Pre-and post-tests

As noted earlier, the pre-test was divided into three sections with a total of five tasks (or questions), namely: Problem-solving (PS) tasks (three tasks), one task each under Real- life mathematical word problems without real meaning (PWRM), and Real-life mathematical word problems without real context (PWRC) sections respectively. The questions used in the test were adapted from Verschaffel, et.al. (2009) and satisfy the assessment standards as reflected in the South African National Curriculum Statement (NCS). The questions are standardised, criterion-referenced measures of problem-solving skills with proven reliability and validity devised and verified (Maxwell, 1992).

Apart from producing a numeric solution, learners were asked to write down the solution process and/or some explanations for each problem-solving (PS) task. Learners‘ answers to the three PS tasks were coded using a schema that was an elaboration of the classification schema developed by Verschaffel, et al. (1994). The classification schema comprised fourteen categories, but for the purpose of this study, the categories were reduced to three general categories:

 Realistic reaction (RR): comprises all cases wherein a learner either gave the (most) correct numerical solution that also took into account the real-world aspects of the problem context, as well as cases wherein there was a clear indication that the learner tried to take into account these real-world aspects, without giving the mathematically and situationally (most) accurate numerical answer. The realistic reaction responses give a clear picture of the abilities of

learners to make sense (or meaning making) of the problem statement in their solution processes.

 Other reaction (OR): all those cases without any indication that the learner was aware of the realistic modelling difficulty, for example, mathematically correct but situationally inaccurate and/or incorrect or inappropriate responses, computational errors, etc. This category also provides a measure of the word problem-solving abilities of the learners.

 No reaction (NR): are all cases wherein a learner did not provide a numerical response and did not give any further written comment that indicated that the learner was aware of the realistic modelling difficulty that prevented them from answering the problem, as well as instances where learners generated incorrect responses with mathematical (or computational) errors.

The purpose of the pre-test was to help the researcher establish how the learners use language, and the problems they experience, when solving mathematics word problems prepared in isiXhosa, learners‘ home language and English, language of learning and teaching. Moreover, it assists the researcher to identify problems they may have mathematically (how they go about solving the problem) and situationally in response tasks with real-world contexts. The post-test investigates if there are any changes after the treatment on the experimental group, and possibly why there are changes.

6.2.2. Semi-structured interviews

The researcher conducted interviews in two different sub-phases: the focus group learner interview of six participants, who were purposefully selected by the teacher and learners - one from each school. The researcher, at this stage, did not have measurable

qualitative constructs, and therefore, used the interview responses to analyse inductively the emerging real-life constructs.

The open-ended unstructured and semi-structured interviews, which are described below, were then undertaken to clarify and understand issues emerging from the pre-test results. Both the teachers and learners were purposefully selected by the researcher and his assistants after capturing the results of the pre-tests. The following questions were asked:

 If the same thing happens to you, would you respond in the same way in

real life as you did in solving the problem? Why?

 Your solution may not work in real life because of realistic considerations.

Why did you answer that way?

 Please think about on what condition your answer could become realistic.

Could you come up with any assumptions or explanations that can make your answers justifiable?

 Do you think the contexts used in the content of tasks (or problems) that

you solved in the pre-test are familiar and/or relevant to your everyday life experiences? Why?

Issues of language of learning and teaching, language spoken at home, language in mathematics and word problem-solving, addressed in this study, form the basis of the research questions and sub-questions (Creswell & Plano Clark, 2007). The open-ended interview questions were also used to measure the extent at which the language policy in their schools influences their current practice regarding the use of languages in their multilingual mathematics classes. The questions were as follow:

Teacher Level

 Which language(s) do you use to support communication in your classroom

and why?

 Which language do you prefer to use when clarifying concepts that are being

taught in the classroom? Why?

 Which language do learners use as a resource in order to understand word

problem-solving? Why?

 Do you provide learners with opportunities to talk, discuss, argue and engage

in dialogue when you teach? How?

 Which language do you mostly use to teach word problem-solving? Why?

 Which language is actually the Language of Learning and Teaching (LoLT) in

mathematics at your school? Why?

Learner Level

 Which language do you use to communicate in your classroom? Why?

 Which language (s) do you prefer to use when you solve word problems?

Why?

 What problems do you usually have when understanding and solving word

problems?

 What difficulties did you experience when solving word problems in isiXhosa

test? What about English test? Why?

 Which language will you choose for your assessments (e.g., tests and

examinations)? Why?

The interview process was divided into two levels: teacher and learner questions as the researcher wanted to distinguish between and compare the perceptions of the two groups of participants so that the results of the survey could guide and influence the planning of the intervention for (or treatment on) the experimental group. Interview responses were sorted into themes that are discussed in the qualitative results section of this study. The reasons that were provided by both teachers and learners on their personal language preferences and/or choices were analysed qualitatively. A classroom observation schedule was also used to triangulate the qualitative data gathered from interviews, and is described in the next sub- section.