paper in terms of context to examine whether performance varied across the different contexts.
4.3 DOCUMENT ANALYSIS OF THE 2009 GRADE 12 TRIAL EXAMINATION
The table below summarises the data from the above table.
Type of Contexts Mark Allocated % of total % with full marks
% with zero marks
% with part marks
Context Free 18 12% 48.9 32.3 18.9
Real 18 12% 34.6 56.9 8.4
Cleaned 52 34.7% 37.2 45.3 17.5
Parable 26 17.3% 37.0 42.5 20.5
Contrived 36 24% 28.3 50.4 21.3
TOTAL 150 100% 37.2% 45.5% 17.3%
Table 4.4(b): Summary of performance based on types of contextual questions.
In classifying the contexts as one of the five types, I discovered that it is not always a clear- cut process. For each of these categories, I discuss some considerations when doing the classification.
Context Free:
Although question 1 began with a scenario, question 1.1 did not require the scenario to perform the conversions. Hence, I classified question 1.1 as context free.
Real:
Real contexts should have a source or the source should be able to be found. I classified question 4.1 as real, as it was based on the growth chart. Although the source was not acknowledged, the chart itself is real and is provided by clinics and hospitals. It belonged to a child called Peter Brown who is a fictitious person. Nevertheless, the chart itself was real.
Cleaned:
Questions 2.1; 2.2 and 4.2 were classified as a cleaned context. Question 2.1 was based on the scenario of the soccer World Cup. The 2010 World Cup was a real phenomenon in South Africa at the time. Stadiums were being built, workers were being employed to build the stadiums, and target dates for completion were set. However, the number of workers required to complete the stadium may be questionable. Therefore I classified this scenario as a cleaned context.
Question 2.2 dealt with matches played, goals scored and the log table. It is true that in the World Cup round robins are played before the knockout stages. It is true that teams are awarded 3 points for a win, 1 for a draw and zero for a loss. These are real. However, the
teams who are playing each other and the goals scored are invented. The proposed scoring by the fanatics is invented but NOT inappropriate to the scenario. I therefore classified this question as a cleaned context.
Question 4.2 dealt with statistics on infant mortality between 2004 and 2008 due to different illnesses. Had a source been acknowledged, the context could have been a real context.
Nevertheless the context is a real situation in South Africa with a high rate of infant mortality as well as HIV/Aids, Polio, Measles and Hep-B. The actual number of babies who died, however, cannot be confirmed without a source. Hence I classified it as a cleaned context.
Parable:
Questions 1.3; 3.3 and 5.3 were classified as parables. Question 1.3 is a fictitious context. A worker, John had been invented. He worked for an unnamed employer and earned an amount that had been made up in order to test some mathematics, particularly percentages.
Question 3.3 centres on the context of a bank (Standard Bank) that offers two types of accounts (SUM1 and ACHEIVER), and their respective fee structure in tabular form. The fee structure is not real and therefore cannot be a real context. The achiever account, for example, offers free deposits and withdrawals yet the context indicates otherwise. Thus the context is fictitious with the intent of testing the percentage of an amount and manipulating transactions.
Contrived:
Questions 3.1; 3.2; 5.1 and 5.2 were classifies as contrived contexts. Question 3.1 was based on a contrived scenario about Sipho and Themba looking after cows on a farm and earning pocket money. The context has been invented to test aspects of ratio in mathematics.
Question 3.2 is an extension of the scenario in 3.1, with Themba having to milk 10 cows and carry and empty the bucket into a bigger container in the farmer’s house. The time taken to milk the cow is invented, the dimensions of the bucket is invented to test capacity and volume. I therefore classified this question as contrived.
Questions 5.1 and 5.2 are about deciding to buy CDs at three possible shops as well as investing money to buy a CD player. Both these questions are contrived. The names of the
shops are invented and so too are the prices of CD players and the discounts on them. The amount received by the younger brother for passing Grade 10 was invented, as well as the number of years invested. The contrived context functioned to test percentages, discounts, and compound interest. I classified these questions as contrived contexts.
More than a third of the examination paper comprised of cleaned contexts. Context free question and real context questions were at a minimum, with each comprising 12% of the paper. It is understandable that context free questions should be at a minimum since this is the second paper in mathematical literacy. Questions in the second paper comprise more of levels 3 and 4 questions with very few level 1 and 2 questions, which are allocated to paper 1.
Twenty-four percent of the paper is based on contrived contexts with the remaining 17.3%
parables.
Detailed marking of the learners’ scripts indicates that learners performed best when questions were not embedded in a context. The worst performance involved contexts that were real, with 56.9% of learners not being able to score any marks. Contrived contexts also posed problems to learners with only 28% of learners being able to score full marks. It is possible that learners were not able to relate to questions that were made up and that they had no meaning for them. Almost 40% of learners were able to score full marks with respect to cleaned contexts, perhaps because the contexts were cleaned so that the questions became accessible to the learners in terms of the language used, the figures given and the provision of additional information such as formulae. Another reason in this case could be that these contexts were based on real events (the World Cup and infant mortality), and hence learners are able to relate to them. Very few learners (8.4%) scored part marks for questions based on real context (most either got full marks or zero), indicating that when it came to questions based on real contexts, learners either understood them or were not able to understand these questions at all. To establish when language was a determining factor for success in questions rooted in real context, I attempted to compare the performance in question 4.1 (classified as real context) across English first and English second language learners, reflected in the table below as a percentage of the class.
To examine the language issue, I thought I would first compare the performance of English First and Second language learners across all the questions and thereafter look at question 4.1, which I classified as real-life context, in isolation. Since Paper 2 consisted predominantly of
questions embedded in context, I compared the final average mark obtained by English First and Second language learners. The table below summarises the information.
English First Language Learners
English Second Language Learners
Female 50% 33%
Male 45% 39%
Total 48% 36%
Table 4.5: Average marks obtained by English First and Second Language males and females
An independent sample t-test was performed to compare the performance of the English first language (Indian) and second language (African) speakers. There was a statistically significant difference in scores between the Indian students (M= 47.98; SD= 4.91) and the African students (M =35.22; SD= 15.02), with t(71) = -3.621 and p = 0.01, two–tailed with both English First language males and females performed significantly better than their English Second language peers in the examination task. The fact that the total average of English First language learners was 48% means that they also must have struggled with the questions in the examination task. A qualitative analysis based on the learners’ responses in their answer scripts and the subsequent interviews (presented in Chapter 5), will perhaps elucidate this aspect.
The table below summarises the performance of learners in Q4.1 according to whether English is a first or second language.
% with full marks
% with zero marks
% with part marks
English First Language (Indians) 35.7 54.0 10.3
English Second Language
(Africans) 32.3 63.4 4.3
Table 4.6: Average Performance of English First and Second language learners on questions based on real contexts.
The above table shows no significant difference between English First and English Second language learners who obtained full marks for this particular contextually based question, implying that language was not a barrier to learners who “understood” the context. It would be interesting to know how many of the 32.3% of English second language learners, who obtained full marks in the real-life contextually based questions, had studied in an English
medium school from inception, and thus had a better command of the English language, compared with the 63.4% of English second language learners who scored zero.