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

- Jennifer Cooper,
*University of Wisconsin - Madison*
- Candace Walkington,
*University of Wisconsin - Madison*
- Caroline Williams,
*University of Wisconsin - Madison*
- Olubukola Akinsiku,
*University of Wisconsin - Madison*
- Charles Kalish,
*University of Wisconsin - Madison*
- Amy Ellis,
*University of Wisconsin - Madison*
- Eric Knuth,
*University of Wisconsin - Madison*

## Abstract

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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