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Conditional and biconditional reasoning : a developmental study using new norms

University of British Columbia

The present study attempted to answer the question of the extent to which idiosyncratic interpretations of premises affected performance on syllogistic reasoning tasks. A model was developed which accounted for both linguistic factors and logical factors. The constructs in the model were incorporated into a new set of norms for syllogistic reasoning. Two tests were developed for this study. The Referential Test measured interpretations of given logical expressions using physical referents. The Syllogism Test contained standard syllogisms in which a specific logical expression was embedded as the first premise of each syllogism. One version of each of these two tests was constructed for each of four logical expressions. One logical expression was a conditional proposition, and the other three were syntactically different biconditional propositions. One version of each test was administered to 916 students in Grades 6, 8, 10 and 12, one proposition for each student. The criterion measures for the Referential Tests revealed (a) many different interpretations of the same proposition, and (b) clear differences among all four propositions. Developmental trends were unclear. The criterion measures for the Syllogism Tests revealed (a) clear developmental trends for the ability to reason consistently, independent of apparent interpretations of premises, and (b) some differences and some similarities among the four propositions, almost all of which contravened norms of formal logic. Intrasubject comparisons between Syllogism Tests and Referential Tests (using the same logical proposition for each student), demonstrated that for almost all students, syllogistic reasoning was governed by both the interpretation of the first premise and the ability to generate that interpretation rather than a truncated version. These comparisons also suggested that some apparently regressive behaviour of Grade 12 students could be attributed to developmental changes in meanings of logical propositions which were not accompanied by corresponding changes in reasoning strategies. Implications were discussed for natural language, mathematics education, and research in logical reasoning (and hence critical thinking), concept formation rule learning, and Formal Operations. Particular attention was given to formal logic and Formal Operations as competence models.

Text

2010-04-19

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http://hdl.handle.net/2429/23867

Mathematics Education

University of British Columbia

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