An analysis of Euclidean geometry learning opportunities in Grade 11 mathematics textbooks

Abstract

In the present study, Euclidean geometry learning opportunities in four Grade 11 mathematics textbooks used in South African schools were investigated. The study adopted the Kurz Opportunity to Learn (OTL) Model as the theoretical foundation with a focus on content coverage and the quality of tasks (cognitive levels, nature, and contextual features of tasks in the textbooks). The study was a qualitative case study. Four approved Grade 11 mathematics textbooks were explored through deductive content analysis. The study revealed that the four textbooks covered almost all the Euclidean geometry topics in depth, but that there was no balance among different cognitive levels of questions. Most of the Euclidean geometry questions in the textbooks were focused more on routine and complex procedures, with very few questions focused on knowledge and none of the four textbooks providing learners with an opportunity to solve problems. It is recommended that the textbook writers include this content in updated versions of these textbooks. Moreover, the Euclidean geometry tasks provided in the four textbooks were mostly routine and interpretation tasks. The researcher advises that the textbooks should provide a balanced range of cognitive levels of questions, and that more representation, modelling, and interpretation tasks should be included to help learners improve their interpretation, representation, modelling, and understanding abilities. Finally, all the questions were of intra-mathematical context (non-application context). Therefore, it is also recommended that more tasks with realistic (fictitious) and authentic context be integrated in the textbooks, rather than using only intra-mathematical context.