An Investigation into the Determinants of Underperformance in Mathematics among Grade 12 Learners in a High School in the Eastern Cape

Abstract

Learners in the Eastern Cape Province have over the years performed poorly in the National Senior Certificate Mathematics examinations. This study sought to investigate the determinants of under-performance of Grade 12 learners in Mathematics. The study adopted a qualitative case study in which data were gathered through interviews with teachers and learners. The purposely selected sample comprised three teachers and nine learners from the same school. The findings showed factors that have a direct influence on teaching strategies such as the inadequacy of resources and under-qualified teachers. The other factors associated with learners were learners’ attitudes and general understatement of the subject contributing to undesirable results. Recommendations, as well as suggestions for further research aimed at addressing the factors identified, are advanced.

1. Introduction

The National Development Program 2030 of the National Planning Commission aims at addressing the injustices of the past in South Africa. This policy shifts towards the promotion of science, technology, and mathematics–oriented education from basic education levels. This is motivated by the assertion that tertiary education institutions need to produce more STEM-oriented graduates successfully. The attainment of the set targets in the long term all hinge on the capacity of the country to improve technology and scientific research. These are ultimately expected to be a product of improvements in pass rates and uptake of Mathematics education from basic and pre-tertiary education stages. As directly noted and presented, Mathematics provides society with a rigorous foundation and grasp of scientific thought and theory capacitating individuals for robust economic growth [1]. Lemaire [2] states that mathematical thought and concepts would eventually become the drivers of world development and management.

Maliki, Ngban and Ibu [3] postulate that favourable and desired economic development are direct outcomes from elevated uptake and success in sciences and in particular, mathematics. The rapid development of the global ecosystem across all sectors has fostered an environment where not only economic development but also global and national security are hinged on the deepening and extensive uptake of mathematics-oriented subjects. These views, therefore, mean that there is a need to not only advance the Mathematics school curriculum but also to encourage uptake and throughput of the subject. However, the academic performance in mathematics has varied across national frontiers. In an international study, it emerged that the number of students in the USA and Australia taking up advanced Mathematics courses declined significantly as students’ progress in high school [4]. Ysseldyke et al. [5] revealed that more than 66% of learners from low-income urban households failed to demonstrate a grasp of even the most mundane mathematical concepts. These studies present worrisome scenarios where the world’s most advanced economy which has abundant resources also suffers the scourge of problematic Mathematics grasp among its learners.

These undesired standards and lack of target achievement are not unique to the developed world alone. In Tanzania, the majority of learners consistently fail to match the required pass results, for four national examination results for the years 2004, 2005 and 2006 Mathematics had failure rates of 70%, 77% and 76% respectively [6]. Bahri and Corebima, [7], in a Nigerian study, states that learners’ attitudes and fears towards the subject, under-qualified educators and insufficient classroom teaching and learning material grossly affected performance. In the South African context, learners have consistently performed badly in Mathematics examinations. The table below shows the overall performance of the Mathematics candidates in the National Senior Certificate from 2016 to 2020 (Table 1).

Year	No. wrote	No. achieved at 30% and above	% achieved at 30% and above	No. achieved at 40% and above	% achieved at 40% and above
2016	265 810	135 958	51,1	89 084	33,5
2017	245 103	127 197	51,9	86 096	35,1
2018	233 858	135 638	58,0	86 874	37,1
2019	222 034	121 179	54,6	77 751	35,0
2020	233 315	125 526	53,8	82 964	35,6

Table 1.

The overall performance of candidates in National Senior Certificate Examinations 2016–2020.

(Adapted from [8])

The table above shows a steady decline in the number of learners taking up Mathematics at the Grade 12 level since 2016. This is the same trend as that reported by Freeman, et al. [4].

