Organization of Knowledge and Conditional Reasoning - CiteSeerX

Journal of Educational Psychology 1990, Vol. 82, No. 4, 832-837

Copyright 1990 by the American PsychologicalAssociation,Inc. 0022-0663/90/$00.75

Organization of Knowledge and Conditional Reasoning Shawn L. Ward

James P. Byrnes

LeMoyne College

Department of Human Development University of Maryland

Willis F. Overton Temple University The authors considered how the way in which knowledge is organized influences scientific reasoning. They adopted a constructivist approach to reasoning in which many-to-one schemata, linguistic mapping, and meaningful relations are assumed to be important components of hypothesis-testing skill. College students received a variant of Wason's selection task in which the semantic content was either familiar or unfamiliar and the interclause relations either did or did not express entailment. Results showed that entailment, which reflects knowledge organization, was more important than familiarity in determining adequate performance. These findings imply that the constructivist view proposed here is a more adequate account of reasoning than others because it alone emphasizes the organization of knowledge as important.

nization of knowledge and familiarity of content as they influence deductive reasoning performance. Piaget (1983/ 1987; Piaget & Garcia, 1987/1989) detailed how the organization of knowledge--as reflected in formal reasoning--develops out of systems of meaning schemes. A key element of these meaning systems are many-to-one schemata in which multiple alternatives are related through an integrative concept. For example, many subclasses (e.g., "dog," "cat," etc.) are integrated through a single superordinate category (e.g., "mammal"). Meaning systems, then, become organized into propositional systems involving conditional statements through entailment, linguistic mappings, and relevance conditions. At the level of formal thought, linguistic mappings of conditional "if...then" statements are used to articulate many-to-one schemata. In particular, the "if' clause conveys that the antecedent is one of several possibilities (Byrnes, in press). In addition, "if...then" statements permit the possibility of both p and not-p, and these propositional clauses map onto the multiple alternatives in a many-to-one schema. In the example "If it is a dog, then it is a mammal," a speaker implies that the case "it is a dog" (p) is only one of several possibilities. Moreover, if the case "non-dog mammal" (notp and q) turned out to be true (e.g., "cat"), the statement would not be false. The term entailment refers to the specific nature of the relation between the antecedent and consequence clause in conditional statements. In those cases in which there is a necessary rather than a contingent relation, an entailment exists (Ricco, 1990). Thus a conditional statement constitutes an entailment if and only if it is impossible to have a situation in which, given the statement "If p, then q," p and not-q cooccur. For example, for the statement "If it is a dog, then it is a mammal," an entailment relation exists between the antecedent and the consequence because it is impossible to find the case of a "non-mammal dog." Stating this in terms of linguistic mapping, when an "if' statement maps onto a many-to-one arrangement, entailment is present. However, when a conditional statement maps onto a one-to-many statement, entailment is not present. For example, the state-

Conditional reasoning--that is, reasoning with propositions of the form "if p, then q"--represents a critical form of deductive thought (Mayer, 1983; Overton, 1990). The importance of conditional reasoning to educational issues derives from the fact that scientific reasoning consists of the formation and testing of "if...then" hypotheses and of the drawing of valid conclusions from conditional premises (Inhelder & Piaget, 1958). Students need to become proficient in such conditional reasoning in order to become successful practitioners of the scientific method and to evaluate the validity of theoretical assertions in any of the scientific disciplines. A considerable body of research has demonstrated that during adolescence, most people develop the ability to reason in a formal deductive fashion (Byrnes & Overton, 1988; Overton, Ward, O'Brien, Black, & Noveck, 1987; Ward & Overton, 1990). What remains less clear is the specific nature of the processes involved in this reasoning. According to information processing accounts (e.g., Cheng & Holyoak, 1985; Griggs, 1983), real-world experiences stored in memory are sufficient to explain successful reasoning. In some accounts (e.g., Griggs, 1983), direct experiences are stored in the form of counterexamples. In others (e.g., Cheng & Holyoak, 1985), moderately general "pragmatic" schemata are abstractions across real-world experiences. On the basis of these accounts, the familiarity of the content contained in a conditional statement is the primary determinant of logical reasoning. According to other accounts--including Jean Piaget's developmental theory--how the person organizes knowledge represents a necessary feature in the explanation of deductive reasoning. Our investigation is framed by Piaget's perspective on the development of formal thought (see Byrnes, 1988; Overton, 1990), and we examined the relationship between the orgaPortions of this article were presented at the biennial meeting of the Society for Research on Adolescence, Atlanta, Georgia, March 1990. Correspondence concerning this article should be addressed to Shawn L. Ward, Department of Psychology, LeMoyne College, Syracuse, New York 13214-1399. 832

