Mathematical Knowledge for Teaching Slope: Leveraging an Intrinsic Approach

ABSTRACT

This paper leverages an intrinsic approach to the conception of mathematical knowledge for teaching (MKT) to show how it can be used to examine teachers’ MKT. In this qualitative study, I interviewed eight practicing teachers using tasks designed to generate data regarding their (a) personal interpretations of slope, (b) understanding of how others develop similar interpretations, and (c) understanding of the discussions and activities that serve that development. Five participants provided evidence they had transformed their personal interpretations of slope into MKT slope. Interestingly, two of the three participants who did not were inspired to begin transforming their interpretations into MKT during the interview suggesting methods teacher educators might use to support the development of mathematics teachers’ MKT.

KEYWORDS:

• Mathematical knowledge for teaching
• slope
• intrinsic approach

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ “MKT_slope” should be read as “mathematical knowledge for teaching slope.”

² Here and elsewhere, quantity is used to refer to measureable attributes of an object or phenomenon and more specifically to one’s capacity or propensity to measure those attributes (Smith & Thompson, 2008).

³ I used pseudonyms for all participants in the study.

⁴ This question is later referred to as The Slope of ½ Task.