Assessing First Year Pre-service Teachers' Geometric Reasoning Ability on Two-Dimensional Shapes (1 - 12)

Abstract

Geometry serves both as an essential instructional tool in mathematics and a visualizing medium for regulating theoretical and real world constructs. Every mathematics teacher must be adequately equipped with the ways of understanding and thinking of the subject matter required to teach geometry. Relevantly, development of the underlying geometrical reasoning is often subject to the overarching concept of two-dimensional geometric shapes. The purpose of this study is to examine the first-year pre-service undergraduates’ reasoning ability about triangles and quadrilaterals. 140 second-semester undergraduates in lecture setting were given a standardized geometry test, namely the van Hiele Geometric Test (VHGT) which contains 20 multiple-choice questions. A descriptive analysis of the dichotomous data was conducted using SPSS and Winstep programs. The findings suggested that among those pre-service teachers, (a) at least 7.1% performed under the basic, visualization level, (b) at most 5.0% attained the required abstraction level, and (c) the rest belongs to group whose analysis level ability remained largely undifferentiated from the aspect of criterion used. This study indicated that reconstruction and reevaluation of textbook content may foster awareness towards rethinking about teachers’ own mathematical dispositions. By collectively or individually challenging their old belief structure, it is hoped that they could realize the epistemic value of having the shapes and its properties be related to each other as well as gaining ownership of such reconstructions of the concepts.