariance of the Number of Correct Responses for Each CSR Argument Type of Set 2 by Grade, with Students' BDS and Mastery Level of Conditional Rule Based on CSR Set 1 (N = 77; Mastery N = 16, Non-mastery N = 61) Argument Type of CSR Set 2 Effect F(2, of Grade 72) P BDS Regression Coefficient _t P Mastery Level Regression Coefficient t P [p» q] 9.18 0.01 0.10 -1.30 0.20 0.95 2.73 0.01 [p, Not-q] 19.69 0.01 0.12 1.54 0.13 1.18 3.31 0.01 [Not-p, q] 5.17 0.06 0.94 0.10 0.92 1.29 3.08 0.01 [Not-p, Not-q] 2.34 0.10 0.80 -0.81 0.42 1.42 3.22 0.01 [q» p] 7.56 0.01 0.37 0.41 0.68 0.96 2.37 0.02 [q, Not-p] 1.34 0.26 0.15 1.34 0.18 0.64 1.32 0.19 [Not-q, p] 12.40 0.01 0.15 1.85 0.07 0.96 2.61 0.11 [Not-q, Not-p] 6.41 0.05 0.01 0.07 0.95 0.93 2.03 0.05 A l l Arguments 535.95 0.01 0.44 1.30 0.20 8.31 5.23 0.01 TABLE 3 Mean Number of Correct Responses, Mean V a l i d a t i o n Time, and Rank. Order f o r Each Argument Type of CSR Set 2 Items by Mastery L e v e l Argument Predicted Rank Non-mastery (N = 61) Rank VT Rank Mastery (N = 16) Rank VT Rank Type Order Corrects Order (Sec) ( Drder Corrects Order (Sec) l Drder [p. q] 1 Mean 7.07 1 1.28 3 .9.44 1 1.49 2 S.D. (2.04) (0.69) (0.81) (0.59) [p, Not--q] 1 5.38 2 1.22 3 9.56 1 1.37 2 (2.45) (0.87) (0.63) (0.61) [Not-p, q] 3 5.51 2 1.06 2 8.44 2 1.26 2 (2.01) (0.67) (1.21) (0.55) [Not-p, Not-q] 3 5.56 2 1.35 3 8.38 2 1.45 2 (2.22) (0.86) (1.26) (0.55) [q, p] 3 3.38 4 0.84 1 7.31 2 1.05 1 (1.90) (0.86) (1.62) (0.42) [q, Not--Pi 3 5.28 2 2.08 4 7.63 2 1.44 2 (2.27) • (1.16) (1.45) (0.66) [Not-q, P] 2 4.33 3 0.88 1 8.25 2 1.25 2 (1.93) (0.55) (1.29) (0.50) [Not-q, Not-p] 3 3.12 4 0.74 1 6.13 3 1.12 2 (2.15) (0.70) (1.86) (0.54) 33. TABLE 4 Percent of Correct Responses for Each of Eight Conditional S y l l o g i s t i c Arguments by Grade; Comparison with Previous Studies Taplin, Staudenmayer Conditional Current Study and Taddonio Taplin & Staudenmayer S y l l o g i s t i c Grade Grade Grade Arguments 5 7 College 5 7 8 11 College [p,q] 60.4 76.8 88.5 90.0 81.0 89.2 94.3 99.1 [p,Not-q] 42.0 56.8 85.9 75.0 70.5 80.2 91.0 99.2 [Not-p,q] 49.6 60.8 72.2 24.0 28.5 30.8 46.3 88.4 [Not-p,Not-q] 62.0 52.0 69.2 10.3 19.3 26.0 37.9 18.0 [q,p] 38.8 31.6 54.1 7.5 13.2 34.6 51.5 16.2 [q,Not-p] 54.8 50.8 66.7 21.8 26.3 37.3 54.2 91.2 [Not-q,p] 37.2 47.2 68.5 66.6 63.8 69.8 66.9 90.3 [Not-q,Not-p] 22.8 38.4 50.0 58.7 54.6 61.4 59.3 86.8 34. Stage 1 Encode premises and conclusion Syllogism about which a conclusion can be drawn at model stage YES; Conclusion = Q 6 NO K - Respond Always True Stage 2 Does second premise equal P? NO Stage 3 Is conclusion consistent with with f i r s t and second premises? V Y E S Stage 4 Is negation of conclusion consistent with f i r s t and second premises? 5 6 YES Respond Sometimes True YES; Conclusion Not-Q NO Respond Never True" Cluster 1 [p,q] p, Not-q] Cluster 2 [Not-q, p] Cluster 3 [Not-p, q] [Not-p, Not q] [q» p] [q, Not-p] [Not-q, Not-p] Figure 1. Marcus & Rips four-stage model for v e r i f i c a t i o n of conditional syllogisms; the point of which a conclusion can be correctly drawn for each syllogism i s also shown. APPENDIX A EIGHT CONDITIONAL SYLLOGISTIC ARGUMENTS ARGUMENT FORM CONCLUSION FIRST PREMISE SECOND PREMISE CONCLUSION NOTATION RESPONSE CONDITIONAL PATTERN BICONDITIONAL AFFIRMING THE ANTECEDENT AFFIRMATIVE If P, then q P q [p. q] Always true Always true NEGATIVE If P. then q P q [p, Not-q] Never true Never true DENYING THE ANTECEDENT AFFIRMATIVE If P. then q P q [Not-p, q] Sometimes true Never true NEGATIVE If P, then q P q [Not-p, Not-q] Sometimes true Always true AFFIRMING THE CONSEQUENT AFFIRMATIVE If P. then q q p [q, p] Sometimes true Always true NEGATIVE If P, then q q p [q, Not-p] Sometimes true Never true DENYING THE CONSEQUENT AFFIRMATIVE If P. then q q p [Not-q, p] Never true Never true NEGATIVE If P. then q q p [Not-q, Not-p] Always true Always true U l APPENDIX B SELECTED SPANS FOR BACKWARD DIGIT SPAN TASK n Sequence 6 4 , 2 , 9 , 3 , 7 , 5 , 5 9 , 7 , 4 , 1 , 6 3 3 , 5 , 2 8 8 , 5 , 3 , 6 , 4 , 7 , 9 , 2 5 5 , 2 , 6 , 8 , 3 2 8 , 5 9 5 , 7 , 4 , 6 , 1 , 9 , 3 , 8 , 2 3 8 , 1 , 4 6 8 , 5 , 7 , 3 , 9 , 1 2 3 , 7 7 7 , 4 , 2 , 6 , 8 , 3 , 5 9 9 , 4 , 8 , 1 , 6 , 2 , 6 , 7 , 3 7 9 , 2 , 4 , 1 , 5 , 3 , 8 4 3 , 9 , 4 , 6 8 5 , 9 , 3 , 7 , 2 , 6 , 4 , 8 4 2 , 8 , 1 , 7 37. APPENDIX C INITIAL INSTRUCTIONS TO SUBJECTS Hello. My name i s and we're going to play two games on the computer i n front of you using the numbered keys. F i r s t , I would l i k e you to type i n your given names and press the RETURN key at the right of the keyboard. (Subject types i n c h r i s t i a n names...) Good! Now, enter your surnames and then, again, press the RETURN key. (Subject types i n surname ...) OK. Now, the games you w i l l be playing w i l l require no more knowledge of the computer than that. You w i l l each have two quite different tasks; one w i l l be remembering a l i s t of numbers and the other w i l l be a true/false quiz. Some of you w i l l have the numbers task f i r s t and others, the true/false. In both cases, you w i l l have four practice problems f i r s t . Let's st a r t with the f i r s t task by pressing the spacebar. 38. APPENDIX D INSTRUCTIONS FOR BACKWARD DIGIT SPAN TASK The computer w i l l show you a series of d i g i t s , or numbers, one at a time. At the end of each series, your job w i l l be to try to remember a l l the d i g i t s and to l i s t them back to the computer by using the appropriate number keys. However, you are to l i s t them i n the reverse, or backwards, order to which they were shown. For example, you may see a series such as: 1 2 3 4 The computer w i l l then show you these symbols •***' displayed i n the middle of the screen. Your job w i l l be l i s t the d i g i t s back to the computer i n the following order: 4 3 2 1 If you cannot remember one or more of the d i g i t s , you should enter a *-' i n i t s place. Let's say that you forgot the d i g i t , 3, you should then have entered the following: 4 - 2 1 The computer w i l l give you time to remember each d i g i t and w i l l then go on to the next series. The word 'READY' w i l l show just before a new series i s about to s t a r t . There are 4 practice and 16 actual items. You should work as quickly as you can but without making mistakes. Now, l e t ' s t r y the f i r s t 4 practice items. 39. APPENDIX E INSTRUCTIONS FOR THE CONDITIONAL SYLLOGISTIC REASONING TASK This task w i l l help your l o g i c a l thinking a b i l i t y improve, i f you follow the instructions very ca r e f u l l y . Your job i s to determine the correct conclusion that can be drawn from two premises (or clues). For example, here are two clues. The f i r s t clue: If P, then Q. The second clue: P From these clues, you are to determine whether, The conclusion: Q, i s 'always true (A),' 'sometimes true (S)' or 'never true (N).' The important thing i s to understand the meaning of each clue. To ensure your understanding, i t i s suggested that you read each clue c a r e f u l l y for up to 5 seconds and then think about what you have read for another 5 seconds. Of course, i f you f i n i s h reading and are sure of your answer, then you can immediately go to the next step by pressing the spacebar. If you don't f i n i s h within 10 seconds, the computer w i l l go on to the next step. The most important thing i s to see whether or not your answer to each conclusion i s correct. If your answer was incorrect, the corrected answer w i l l f l a s h on the screen and you should try to understand why that answer i s r i g h t . Good luck.

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
United States 9 0
Germany 6 1
France 5 1
China 4 5
Russia 3 0
Serbia 1 0
City Views Downloads
Unknown 15 1
Beijing 4 0
Ashburn 2 0
Mountain View 2 0
Sunnyvale 1 0
Seattle 1 0
Phoenix 1 0
Redmond 1 0
Chicago 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0054511/manifest

Comment

Related Items