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.
Highlights
Mathematics textbooks have been found to have a strong influence on classroom practice (Fan, 2013; Howson, 1995; Stylianides, 2014; Valverde, Bianchi, Wolfe, Schmidt, & Houang, 2002) and the tasks that they include can stimulate different levels of mathematical thinking and learning (Watson, & Ohtani, 2015; Stein, Smith, Henningsen, & Silver, 2000; Sullivan, Clarke, Clarke, & O’Shea, 2010)
The other, which was taught according to the South African CAPS curriculum, used Classroom Mathematics Grade 9 (Rhodes-Houghton et al, 2013)
The analysis of the microstructures focuses on the affordances for learning presented in the textbooks regarding the interplay between procedural and conceptual knowledge, the integration of the multiple representations of functions and links established to other mathematical content areas and the real world
Summary
Mathematics textbooks have been found to have a strong influence on classroom practice (Fan, 2013; Howson, 1995; Stylianides, 2014; Valverde, Bianchi, Wolfe, Schmidt, & Houang, 2002) and the tasks that they include can stimulate different levels of mathematical thinking and learning (Watson, & Ohtani, 2015; Stein, Smith, Henningsen, & Silver, 2000; Sullivan, Clarke, Clarke, & O’Shea, 2010). At a South African school (the context of this study), learners in two language-based streams are taught mathematics using different textbooks up until the end of Grade 9. In Grade 10, learners who choose to write the National Senior Certificate examinations merge from both streams and are thereafter taught together. Both groups of learners have encountered similar mathematical content en route to Grade 10, the textbooks utilised respectively in the two language-based streams do not necessarily approach this content in the same way. In a larger study (Mellor, 2015), a comparative textbook analysis was undertaken as a means of attempting to interrogate the affordances for learning experienced by the two groups before progressing to Grade 10, with the ultimate aim of helping her, and other Grade 10 teachers at the school, have a deeper understanding of their learners’ mathematical backgrounds, avoiding potential ‘mathematical mismatches’ between the teachers and their learners (Skemp, 1976)
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