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KNOWLEDGE ORGANIZATION ment " If it is a mammal, then it is a dog" does not express entailment because the case o f "non-dog m a m m a l " is quite possible. Relevance is a logical concept that refers to some identifiable, meaningful relation between the antecedent and consequence clauses o f a conditional statement. For example, "I f it is a dog, then it is a m a m m a l " meets the relevance condition because dog and m a m m a l are linked by definition in the sense that a dog is a part o f the class o f mammals. On the other hand, " I f it is a zebu, then it is a m a m m a l " does not meet the relevance condition because there is no meaningful linkage between the clauses. In logic, the relevance condition is particularly important because it distinguishes stronger (relevance-present) and weaker (relevance-absent) forms o f entailment. Relevance is also a specific type of familiarity. Here, f a m i l i a r i t y is defined as the meaningfulness o f the linkage rather than as the simple exposure to the content o f the clauses (Ward & Overton, 1990). The information-processing approach to reasoning denies the importance of structural or organizational features of knowledge as important determinants of reasoning performance. As a consequence, this approach would not predict differences on the basis of entailment. The organizational approach, on the other hand, leads to the prediction that the inclusion o f entailment relationships in conditional reasoning tasks will facilitate performance. Because relevance is a form of familiarity, both the organizational and the informationprocessing approaches predict a facilitating effect when this feature is included in reasoning tasks. In our study, late-adolescent subjects were presented with a modified version of Wason's (1983) selection task. Four types of conditional statements were used in this task, and we constructed them by crossing familiarity with entailment. We predicted that entailment would be a stronger determinant o f correct performance than would familiarity. We specifically predicted that the familiar entailment condition would yield better reasoning performance than would the familiar nonentailment condition. We also predicted that the unfamiliar entailment condition would similarly yield better reasoning performance than the unfamiliar nonentailment condition. Three distinct types of relevance relationships were also used (legal, class inclusion, and object property relations) in an effort to further explore the influence o f this feature. Method Subjects

One hundred thirty-two (132) college students (age M = 20 years, 4 months) participated. Subjects were recruited from Introductory Psychology classes from a private liberal arts college in New York state and from a large public university in Maryland. Design

We used a between-subjects design in which subjects were randomly assigned to one of four conditions, which we formed by crossing the familiarity of antecedent consequent relations with entailment (n = 33 per group). Before engaging in a reasoning task, subjects were given a familiarity task, by which we assessed how

familiar they were with the relations expressed in the rules used in each of the conditions, and an entailment task, by which we assessed their recognition of the impossibility o f " p and not-q" cases for these rule relations. Tasks and Procedure Familiarity task. Subjects were asked to rate their knowledge of information described in 20 statements. Six statements were true facts thought to be familiar, six were obscure but true facts, and the remaining eight were erroneous (see in Table I). The relations expressed in each of the six familiar statements constituted the semantic content of the familiar rules found in the familiar entailment and familiar nonentailment conditions of the selection task. Thus we directly determined familiarity rather than simply assuming it. The relations expressed in the six unfamiliar statements constituted the semantic content of the unfamiliar rules found in the unfamiliar entailment and unfamiliar nonentailment conditions of the selection task. The eight erroneous statements were included deliberately in order to check whether subjects were attending to the task. Subjects were asked to judge each statement for its correctness by using a 5point scale presented to the fight of each statement. Subjects were expected to respond either very sure it's right (5) or pretty sure it's

