RESEARCH METHODOLOGY
3.5 RESEARCH INSTRUMENTS
In the quest for answers to the first two research questions, the study used the research instruments:
a) Questionnaires (for teachers),and b) Observation of lessons.
The remaining research questions, 3 and 4, were directly related to the learning of fraction division and the learner.To find answers to them, the study required the use of research methods that directly involved learners. Those methods were:
c) Experimentation, and d) Group interviews.
3.5.1 Questionnaires
Questionnaires (Appendix A) were administered to teachers to find out their perceptions on practical work and fraction division.This called for the inclusion of
questionnaire items directly linked to perceptions of practical work by teachers.
Although the questionnaire mostly consisted of closed items, eight items allowed for open-ended responses for teachers to express their opinions. This immediately rendered the questionnaire less structured. However, its use was justified by the suggestion that "If a site-specific case study is required, then qualitative, less structured, word-based and open-ended questionnaires may be more appropriate as they can capture the specificity of a particular situation" (Cohen et al., 2002, p.247).
This particular questionnaire, however, tried to find a balance between a highly structured questionnaire (with closed items only) and an unstructured questionnaire (open-ended items) to serve the purpose of the study, i.e. finding in-depth information about the effectiveness of practical work in the learning of fraction division. The questionnaire was designed, piloted and refined before the actual fieldwork. Inclusion of open-ended items was the product ofthese efforts. Teachers were given a week to complete the questionnaire. In line with ethical requirements, terms and conditions for their participation were fully explained to them in the company of the procedural letter of consent, which they signed and returned with completed questionnaires.
3.5.2 Observation
Teachers were observed teaching division of fractions to test assumptions on their practices. To capture unfolding events in depth, a semi-structured type of observation was deemed as suitable. According to Cohen et al (2000), a semi- structured observation has an agenda of issues of interest but gathers data in a far less pre-determined and systematic manner. This semi-structured character of the observation suited the qualitative nature of this study. The roleof the researcher was made clear to the teacher and his learners before the observation of lessons. At the
initial stage of the research (before the experimental stage) the most appropriate role of an observer was observer-as-participant. A definition of this role states that "The 'observer-as-participant', like the participant-as-observer, is known as a researcher to the group, and maybe has less extensive contact with the group" (Cohen, Manion &
Morris, 2000, p.310). Such a role allowed for the capture of events as they unfolded, with a special focus on what teachers did in relation to their practicesassumed in the motivation. This implied that while the observer had specific issues of interest, the observation process itself was open to events as they unfolded.
3.5.3 The Experiment
Finding reliable data on the effectiveness of practical work in fraction division required engagement of learners with practical activities to determine their effect on learners' learning. It entailed determining the difference in the understanding of fraction division between those learners who had been exposedto the use of practical work and those who had not. This required the study to take on an experimental shape at that particular stage. The most appropriate kind of experimentfor this study was the quasi-experimental design, regarded as the closest compromise of the true experiniental design. It is acknowledged that" ... often in educational research, it is simply not possible for investigators to undertake true experiments"(Cohen, Manion
& Morris, 2000, p.214). However, the salient and fundamental characteristics of an
experimental study are still prominent in the quasi-experimental study. They include:
(a) the experimental and control groups, (b) the treatment that the experimental group is exposed to (practical activities), (c) the pre-test and post-test that both groups undertake before and after the treatment to determine the difference it has made in the experimental group. The formation of the two groups was discussed under sampling. The treatment was the use of practical work in the division of
fractions. This came in the form of worksheets with exercises on the practical division of fractions, which the treatment group had to work on. Exercises included the use'of a drawing ruler and sets of bottle-tops. Both ~roups wrote a pre-test and post-test (see Appendices C and D) before and after the treatment to measure levels of performance.These tests were set in accordance with the requirements of testing for research purposes. Since they were designed for a specific group, these tests of a non-parametric nature (Cohen et al., 2000) were designed by the researcher. The tests focused on three basic categories:
a) Fraction identification (multiple choice items)
b) Fraction representation (shading appropriate fraction parts),and c) Division of fractions.
With the subject domain clearly prescribed, the tests were domain-referenced. A domain-referenced test was defined by Cohen et al (2000) as one where: (a) considerable significance is accorded to meticulous specification of content to be assessed,and (b) the domain is the particular field or area of the subject that is being tested. By virtue of seeking to establish whether learners could carry out the tasks listed above, the tests required learners to meet certain criteria and were therefore criterion-referenced. Bentley & Malvern (1983) defined criterion-referencing as testing where performance is measured against a description or model and judged as worthy or otherwise by how it matches that description. With learners expected to match specific response standards and models, both tests fitted into this category of testing. The normal duration for each test was 30 minutes to any average learner. But for purposes of removing time constraints as possible impediments to a true reflection of learners' abilities, learners were given I hour to write each test.
3.5.4 Interviews
After exposing learners from the experimental group to division of fractions by practical means,and evaluating each group's performance, the investigation focused on the views of learners about their experiences with practical work. Interviewees were drawn from the experimental group that had experience with the practical division of fractions.The interview was a group interview. The size of the group was six members drawn across the spectrum of performance levels.Included in the group were below average,average and above average learners. Post-test performance was used as the basis for the selection of interviewees. Areas that the interview focused on included the benefits and challenges, if any, that learners experienced with the practical division of fractions. The interview sought to find out learners' preferences between the two modes of fraction division that they had been exposed to Le. the ruler (part whole) and bottle-tops (subsets). General comments by learners were also catered for.