Abstract
Background: Gifted learners are South Africa’s future leaders and investment in the skills of disadvantaged learners would benefit the country.
Objectives: This study investigated whether Olympiad participation could develop problem-solving skills in mathematically gifted disadvantaged learners.
Methods: The methodology of the study was quantitative. A total of 100 mathematically gifted Grade 7 learners from two quintile two schools in the same disadvantaged area of South Africa were exposed either to Olympiad-style questions (South African Mathematics Challenge past papers), or traditional Department of Education worksheets. Five aspects of Study Orientation, including problem-solving behaviour, were assessed using the Study Orientation in Mathematics (SOM) before and after the intervention.
Results: The findings revealed a correlation between success in traditional mathematics and study attitude, study habits, and overall study orientation, as well as an interaction between disadvantage and success in mathematics. The intervention did not increase problem-solving skills. Participants found the Olympiad-type questions unfamiliar and difficult, which is indicative of the limited enrichment opportunities for mathematically gifted learners in disadvantaged areas of South Africa.
Conclusion: Poverty and giftedness were shown to interact: the gifted disadvantaged learners in this study were less disadvantaged by their surroundings than one would expect and conversely had higher mathematics anxiety than expected for their achievement level.
Contribution: This study highlights the need to nurture the skills of mathematically gifted disadvantaged children.
Keywords: mathematically gifted; gifted disadvantaged; problem-solving skills; mathematics Olympiad; South Africa.
Introduction
Gifted disadvantaged learners in South Africa
Gifted children are South Africa’s future leaders, scientists and researchers. Gifted children in South Africa are typically ‘undervalued and under-served’ (Van der Westhuizen, 2007, p. 1), particularly disadvantaged children, who do not have access to quality education. According to Statistics South Africa (2017), 66.8% of children aged 0–17 in South Africa were living below the upper-bound poverty line (UBPL) in 2015. Definitions of giftedness vary from 2% to 5% of the population, which means that roughly 260 000 to 650 000 children in South Africa have untapped potential as both gifted and disadvantaged.
Education potentially facilitates an escape from a poverty ‘trap’ in South Africa: only 8.4% of adults with higher education are living below the UBPL compared with 79.2% of those with no education and 69.2% of those with only primary school education (Statistics South Africa, 2017). In South Africa, the Department of Basic Education categorises schools according to quintiles or fifths of the population, based on the poverty level of the communities surrounding the schools, with quintile 1 being the poorest, and quintile 5 the richest (Murray, 2017). Quintile 1–3 schools are non-fee-paying. For the purpose of this study, a child attending a non-fee-paying school was defined as disadvantaged. Van Broekhuizen et al. (2016) found that:
[W]hile attending a quintile 1–3 school largely precludes learners from gaining access to university, those who do make it into university tend to perform almost on par with their quintile 4 and 5 counterparts. (p. 66)
This finding implies that investment in the skills of gifted disadvantaged learners at school level (resulting in more learners entering university) would pay off with more university passes.
Identification of the gifted in South Africa
Many difficulties are associated with intelligence testing in multilingual and multicultural countries with widely varying access to education (such as South Africa). The country has 11 official languages, namely English, Afrikaans, and nine African languages (Jordan, 2015; Maree et al., 2011). Although English is the dominant language in business and government in South Africa, 76.9% of the population speaks an African language as a home language (Jordan, 2015). Intelligence quotient (IQ) tests available for African language speakers in South Africa are limited. The New South African Individual Scale (NSAIS) (1962) was translated into isiXhosa in 1988, and from there into four other African languages, and normed on black children from 9 to 19 years of age (Mayaba, 2016). These translations of a 1962 test remain the only IQ tests available in these languages. The Junior South African Individual Scale (JSAIS) (Madge, 1981) was translated into isiZulu and SeSotho in 2010 (Mawila, 2012). However, these versions are not yet commercially available (Health Professions Council of South Africa, 2017). Van Eeden published studies in 1993 and 1997 on black children attending private and former white schools, who were educated in English and took the Senior South African Individual Scale Revised (SSAIS-R) (Van Eeden, 1991) in English. She concluded that norms for environmentally disadvantaged learners should be used when evaluating children whose home language is not the testing language (Cockcroft, 2013).
Non-verbal tests, such as the Raven’s Standard Progressive Matrices (SPM), the Naglieri Non-Verbal Ability Test (NNAT) and Form 6 of the Cognitive Abilities Test (COGAT) are often suggested as a culture- or language-fair option for use in multicultural and multilingual societies such as South Africa (Laher & Cockcroft, 2017; Sarouphim, 2009). However, Lohman and Gambrell (2012) found a 7.3 and 9.5 point difference in scores between first- and second-language English speakers and that ‘reducing the language demands may actually increase the cultural loading of the test’ (Lohman, 2013, p. 274). In South Africa, studies by Israel (2006) and Knowles (2008) found substantial language bias in the Raven’s Advanced Progressive Matrices (RAPM) and RPM. Similar results have been found in Zambia and Kenya (Maree 2018).
