Reflections on the introduction of Algebra in Grade 8 : a teacher's perspective
This dissertation looks at the early learning of algebra from a classroom teacher's perspective. There are three aspects that inform the topic: the actual classroom, the literature on beginning algebra and a sample of some of the current textbooks used in South Africa. From my reflections on my own teaching of a Grade 8 class, I was able to identify those definitions and beliefs about algebra which were shaping my teaching. Based on the literature I classified the approach to algebra that I was foregrounding in my classroom. I saw that this traditional methodology was limiting the scope of my students' outlook on algebra. I discovered more approaches to the early learning of algebra which could broaden my students' view of the subject This dissertation presents the followmg four approaches to introducing algebra: generalisation; problem solving; modeling and functions. The traditional approach is discussed as a part of generalisation. My research shows that elements of all of these approaches need to be included when introducing algebra. Often the approach to algebra is largely determined by the choice of textbook used. My analysis shows that many widely used textbooks tend to emphasise only one of the above four approaches. The dissertation notes the mistakes that are typically made by following each approach in addition to the haphazard errors made by students who are starting to learn algebra. Further light on the mistakes made by students is given by looking at how standard algebraic symbols developed over centunes of time. A teacher who is aware of the processes of her students learning algebra should be able to see beyond the mistakes that are made. She should encourage the learning of algebra as giving a broad conception of its disciplines and applications, and not as a narrow set of prescribed learned manipulations.
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