# Principles Used to Evaluate Mathematical Explanations

- Samuel Johnson,
*Yale University*
- Angie Johnston,
*Yale University*
- Marissa Koven,
*Emory University*
- Frank Keil,
*Yale University*

## Abstract

Mathematics is critical for making sense of the world. Yet, little
is known about how people evaluate mathematical explanations. Here, we use an
explanatory reasoning task to investigate the intuitive structure of mathematics.
We show that people evaluate arithmetic explanations by building mental proofs
over the conceptual structure of intuitive arithmetic, evaluating those proofs
using criteria similar to those of professional mathematicians. Specifically, we
find that people prefer explanations consistent with the conceptual order of the
operations (“9÷3=3 because 3×3=9” rather than
“3×3=9 because 9÷3=3”), and corresponding to simpler proofs
(“9÷3=3 because 3×3=9” rather than “9÷3=3
because 3+3+3=9”). Implications for mathematics cognition and education are
discussed.

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