An analysis of mathematical processes and understanding in a tutoring intervention : the case of trigonometry

Trigonometry is a topic that teachers often find hard to teach, and students can find it difficult and confusing. The topic of trigonometry is a topic that links algebraic concepts, number skills and geometric meanings together, and many students are not accustomed to this integrated way of learning different mathematical strands. Relational understanding, as defined by Skemp, has received a lot of attention from researchers and teachers, but it is very difficult for students to achieve relational understanding, especially in trigonometry. In addition, there is a scarcity of methods and approaches for explaining introductory aspects of trigonometry. As such, many researchers suggest that schools should encourage secondary students to learn the subject of trigonometric functions through different representations and, in the process, develop an effective way of teaching to build relational understanding, in particular through mental modelling approaches. The purpose of this study is to explore ways of helping students to learn the subject of trigonometric functions at the introductory level leading to relational understanding. This study takes the view that learning is a process that integrates the manipulation of mental models and construction of schemas in order to foster relational understanding. For this purpose, this research uses a multi-case study analysis to document three students who attempted to learn introductory trigonometry. The main process of this study is the tutoring process. During this process, the research was conducted via an intervention consisting of tutoring lessons for three high school students, ranging from Year 10 to Year 11, in a one-on-one context. The author of this thesis was the teacher during the tutoring process. During the tutoring interventions, the students were encouraged to draw diagrams, discuss their ideas, and if necessary to summarise their ideas. At the same time, the students learned to articulate their ideas about trigonometric functions through the process of employing additional Small Problem Solving tasks. The mental models proved to be useful in order to help students to construct their mental representations of trigonometric functions and to develop understanding during active participation in the process of solving small problems