Research methodology

A pilot study was carried out at one school prior to the actual fieldwork in this research. The school resembles the ones used in the research in terms of area where they are situated, child problems and teacher challenges in teaching mathematics. The purpose of the pilot study was to test the research instrument and gain more insight into the mathematics teaching problem.

The aim of conducting a pilot study was also to test if participants would be able to answer the interview questions as expected and to allow the researcher to re - phrase them where necessary and also note if the participants needed further clarification. The outcome of the pilot study indicated those questions that were not clear enough and these were paraphrased to enable the current participants to answer them appropriately. The qualitative method was selected as appropriate for this research for reasons explained below.

4.2.1 The qualitative method

McMillan and Schumacher (2010:320) describe qualitative research as an analysis of people’s individual and collective social actions, beliefs, thoughts and perceptions and are primarily concerned with understanding the social phenomena from the participant’s perspective in addition to this definition. Creswell (2010:56) charges that the aim of qualitative research studies is to engage in research that probes for a deeper understanding of a phenomenon rather than to search for causal relationships. Qualitative research sets out to penetrate the human understanding and the construction thereof.

The qualitative approach was used in this study to explore the views of Grade 3 teachers regarding challenges they faced when teaching Mathematics. The approach was followed because it is an approach that allows researchers to gain insight into the inner experience of participants, to determine how meanings are formed through culture, and to discover rather than test variables (White 2005:81 and Corbin and Strauss 2008:12).

As a researcher using the qualitative method, it is important to describe the context in which this study was conducted. According Terre Blanche (2001:271), in any qualitative study, the context was accepted in a naturalistic manner where a researcher was physically present. In the case of this research the contention is that it will be best for understanding children’s problems and teacher challenges in the teaching of mathematics. It would be best to visit the schools and observe teacher child interactions. Thus, this context is viewed as influencing both the participants and the data that was collected.

Merriam (2009:13) concurs with this view and adds that events could be understood adequately if they are seen within a context. Thus any context is unique and is characterised by a unique time, geographic setting, social and historical settings and that these aspects impact on both the researcher and the participants.

Babbie (2003:272) also states that the qualitative researcher has a preference in understanding events, actions, and processes in their context and adds that other writers refer to this as the contextualist or holistic research strategy of qualitative research. Thus, the qualitative researcher aims to describe and understand events within the concrete, natural context in which they occur. Therefore, it is only when one understands events against the background of the whole context and how this context confers the meaning to the events concerned, that one could truly claim to “understand” the events.

Since this research was about establishing how mathematics computations were taught, it became important to consider a study design that would best yield the desired answers. (Creswell 2010:78).

4.2.2 Study Design

Mouton (2006:55) defines design as a plan of how one intends conducting the research. According to his explanation, a research design focuses on the end product, formulates a research problem as a point of departure, and focuses on the logic of the research. Thus a research design ensures that there is a structure for the way in which data will be collected and analysed as well as the procedure to be followed.

David and Sutton (2004:133) and McMillan and Schumacher (2010:345) argue that the purpose of the research design is to provide a framework for the collection and analysis of data and to improve the validity of the study by examining the research problem. The present study was designed as a case study investigating which approach teachers used when they taught computations in mathematics. The rationale for the choice of the design would allow the researcher to focus closely on the issue at hand. The design would also make it possible to establish which aspects of mathematics teaching are problematic. Yin (2009:18) argues that a case study is used in order to understand a real-life phenomenon in depth; however, such understanding encompassed important

contextual conditions, because they are highly pertinent to the phenomenon of the study. Contextual issues in this study would be the learning environment, especially those classroom variables that are related to mathematics teaching. The case study was preferred because Baker (1999:321), McMillan and Schumacher (2010:344) and Creswell (2010:75) indicate, it could afford the researcher a better understanding of the problem.

Another important fact is that a case study has to do with a limited number of units of analysis (often only one) such as an individual, a group or institution, which are studied intensively, (Welman and Kruger 2001:105 and Creswell (2010:75). In this study, the units of study constitute the Grade 3 classes in the Foundation Phase of schools in Mamelodi Township in Tshwane South district.

The schools and teachers were selected according to the sampling procedure outlined below.