Problem-solving skills in South Africa
Problem-solving skills are higher-level, creative skills. These skills are beneficial at university and in the workplace (Griesel & Parker, 2009). Good problem-solvers have meta-cognition developed through problem-solving experience (Nieuwoudt, 2015). Mathematics competitions expose learners to problem solving (Engelbrecht & Mwambakana, 2016). Various mathematics competitions are open to learners in South Africa. Most of these competitions are free or have free entry for learners from no-fee schools (South African Mathematics Foundation [SAMF], 2020b; University of Cape Town, 2019; University of Pretoria, 2019; University of Witwatersrand, 2019). There are also several free Olympiad training programmes provided by the SAMF, namely the Siyanqoba training and SAMF Olympiad training (Grades 7–12) (SAMF, 2020a). The South African (SA) Mathematics Challenge is the biggest of these Olympiads for Grades 4–7 learners, with 80 000 learners having participated in 2019 (SAMF, 2020b).
South African learners lack problem-solving strategies and skills, and mathematics textbooks used in South African schools use routine problems (Chirove & Mogari, 2014). The general level of problem-solving skills at school level in South Africa is demonstrated in South Africa’s performance in the Trends in International Mathematics and Science Study (TIMSS), which ‘assesses a range of problem-solving situations within mathematics, with about two-thirds of the items requiring students to use applying and reasoning skills’ (Grønmo et al., 2013). South Africa came in second-last in mathematics (Business Tech, 2016). Additionally, in South Africa, not only learners but also teachers find non-routine problems difficult (Chirove & Mogari, 2014). In a study by Govender (2014b), 14 second-year trainee teachers wrote the Grade 7 SA Mathematics Challenge. Only 28.7% of the trainee teachers scored over 60% (the score required for a Grade 7 learner to progress to the second round of the Olympiad). South African Mathematics teachers even lack basic skills: Venkat and Spaull (2015) found that 79% of South African Grade 6 Mathematics teachers were classified as having content knowledge levels below Grade 6. Maree and Erasmus (2006) stress the need for informal mathematics learning to develop problem-solving skills. This is hard to achieve in a country where parents work long hours and have low levels of mathematics education themselves. Even South Africa’s best performers in the TIMSS did poorly in problem solving (Long & Wendt, 2017).
Rationale for the study
Mhlolo (2015, p. 166) identifies mathematical competence as ‘the key to the welfare of a nation in a global economy’ and warns of two groups that are in high risk of not realising their full potential: mathematically gifted children and economically disadvantaged children. Research in South Africa has largely neglected mathematically gifted disadvantaged children (Stones, 2020). Although there is extensive research on mathematics education in South Africa, ‘little research has been done on the impact and efficiency of mathematics olympiads’ (Engelbrecht & Mwambakana, 2016, p. 2). There was a gap at the intersection of these two areas of research, namely gifted disadvantaged children and the impact of mathematics Olympiads. There have been no studies on the potential benefits of the SA Mathematics Challenge or Olympiad for gifted disadvantaged children (Stones, 2020). This research aims to fill this gap in the body of knowledge on giftedness.
Research questions
The purpose of this study was to examine the possible effects of Olympiad participation on gifted disadvantaged children, particularly to explore whether Olympiad participation could develop problem-solving skills in mathematically gifted learners from disadvantaged schools. The primary research question was as follows: How valuable is participation in the SA Mathematics Challenge for developing problem-solving skills in mathematically gifted disadvantaged learners? This gave rise to the following secondary research questions:
- What are the essential aspects of current (group-based) programmes aimed at enhancing the problem-solving skills of mathematically gifted learners in disadvantaged schools?
- What is the impact of 3 h-long facilitated sessions doing SA Mathematics Challenge past papers on mathematically gifted disadvantaged learners’ study orientation in mathematics in general?
- What is the impact of 3 h-long facilitated sessions doing SA Mathematics Challenge past papers on mathematically gifted disadvantaged learners’ problem-solving skills in particular?
Research methods and design
Research paradigm and design
This study was viewed through the lens of critical realism (Cruickshank, 2011). To examine matters from multiple cultural stances, research in a multicultural society needs to adapt from a Eurocentric view. The advantage of the pragmatic prism to one’s lens is the emphasis on the practical: research does not have to reach an ideal that might be unattainable to contribute to the body of knowledge on gifted education in South Africa, or to benefit gifted disadvantaged children. The methodological approach of the study was quantitative.
As shown in Figure 1, the study utilised a non-equivalent comparison group design, which is a quasi-experimental version of the pretest-posttest comparison group design (Engel & Shutt, 2014). There are two groups in a comparison group design, one of which receives the intervention and one that receives a different intervention. The disadvantage of comparison group design compared to using a traditional control group is that it is a comparison of interventions, rather than comparing an intervention against no intervention. However, it is generally accepted that it is right and ethical to offer both groups some benefit in the study (Maree & Pietersen, 2016).
