An analysis of students' understanding of circle theorems and angle properties

Abstract

This study explores the mathematics understanding of Form 4 students in two areas of geometry - Circle Theorems and Angle Properties. An insight is gained into students' understandings, difficulties and misconceptions in the two mathematical topics, and the strategies they use to apply their understanding to solve geometric problems. Data was initially collected through self-designed tests distributed to ninety Form 4 students in one school. A sample of eight students was then selected using stratified random sampling based on their test performance. Semi-structured individual interviews, in the form of mathematical sessions were conducted with the selected students in which interviewees explained their line of reasoning used in the tests, whilst probing aimed for deeper exploration into their understanding, difficulties, misconceptions and strategies. By analysing the data using a thematic approach, it was revealed that students focus on procedural skills and tend to disregard the importance of conceptual understanding. Additionally, participants lacked the ability to put logical reasoning into writing and struggled to compile simple proofs. The language of instruction was one of the main criteria for students struggling to present knowledge, together with them tending to be better at presenting verbal rather than written responses. A number of implications are presented in the concluding chapter.