CHAPTER ONE STUDY BACKGROUND
- Introduction
I loved grade ten algebra. I’ve never been more sure
About the world and my place in the world Than I was in grade ten math class.
I teased out intricate equations With unknowns of x and y,
And glowed with the confident knowledge I could always find the correct answers
In the back of the book.
(Poem by Leggo, 2008:187, in response to Skovsmose, (2008:168) )
The learner in the above poem loved grade ten algebra because he could “tease out intricate equations with unknowns of x and y.” Is this all there is to grade ten algebra? The grade ten math class described sounds like a mysterious place where one performs tricks of seemingly no value as the answers were printed at the back of the book. The learner’s confidence depends on this knowledge. The learner appreciates the opportunity for self-evaluation because he can find the answers in the back of the book. It seems as though the learner has little understanding about what is actually taking place and is consequently denied the opportunity to learn algebra meaningfully. The educator is absent from the poem and the textbook is the only authority recognized, especially as it confirms his learning. It is possible that this is the kind of learner who is independent and frequently works out problems on his own during the mathematics lessons. The learner’s situation must be understood in the context of the view that education is a multilevel, complex and highly contextualized system (Gau, 1997). The question to ask is to what extent is this learner’s experience and practice typical of most grade ten learners?
Motivation
My interest is in studying curriculum in general and the learning and teaching of secondary school mathematics in particular. Within the subject of mathematics, algebra is of special concern. Early on in my teaching career, I realized that algebra plays an important role in the general performance of learners of mathematics. Consequently, I often used an algebra test to select students for any advanced level mathematics course. These days I teach in an education system where the screening of learners on the grounds of performance in algebra is neither desirable nor permitted. I am motivated to provide opportunities to learn (OTL) mathematics to all our learners.
Though the term OTL will be explained in greater detail in the chapters that follow, it is appropriate to refer to it as an ideal for the learning situation. As a concept in education OTL can help in the pursuit of good practice in the learning and teaching situation because it takes into consideration all stakeholders, from those who make decisions about what is to be taught, those who implement it, to the learner and the supporting materials available to all. For this reason, I wished to better understand how groups of grade ten learners comprehend and learn algebra, an important section of mathematics. Three secondary Catholic schools in South Africa were identified in which this study could take place. Many questions were posed, for example, what opportunities does the system provide to actually develop competence in this area of mathematics?
Algebra is one of the main branches of mathematics to which learners are gradually exposed throughout high school. It is described as a generalized form of arithmetic where symbols, letters and signs are used in place of or together with numbers. These symbols have different meanings and interpretations in different situations. Many students seem to have different perceptions about these symbols, letters and signs and this affects their understanding of the mathematics involved. In South Africa for example, within the Further Education and Training (FET) band (Grades 10-12), as part of Learning Outcome 2 (Functions and Algebra), learners are expected to multiply, factorize, and simplify different algebraic expressions up to and including trinomials, solve linear equations, quadratic equations by factorisation,
exponential equations of the form kax+p = m, linear inequalities in one variable and illustrate the solution graphically, and linear equations in two variables simultaneously (numerically, algebraically and graphically) (Department of Education, 2005). This suggests a skills-based perspective on algebra.
