Sense making or coding

The next step, sense making, is referred to as coding. According to Cohen and Manion (1994:286), coding is the “translation of question responses and respondent information to specific categories for the purpose of analysis”. Rule and John (2011:77) refer to the use of codes as labels that are assigned to different themes or foci within the data. Moreover, Dana and Yendol-Hoppey (2009:118) refer to Schwandt’s definition of coding as “a procedure that disaggregates the data, breaks it down into manageable segments and identifies or names those segments”. Coding is “a database of connections between various terms and data items selected from among the whole basket of evidence” (Olsen, 2012:46). This understanding of the process of coding guided this part of the analysis process.

There are various steps to coding data including determining the size of text segments, developing a list of codes for basic retrieval and then detailed retrieval (Olsen, 2012:80). For the purpose of this study, data were coded using ATLAS.ti, a computer-assisted qualitative data analysis programme.

“Computer packages allow the user to store notes about the definition of their codes and to retrieve segments of data that have been assigned different codes, allowing you to gather together all instances of a particular code in order to compare these” (Barbour, 2014:262). ATLAS.ti proved a useful tool which provided a comprehensive overview of large amounts of text in the form of the learners’ written work as well as transcriptions of audio-recordings and interviews (Henning, 2004:126). Although computer-assisted analysis was used in this study, it remained the primary responsibility of the researcher in ensuring systematic, thorough analysis of the data (Barbour, 2014:260).

about them, and then coming up with insightful results” (Friese, 2014:12). Referring to NCT analysis, Friese (2014:13) describes noticing things as “the process of finding interesting things in the data…and nam(ing) them”. In this study, as patterns were noticed in the data, they were assigned or attached to codes. The codes were largely determined before data were collected in order to provide a provisional coding frame for the data analysis. These codes developed from the relevant literature read in this field of research. The codes were established to attempt to answer the research questions of this study. The provisional coding frame included: representations of mathematical problems, demonstration of understanding through writing, individual writing and collaborative writing, the use of prompts when writing, the use of specific topics to develop writing and conceptual understanding, the usefulness of Burns’s types of writing in a South African context and the development or change in learners’ abilities to solve mathematical problems. However, these codes were adapted and additional codes considered while data were analysed. Barbour (2014:260) adds that one moves “back and forth between provisional and revised coding frames and transcripts or coded extracts in order to interrogate themes and build up explanations”. Codes were developed deductively before data collection and inductively during data analysis. Some codes were merged into themes for the purpose of addressing the research questions in the findings and discussion in chapters 4 and 5 while others became themes on their own. Themes were used to search for a detailed description of the use of writing when solving mathematical problems (Creswell, 2014:199).

Barbour (2014: 278) argues theoretical frameworks that inform data analysis are often “referenced in terms of guiding the general approach taken in research, in formulating the questions to be asked and in determining what counts as ‘data’”. In this study, the theoretical framework largely concerned social constructivism since learners participated in collaborative work and group discussions where they engaged with the teacher and their peers. Through social constructivism, learners developed their mathematical problem-solving abilities in their ZPD’s through the introduction and implementation of various writing tasks. Scaffolding was used to assist learners while they developed their use of writing in mathematics. Through encountering the writing tasks, learners’ procedural knowledge and conceptual knowledge were drawn upon and developed. According to Thorn (2000:68), this theoretical lens determines how the researcher approaches and collects data which is relevant in answering the research questions so that raw data can be transformed to depict the focus of the study.

As discussed in the literature review in chapter 2, the Learning Framework in Number (LFIN) incorporates the Stages of Early Arithmetical Learning (SEAL), the Structuring Number Strand (SNS), conceptual place value and early multiplication and division (Wright, Martland

& Stafford, 2006). The LFIN, in conjunction with the theoretical framework, was used to guide the process of data analysis. Using the different stages and levels of the various components of LFIN, the researcher analysed the strategies that learners employed when solving mathematical problems, particularly when analysing their strategies in the pre-test and post-test. The LFIN supplied clear indicators of the stage or level of strategies that were used in the pre-test when compared to the post-test. This process made it possible to gauge what developments or changes there were in learners’ strategies when solving mathematical problems.