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FIGURE 1: Non-equivalent comparison group design. |
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Sampling
Selection of schools
A two-step approach to sampling was used. Purposive sampling was used to select two large quintile 2 schools in the same township in Gauteng (Department of Basic Education, 2017). All schools in quintiles 1–3 are no-fee schools, so children attending them would be considered to be disadvantaged.
Selection of learners within the chosen schools
The participants were Grade 7 learners. Because of the limitations of IQ tests available in South Africa for black learners, an IQ test was not used for selection (Bouwer, 2014; Erasmos, 2013; Knowles, 2008; Maree, 2018; Mawila, 2012; Zygmont, 2006). Teacher identification could have been used, but giftedness is given little emphasis in teacher training in South Africa (Van der Westhuizen & Maree, 2006). Parent identification of the gifted is generally better than teacher identification (Daǧlioǧlu & Suveren, 2013; Gross, 1999). However, contact with parents in a quantitative study with large numbers of learners would have been impractical.
The study required that the learners have a sufficient grasp of the basic concepts of mathematics for their grade. It is impossible to access higher-level learning such as problem solving without a basic understanding of concepts (Johnson & Schmidt, 2006). Taking the issue of gifted identification together with the requirement for basic mastery of mathematical concepts, the learners’ mathematics marks were used to identify mathematically gifted learners. Therefore, for the purposes of this study, the definition of mathematically gifted was the top 50 of the grade by mathematics year mark at the end of Grade 6. The top 50 equated to the top 14.1% of the grade at the intervention school (355 learners) and the top 14.7% of the grade at the alternative intervention school (340 learners).
Data-gathering instruments
The Study Orientation for Mathematics (SOM) (Maree et al., 2011) was used as the pre-test and post-test. The SOM is designed for Grades 7–12 learners (Maree et al., 2011). Advantages of the SOM include that it was normed on learners from different language and socio-economic groups in South Africa (Maree et al., 2009), reliability and validity are highly satisfactory (Maree et al., 2011), it is quick to administer, and can be administered by a teacher rather than a psychologist (Maree, 2020).
The sub-tests of the SOM for Grades 7–9 learners consist of study attitude, mathematics anxiety, study habits, problem-solving behaviour (PSB), and study milieu. Study attitude (14 questions) covers the feelings and attitudes that learners have towards mathematics. Mathematics anxiety (14 questions) covers the degree to which the learners exhibit anxious behaviours. Study habits (17 questions) refers to consistent study habits such as practicing examples, learning theorems and doing assigned work diligently. Problem-Solving Behaviour (18 questions) includes the act of self-reflection when approaching problem solving in mathematics. Study Milieu (13 questions) highlights the impact of the socio-economic situation and home language versus the language of learning on learners.
The SOM was normed on 3013 Grades 8–11 learners at high schools across South Africa, and the Grades 8 and 9 norms were extended for Grade 7 learners (Maree et al., 2011). The samples in the initial study by Maree et al. (2011) were chosen randomly on three levels: the education department of the learner (which until only a few years previously had been racially segregated, and so could be used as a proxy for race), language of instruction, and area (urban or rural). This sampling resulted in a spread of race and language groups reflecting the general high school population, including black learners from disadvantaged urban schools such as the participants in this study.
The reliability and validity of the SOM are high. In the original study by Maree et al. (2011), the reliability coefficients for the different fields for African language learners who did the test in English (the same demographic as the learners in our study) ranged from 0.67 to 0.77, with the overall reliability of all the fields together at 0.89. Table 1 in the results section shows the pre-test dataset compared with the African language norm group from the original study.
| TABLE 1: Reliability coefficients for the different fields for the pre-test compared with the Study Orientation in Mathematics African languages norm group. |
The authors of the SOM tried to ensure the content validity of the SOM by reviewing the literature on the subject, getting experts to check the ordering and wording of questions, checking the item field correlations, and checking with experts whether all the important aspects of each item were included (Maree et al., 2011).
In terms of construct validity, study attitude correlated with study habits; study attitude correlated with problem-solving behaviour; study habits correlated with problem-solving behaviour, and mathematics anxiety correlated with study milieu (Maree et al., 2011). In addition, there was a low correlation between two distinct groupings of items. study habits, study attitude, and problem-solving behaviour combine to measure ‘academic behaviour in mathematics’ and mathematics anxiety and study milieu combined to measure ‘helplessness, anxiety and lack of control… in Mathematics’ (Maree et al., 2011, p. 45).