According to Reddy [9], poor performance is highest among black Africans. The subject itself is believed to be difficult even to parents [9]. Consequently, many schools in the country, along with their learners, have opted for mathematical literacy, which is viewed as a less complicated subject. While this may be so, the concepts taught and learnt through mathematical literacy are considered inadequate for advanced study in STEM-related subjects at university level. A typically notable scenario is that of the Bohlabelo cluster in Sekhukhune of Limpopo province in South Africa comprising of four circuits, with 47 secondary schools: Mathematics in Grade 12 has been declared “a killer subject” and as such, learners begin to fear Mathematics. This view is largely ubiquitous in the country’s secondary education sector including the Eastern Cape Province. Therefore, this primary purpose of this study is to determine the causes of poor performance among Grade 12 learners in an attempt to mitigate the low levels of performance. At secondary level, along with other related studies, the study will form a base of literature upon which future studies and references may be based.

2. Literature review

2.1 Mathematics teaching strategies

Teaching strategies encompass all actions in and out of the classroom such as organising and planning of lessons, arrangement of learners, delivery of lessons based on learners’ experiences, effective communication using appropriate language and material, as well as lesson assessment based on the outcomes of the lesson [10]. In a Chinese study that compared the effectiveness of constructivist teaching approaches to the traditional transmission style teaching, it emerged that the constructivist approach resulted in significantly higher learning gains [11]. Ifamuyiwa and Akinsola [12] state that cooperative learning strategies are useful strategies when conducting and delivering lessons on complex principles in Mathematics. In addition, Kodisang [13] advises that to foster a productive learning environment, educators must allocate duties and roles to learners in highly functional groups to encourage debate and ultimately higher-order responses from learners. Muradya [14] indicates that during active learning of Mathematics, the selection and application of inappropriate teaching strategies often results in poor performance by learners. The study revealed that students were performing poorly because of how the subject was taught [14]. In support of this notion, Wabwoba, [15] observes that poorly motivated teachers utilising inappropriate and incorrect teaching methods often resulted in learners performing badly.

2.2 School/teacher-related factors

Hanushek and Rivkin [16] investigated the teacher-related factors that affect learning achievement in Mathematics. Among those factors is the motivation to teach and mediate the construction of mathematical concepts by the learner. The author contends that a positively motivated teacher can help learners minimize mathematical anxiety referred to in the previous section and go an extra mile to help learners address their difficulties in learning the subject and demystify the concepts.

According to Pereira [17], the language of instruction often influenced the performance of learners in all subjects during schooling. Performance was poor, particularly among rural learners or those who have been subjected for long periods to tuition using a different language. There is, therefore, a strong correlation between the language proficiency of learners with their performance in other subjects. However, the implementation in schools has not been sufficiently conducted [18]. In many cases, educators rely on inapplicable teaching practices which affect the learners’ grasp and outcomes. There is a risk of a high failure rate in Mathematics as core concepts may not be understood, or are lost. Learners need not have advanced proficiency in the language of tuition, but rather should have a deep grasp of the language to grasp concepts in Mathematics and related subjects. Rammala [19] also indicated the importance of language in the performance of learners in Mathematics. Most Grade 12 learners in South African schools struggled and performed poorly in the language of tuition, therefore, likewise most learners failed to grasp key concepts in the subject and barely understood what was required of them [19].

A compounding factor is the lack of resources in some schools in South Africa. There are cases of schools in the country which are poorly resourced but manage to perform well regardless of the obvious shortcoming. Conversely, in the long term and on a day-to-day basis, lack of adequate funding can have a disastrous effect on achievement [20]. While qualified Mathematics teachers may be able to teach and deliver classes with limited resources like textbooks, problems emanate from the limited examples and practice work that an individual teacher may develop [21]. Additionally, the lack of resources only compounds the workload of the already burdened teaching staff. Educational institutions that lack textbooks fail to achieve the independent enquiry level and higher-order thinking attained through self-learning [22]. In the study conducted by Van der Linde [23], lack of resources features very strongly as the cause of the poor performance in Grade 12 Mathematics.

