Adolescent Reasoning in Mathematics: Exploring Middle School Students’ Strategic Approaches in Empirical Justifications


Twenty middle-school students participated in semi-structured interviews in which they were asked to assess the validity of two mathematical conjectures. In addition to being free to develop a valid proof as a justification, students were also asked to generate numeric examples to test the conjecture. Students demonstrated strategic reasoning in their empirical approaches by varying the quantity, parity, magnitude, and typicality of the numbers selected. These strategies were more developed in students who initially believed in the truth of the conjecture as well as in students who generated a valid, deductive proof. Emphasizing students’ strategic selection of diverse examples parallels inductive reasoning in other domains. Strategic use of examples in justifying conjectures has the potential to assist students’ development of deductive proof strategies.

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