Mathematical Reasoning: Adults' Ability to Make the Inductive-Deductive Distinction

Abstract

In this study, I examined adults' ability to distinguish necessary deductive and indeterminate inductive forms of argument in mathematics. Only 30% of a sample of college students distinguished deductive and inductive forms of argument and experienced deductively derived conclusions as necessary and inductively derived conclusions as uncertain. Forty percent failed to distinguish deductive and inductive forms and experienced inductively derived and deductively derived conclusions as necessary. Thirty percent distinguished deductive and inductive arguments but experienced deductively derived and inductively derived conclusions as uncertain. As observed in other reasoning domains, the introduction of personal beliefs or knowledge about the argument content appeared to affect adult reasoners' application of knowledge about forms of argument and judgments of necessity. The results suggest the following conclusions. Adults' experience of the conclusions from mathematical inductive and deductive arguments as provisional conclusions or necessary conclusions depends on a complex coordination involving ability to attend to abstract premise-conclusion relations and beliefs about the nature of mathematical objects and regularities. Thus, two major achievements are involved, explaining the low numbers able to judge necessity in mathematics.