2.3 Learner personal factors

Various learner-specific factors were discovered to be significant in influencing the performance of learners in Mathematics. These included gender, economic status and attitudes of learners [21]. A study conducted in Nepal by Acharya [24] revealed some of the factors affecting learner performance in Mathematics. Learner related factors will be discussed in this section while school/teacher-related factors will be discussed in the section that follows. According to Acharya [24], Mathematics anxiety is one of the key factors affecting students’ ability to successfully learn Mathematics. Mathematics anxiety is a general negative feeling towards the process of the learning of the subject and it affects the students’ learning negatively. This finding adds weight to findings by Mensah et al. [21] who indicated that the attitude presented by learners towards attaining knowledge in Mathematics was vital in determining the learners’ outcomes in the subject. Additionally, Beilock and Willingham [25] state that many students struggle with Mathematics at some point. It is not uncommon to hear them complain that they hate Mathematics: “it’s hard,” they are quick to give up when they do not understand something. A negative mindset like this can quickly turn into cycles of low confidence, reduced motivation and poor performance [25].

The second factor reported by Acharya [24] is the level of relevant prior knowledge from earlier grades. Mathematical concepts are cumulative and lack of mastery in lower grades makes it very difficult for a learner to construct concepts in higher grades. The third factor affecting performance in Mathematics identified by Acharya [24] is the ‘lack of students labour’ (p. 11). This refers to a lack of enough effort on the part of the learner when they study Mathematics which leads to a lack of practice in the application of concepts in different scenarios.

In a South African study involving Grade 3 learners, it emerged that only 16% of the learners involved in the study performed at the appropriate standard for Grade 3 level. The rest of the learners performed below the expected level in Mathematics [26]. The same study also revealed that the poorest 60% of the Grade 3 learners are three Grade levels behind the wealthiest 20% of learners in Grade 3. Furthermore, the study showed that by Grade 9, the gap between the poor and wealthy learners grows to four grade levels. The Eastern Cape Province in which this present study was conducted is one of the poorest provinces in South Africa. Spaull and Kotze [26] concluded that this learning deficit is difficult and costly to rectify later in life (for example in Grade 12 which was the focus of this study).

In another South African study of township schools like the one in the present study, Mkhize [27] explores the reasons that learners in high school did not do well in Mathematics Grade 12 examinations. According to teachers in the study, the reasons for the poor performance was due to the following reasons:

• Learners are not motivated, this may be because of the families and societies they are being raised in where no one probably would have achieved anything related to Mathematics so no one will push them to do better.

• Learners are generally lazy and this may be attributed to poor learner management from a tender age.

• Learners have illiterate parents who cannot assist them with their school work and often leave the teacher to deal with their child’s shortcomings in Mathematics

• Learners do not know how and what to study which could have been attributed to how they were taught from elementary stages of Mathematics and school in general.

• Learners believe Mathematics is difficult because they would be discouraged by the amount of energy and effort required to master the general concepts.

• Learners have a negative attitude towards Mathematics since in most social circles, it is regarded as difficult by many.

When asked about the reasons they failed Mathematics, the learners in the study indicated that the reason they appeared lazy and demotivated was because of the constant failure in solving problems when they studied on their own. Mkhize [27] further reports that according to the learners, teachers always tell them that Mathematics is easy but they do not show them how it is easy.

2.4 Theoretical framework

This study is based on the theory of constructivism. Constructivists contend that learning is a process of constructing meaning from personal experiences [28]. In addition, Taber [29] posits that learning is a ‘process of constructing internal mental representations of the world’ (p. 45). The constructivist’s view emphasizes the need for the learner to be present and to experience events for them to be able to acquire knowledge and learning [28]. This view entails that Mathematics learners will learn more from problem-solving as this will afford them chances to experience the subject as opposed to being told or shown how to do it on the board only. Riegler [30] states that the term constructivism is probably derived from Piaget’s “constructivist” views. Mvududu and Thiel-Burgess [31] state that constructivism is an approach to probe learners’ understanding and elevate them from lower levels of learning to much higher levels of learning through the application and synthesis of experienced events.