To test concurrent validity, Maree et al. (2011) compared the SOM to two existing tests, the Diagnostic Tests in Mathematical Language (DTML) and the Achievement Test in Mathematics (ATM) and all the items except Problem-Solving Behaviour correlated at the 1% level. Maree et al. (2011) speculate that the lack of correlation in this sub-test is because of the questions in the DTML and the ATM not requiring problem-solving skills to answer successfully, which far from being a drawback of the SOM, shows its unique benefit.
A study of the SOM in relation to school mathematics results in the Northern Cape province of South Africa found that for:
[B]oth genders and across all three race groups, the set of study orientation scales contributed significantly (at the 1% level) to the explanation of variance in mathematics achievement for Grade 9 learners. (Moodaley et al., 2006, p. 652)
These results show clear predictive validity for the SOM for white, black and so-called ‘coloured’ (mixed-race) learners in previously white schools.
Procedure
Intervention
The intervention consisted of 3 h-long facilitated sessions where the learners worked through past papers of the SA Mathematics Challenge for Grade 7 (SAMF, 2018). Because of the low problem-solving skills of mathematics teachers in South Africa (Chirove & Mogari, 2014; Govender, 2014b) and because of the success of Govender’s (2014b) study of the SA Mathematics Challenge without overt teaching of problem-solving skills, facilitation was kept to a minimum. The three past papers covered the first-round papers from 2013, 2014, and 2018. Figure 2 shows examples of questions in the intervention and the alternative intervention.
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FIGURE 2: Example questions from SA Mathematics Challenge intervention and the alternative intervention. |
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Learners in the intervention group completed on average 42.07 questions during the study, of which they got 8.85 correct (21%). Learners were encouraged to work in pairs and to discuss their answers but were also allowed to work alone if they preferred. Over 90% of learners in the intervention group chose to work in pairs. Learners were also encouraged to take home the past papers to complete at home. Six learners did this after each of the first two sessions (participants 6, 9, 10, 11, 22, and 42 after session 1 and participants 6, 9, 10, 11, 18, and 19 after session 2), and two (participants 18 and 19) after the last session.
After each session, the past papers were marked. However, to avoid emphasising scores rather than on the process of learning, these marks were not given to the learners. Instead, the following week, learners received an answer sheet printed from the SA Mathematics Challenge website, giving both the correct answer and a brief explanation. After the learners had been given the answer sheet, the primary researcher explained a selection of common mistakes.
Alternative intervention
The alternative intervention followed the same format as the intervention. Worksheets 1–6 from Mathematics in English Book 1: Grade 7 book 1 terms 1 and 2 (Department of Basic Education, 2018a) were used. Example questions are shown in Figure 2.
In contrast to the intervention group, fewer than 20% of the participants chose to work in pairs. Five learners took worksheets home after the first session and six after the second session, with three in common between the two sessions. There were far more questions in the alternative intervention worksheets than in the SA Mathematics Challenge worksheets because the questions were simple drill questions, rather than complex problem-solving questions. On average the participants in the alternative intervention completed 105.8 questions in total, compared with 42.07 in the SA Mathematics Challenge intervention. The average number of questions answered correctly was 87.23 (82%). Once again, after each session, the papers were marked, learners were given an answer sheet, and lastly, the primary researcher went over a few common errors on the board. The number of common errors was fewer than in the SA Mathematics Challenge intervention because the learners got fewer questions wrong than in the SA Mathematics Challenge past papers.
Ethical considerations
The ethics of this study were guided by the American Psychological Association’s (APAs) five general principles: beneficence and non-maleficence; fidelity and responsibility; integrity; justice; and respect for people’s rights (Elias & Theron, 2012). The study also conformed to the APA requirements for research, publication and assessment (American Psychological Association, 2017). Lastly, ethical clearance was required from the University of Pretoria and the Department of Basic Education, which included vetting of the study design and all letters sent to schools. Ethical clearance to conduct this study was obtained from the University of Pretoria Research Ethics Committee. (No. EP 18/06/01.
Rigour of the study
The study considered internal and external validity and reliability of the data. The following threats to internal validity were considered: history, maturation, instrumentation, testing, selection bias, mortality, contamination and treatment misidentification. To reduce the effect of history, the interventions ran just 13 days apart. Maturation was not a concern as the study was only 5 weeks in duration. The SOM is highly reliable (Maree et al., 2011) so instrumentation was not a problem. A testing disadvantage was that the pre- and post-tests were administered only 4 weeks apart, which could result in learners remembering what they answered the previous time, but this effect was assumed to be the same for both groups. Selection bias is usually countered by randomisation (Maree & Pietersen, 2016; Mertens, 2015). Because of the practicalities randomisation was not viable, so the schools were as closely matched as possible. In terms of mortality, there was a greater attrition rate at the intervention school than at the alternative intervention school. Contamination was avoided by not revealing to either school the other school taking part in the study. Also, although the schools were in the same overall area, they were not close to each other. Lastly, the primary researcher attempted to counter treatment misidentification by interacting with the alternative intervention group in the same manner as with the intervention group. The placebo effect applied to both groups, as participants, parents and teachers at both schools were aware of being chosen to participate in the study.
