Learners’ written work

In the case of this research study, the learners’ written tasks were in the form of journals and work done on paper. The types of writing tasks included writing to solve mathematical problems, writing to record (keeping a journal or log), writing to explain, writing about thinking and learning processes, and shared writing.

According to Swanborn (2010:73), the advantage of documents, in this case the learners’ written work, is that they provide a stable source of data: they are outside the researcher’s influence. Rule and John (2011:67) suggest that the documents may prompt important questions which could be pursued further in interviews. In this study, learners’ written work during the pre-test was used to select eight learners to be interviewed. The interview questions (Appendix H) referred to the writing these learners used when they solved mathematical problems of the pre-test. However, disadvantages of this data collection instrument include a biased selectivity as well as the possible bias of the researcher herself (Yin, 2003:86). As the teacher of the selected class, the researcher had to be aware of selecting learners based on their use of writing in the pre-test, considering their mathematical abilities and not their literacy abilities.

The eight learners’ written work was collected over the duration of the data collection period when they engaged in various writing tasks. Written work was analysed to determine how writing tasks supported Grade 3 learners in mathematical problem-solving. Added to this, the mathematical problems learners solved during the pre-test and post-test were included as part of this data collection instrument.

3.5.2 Audio-recordings

In this study, audio-recordings were made throughout the data collection period since all the learners in the class engaged with writing to solve mathematical problems. Learners solved differentiated problems (listed in Appendix G) according to the mathematical ability group of which they were a part. They were given time to solve the problems and write their solutions and explanations in their journals. The different ability groups discussed their solutions and strategies on the carpet while the rest of the learners continued working on their solutions or completed other mathematics activities. Audio-recordings were made of the ability group

discussions. It was decided that audio-recordings would be beneficial as an instrument for collecting data because it may not have been possible to capture as much of the discussions as possible through taking field notes alone. Additionally, audio-recordings were inconspicuous (Creswell, 2014:192) since they allowed learners to explain their strategies and participate in discussions more freely. Learners were not as distracted by the audio- recordings as they would have been had field notes been made during the discussions. The use of audio-recordings allowed facilitation of the group discussions: it was not necessary to take field notes during discussions. The audio-recordings were transcribed, coded and analysed.

3.5.3 Field notes

Dana & Yendol-Hoppey (2009:74) explain that field notes capture what is occurring without commenting on or judging a particular act where no interpretations are made. Particular forms of field notes used in this study include scripting dialogue and conversation during the ability group discussions as well as when learners worked collaboratively in pairs. Field notes were used to record what learners were doing at particular times. How learners used different types of writing tasks in mathematics was noted. In this study, field notes captured the preferences learners had towards using different types of writing tasks, if any, and how writing can support mathematical problem-solving.

3.5.4 Interviews

Simons (2009:43) describes interviews as a means of exploring core issues quickly and in- depth. Interviews provide opportunities to ask follow-up questions and probe motivations. As a data collection method, “interviews can be time consuming to arrange, carry out and to analyse and yet interviews can also provide some of the richest data” (Hamilton & Corbett- Whittier, 2013:104).

The eight Grade 3 learners selected in this study were interviewed individually regarding their use of writing and how it influences and supports their thinking when solving mathematical problems. They were interviewed on two occasions. They were first interviewed after the pre-test and again after the post-test. Interviews were semi-structured with a flexible list of questions and key themes (Appendix H). Silverman (2011:162) highlights the skills needed to conduct semi-structured interviews as probing, rapport with the interviewee and understanding the aims of the study. As the teacher of the selected Grade 3 class, the

care had to be taken not to influence their responses in a particular direction. The interview questions related to specific writing episodes the learners experienced during the pre-test and the post-test. Olsen (2012:33) explains the use of questions and prompts in semi- structured interviews: both need to be planned in advance. Learners were selected based on their use of writing during the pre-test, so their strategies were considered in the planning of possible prompts. Interviews were audio-recorded to ensure that analysis of interviews was not limited; rather that data were captured in their entirety. Interviews were transcribed, coded and analysed. This process is elaborated upon during discussion of the data analysis of this study.

3.6 DATA ANALYSIS

The process of analysing data makes sense of what has been collected. Rule and John (2011:75) state that the “key research questions…developed at the start of the study should serve as a guiding force in the analysis process”. Data collected for this study were explored in relation to the research questions stated below.

Research question:

How do various types of writing tasks support Grade 3 learners in solving mathematical problems?

Sub-questions:

1. What support do writing tasks give to the development of conceptual understanding? 2. What support do writing tasks give to the development of problem-solving strategies? 3. How are writing tasks useful in the Foundation Phase mathematics classroom? 4. What challenges do learners experience when writing in the Foundation Phase

mathematics classroom?

A four step approach to analysis of data was used: description, sense making, interpretation and implications which are commonly used in case studies (Dana & Yendol-Hoppey, 2009:120). This process enabled management of data analysis. The steps of description and sense making were used to organize and prepare the data for interpretation (Rule & John, 2011:76).

3.6.1 Description

Audio-recordings of the group discussions as well as interviews with the eight Grade 3 learners were transcribed in preparation for data analysis. Olsen (2012:39) describes

transcription as “writing down or typing out the text of an interview or other sound file”. Pseudonyms were used during transcription in order to maintain participants’ anonymity. Olsen (2012:35) adds that transcripts enable the researcher to have “insight into mechanisms, processes, reasons for actions, and social structures as well as many other phenomena”. Once data were organized and prepared, data were read and re-read to develop a descriptive sense of what was happening, describe initial insights and reflect on the overall meaning (Creswell, 2014:197). In doing so, empirical information was converted into a description of the data in order to draw meaning from them (Henning, 2004:6).