Table 1 Familiarity Task Items Item

M

Familiar items (overall M = 4.66) Gasoline is a flammable liquid 4.86 People must be 16 to have a driver's license 4.45 People must be at least 18 in order to vote for President 4.95 A diamond is a very hard precious stone 4.55 A lizard is a kind of reptile 4.66 A dog is a kind of mammal 4.51 Unfamiliar items (overall M = 3.13) A zebu is a kind of mammal 3.08 A potato is a nightshade herb 2.64 People must be at least 25 to run for Congress 3.33 People buying a house must have a title search done 3.19 A male Brazilian hummingbird has a red throat 3.13 The luster of an onyx is waxy in appearance 3.39 Incorrect items (overall M -- 1.42) The planet Jupiter is the smallest planet in our solar system 1.83 There are 31 days in February 1.30 A grasshopper is a kind of mammal 1.58 Apples are a kind of vegetable 1.17 St. Louis is the capital of the United States 1.02 There were 15 original colonies after the American revolution 1.50 Abraham Lincoln was the first President of the United States 1.16 There are 36 letters in the English alphabet 1.80

SD

0.71 I. 13 0.38 1.11 0.58 1.12

0.70 0.89 1.11 0.96 0.38 1.05

1.19 0.85 0.99 0.52 0.13 0.82 0.72 1.50

Note. I = very sure it "s wrong, 2 = pretty sure it's wrong, 3 = don't know, 4 = pretty sure it's right, 5 = very sure it's right.

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S. WARD, J. BYRNES, AND W. OVERTON

right (4) for the familiar statements, to respond pretty sure it's wrong (2) and very sure it's wrong (1) to the incorrect statements, and to respond don't know (3) for the unfamiliar statements. Subjects were told that some statements could be right and some could be wrong. If they did not know whether a statement was right or wrong, they were to respond don't know. The statements were presented in random order. Relations that were expected to be familiar and unfamiliar to subjects were demonstrated to be so (see Table 1). These findings support the use of "familiar" and "unfamiliar" on the selection task. Entailment task. This task was used to assess a subject's belief in the necessary relation between antecedents and consequents used in the selection task. It consisted of a set of 24 statements derived from the familiar and unfamiliar facts found in the familiarity task. Each of these facts were presented as entailment and nonentailment statements (see Table 2). Whereas in the familiarity task subjects were asked simply whether they thought a relation was true, in the entailment task they were asked whether it was necessarily true. Subjects were presented with cases and were asked how possible these cases were by using a 5-point scale. For example, they were asked how likely it was that "something was a dog but not a mammal." Their choices were impossible (1), pretty unlikely (2), don't know (3), pretty likely (4), and extremely possible (5). There were four kinds of statements (see Table 2). Familiar entailment statements described "impossible" cases, such as a dog that is not a mammal. Subjects were expected to select either the impossible or the pretty unlikely alternative. The familiar nonentailment statements were created by means of a many-to-one arrangement (e.g., "dog," "cat," etc., to "mammal") considered from the standpoint of one-to-many (e.g., "mammal" to "dog," "cat," etc.). We expected subjects to respond with very likely to these familiar nonentailment items. For unfamiliar entailment items, we expected subjects not to know the "impossibility" of these outcomes. Finally, for unfamihar entailment items, we expected subjects to recognize the high probability of these outcomes even though the relations described were unfamiliar. This is because subjects were expected to be possibly familiar with a component of each item (e.g., being a mammal). These expectations were confirmed with few exceptions (see Table 2). The ratings for the four kinds of items suggest that subjects distinguished between necessary (i.e., entailment) and nonnecessary (i.e., nonentailment) relations and support the use of the terms "entailment" and "nonentailment" as labels for conditions of the selection task. Selection task. Test booklets were constructed to contain an instruction page and eight variations of Wason's (1983) selection task. Subjects in each condition received six "if...then" rules and were asked to determine violations of that rule. Each problem was presented on a separate page of a booklet. For each problem, four response alternatives displayed on cards were presented along with the rule for that problem. These response alternatives corresponded to the affirmation of the rule's antecedent (p), the affirmation of its consequent (q), the denial of the antecedent (not-p), and the denial of the consequent (not-q). Each card was depicted as a rectangular box with words printed in it. Therefore, only one side of each card was visible, and subjects had to imagine possible reverse sides. As stated earlier, there were four conditions. Examples of specific rules for each condition are listed in Table 3. Two tokens of three many-to-one contents were used in each condition; that is, two rules were constructed from class inclusion relations, two rules were constructed from object-property relations, and two rules were constructed from legal relations. For each of these contents, multiple alternatives were organized around a single, integrative term. The experimenter read aloud the instructions while the subject read them. The instruction page informed the subject that the booklet contained several problems and that each presented a rule that was

