Logical Reasoning in Mathematics Students: Conditional Inference with Mathematical, Abstract and Everyday Content

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Data, analyses and material associated with the manuscript “Logical reasoning in mathematics students: Conditional inference with mathematical, abstract, and everyday content”.Abstract. In standard mathematical logic, conditionals – sentences of the form ‘if p then q’ – are treated as false if p is true and q is false, and true otherwise. In everyday life, in contrast, conditionals are rarely true or false; they vary in believability, and believability affects evaluation of conditional inferences. Might this mean that conditional inference in mathematics is also influenced by believability? We investigated this question in three studies. Study 1 used comparative judgement to score mathematical conditionals for believability, then showed that mathematics undergraduates accepted more inferences from more believable conditionals. Study 2 demonstrated that mathematics undergraduates evaluated conditional inferences similarly across mathematical, abstract and everyday content, but treated inferences from believable mathematical conditionals more normatively. Studies 1 and 2 also found educationally relevant individual differences, with some participants more likely to accept invalid inferences and more affected by believability. Study 3 established that the results of Studies 1 and 2 are sensibly attributed to believability rather than to easiness. We consider educational implications for the development of reasoning skills, and the meaning of believability as a theoretical construct in mathematics.Information about the repository content is available in the file "codebook.txt"© the authors

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