An analysis of the cognitive demands of examples presented in grade 7 textbooks in geometry

Abstract

The use of textbooks in teaching and learning is very crucial, and in some cases, textbooks are the only resources available for both teachers and learners. Well-constructed textbooks should include examples that support learning, particular in subjects with an abstract nature, like mathematics. This research study is aimed at the analysis of examples in two lower-secondary level (grade 7) mathematics school textbooks in geometry. The selected textbooks were: Curro Grade 7 Mathematics and Mindbourne Grade 7 Mathematics. The work included an investigation into the levels of cognitive demands of examples, frequency of examples, the types of examples, and the order of thinking required in solving the mathematics problem presented in examples. This was followed by a discussion about real-life examples and how they can be used to enhance the understanding of geometry concepts. This study is important as it contributes to the crucial role of examples in school mathematics textbooks, particularly at the lower-secondary level in a Sount African context; thereby contributing to the literature and classroom practice as both teachers and learners interact with textbooks in a mathematics classroom. A constructivism paradigm informed the study, through the use of a qualitative research design. All examples in geometry in the two selected textbooks were analysed using an analysis tool adopted from literature and further developed for the purpose of this study. The researcher has drawn on the framework by Stein, Henningsen and Silver (2000) to analyse the cognitive demands of tasks, and the work from Michener (1978) to classify the types of examples in mathematics. Thus, the overall analytical framework is a merger between the Stein et al. (2000) framework and Michener’s (1978) work. The main findings were that there are some similarities and fundamental differences in terms of frequency and presentation of examples in the two textbooks, which may benefit learners as they use both books. There were no counter examples in both textbooks. This might indicate that both textbooks require more examples. One limitation of this study is that only two textbooks formed part of the analysis, due to practical reasons, yet there are so many textbooks being used in South African schools at this level. It is recommended that more research should be done in analysing examples as it is presented in mathematics textbooks; through selecting a larger sample, also focusing on other content areas, and using other theoretical frameworks for analysis. It might provide more insights in how examples in textbooks contribute to teaching and learning in mathematics. Key words Cognitive demands, Examples, Grade 7, Higher Order Thinking, Lower Order Thinking, Geometry