Affordances for learning linear functions: A comparative study of two textbooks from South Africa and Germany

Abstract

Textbook content has the ability to influence mathematical learning. This study compares how linear functions are presented in two textbooks, one of South African and the other of German origin. These two textbooks are used in different language-based streams in a school in Gauteng, South Africa. A qualitative content analysis on how the topic of linear functions is presented in these two textbooks was done. The interplay between procedural and conceptual knowledge, the integration of the multiple representations of functions, and the links created to other mathematical content areas and the real world were considered. It was found that the German textbook included a higher percentage of content that promoted the development of conceptual knowledge. This was especially due to the level of cognitive demand of tasks included in the analysed textbook chapters. Also, while the South African textbook presented a wider range of opportunities to interact with the different representations of functions, the German textbook, on the other hand, included more links to the real world. Both textbooks linked ‘functions’ to other mathematical content areas, although the German textbook included a wider range of linked topics. It was concluded that learners from the two streams are thus exposed to different affordances to learn mathematics by their textbooks.

Keywords

• Linear functions
• Cognitive demand
• Textbooks
• Tasks