The factors influencing external validity include time, selection and setting (Creswell, 2014). As time passes, the results of the study could become less relevant. Because only two schools from the same area in Gauteng were selected for this study, it is not possible to generalise beyond this area, without replication of the study in other disadvantaged areas of the country. Lastly, as only one researcher was involved in the sessions, results may be bound by the setting. Only replication in other settings can counter this threat to external validity.
The reliability of quantitative data is the extent to which research findings or results from a test instrument can be replicated (Maree & Pietersen, 2016). As mentioned earlier, the reliability of the SOM has been established, and the reliability of the dataset for the study was examined in the data analysis.
Data analysis procedures
To check the reliability of the dataset from the study, Cronbach’s alphas were calculated on the pre-test dataset (Tavakol & Dennick, 2011), which consisted of all the participants who completed both the pre- and post-test (27 from the intervention group and 40 from the alternative intervention group). The pre-test dataset was compared with the African language learners in the original sample used for norming the SOM. As can be seen from Table 1, the reliability of this study’s sample compared well with the original sample. The PSB sub-test had a reliability of 0.78, which is above the acceptable cut-off of 0.7 (Muijs, 2004).
A demographic comparison was made of the two schools, comparing gender, age and home language. The Pearson’s chi-square test on the cross-tabulation of gender by school showed that gender distribution did not differ significantly between the two schools (p-value = 0.34). In both schools, there were many more girls than boys in the top 50 in the grade. The age range was from 11 to 14 years in the intervention group, and 11 to 13 years in the alternative intervention group. The median age for both groups was 12.00 years; the mean for the intervention group was 12.30 years (s.d. = 10.9 months), and for the alternative intervention group was 12.08 years (SD = 7.4 months). Because age was not normally distributed, the non-parametric Mann–Whitney U test was used to analyse the data (Mat Roni et al., 2020; Pietersen & Maree, 2016). There was no significant difference between the two school samples in terms of age (p-value = 0.35). The number of home languages was extensive, with all 11 official languages, and ‘other’, represented between the two schools. There was some difference in terms of the spread of language groups at the two schools, with the intervention group having more learners from the Sotho–Tswana language group, and the alternative intervention having more Nguni language speakers, but both groups could be described as African language speakers taking the SOM in English.
The Mann–Whitney U test, which is a non-parametric test used in place of an independent t-test for small or non-normal samples (Pietersen & Maree, 2016), was used to compare the Grade 6 marks for the two schools. The sample from the intervention school had a much broader range of marks (51% to 90%) than that of the alternative intervention school (58% to 84%), and the median of the intervention group (72%) was considerably higher than the alternative intervention group (65%). The mean for the intervention group was 71.26% (SD = 10.97) and the mean for the alternative intervention group was 66.28% (SD = 6.46). The distribution of Grade 6 marks was not the same across schools (p-value = 0.04).
Furthermore, the pre-tests of the SOM for the two schools were compared. Descriptive statistics were computed across the two schools and then a non-parametric test (Mann–Whitney U) was performed. These tests aimed to find out if the schools could be considered to be equivalent in terms of problem-solving skills before the interventions. The p-values greater than 0.05 were obtained for all three tests, across all fields of the SOM. This shows that before the intervention, the two groups can be considered to be on par in terms of all sub-tests of the SOM, and in terms of overall mathematics study orientation.
Results and discussion of findings
The main null hypothesis for the study was: There is no significant difference between the pre-test and post-test mean scores for the two groups. To evaluate this hypothesis, the change in the score of the PSB sub-test of the SOM from the pre-test to the post-test in both schools was examined.
Comparing pre- to post-test
A Related-Samples Wilcoxon Signed Rank Test was chosen as a non-parametric test to investigate whether there was a significant change from the pre- to the post-test in the intervention group (Maree & Pietersen, 2016). Particular emphasis was placed on the results for the PSB sub-test of the SOM, as this was being used to assess whether the SA Mathematics Challenge intervention had improved the participants’ problem-solving skills. The null hypothesis investigated was ‘the median of differences between SOM PSB post-test and SOM PSB pre-test equals 0’, with a one-sided alternative hypothesis. The median was chosen rather than the mean because the Wilcoxon Signed Rank Test, as a non-parametric test, utilises ordinal data (Mertens, 2015; Muijs, 2004). The significance of this test was 0.21, so there was no significant improvement in problem-solving skills from the SA Mathematics Challenge intervention, which was against expectations. There was also no significant improvement in problem-solving skills from the alternative intervention (p-value = 0.07).
