Abstract:

There is plenty of literature that presents difficulties demonstrated by students in learning geometry. Geometry is one of the areas of mathematics that challenges students a lot, however, at its heart is exploring and understanding space. This space is first encountered by students from conception. This paper contributes to the literature by investigating the teachers’ role in developing geometric concepts, highlighting students’ alternative geometric vocabulary, conceptual, terminology misunderstandings and their demonstrated challenges. This paper is part of a larger project that focused on numerous elements of developing geometric knowledge; however the paper only focuses on Grade 8 students’ alternative geometric understanding with the aim of informing instruction. Using the diagnostic test and reflective tests we traced alternative geometric vocabulary, conceptual and terminology misunderstandings. We targeted three groups of students based on the diagnostic test’s results (three high, three average and three low achievers). The responses to the diagnostic and reflective tests which focused on properties of triangles provided the data for the study. Van Hiele theory provided the lens for the study. A qualitative approach was used to analyse the performance of the students in the diagnostic and reflective tests. The findings show that daily reflective tests can serve as essential tools in helping that mathematics teacher discover more and more in-depth students’ alternative geometric vocabulary, conceptual and terminology misunderstandings. In conclusion this paper recommends mathematics teachers to make optimal use of diagnostic and reflective tests to guide them in identifying students alternative geometric vocabulary, conceptual and terminology misunderstandings in learning geometry. The discovery of students’ alternative geometric vocabulary, conceptual and terminology misunderstandings can help mathematics teachers to design intervention activities that allow the enhancement of students’: self-exploration of geometric ideas, geometric language proficiency, geometric concepts and terminology.

Keywords:

Reflective test, mathematical terminology, geometric concepts, language proficiency, diagnostic test.