Slope conceptualizations in mathematics textbooks

Abstract

This paper reports the results of an investigation whose objective is to find which slope conceptualizations have a presence in high school mathematics textbooks and which are the predominant ones. For this, we used the Content Analysis method, where the objects of analysis are found in content exposition, worked examples, and in the exercises or problems proposed in the textbooks. As a reference framework we used the eleven slope conceptualizations identified by Stump (1999) and Moore-Russo, Conner and Rugg (2011). Our findings indicate the presence of most of the conceptualizations identified in the previous research, however, there is a notable predominance of those that emerge from the analytical definition of slope, such as the parametric coefficient, algebraic ratio, and trigonometric conception and its internal application in determination of parallelism or perpendicularity between lines as is the determining property. These conceptualizations, on the one hand, induce to formation of the idea that slope makes sense only in intra-mathematical context, and on the other hand, they favor the development of procedural knowledge on detriment of conceptual knowledge. Understanding the slope requires the creation of internal networks as a product of connections between conceptualizations intra and extra mathematical plane, in addition to the harmonious development of conceptual and procedural knowledge. Achieving the understanding of the concepts is essential for Mathematics Education, however, our results indicate that the texts used by teachers can hardly contribute to this achievement.