Table 2 Entailment Task Items Item

M

SD

Familiar entailment items ( M = 1.83) Someone who is 14 but has a driver's license Something called gasoline that doesn't burn Something that is a lizard but is not a reptile Something that is a dog but is not a mammal Someone who is 16 but who legally voted A precious stone called a diamond that is not very hard

1.97

0.94

1.86

1.17

1.89

1.21

1.84

1.41

1.55

0.96

1.86

1.18

Familiar nonentailment items (M = 4.32) Someone voted legally for President but is not 18 Something that burns but is not gasoline Someone has a driver's license but is not 16 Something that is very hard but is not a diamond Something that is a mammal but is not a dog Something that is a reptile but is not a lizard

2.56 4.86

1.79 0.75

3.75

1.53

4.84

0.31

4.94

0.39

4.91

0.43

Unfamiliar entailment items (M = 2.90) Someone bought a house but did not have a title search done 3.25 Something that is a zebu but is not a mammal 2.94 A stone called an onyx that does not have a waxy luster 3.05 Someone who is 21 but who ran for Congress 1.81 Something called a potato that is not a nightshade herb 3.34 A male Brazilian hummingbird that does not have a red throat 2.98

0.84 0.71 I. i 2 0.87 0.91 0.72

Unfamiliar nonentailment items (M = 4.06) Something has a waxy luster but is not an onyx Something is a nightshade herb but is not a potato Something has a red throat but is not a male Brazilian hummingbird Someone who had a title search done but who is not buying a house Someone who ran for Congress but who is not 25 Something that is a mammal but is not a zebu

4.13

0.86

3.59

0.87

4.38

0.76

3.73

1.03

4.09

1.07

4.44

0.91

Note. l = impossible, 2 = pretty unlikely, 3 = don't know, 4 = pretty likely, 5 = extremely likely.

supposed to be followed. Subjects were instructed to select only those cards that should definitely be turned over in order to decide whether the rule for that specific problem was being broken. Over multiple studies, we have found that some initial practice in the mechanics of the selection task is necessary to maximize performance. Therefore, all subjects attempted to solve two practice problems before trying to solve the six test items. One practice rule was "If a

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KNOWLEDGE ORGANIZATION Table 3

Examples of Rules Used in the Selection Task by Condition and Rule Type Rule type

specific combination of response alternatives selected by the subjects. There were 16 possible selection combinations that could be given for each problem.

Example Results

Familiar entailment condition Class inclusion Object-property Legal Familiar nonentailment condition Class inclusion Object-property Leg~ Unfamiliar entailment condition Oass inclusion Object-property Legal Unfamiliar nonentailment condition Class inclusion Object-property Legal