Jean Claude Piaget is considered the father of the constructivist movement, particularly cognitive constructivism [28]. According to Amine and Asl [28], ‘as learners encounter an experience or a situation that challenges the way we think, a state of disequilibrium or imbalance is created’ (p. 10). The mental imbalance necessitates that there be a rearrangement of mental structures to accommodate the new experiences. In Mathematics, this is the problem-solving process, which will build new mental structures. Constructivism is, therefore, a practice-based model of learning [32]. Piaget’s constructivist approach is based on radical constructivism which focuses on individual cognitive processes combined with social interaction [33]. From a Piagetian point of view, knowledge construction occurs at a personal level. The environment and others serve as a source of the disequilibrium that triggers the construction of new knowledge.

3. Methodology

3.1 Research design and justification

The researcher adopted a qualitative case study approach. Stake [34] asserts that in a case study, the researchers use multiple data gathering techniques to get a deeper understanding and a rich description of the case. The advantages of using qualitative research are that the researcher has the first-hand experience of the participant during observation, the information can be recorded as it occurs during observation, and the researcher can control the line of questioning in an interview. Qualitative research is value-laden.

3.2 Population and sampling

The population consisted of three Mathematics teachers and nine Grade 12 learners. The study utilised non-probability sampling techniques. The purposive sampling was used to select participants who contributed to the qualitative data because of their relevant knowledge. To attain quality and reliable information, the most experienced Mathematics teachers, both general and specific to Grade 12, were selected as the appropriate sample units. The first participant, TR-1 was a female educator holding a Bachelor of Education in Mathematics teaching qualification with 23 years of experience and 16 years teaching Grade 12. TR-2, also a female educator held a Bachelor of Education Honours qualification and 17 years total teaching experience with 12 of those in Grade 12 classes. The third participant, a male TR-3, held a Bachelor of Education qualification and had 31 years of experience and 27 of them in teaching Grade 12 Mathematics.

The learners included as participants in the study were randomly selected from within the purposively selected Grade 12 group. No particular trait or demographic characteristic among the Grade 12 participants was considered as critical above the others to warrant specialized grouping. The learners were randomly selected regardless of age, gender and social status as it was deemed to be generally consistent among the likely participants and little chance of exclusion was possible given the sampling technique. For the presentation of narratives, teachers were coded using prefixes as follows: TR-1, TR-2 and TR-3 while the learners were LN-A to LN-I.

3.3 Ethical approval statement

The participants in the study were informed about the purpose and nature of the study in writing and it was stated that they had the right to choose not to take part in the study without facing any negative consequences. Guarantees were given that all information would be private and confidential. Participants gave their consent in writing.

3.4 Data collection procedures

Data were collected using one-on-one interviews and focus group discussions. According to Mentz and Wolhuter [35], an interview is a goal-directed attempt by an interviewer to obtain reliable valid measures in the form of verbal responses from one or more interviewees. The interviews were semi-structured, allowing the researcher to probe respondents’ answers for clarity and more detail. The researcher conducted focus group discussions with the learners on the contributing factors that underpin under-performance in Mathematics.

3.5 Data analysis

According to Kothari [36], data analysis is a process of generating useful information from the data through tabulation, screening and coding. The process involves operations that are performed to summarise and organise the data collected from the field. Since the study involves qualitative data, the data analysis process was done through transcription and recording of participants’ assertions and responses during interviews. The data analysis was inductive as there were no predetermined themes. Therefore, themes emerged from the data sets. Analysis of the qualitative data obtained was undertaken through the development of thematic focus areas which jointly provide answers to the research questions. This helped the researcher to make a description of the data collected from the field based on research objectives and to derive conclusions on what to take regarding its usefulness.

4. Results

The following section provides the determinants of underperformance in Mathematics among Grade 12 learners through interviews conducted with the participants and data gathered through observations. In analysing the data, the researchers read and independently categorised responses from both the learners and their teachers. In categorising the responses, statements projecting similar ideas were grouped. Four major themes that emerged in the data analysis are used as headings to present data.

