Mathematical knowledge for teaching: a focus on the mathematical work of a grade 8 teacher when introducing algebra

Abstract

This study investigates mathematical knowledge for teaching. One Grade 8 teacher was interviewed and observed for one week while teaching algebra to 8th graders. I focused on mathematical problems that confronted her as she went about her work, the mathematical work of teaching she grappled with, the knowledge resources she called on as well as the algebraic activities that she presented to her learners. The analysis shows that she wrestled with explaining, representing, questioning, defining, working with learners’ ideas while restructuring tasks was entirely absent in this practice. It was interesting to see that learners were exposed to representational, transformational and reading activities of algebra and not the generalizing and justifying activities of algebra. The analysis further shows that this teacher drew on mathematics, curriculum and her experience in order to sustain her practice. Based on the findings of this study I argue that mathematical knowledge for teaching in this practice is empirical, with a strong focus on conventions as well as terminology; and is characterized by representational, transformational and reading activities.