The other sub-tests of the SOM were examined to see the impact of the interventions on the participants’ study orientation in mathematics in general. As can be seen from Table 2, there was no significant change in study orientation after the intervention, with minimal effect sizes for all sub-tests, and there was a significant change in study habits and overall study orientation in Mathematics, with small effect sizes, after the alternative intervention.
| TABLE 2: Related-Samples Wilcoxon Signed Rank results showing differences between pre- and post-tests of the Study Orientation for Mathematics. |
To investigate whether low mathematics skills were a limit to developing problem-solving skills, the authors examined the top stratum of study participants. To do this, the authors went back to the original sample and took the top 5% (17 learners) in each school. Then, learners who did not complete both the sessions of the SOM were excluded, leaving a sample of 12 learners (2 boys and 10 girls) from the intervention school and 14 learners (2 boys and 12 girls) from the alternative intervention school. The lowest Grade 6 mark in this sample was 74% at the intervention school and 68% at the other school. The 5% sample was less affected by the dropout rate at the intervention school than the larger sample. However, neither the intervention nor the alternative intervention resulted in a significant difference in problem-solving skills. The p-value for the 5% group at the intervention school was 0.36 and the p-value for the 5% group at the alternative school was 0.17.
Discussion of results
Problem-solving behaviour
Studies of problem solving in mathematics vary in their approach on a continuum from overtly teaching problem-solving strategies to the pure experience of problem solving. This study was on the experiential end of the spectrum, with no overt teaching of strategies and learners were not asked to formally categorise their problem-solving methods. For the SA Mathematics Challenge group, there was a very slight decrease in PSB from the pre-test to the post-test, with a negligible effect size, as shown in Table 2. The participants also did not improve their average marks from the first to the third session of the SA Mathematics Challenge past papers, which contrasts with Govender’s (2014b) study, where the in-service teachers improved their marks on the SA Mathematics Challenge after his intervention.
Problem-solving behaviour improved slightly from the pre- to the post-test for both the full alternative intervention group and the 5% sample. As can be seen in Table 2, there was a small effect size for the larger group and a negligible effect size for the 5% sample. This slight improvement in skills in a 3 h intervention correlates positively with the findings by Reder et al. (2020), Wang et al. (2017), and Gladwell (2008), who found that practice improves skills, but practice needs to be long term to have a significant effect.
Study attitude
Scores for the intervention group decreased slightly from the pre-test to the post-test, but the study attitude of the learners was still high, with participants scoring at the 80th percentile in study attitude compared with the Grades 8 and 9 norm group. The participants were above the 86th percentile of their class by mathematics achievement, so scoring at the 80th percentile is slightly less than expected. However, study attitude increases with age so these findings could be said to correlate with those of Maree et al. (2003, 2011) and Moodelay et al. (2006) that study attitude correlates positively with success in mathematics. In addition, as can be seen in Table 2, the learners in this study who were in the top 5% of the class scored higher in study attitude than those in the larger sample (top 14.1% of the class). This finding is also in line with the finding by Palomar-Lever and Victorio-Estrada (2017) that disadvantaged learners’ attitude towards school correlates positively with achievement at school, and findings by Maree et al. (2003, 2011) and Moodelay et al. (2006) that Study Attitude correlates positively with achievement in mathematics.
Like with the intervention group, the study attitude scores were high both before and after the alternative intervention, which is in line with research that correlates academic success positively with study attitude (Goodman et al., 2011; Heuser & Wang, 2017; Maree et al., 2003, 2011; Moodaley et al., 2006; Palomar-Lever & Victorio-Estrada, 2017).
Mathematics anxiety
People are more likely to persist with a task if they believe they can succeed at it (Pajares, 1996). Anxiety interferes with this self-belief. In the SOM, a high score in the mathematics anxiety sub-test indicates high confidence in mathematical ability or low mathematics anxiety. The scores of the intervention group decreased slightly between the pre- and post-test, indicating a slight increase in anxiety levels, with a negligible effect size. The mean mathematics anxiety score for both the pre- and post-test was at the 60th percentile, which indicates quite high anxiety for learners who were above the 86th percentile in mathematics achievement. The vast majority of the participants in both interventions were girls, and the literature has shown that gifted girls tend to underestimate their mathematical ability (Pajares, 1996). This relatively high level of anxiety in high-performing students contradicts the findings of Hart et al. (2016) and Lindskog et al. (2017), who found that mathematics anxiety is inversely related to success in mathematics. Conversely, the mathematics anxiety scores support the findings that educationally disadvantaged high school and university students in a rural area all experienced mathematics anxiety to some degree (Hlalele, 2012, 2019).
The mean score on the mathematics anxiety sub-test of the SOM increased (i.e. indicating an improvement in confidence in mathematics) slightly for the intervention participants, with a negligible effect size, as can be seen in Table 2. This finding contrasts with Newstead (1998), who found that discovery teaching methods result in higher levels of mathematics confidence. The worksheet content was traditional, and although the way that it was presented to the learners with minimal input from a teacher could be described as experiential, it was less experiential than the SA Mathematics Challenge intervention, as most learners chose to work alone.
