Beginning mathematics teachers' purposes for making student thinking public

Abstract

Although having students make their mathematical thinking public has become a commonly encouraged practice in U.S. schools, little is known about how teachers perceive this practice. This study examined 14 beginning mathematics students' thoughts about making student thinking public using a framework for assessing the extent to which a practice supports students' mathematical learning. Analysis of the data revealed nine themes in the students' purposes for making student thinking public, ranging from affective concerns to those that had the potential to transform student learning. The findings highlight the fact that students' and teacher educators' use of common terms to label pedagogical practices does not necessarily imply a common understanding of the purpose of those practices. Describing pedagogical practices in ways that highlight differences in the purposes for which they can be used is proposed as a way to contribute to improving both students' and teacher educators' classroom practices.

Keywords:

• beginning teachers
• student thinking
• pedagogical practices

Acknowledgements

The research reported on in this article was supported in part by U.S. National Science Foundation award ESI-0243558. Opinions expressed are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Notes

1. We use the term ‘thinking’ broadly to represent students' ideas about approaching problems, what led them to their solutions, their justifications for solutions, and their reflections on mathematical activity, as well as their solution methods and answers to problems.

2. By ‘mathematical understanding’ we mean being able to solve a problem using a mathematical concept or skill and being able to justify why the process worked, rather than merely describing the process. This distinction between description and justification has been discussed elsewhere (Hill et al. 2008), and seems to be a critical piece of teacher development (Lo, Grant, and Flowers 2008).

3. For more details about this course, see Van Zoest and Stockero (2008a, 2008b, in press).

4. In the state where the study took place, graduates of secondary teacher education programs are certified to teach grades 6–12 (12–18 years old).

5. Transcript references include the participant number (if not already mentioned), followed by the type of data source – focus group written work by page number (FGW#), focus group video discussion (FGV), focus group follow-up interview (FGInt), post-observation interview 1, 2, or 3 (POInt#) – followed by the HyperResearch character number that begins the idea unit from which the quote is taken.