Data collection

The researcher used primary and secondary written sources of data. Primary sources of data are original records of events and experiences, as seen through the eyes of and as interpreted by the researcher. Primary sources of data allowed the researcher to be as close as possible to what actually happened. Examples of such include past examination question papers, and marking scheme.

Secondary sources of data are derived sources written by people who did not experience the event first hand. Secondary data sources can also be defined as existing data collected at an earlier time by a different person who had a different purpose (Johnson & Christensen, 2011) for example, examination reports. Official

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documents, such as past examination question papers, past examination marking schemes, curriculum guides, and examination reports were the major sources of data in this research.

3.4.1 Schedule for analysing the mathematization of real-life situations

The schedule for analysing the mathematization of real-life situations was developed by the researcher as informed by the theory of authentic task situations. It was based on contextual subjects, theme, significance, horizontal mathematization, vertical mathematization and the eight crucial aspects of the theory of authentic task situations (see section 2.2). This schedule has twelve columns. The number of rows depends on the number of contextual word-problems included in the given question paper (see Appendix 3.1.1 – 3.1.24).

The first column indicates the examination body, the year, the month, and the relevant paper (Paper 1 or Paper 2). The second column indicates the quantity of marks and the level of the contextual word-problem under consideration. A contextual word-problem that is exclusively solved through horizontal mathematization is a level-1 contextual word-problem. A contextual word-problem which is exclusively solved through vertical mathematization is a level-2 contextual word-problem. A contextual word problem that is solved through progressive mathematization is a level-3 contextual word-problem. The third column identifies the theme of the relevant contextual word-problem. The fourth column indicates the contextual subject of the given contextual word-problem.

Columns five to twelve present the eight crucial aspects of real-world problems. The fifth column indicates whether the event described in the contextual word-problem has taken place, or if it has a fair chance of occurring, or if it cannot take place in the real world. The sixth column indicates whether or not the question posed in the contextual word-problem has a fair chance of being asked in a real-world situation. The seventh column indicates the existence, as well as both the realism and specificity of the information presented in the contextual word-problem.

The eighth column indicates the way the task is conveyed to students in terms of mode and language. The ninth column indicates the role and purpose of someone solving the task in terms of availability and expanded plausibility. The tenth column

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mentions factors in the social context. These include the availability of external tools, guidance, consultation and collaboration, discussion opportunities, time, and implications of the success or failure to solve the task. The eleventh column indicates solution requirements. The twelfth column indicates the purpose in the figurative context.

It must be noted that one schedule for analysing the mathematization of real-life situations was completed for each question paper. One schedule was devoted to each 2008-2013 past examination question paper. Consequently, a total of twenty four schedules for analysing the mathematization of real-life situations were completed: twelve for IEB and twelve for NSC. Tables 3.1.1 to 3.1.24, in the appendix, illustrate data collected using the schedule for analysing the mathematization of real-life situations included in past IEB and NSC examination question papers.

3.4.2 Schedule for the total marks of contextual word-problems and national performance

The schedule for the total marks of contextual word-problems and national performance was developed, by the researcher, from the total marks of contextual word-problems included in past examination question papers and the national mathematics pass rate. One schedule for the total marks of contextual word- problems and national performance was completed for both IEB and NSC examinations.

The abovementioned schedule has five columns and seven rows. The first column indicates the year. The second column shows the total marks of IEB contextual word-problems for each year. The third column indicates the IEB national performance for each year. The fourth column provides the total marks of NSC contextual word-problems for each year. The fifth column provides the NSC national pass rate for each year.

The first row presents column headings. The second row indicates the year 2008. The third row represents the year 2009. The fourth row shows the year 2010. The fifth row indicates the year 2011. The sixth row represents the year 2012. The seventh row indicates the year 2013. The eighth row shows the totals. Finally, the

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ninth row indicates the averages. Table 3.2 shows the rows and columns of the schedule for the total marks of contextual word-problems and national performance. Table 3.2 shows the relationship between total marks allocated to contextual word problems and national performance.

Table 3.2: Schedule for the total marks of contextual word-problems and national performance

Year Total marks of contextual word-problems (IEB) National pass rate (IEB) Total marks of contextual word-problems (NSC) National pass rate (NSC) 2008 115 95.8 66 45.7 2009 104 95.5 98 46 2010 101 96.3 77 47.4 2011 74 96.6 65 46,3 2012 54 96.9 91 54 2013 61 96.8 76 59.1 Total 509 577.9 473 298.5 Average 84.8 96.3 78,8 49.8

(This schedule was developed by the researcher)