Study habits
Study habits have been correlated with academic success (Maree, 2015; Maree & Ebersöhn, 2002; Moodaley et al., 2006; Sikhwari, 2016). The SA Mathematics Challenge intervention did not result in improved study habits for the participants. Scores in Study Habits decreased slightly from the pre- to the post-test, with a negligible effect size. However, the participants in this study were somewhat younger than the norm group, and study habits increase with age (Maree et al., 2009). Taking the younger age of the participants in the study into account, these findings could be said to agree with the findings of Maree et al. (2011).
Table 2 shows that there was a statistically significant improvement in the study habits scores from the pre- to the post-test for the alternative intervention participants, with a small effect size. There was also an increase in the study habits score for the alternative intervention 5% sample, although it was not statistically significant, with a small effect size. Studies correlating study habits and success (Maree, 2015; Maree & Ebersöhn, 2002; Moodaley et al., 2006; Onoshakpokaiye, 2015; Sikhwari, 2016) are concerned with better study habits resulting in success, rather than the other way round. But, if the mathematical practice of routine worksheets improves study habits, it could be part of the reason why practicing mathematical skills in a structured way improves academic success, as has been shown by the Kumon method (Usmadi et al., 2020). The other reason would be practicing a particular algorithm to develop automaticity (Department of Basic Education, 2018b).
Study milieu
The mean study milieu score for both the intervention group and the alternative intervention group was higher than the 20th to 40th percentile that one would expect considering the socio-economic area where the school was situated (see Table 2). This contradicts the findings that poverty is directly related to the standard of education (Nortje, 2017) and that there is a positive relationship between both school resources and academic success (Lemmon, 2017; Letsoalo et al., 2019) and family resources and academic success (Gaillard, 2019; Uleanya & Bunmi Omoniyi, 2019). However, various factors have been shown to protect disadvantaged children from the poverty trap, namely being identified as gifted (Bolland et al., 2019); good child-rearing methods (Lipina, 2016), a positive relationship with a teacher; support from family or the community (Williams et al., 2017); a positive attitude to school (Palomar-Lever & Victorio-Estrada, 2017), and having a goal on which to focus (Kotzé & Niemann, 2013). The learners from this study had been identified as gifted by their selection to the study, had above-average scores in study attitude, and may have had some of the other protective factors despite the poverty of their community. Taking the protective factors into account, these findings could be said to be in line with both the findings that there is a positive relationship between resources and academic success (Gaillard, 2019; Lemmon, 2017; Letsoalo et al., 2019; Uleanya & Bunmi Omoniyi, 2019) and the findings on protective factors mitigating the effects of poverty (Bolland et al., 2019; Palomar-Lever & Victorio-Estrada, 2017).
Overall study orientation
Overall study orientation in mathematics predicts success in Mathematics (Maree et al., 2009; 2011; Moodaley et al., 2006), Engineering (Maree et al., 2003) and Natural sciences (Maree, 2015). The SA Mathematics Challenge intervention did not improve overall study orientation in the participants, but the alternative intervention resulted in a statistically significant improvement in overall study orientation, with a small effect size, that can be seen in Table 2. The improvement in the 5% sample of the alternative intervention was smaller, although starting from a higher base. The available studies on study orientation did not investigate improvement in study orientation brought about by an intervention, but these findings did concur with the prior findings that a positive study orientation in mathematics is correlated with academic achievement (Goodman et al., 2011; Maree et al., 2003, 2009, 2011; Moodaley et al., 2006; Palomar-Lever & Victorio-Estrada, 2017).
Integration of findings
Success in traditional mathematics
The study found a positive relationship between success in traditional mathematics and study attitude, study habits, and overall study orientation, in line with research on these aspects of study orientation (Heuser & Wang, 2017; Maree, 2015; Maree et al., 2003, 2011; Maree & Ebersöhn, 2002; Moodaley et al., 2006; Onoshakpokaiye, 2015; Palomar-Lever & Victorio-Estrada, 2017; Sikhwari, 2016).
The influence of poverty
The participants in this study were less disadvantaged by the poverty of their surroundings than would be expected, scoring at the 65th percentile in Study Milieu when their school was in a quintile 2 (20th to 40th percentile) area in terms of socio-economic status (SES). These study milieu scores contradict studies that show a positive relationship between study milieu and success in Mathematics (Gaillard, 2019; Lemmon, 2017; Letsoalo et al., 2019; Serrano Corkin et al., 2019; Uleanya & Bunmi Omoniyi, 2019; Van der Berg, 2015). However, these results are in line with studies that certain factors protect against poverty, including being identified as gifted (Bolland et al., 2019), study attitude (Palomar-Lever & Victorio-Estrada, 2017) and study habits (Kotzé & Niemann, 2013; Williams et al., 2017).
