# Relationships among prospective secondary mathematics teachers’ skills of attending, interpreting and responding to students’ understanding

## Abstract

This study explores relationships among prospective secondary teachers’ skills of attending to relevant mathematics elements in students’ answers, interpreting students’ mathematical understanding, and proposing instructional actions. Thirty prospective secondary mathematics teachers analyzed three high school students’ answers to three problems of derivatives of a function at a given point and proposed instructional actions to help them progress in their understanding. Findings indicate that the more prospective teachers identified links between the mathematical elements and characteristics of students’ understanding, the more suitable the instructional activities were. Furthermore, our results suggest practical implications for teacher education programs since the type of task presented in this research may help to foster prospective secondary teachers’ noticing of students mathematical understanding.

## Keywords

Derivative concept Noticing Prospective secondary teachers Prospective teacher education Students’ mathematical understanding## Notes

### Funding information

The research reported here was financed in part by Ministerio de Educación y Ciencia, Dirección General de Investigación, Spain, under Grant no. EDU2014-54526-R and EDU2017-87411-R, and in part by Generalitat Valenciana project no. GV/2015/115.

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