Publication Date


Document Type

Book Chapter


Teacher educators need to support middle grades teachers in developing mathematical knowledge for teaching algebraic concepts. In particular, teachers should become familiar with possible introductions and sequencing to the concept of slope, and common middle school students’ limited conceptions about measuring the steepness of an incline. Steepness can be expressed directly in terms of an angle or indirectly as a slope. Encouraging middle school students to find a measure of steepness using a ratio may help support students’ transition to multiplicative thinking. This mixed – methods study explores middle school students’ responses in solving a comparison problem involving the steepness of two inclines, in order to gain insight into common student strategies. The quantitative portion of the study involved written surveys distributed to 256 Grade 7 participants in the United States. We examined the frequency and types of solutions offered by these participants. We found that 27% of the participants provided an incorrect solution which was consistent with additive reasoning. The qualitative portion of this study consisted of small group interviews of 19 Grade 7 participants, who were conflicted in the different solutions they produced from using additive reasoning and their geometric knowledge.

Original Citation

Cheng, D. & Sabinin, P. (2011). Making Algebra More Accessible: How Steep Can it be for Teachers? In B. Boufoy-Bastick (Ed.), The International Handbook of Cultures of Teacher Education: Comparative International Issues in Curriculum and Pedagogy (pp. 87-101). Strasbourg, France: Analytrics.

Included in

Mathematics Commons