Problem solving
The study showed that Olympiad-type questions were more difficult for the participants than the alternative intervention. The finding that the SA Mathematics Challenge was difficult to the participants in this study was in line with other research into problem solving in South Africa (Engelbrecht & Mwambakana, 2016; Govender, 2014a; Mochesela, 2007) and abroad (Schoevers & Kroesbergen, 2017), and can be linked to findings that teachers in South Africa are themselves unfamiliar with problem solving and Olympiad-type questions (Govender, 2014b). Problem solving can be exacerbated by language difficulties (Mochesela, 2007; Sepeng, 2013; Sepeng & Webb, 2012; Tambychik & Meerah, 2010) so this angle of difficulty with problem solving would be worth investigating in future studies.
Strengths and limitations of the study
The strengths of this study were the selection of the schools and the use of the SOM for assessment. The two schools were well-matched in demographics as well as results on the pre-test of the SOM. The SOM was normed on disadvantaged South African learners and is a valid and reliable scientific instrument, which has been used in several studies in South Africa (Jagals, 2013; Molepo et al., 2005; Moodaley et al., 2006).
The limitations of the study were the sample size and area, the selection by Grade 6 marks, the short duration of the study, the lack of overt teaching and the relative difficulty of the interventions. Although the sample size was sufficient for statistical purposes, it was not large, and the two schools chosen were from the same township in Gauteng, so results cannot be generalised beyond the area where the study took place. Because of the difficulties of using IQ tests to assess disadvantaged learners and practical considerations, Grade 6 mathematics marks were used for selection. Additionally, the intervention took place at one school and the alternative intervention at the other, which precluded random assignment of participants to the intervention or alternative intervention group. The Grade 6 marks were not equivalent at the two schools and did not correlate with the SOM pre-test results. The study was very short, with no teaching of problem-solving skills. Overt skills building as offered by the Siyanqoba regional training for high school learners or the online SAMF Olympiad training for Grades 7–12 (SAMF, 2020a), in conjunction with practice of past papers, might have resulted in better skills acquisition. Lastly, the intervention and the alternative intervention were not equivalent in terms of difficulty.
Recommendations for future research
If this study were to be repeated, it is suggested that learners are not selected by marks, but rather by IQ test, the Grade 6 standardised Annual National Assessment (ANA) results or the PSB sub-test of the SOM. The reason for this is that this study showed that end-of-year marks are not comparable across schools.
Future repetitions of this study should include 10 or more sessions of SA Mathematics Challenge practice rather than just three. This would give learners a chance to self-develop skills over time. Additionally, overt teaching on how to approach various types of Mathematics Olympiad questions is recommended to scaffold the development of problem-solving skills in learners. Future researchers could analyse the success of the SAMF Olympiad training materials, other materials, or develop their own.
Lastly, it is recommended that schools in disadvantaged areas that are successful in the SA Mathematics Challenge are researched. Investigation of Olympiad preparation techniques used by no-fee schools that are successful in the SA Mathematics Challenge or Mathematics would potentially give a blueprint that could be rolled out to other no-fee schools. A comparative study of SOM PSB scores of learners at two disadvantaged schools, one that is successful in the SA Mathematics Challenge, and one that is not, could test the relationship between SOM PSB scores and success in the SA Mathematics Challenge.
Conclusion
This study found a positive relationship between success in traditional mathematics and study attitude, study habits, and overall study orientation. Poverty and giftedness were shown to interact: the gifted disadvantaged learners in this study were less disadvantaged by their surroundings than one would expect, and conversely had higher mathematics anxiety than expected for their achievement level.
More importantly, the study highlights that while opportunities for mathematically gifted learners in disadvantaged areas of South Africa do exist, much more could be done. The participants in this study found the problem-solving questions in the SA Mathematics Challenge difficult. Greater experience in Mathematics Olympiads, possibly coupled with teaching problem-solving techniques, may help mathematically gifted disadvantaged learners live up to their potential as South Africa’s problem-solvers.
Acknowledgements
This article is partially based on the author’s thesis entitled South African Mathematics Challenge participation : developing problem-solving skills in Mathematically-gifted disadvantaged learners submitted at the University of Pretoria, South Africa. with Prof. J.G. Maree as the supervisor, available here: http://hdl.handle.net/2263/78379.
Competing interests
The authors declare that they have no financial or personal relationship(s) that may have inappropriately influenced them in writing this article.
Authors’ contributions
B.S and J.G.M contributed to the article. J.J. contributed towards the statistical analysis of the article.
Funding information
The authors received no financial support for the research, authorship, and/or publication of this article.
Data availability
The data that support the findings of this study are available on request from the corresponding author, B.S. The data are not publicly available because of their content that could compromise the privacy of research participants.
Disclaimer
The views and opinions expressed in this article are those of the authors and are the product of professional research. It does not necessarily reflect the official policy or position of any affiliated institution, funder, agency, or that of the publisher.
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