A Study of Slope Explanations across a Standards-Based Textbook Series

Abstract

This study analyses a standards-based textbook series to investigate how slope is presented across seven sequential textbooks in a secondary mathematics curriculum. Analysis of the expository content across the textbooks shows that slope is covered in all seven books, is frequently described as a Constant Parameter or Ratio, is frequently used in real world contexts, and is often described alongside covariational language of how inputs and outputs change in relation to one another. Results indicate that Determining Property and Steepness components of slope are less prevalent and disproportionately unlikely to be accompanied by covariational language and applications compared with the other slope components. Although many consistencies were found across the textbook series, differences in emphases from one textbook to another are also discussed and connected to the recommendation that future work around slope investigate its development across the secondary curriculum. Results are discussed relative to students’ preparation for specific calculus topics that build on prior knowledge of slope. Implications for both teachers and researchers are provided.

Components and Subcomponents of the Slope used by High School Mathematics Teachers

“…The concept of slope has several ways of being conceptualized, each of which holds fundamental importance across multiple domains (Cho & Nagle, 2017;Nagle et al, 2022;Stump, 1999). These conceptualizations can be categorized into two notions: a geometric notion and a variational notion.…”