If it is a lizard, then it is a reptile If it is gasoline, then it is flammable If someone voted, then that person is at least 18 If it is a reptile, then it is a lizard If something is flammable, then it is gasoline If someone is at least 18, then that person has voted If something is a potato, then it is a nightshade herb If it is an onyx, then it has a waxy luster If someone is buying a house, then that person has had a title search done If something is a nightshade herb, then it is a potato If something has a waxy luster, then it is an onyx If someone has a title search done, then that person is buying a house

student is watching television, then the student's homework is finished." The cards displayed "homework finished ~ (q), "watching television" (p), "not watching television" (not-p), and "homework not finished ~ (not-q), respectively. After making selections, they were told The "watching television" card should be turned over because it could have "homework not finished" on the other side and that would mean that the rule was being broken. Also, the "homework not finished" card should be turned over because it could have "watching television" on the other side and that would mean that the rule was being broken. The other two cards should not be turned over because what could be on the other side does not help you determine whether the rule is being broken. After this feedback, subjects were asked to solve the second practice problem, which had the rule "If a person is swimming in the public pool, then a lifeguard is present." The four cards showed "swimming" (p), "lifeguard" (q), "sunbathing" (not-p), and "no lifeguard" (not-q). After making selections, they were given feedback similar to that for the first practice problem. No other forms of more specific feedback were provided. Upon completion of the second practice trials, subjects worked on the six test trials at their own pace. Within each condition, rules were presented in a counterbalanced order. Subjects were tested in groups ranging in size from 1 to 4. Scoring. The correct logical response is the selection of the p and the not-q alternatives and not the selection of the q and the not-p alternatives. This selection combination, referred to as the "complete falsification solution," was awarded 1 point. If this was not the response given for a rule, a score of 0 was given. Therefore, scores ranged from 0 to 6. In addition, each problem was scored for the

Pre-Existing Differences Before we considered the m a i n results for the selection task, it was necessary to demonstrate that r a n d o m assignment effectively neutralized pre-existing individual differences in knowledge o f the content o f rules. Analysis o f the familiarity task showed that all groups were equally familiar and unfamiliar with the rule content used in the selection reasoning task (ps < 2.0). F o r the entailment task, no significant group differences were found in subjects' rating o f the possiblity o f the o u t c o m e s described by familiar entailment, familiar n o n entailment, unfamiliar entailment, and unfamiliar nonentailm e n t items. Therefore, all groups recognized the e n t a i l m e n t and n o n e n t a i l m e n t o f rule relations to the same degree.

Selection Task As a first analysis, we considered the effect o f feedback given on the two practice trials. A 4 x 2 (Condition x Practice Trial) analysis o f variance (ANOVA)revealed a significant m a i n effect o f practice trial, F(1, 128) = 64.73, p < .001: Subjects m a d e significantly m o r e " p and not-q" selections in the second practice trial (64%) than in the first practice trial (33%). As m e n t i o n e d earlier, the first practice trial represents spontaneous performance, and the second trial represents performance after the first feedback was given. In essence, feedback was necessary to elicit a high level o f performance. In order to explore the independent effects o f familiarity and entailment relations, planned contrasts were performed on the frequencies o f " p and not-q" selections in each o f the four conditions. In Table 4 we present the incidence o f " p and not-q" selections and other selections generated by subjects in each condition. W e first considered the effects o f familiar content while holding entailment relations constant. We contrasted the familiar entailment group ( M = 2.85, correct solutions, SD = 2.12) with the unfamiliar e n t a i l m e n t group ( M = 2.30, SD = 2.13). In each o f these conditions, the antecedents were one o f several alternatives ("many"), and the consequent was an integrative term ("one"). W e found

Table 4

Response Patterns for Each Condition (N = 33) Collapsed Across Rule Type Condition Pattern

FE

UFE

FNE

UFNE

Total

p and not q p and q p Not p and q Other

47 18 12 5 18

38 23 15 3 21

21 30 10 12 27

5 34 20 7 34

28 26 14 7 25

Note. Entries are percentages. FE = familiar entailment; UFE = unfamiliar entailment; FNE = familiar nonentailment; UFNE = unfamiliar nonentailment.

