CHAPTER 4: DATA ANALYSIS

The discussion in the previous chapter focuses on research methods and techniques used to collect data for the study. This discussion entailed a mixed method research, hence data collection strategies, site selection, sampling, credibility, a pilot study and ethical issues were based on both qualitative and quantitative paradigms. This chapter discusses how data were analysed and presented. Data were collected, processed and analysed in response to the problems posed in chapter one. Two fundamental research questions guided data collection goals and subsequently data analysis. These goals were to explore the difficulties learners and teachers experience with mathematics symbols during teaching and learning and the possible instructional strategies to mitigate the effects of symbolic obstacles.

Data Analysis 4.1

The researcher presents the findings resulting from an exploration of difficulties learners and teachers experience with mathematical symbols during teaching and learning. Data were gathered from two main of sources: questionnaires and interviews. Additional data were collected by compiling field notes during the observation with comments written after the field. In addition, discussions in the interviews were recorded with a digital voice recorder. The formal conversational focus group interviews were mainly conducted between the researcher and learners with interview scripts. Due to time constraints, learners at each grade level were engaged in focus group interviews. Focus group interviews are used when it is better to obtain information from a group rather than individuals (Gill et al, 2008). Focus group interviews were chosen as they can reveal a lot of detailed information and deep insight since several perspectives about the same topic can be drawn from the group participants simultaneously. The researcher created a conducive discussion environment where participants were ease to discuss their views, allowing then to respond to questions in their own words and add meaning to their answers. The benefits of focus group interviews research include gaining insights into participants’ shared understandings of the phenomena (Anderson, 2010). The group sizes were restricted to a maximum of 12 learners, which was deemed large enough to generate rich discussions. The responses of learners were audio recorded and transcribed.

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4.2

The analysis of data in this study follows mainly a qualitative approach. The aim of using a qualitative approach is to uncover hidden details of a phenomenon and understand the big picture by using the data to describe the phenomenon and what it means (Cassidy et al, 2011). Qualitative data analysis strategies for fall into three main groups: Categorising strategies such as coding and thematic analysis; connecting strategies (such as narrative analysis and individual case studies); and memoranda and displays (Maxwell, 2005). These methods can be combined. The strategies used to analyse the data in this study were inductive analysis “bottom up” (Braun & Clarke, 2006), and typological “top down” (deductive) analysis (Buckley, Halbesleben & Wheele, 2015). The use of inductive analysis is to code the data without fitting it into a pre-existing coding frame, or the researcher’s analytic pre-conceptions, themes identified are strongly linked to the data themselves. This type of analysis is derived from the collected data.

Typological (deductive) analysis on the other hand involves splitting the data set into several groups or categories based on pre-determined categories which are generated from theory, common sense, and research objectives (Hsieh and Shannon, 2005). A topological analysis is normally driven by the researcher’s theoretical or analytic interest in the area. This was the case after obtaining preliminary results from the closed- ended questions. The research utilised interviews that were analysed using typological analysis. The researcher was careful in order to avoid bias in the whole analysis process as the coding framework has been decided in advance, thus severely limiting theme and theory development. Furthermore, the use of typological analysis usually blinds the researcher from looking into other important dimensions in the data. This weakness was counter- balanced by the use of inductive analysis that analyses actual data without taking a predetermined theory into consideration. This approach is deemed comprehensive and most suitable when there is little prior knowledge about the phenomenon of interest (Ghauri & Grønhaug, 2005).

Inductive Analysis 4.3

Inductive analysis is a data processing approach that uses raw data to derive concepts, categories and themes (Bernauer, Lichtman, Jacobs & Robinson, 2013). This inductive procedure for analysing qualitative data is guided by specific objectives that are

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determined by the researcher in advance (Thomas, 2003). The main reason for selecting inductive approach is that it allows research findings to emerge from frequently occurring responses inherent in raw data. Furthermore, the approach is not affected by the restraints as in structured methodologies. Structured methodologies use a formal methodical approach to the analysis and design of information systems. To carry out inductive analysis data were scanned for categories and relationships among those categories were further grouped into typologies, allowing themes to emerge from the data (Scruggs, Mastropieri & McDuffie, 2007). The main idea was to allow research findings to emerge from the frequent, dominant or significant themes inherent in raw data, without the restraints imposed by structured methodologies. The benefit of utilising induction analysis is that key themes, which are often obscured, reframed or left invisible because of the preconceptions in the data collection and data analysis procedures, can emerge. An inductive approach helps to understand meanings of complex data by developing a summary of themes from the raw data (data reduction). Inductive analysis was used to derive nodes from closed questions that were later envisaged using focus group interviews.

Transcription of verbal data 4.4

Verbal data collected from group interviews with learners and individual teacher interviews, was transcribed from the voice recorder into written form in order to conduct a thematic analysis. Transcription is the first step towards familiarisation with the data (Hart, Brannan & De Chesnay, 2014). Bird (2009) also argues that the process of transcription should be taken as:

“…a key phase of data analysis within interpretative qualitative methodology and recognised as an interpretative act, where meanings are created, rather than simply translating spoken words into written statements”(p.227).

Green, Franquiz, and Dixon (1997) also interpreted interview transcripts as a form of data. They focused mainly on their constructed quality and echoed the following sentiments:

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“…. a transcript is a text that “re”-presents an event; it is not the event itself. Following this logic, what is re-presented is data constructed by a researcher for a particular purpose, not just talk written down”. (p. 172)

This study utilised thematic analysis to analyse transcribed data. The researcher read the transcripts several times to locate categories and later uses these categories to extract broad themes. The researcher developed a coding frame that was used to code the transcripts. If new codes emerged, the coding frame was changed and the transcripts were reread according to the new structure. This process was used to develop categories, which were then conceptualized into broad themes afterwards. The themes were categorized. The researcher checks the transcripts against the original audio recordings for accuracy in order to ensure the validity of the data.

Coding 4.5

Codes were used to organise and sort data. Coding involves combining the data for themes, ideas and categories. This is done by marking similar passages of text with a code label or code so that they can easily be retrieved at a later stage for further comparison and analysis. Coding allows the researcher to mark the data, in such a way that it becomes easier to search the data, to make comparisons and to identify any patterns that require further investigation (Taylor & Gibbs, 2010). Codes were used to develop to label or identify issues raised by learners about their encounters with mathematical symbols. Codes also assisted in compiling and organising data. The coding becomes the basis for developing the analysis. It is generally understood, then, that “coding is analysis”. The codes for this study were derived from keywords, ideas and concepts raised by participants as recommended by Ryan and Bernard (2003b). The researchers read learners’ texts and identify passages, phrases and keywords that were judged to represent the same, theme or concept and assigned to a code.

The identified codes were assigned names that give an indication of the idea or concept that underpins the theme or category. Any part of the data that relates to a code topic was appropriately labelled. This process of coding involves close reading of the text. If a theme is identified from, the data that does not quite fit the codes already existing then a

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new code is created. As the researcher read participants’ responses, new codes evolved and grew as more topics or themes become apparent.

The Coding Process

The coding process was derived from two basic sources: a-priori ideas from literature review, pre-existing theories and those that emerge from the data set during analysis (grounded theory). Research questions that were addressed by the study and issues from the interview schedule also informed the coding process. The researcher used his knowledge of mathematics, classroom experience and subject expertise in creating the codes.