# Justifications for choices made in procedures

## Abstract

In any procedural mathematical situation, there are multiple ways of achieving the same answer. Given this observation, we ask, why choose one procedural solution over another? We address this question here with data drawn from interviews conducted with university students engaged in row-reducing matrices. During their tasks, the students voiced a variety of justifications for the procedural steps they enacted. Through a phenomenographical analysis (Marton, *Instructional Science, 10*, 177–200, 1981) of their utterances, we construct a framework for justifications for choices made within procedures with two broad categories, *algorithmic* and *anticipatory*. By comparison, this is similar to the creative/imitative reasoning framework of Lithner (*Educational Studies in Mathematics*, *67*, 255–276, 2008), a framework primarily emerging from less procedural settings. We suggest that, given this richness in justifications brought forth by a procedural setting, when used effectively, instruction in mathematical procedures has the potential to contribute to deeper, more flexible forms of mathematical knowledge overall.

## Keywords

Procedural flexibility Student justifications Mathematical flexibility Use of flexible cognition## Notes

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