# Exploring one student’s explanations at different ages: the case of Sharon

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## Abstract

This study describes the types of explanations one student, Sharon, gives and prefers at different ages. Sharon is interviewed in the second grade regarding multiplication of one-digit numbers, in the fifth grade regarding even and odd numbers, and in the sixth grade regarding equivalent fractions. In the tenth grade, she revisits each of these concepts again. The study investigates the different forms Sharon’s explanations take at different ages as well as how she perceives the nature of mathematical explanations at different ages. Sharon’s explanations are also used to investigate her conceptualization of the number zero, a concept which runs across the curriculum at different ages. Finally, the study explores a method for investigating the long-term mathematical development of one student. Implications for future research are discussed.

### Keywords

Mathematically based explanations Practically based explanations Zero### References

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