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S. WARD, J. BYRNES, AND W. OVERTON

that when entailment existed between clauses, familiarity had no effect, t(128) = 1.29, ns. Subjects in the unfamiliar entailment condition generated only 9% fewer falsification solutions (38%) than did subjects in the familiar entailment condition (47%; see Table 4). Hence familiarity added very little when entailment relations existed. However, familiarity did have an effect when entailment relations were absent. This was evident when we compared subjects in the familiar nonentailment condition ( M = 1.27 correct solutions, SD = 1.44) with those in the unfamiliar nonentailment condition ( M = 0.30, SD = 0.73). When entailment did not exist, subjects performed better when the antecedent-consequent relation was familiar than when it was unfamiliar, t(128) = 2.31, p < .02. Therefore, familiarity significantly improved performance only when the clause relation was a nonentailment relation. In contrast to familiarity, entailment relations do seem to have been necessary for adequate performance regardless of whether the content was familiar or unfamiliar. In particular, when the content was familiar, the presence o f an entailment relation significantly improved performance. Subjects in the familiar entailment condition generated significantly more falsification solutions (M--- 2.85, SD = 2.12) than did subjects in the familiar nonentailment condition ( M = 1.27, SD = 1.44), t(128) = 3.75, p < .001. In essence, if we took away an entailment relation in which "p and not-q" was believed to be impossible, correct selections dropped from 47 % to 21% even though the content was familiar (and identical!). Moreover, even when content was unfamiliar, entailment significantly improved performance. Subjects in the unfamiliar entailment condition generated significantly more falsification solutions ( M = 2.30, SD = 2.12) than did subjects in the unfamiliar nonentailment condition ( M = 0.30, SD = 0.73), t(128) --4.76, p < .001. These results, combined with the finding that familiarity added little without entailment relations, demonstrates the importance of entailment over familiarity. With respect to other selections shown in Table 4, one can see that as falsification solutions decreased from 47% to 5% across conditions, there was a corresponding increase in "p and q" selections from 18% to 34%, x 2 (6, N = 792) = 100.46, p < .001. This so-called matching strategy (see Ward & Overton, 1990) consists of selecting those cards that are positive instances of the antecedent and the consequent of a given rule. Thus for "If it is a dog, then it is a mammal," subjects would select the "dog" and the " m a m m a l " cards. This response pattern tends to reflect a confirmation bias wherein subjects attempt to find evidence that supports a rule rather than violates it.

q" selections for legal rules (39%) than for either objectproperty (25%) or class-inclusion (20%) rules. The incidence of correct selections did not differ between object-property and class-inclusion rules. However, this effect was qualified by the Conditon x Rule Type interaction. The percentages of correct selections categorized by condition and rule type are shown in Table 5. Post hoe tests on the interaction revealed that intergroup differences were due largely to the fact that the two entailment groups performed significantly better than the two nonentailment groups with the legal and object-property rules. No differences emerged between the entailment groups and the familiar nonentailment group for class inclusion rules, but performance was uniformly lower. In addition, whereas the two nonentailment groups generated the similar frequencies of correct selections regardless o f rule type, differences among rule types emerged for the two entailment groups. In particular, for the familiar entailment group, performance was significantly better for the legal rules than for either the objectproperty or the class-inclusion rules. Moreover, performance was significantly better for object property rules than for classinclusion rules. Whereas subjects in the unfamiliar entailment group performed significantly better for legal rules than for object-property or class-inclusion rules, no differences emerged between the latter two rule types. These findings for the two entailment groups suggest that certain kinds of manyto-one schemata are more likely to facilitate hypothesis-testing performance than are others. Finally, differences emerged between the two nonentailment groups. Whereas the familiar nonentailment group performed significantly better than the unfamiliar nonentailment group for class-inclusion and object-property rules, they did not differ for legal rules.

R u l e T y p e Effects

Table 5 Correct Selection Percentages by Rule Type and Condition (N = 33)

A 4 x 3 (Condition x Rule Type) ANOVA with repeated measures on the last variable was performed. This analysis revealed significant main effects for condition, F(3, 124) = 12.87, p < .001, and rule type, F(2, 248) = 18.07, p < .001, as well as a significant Condition x Rule Type interaction, F(6, 248) = 9.05, p < .001. Post hoe analysis of the main effect of condition revealed the same findings as the planned comparisons. With regard to the main effect of rule type, post hoe tests revealed that subjects generated significantly more "p and not-

