CURRICULAR ANALYSES

4.3.1 The concept

In order to analyse any relationships between the results of prior learning variables such as NSC in Mathematics (papers 1, 2 and 3), the NBT in Mathematics, the APM examination and first-year university Mathematics examinations, it was important to be familiar with the curricula assessed in each of these examinations. For this purpose the

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research method of document analysis was used. Document analysis is an analytical method that is used in research on narrative data to gain an understanding of the trends and patterns that emerge from the data (Creswell & Plano Clark, 2007). The analytical procedure entails finding, selecting, appraising (making sense of), and synthesising data contained in documents (Labuschagne, 2003).

Document analysis involves skimming (superficial examination), reading (thorough examination) and interpretation (Bowen, 2009). It requires a systematic and critical examination, rather than a mere description of an instructional document such as a curriculum (Edwards, 2010).

Within the holistic approach, which is the hallmark of the FraIM that underpins this study, the document analysis was used in combination with other research methods, i.e. statistical interpretation of the numerical data and observations made from the narrative data. The researcher attempted to provide a convergence of evidence that breeds ‘credibility'. The advantage of examining data collected through different methods was that the researcher could strengthen findings across data sets and thus “reduce the impact of potential biases towards a specific method, a single source or a single investigator’s opinion” (Bowen, 2009; Patton, 1990).

4.3.2 The sample documents

Plowright (2011, p. 110) describes an artefact, in this study the curriculum, as a “means of encoding or expressing information, knowledge and understanding, in order to make these accessible to and usable by the participants involved in the process”. All the artefacts are imbedded in a particular discourse domain, which is located in one or more specific contexts. The artefacts analysed in this study were the curriculum documents on Mathematics in the South African context. These are the National Curriculum Statement for Mathematics, the Independent Examination Board (IEB) curriculum statement for APM, and the curricula for Mathematics 114, Mathematics 115, Mathematics 144 and Mathematics 145 as described in the 2013 yearbook of the Science Faculty at the SU.

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As these curricula all have common characteristics, the researcher performed coding and category construction, based on the data characteristics, to uncover themes pertinent to the curricula (Bowen, 2009).

The approach used for the analyses of the curricula was derived from a revised Bloom’s taxonomy of educational objectives (Berger, Bowie & Nyaumwe, 2010; Krathwohl, 2002) and had two dimensions, namely content and cognitive demand.

As an introduction the researcher first gave an overview of the curricula of the NSC Mathematics and APM, as well as the first-year Mathematics 114, 115, 144 and 145 at SU. Then the nature of the two prior learning curricula, i.e. those of NSC in Mathematics and APM, were compared by stating their definitions and looking for similarities and differences. The content of all the different curricula was subsequently summarised to detect any overlaps between the respective curricula and specifically to determine the position of the content of the APM course in relationship to the other courses.

Before analysing the cognitive demands of each curriculum, a comparison between the NSC Mathematics and APM curricula was made in terms of examination mark totals, time allocation and comparability with international curricula. Then the learning outcomes were stated. The verbs used to describe what a learner must be able to do were used as keywords or codes to classify the learning outcomes or objectives into different cognitive levels according to the revised Bloom’s taxonomy of educational objective. This taxonomy was represented in a two-way table with the knowledge dimension on the vertical axis of the table and the cognitive process dimension on the horizontal axis. Every learning outcome or objective was classified in one or more cells formed by the intersections of the knowledge and cognitive processes. The cognitive categories were remember, understand, apply, analyse, evaluate and create (Liang & Yuan, 2008), while the knowledge categories were factual knowledge, conceptual knowledge, procedural knowledge and metacognitive knowledge (Krathwohl, 2002). This method clarified the different skills specified in each curriculum.

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To identify the skills required in the different examination papers, the taxonomical differentiation of the Grade 12 papers was analysed according to the taxonomy of categories of mathematical demand, as suggested in the 1999 Trends in International Mathematics and Science Study Mathematics survey, which includes four cognitive levels. This was done in order to determine the emphasis of each curriculum in terms of the cognitive levels knowledge, routine procedures, complex procedures and problem solving. The final analysis in this section was an analysis of the verbs used in each of the questions to describe the skills required in the different examinations.

4.3.4 Ethical issues

The researcher aspired to demonstrate objectivity (seeking to represent the outcome of the analysis fairly) and sensitivity (responding to even subtle cues to meaning) in the selection and analysis of data from the curricula (Bowen, 2009). As the subjective interpreter of data contained in the documents, the researcher aspired to make the process of analysis as rigorous and as transparent as possible.