Academic journal article Asian Social Science

The Teaching of Geometric (Isometric) Transformations at Secondary School Level: What Approach to Use and Why?

Academic journal article Asian Social Science

The Teaching of Geometric (Isometric) Transformations at Secondary School Level: What Approach to Use and Why?

Article excerpt

Abstract

The topic of Geometric transformation is topic number 10 out of 11 topics on the national ordinary level mathematics syllabus. It involves both analytic and algebraic geometry. Analytic because it can be approached using the graphical perceptive, and algebraic because matrix theory can be applied. It requires learners to have a good grasp of a number of skills, the so called assumed knowledge. Thus Teachers of mathematics before designing, selecting and implementing a lesson, ought to understand the knowledge that their students already have (or do not have). This is because one mathematical topic depends on another, early strengths support later progress while earlier weaknesses compound into greater debility. Such information is extremely useful for planning instruction. Assumed knowledge base covers topics such as vectors, construction of shapes, symmetry, properties of shapes, Cartesian equations and graphs, similarity and congruency, etc. Because of such demands learners are found wanting especially where it involves deciding the type of transformation. It is thus the thrust of this paper to approach transformations first by using graphs. Such an approach may cause understanding and enjoyment amongst teachers and learners in the topic. This approach aims at exposing the student to real practical experiences with transformations. Brief synopses on issues of the subject content are provided.

Keywords: translation, reflection, rotation

(ProQuest: ... denotes formulae omitted.)

1. Introduction

Transformations are somewhat a difficulty topic of the ordinary level mathematics syllabus. It usually comes barely towards the end of the syllabus, and as such it is either skipped or hurriedly done by most teachers of mathematics. Students and teachers, both, exhibit serious shortcomings in their understanding of transformations. During a workshop which the author conducted with mathematics teachers in Mberengwa district, it emerged that Transformation as a topic gives teachers the least pleasure, yet it is considered important in supporting students' development of geometric and spatial thinking (Hollerbrands, 2008). In this workshop teachers voiced mixed feelings about how they handle the teaching of transformations. Some said they never attempt to teach it because they don't quite understand it, whilst others said they usually teach it when there is very little time leftto finish the syllabus resulting in a crush programme by teachers. However studies have revealed evidence suggesting that teaching geometric transformations is feasible and may have positive effects on students' learning of mathematics (Edwards, 1989).

With transformations, it appears problems encountered by the students are a result of lack of conceptual understanding and might also be a result of the teaching they experience in learning transformations. Nziramasanga commission (1999) lamented the poor state of mathematics instruction in Zimbabwe and averred that the problems of quality of mathematics instruction and learning are from diverse sources. The mathematics teacher, however, has fallen victim by being accused to be responsible for the low quality of student performance in our secondary schools (Curriculum Team Research report, 2010). Foster (2007) highlights that if students are taught abstract ideas without meaning, this might not develop their understanding. Teachers appear to have difficulties with their own content knowledge. If a concept becomes more sophisticated for the teacher, it frequently becomes a barrier to students' understanding. The O-level text books also fail to present the content in such an elaborate way that could provide sufficient room for students to develop relational knowledge (Nziramasanga commission, 1999).

Against such a background it has to be acknowledged that the article comes at an appropriate time, and that there is always much interest amongst the general public about standards of achievement in mathematics. …

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