Discussion In general, the purpose of this study was to examine the role of entailment relations and relevance type familiarity in the solution of conditional reasoning problems. The point of origin of this work was the view that successful formal reasoning requires an organization of knowledge that goes significantly beyond the storage of actual-world knowledge experiences in memory (Overton, 1990). Several major conclusions emerged from the findings. The first concerns the important role that knowledge organization plays in reasoning performance. The responses to the familiarity and entailment tasks demonstrated the existence of many-to-one schemata for our subjects, and these

Condition Rule type FE UFE FNE UFNE Legal 73 61 27 6 Object-prope~y 45 33 18 2 Class indufion 24 21 17 8 M 47 38 21 5 Note. FE = familiar entailment; UFE = unfamiliar entailment; FNE = familiar nonentailment; UFNE = unfamiliar nonentaiiment.

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KNOWLEDGE ORGANIZATION schemata produced some interesting asymmetries in performance. When reasoning from an alternative to an integrative term (e.g., "dog" as a kind of"mammal"), subjects recx~on~ed the necessity of this link. In contrast, when reasoning from the integrative term to the alternatives, subjects recognized the nonnecessity of this link. This characterization of knowledge is quite distinct from one that posits a mere compilation of facts or simple associative links. Associative links by their nature reflect symmetries, not asymmetries. The asymmetrical nature of the many-to-one schemata in turn strongly affected hypothesis-testing performance. This was most deafly demonstrated by the finding that subjects in the familiar entailment condition performed better than those in the familiar nonentailment condition. As stated, we expected that as long as the structure of this content was a many-toone arrangement, subjects would perform well even with unfamiliar content. Given the pervasiveness of hierarchical structures across disciplines, this account could have enormous implications for reasoning in academic subject areas. Second, the findings concerning entailment and familiarity support a general distinction concerning the role of conceptual versus procedural knowledge in scientific problem solving (Bymes, 1988; Overton, 1990; Overton et al., 1987; Ward & Overton, 1990). According to this view successful problem solving derives from having both knowledge of the core concepts for a given domain (conceptual knowledge) and "how to" knowledge of step-by-step solutions, algorithms, or heuristics (procedural knowledge). Inadequate performance can derive from (a) having the requisite conceptual knowledge but lacking procedural knowledge, (b) having procedural knowledge but lacking conceptual knowledge, (c) having both but lacking an integration of such forms of knowledge, or (d) having neither form of knowledge. In our study, the requisite conceptual knowledge consists of the many-to-one schemata. The relevant procedural knowledge consists of the specific linguistic device of both forming an "it" statement that appropriately maps onto schemata and seeking cases of "p and not-q." Whereas the familiarity and entailment tasks elicited near-ceiling levels of conceptual knowledge in subjects, 30%50% of subjects in the familiar entailment condition (depending on rule type) still failed to provide correct responses. Therefore, having high levels of conceptual knowledge alone was insufficient for correct performance. We suggest that some students may require additional training in the specific procedure of forming and evaluating "if" hypotheses. There clearly are alternative ways of stating hypotheses, and the use of"if" may be a novel enterprise. Finally, our study has several implications for education. First, it is clear that older adolescents are fully capable of evaluating the truth of hypotheses when given the opportunity to reason from a basis of familiar (and even unfamiliar, though structurally analogous) many-to-one schemata. This suggests that instruction that emphasizes hierarchical or nested relations among concepts is more likely to foster conditional reasoning about this domain than is instruction that does not emphasize these relations. In particular, this supports Lawson's (1985) argument that instruction in symbolic propositional logic that makes no reference to meaningful content is unlikely to enhance formal rcasoning about some discipline.

Thus with respect to the debate about whether higher order thinking can be elicited through instruction, this research supports those who argue that such instruction be strongly grounded in academic content areas. This content must be richly structured for students in order to promote the construction of many-to-one schemata. In future studies, researchers could contrast one instructional method that is designed to foster integration within an unfamiliar domain with one that is not designed this way, in order to see whether conditional reasoning can be facilitated after instruction is provided.

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