The application of Van Hiele’s theory of instructional design to facilitate the learning of circle geometry in grade 11

Abstract

This study explores the application of van Hiele’s theory of instructional design to facilitate the leaning of circle geometry in Grade 11. Geometry is an essential and compulsory component in secondary school Mathematics. However, learners face problems in understanding geometric concepts; constructing proofs; and in deductive reasoning. The instruction in geometry offered by teachers in most South African schools is inadequate in guiding the learning of geometry. The purpose of this study is the application of van Hiele’s theory of instructional desig to facilitate the learning of circle geometry in Grade 11. This study employed a qualitative approach set within an interpretive paradigm, with a case study design. The emphasis of this study is on exploration, description, explanation, creation of, and testing of instructions based on van Hiele’s theory. The methods of collecting data in this study were document analysis, classroom observation, and interviews. The participants in this study were 35 Grade 11 Mathematics learners and one Mathematics teacher. The findings from document analysis, which largely involved the reading that focused on the Senior Phase (SP) and Further Education and Training (FET) Curriculum and Assessment Policy Statement (CAPS), revealed a disconnect on issues that are covered between SP and FET bands in geometry, curriculum, while content focus for Grade 11 circle geometry requires learners to prove seven theorems and their application, the focus for SP is mainly on the study of space and 2D shapes. Drawing from van Hiele’s five phases of learning, classroom observation data showed that the teacher lacked knowledge of van Hiele’s theory and phases of learning. Analysing some of the student-written responses revealed that, lessons developed and presented according to van Hiele’s phases of learning helped learners to progress through geometric levels of understanding. The findings from the interviews confirmed the findings from classroom observation. One of the recommendations this study makes is that teachers should embrace the use of van Hiele’s theory as a teaching strategy for geometry to ensure that learners understand circle geometry.