## Providing Written Feedback on Students’ Mathematical Arguments: Proof Validations of Prospective Secondary Mathematics Teachers

Source: Journal of Mathematics Teacher Education, Volume 17, Issue 2, pp 105-127, April 2014.

Prior research has demonstrated several weaknesses teachers have with respect to proof validation, but little research has investigated instructional sequences aimed to improve this skill.

In this paper, the authors present the results from the implementation of such an instructional sequence.

A sample of 34 prospective secondary mathematics teachers (PSMTs) validated twelve mathematical arguments written by high school students. They provided a numeric score as well as a short paragraph of written feedback, indicating the strengths and weaknesses of each argument.

The results provide insight into the errors to which PSMTs attend when validating mathematical arguments. In particular, PSMTs’ written feedback indicated that they were aware of the limitations of inductive argumentation.

However, PSMTs had a superficial understanding of the “proof by contradiction” mode of argumentation, and their attendance to particular errors seemed to be mediated by the mode of argument representation (e.g., symbolic, verbal). We discuss implications of these findings for mathematics teacher education.