DATA COLLECTION INSTRUMENTS

Babbie (2004, p. 113), states that “a research design should bring more than one research method to bear on the topic”. To avoid such weaknesses (De Vos, Strydom, Fouché, & Delport, 2005, p.

296), the study made use of semi-structured, teacher and learner interviews (Appendix B and E) to gain a detailed picture of teachers’ methodological beliefs on the importance of and approaches to implementing critical thinking in a mathematic class. The rest of the instruments consisted mainly of learners’ written assessments (Appendix A), field notes, as well as audio recordings of learners’ interviews which addressed how they went about solving word problems. Data was then analysed to determine the effectiveness of teachers’ critical thinking implementation (Appendix D) through the problem-solving techniques of learners in assessment scripts.

According to McMillan and Schumacher (2001, p. 42) , field observations are thorough images of people, and objects within a setting. Data was collected through the written assessments of learners, and teachers were observed in their classrooms, which enabled precise and in-depth analysis of data needed for the study to be successful. Making use of multiple methods facilitated the corroboration of the responses and the data collected, and therefore enhances the validity,

reliability, and accuracy of the data. Data was collected over a period of 10 weeks including a week at the beginning and the end for the post-learners respectively.

3.4.1 Teacher interviews

Interviews can be described as a means of exploring core issues quickly and in-depth (Simons, 2009, pp. 35-36). Interviews provide opportunities to ask follow-up questions and probe motivations. The study started with teacher interviews to record teachers understanding of critical thinking. Two Grade 3 teachers were selected from the sample schools to partake in this case study.

3.4.2 Lesson observations

Following teacher interviews, lesson presentations were observed for a week to identify the various ways in which they promoted critical thinking and enabled learners to solve mathematical problems. This included how lesson objectives were determined, whether teaching occurred through questioning, whether the objectives were practiced with learners before the teacher assessed whether learners grasped the objectives, if the educator reviewed, refined, and improved learners’ understandings, and lastly whether the educator provided feedback and checked for understanding by assessment of learning at the end of the lesson.

3.4.3 Learner Assessments

Learners’ assessments scripts were analysed to identify the various problem-solving skills that they used when writing the assessment. According to Lai (2011), learners’ prior content knowledge is vital but not enough to promote critical thoughts in a subject. The purpose of the assessment was to identify whether learners were on the same SEAL and LFNI levels, with the same mathematical background knowledge before identifying if teachers one and two effectively employed strategies which promote effective critical thinking skills , as well as an indication of how effective the teachers’ implementation of critical thinking during their teaching was (Giannakopoulos & Luneta, 2015).

The nine learners’ written assessments, per teacher, were collected during the data collection period and analysed to determine how the various techniques critical thinking inculcation within teachers’ lessons supported Grade 3 learners in mathematical problem-solving. To maintain anonymity, learners were labelled as Table 3.2 indicates.

Table 3.2 Learner labels

Ability Groups Teacher 1 Teacher 2

Learner Learner labelled as Learner Learner labelled as:

Above Average (AA)

Learner 1 Learner 1.1 Learner 1 Learner 2.1

Learner 2 Learner 1.2 Learner 2 Learner 2.2

Learner 3 Learner 1.3 Learner 3 Learner 2.3

Average (A)

Learner 4 Learner 1.4 Learner 4 Learner 2.4

Learner 5 Learner 1.5 Learner 5 Learner 2.5

Learner 6 Learner 1.6 Learner 6 Learner 2.6

Below Average (BA)

Learner 7 Learner 1.7 Learner 7 Learner 2.7

Learner 8 Learner 1.8 Learner 8 Learner 2.8

Learner 9 Learner 1.9 Learner 9 Learner 2.9

3.4.4 Learner interviews

Nine learners were purposively selected, based on their abilities in previous, assessments and individually interviewed. The nine learners represented the different mathematical ability groups.

Three learners were selected from the above average ability group; three learners each from the average and three from the below average ability groups. The sample of learners were selected based on varying levels of success in solving word problems in the math assessment to obtain a variety of learners’ assessment work. The purpose of the interviews was for learners to explain the various strategies they had used when solving the problems of the assessment. The verbal explanations of their strategies and solutions were compared to their written strategies. The

interviews helped to gauge learners’ understanding of problems because learners verbally explained their strategies.

This process spanned school terms: Data was collected from the beginning of one school term since the normal teaching and learning program of the school was considered and included time for assessments and related interventions. Several public holidays fell within the data collection period.

3.4.5 Audio recordings

Teachers’ and learners’ interviews were recorded throughout the data collection period. Audio-recordings were made of teachers’ and learners’ responses to interview questions.

3.4.6 Field notes

Field notes capture what is occurring without commenting on or judging an act where no interpretations are made (Yin, 2009). Field notes used in this study include scripting dialogue and conversation during interviews and classroom observations. Field notes were used to capture teacher’s methodology in their lessons; as well how learners used different types of methods in mathematics. In this study, field notes captured the preferences learners had towards using different types of problem solving methods, if any.

3.5 SITE AND SAMPLING