What is a Literature review and what is its purpose?

Fraenkel, Wallen and Hyun (1993) define a literature review as a critical analysis of identified documents containing information related to a specific research study. The literature reviewed is identified and analyzed from documents like articles, books, conference proceedings and journals to provide the researcher with a description, summaries and descriptions of what other researchers have done in line with the research problem that needs to be investigated. The purpose of reading this literature is for the researcher to see what has been done, what needs to be done and what gaps needs to be filled in line with what the researcher intends to research on. By reviewing the literature, the researcher is able to identify new and similar ways and to shed light on any gaps or similarities from what other researchers have already done. A good literature review will enable the researcher to support and justify the reasons for studying a particular area using the literature that is already available in research education.

For these reasons, a literature review of studies related to learner errors and misconceptions will help me review and relate these to my research since the area of focus is also on learner errors and misconceptions. Literature on the use and the influence of use of ICT in the learning and teaching of mathematics will also be reviewed and reported on to provide a link and a justification on why ICT should be used to address learner errors and misconceptions in the mathematics classroom.

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In reviewing the literature, it is important that in this research I establish the concepts and the theories that supports and inform my study, hence a conceptual framework and a theoretical framework influencing my study will thus be outlined. Concepts and theories influencing my choice of research will be outlined as they help show the readers how I, as the researcher choose to see the world in general and then more specifically, how I choose to view the research problem I intend to investigate. Liehr and Smith (1999), define a theory as “a set of interrelated concepts, which structure a systematic view of phenomena” p.8. Thus a theory describes some observations on the basis of some prescribed model. In other words, a theory will give a clear picture of the events it seeks to explain within a given frame. Chinn and Krammer(1999) see concepts as those parts of a theory. This then means that a theoretical framework is the frame the researchers chooses to guide them researches, while a conceptual framework allows the researcher to choose those parts in the theory that should guide one’s research (Imenda, 2014). For Evans (2007), there is no difference between a conceptual and a theoretical framework, as these two serve the same purpose. They both serve guide the researcher by showing how a research fits into what has already been established and to show how the research will contribute to the topic at large respectively (Maxwell, 2005),

My intention is to find out learner’s reasoning for their errors and misconceptions on Functions; hence, my focus will be on individuals’ construction of knowledge. I will enquire into learner’s current thinking processes based on what they would have constructed through their experiences in the classroom and through other learning processes. Although there might be some uniqueness in the learners’ individual constructions, it is also very possible for learners to share the same modes of thought. For these reasons, constructivism for me, will provide me with the most appropriate and compatible ways to study learner cognition under these conditions. For the purpose of this study, I will define the theories that guide my study, but in so doing, I will also specify the particular concepts within those theories that will shape my investigation.

This literature review, will “serve as the driving force and the jumping off point” for my own research investigation (Ridley, 2008). I will use the literature to further supports why the problem I have identified is an important problem in mathematics education to be investigated. Iwill also illustrate using literature, the gap that needs to be filled from previous research and to

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justify why there is need for that gap to be filled. It is important in my literature review to look at research on errors and misconceptions in mathematics in general, before coming down to algebra and ultimately functions. I will also review literature on teaching interventions in general as well as interventions using ICT. In so doing, the learning theories will provide for me the lens that I will use to explain and understand my literature in the context of this study. However, it is possible for the lenses to draw certain areas closer to the eye while ignoring other aspects, hence, for this reason it is might not be easy to find a theory that accommodates every aspect about learning functions in this study (Makonye, 2010). My investigation will thus be informed by the following theoretical frameworks: constructivism, socio-cultural theories, variation theory and the technological pedagogic content knowledge theory; the concepts in those theories that direct my study will also be differentiated within the theories as now outlined below.