4.1 School related factors

The findings indicated that limited access to textbooks and practical learning resources was the cause of poor performance. TR-1 indicated that “There are many reasons why learners would not perform the way that the teachers, schools and department want them to perform when it comes to Mathematics. The schools are often lacking adequately qualified and experienced teachers, textbooks, teacher resources among many other things”. Along the same sentiments, TR-2 said “in our school, the learners and teachers do not have adequate time and material to sufficiently undertake a subject, which is as complex as Mathematics. Similarly, TR-3 stated that “many learners have a little or weak foundation in Mathematics. That, mixed with the limited resources and encouragement at the schools automatically means that learners will fail. There are no activities done to encourage an improved grasp of the subject. The participants’ responses to the primary question are indicative of institutional inadequacies, which have fostered environments that are non-conducive for effective teaching and learning of Mathematics and as such result in undesired outcomes. The prominent causal issues identified relate to mostly lack of resources, particularly learner textbooks and LTSM. Ultimately, the extent to which resources are availed and utilized in the schools is a determining factor in Mathematics outcomes.

Regarding inadequate resources, learners indicated their frustration of sharing textbooks. They expressed similar views as articulated, for example, LN-A indicated that “it would be much easier to read more on the topics instead of photocopies of the homework only”. LN-C pointed out that “having more books which are not shared, or which can be taken home to study will give us more time to practise more and more examples”. Related to this view, LN-D said “it can be very frustrating trying your best but not doing well or not being able to do well because of shortages of books. Having all the resources I need motivates me to do better than at present”. LN-F shared the same sentiments “some of the items needed to study Mathematics are easily available for everyone. A lot of the time during the period, especially in Grade 12, we are required to have mathematical sets with compasses, protractors and set squares. Not everyone has these and, therefore, practising at school or after school is not easy”. Notably, both from educators and learners, the data indicated that resource constraints were identified as inducing serious challenges during teaching and learning. Particularly, the unavailability of adequate textbooks, reference sources and practice material severely prejudices learners.

4.2 Teacher related factors

Data from interviewing teachers indicated under-qualified teachers, and the reluctance to accept responsibility and accountability by the appropriate teachers have largely compromised results in Mathematics. Concerning the effect on the composition of educators for Grade 12 Mathematics on learner performance, TR-1 said “from my view, many teachers are not willing to take the responsibility which comes with teaching Grade 12 Mathematics. Here TR-2 pointed out “many teachers are satisfied with the qualifications which they have. Few teachers want to go for skills or content improvement. So, many teachers are using what they learnt a long time ago to teach in modern times. I do not think it works well. Interestingly, TR-3 expressed a similar view: “we have many young teachers in the schools taking Grade 12 classes. Many struggle to control the classes. Many of them also even struggle with content and methods because they are young and new. The data from interviews of teachers indicated that the quality of teachers especially regarding teaching experience at Grade 12 and the reluctance towards continued skills development was noted as having negative impacts on the quality of content and relevance of teaching methods applied in classes.

4.3 Learner personal factors

The findings illustrated a picture of both teachers and learners agreeing that learners have little interest in learning in general. This further worsened their performance in Mathematics. The learner attitudes and the values which they placed upon learning were identified as being below those desired for adequate and satisfactory performance in the Mathematics curriculum. In responding to the question asked on the factors which contribute to poor performance in Mathematics TR-1 said “most of the learners show no interest at all in learning; this makes it worse for Mathematics results. Peer pressure, lack of guidance, poor socio-economic backgrounds, child or elder-headed households affect our learners a lot”. Similarly, TR-3pointed out “poor attitude towards studying is serious among learners. Many of them do not understand the value of learning especially a critical subject like Mathematics in this modern age. In another pertinent instance, learners insisted “I do not see how I can be motivated, there are few textbooks at school … nobody cares.”

Concerning lack of interest in learning Mathematics, learners did not seem to identify shortcomings from their side. Blame was for example apportioned to the content being difficult. Here LN-A pointed out: “Mathematics requires more thinking, knowledge and understanding than what is required in other subjects”. About this LN-C said, “Mathematics is very difficult and most of the time you might think that you have grasped the concepts, but they are easy to forget”. LN-H corroborated this “the subject is a lot more difficult than most people realize. So, it’s not easy to pass it even if you try”.

4.4 School related factors

The findings indicated that limited access to textbooks and practical learning resources were the causes of poor performance. Inasmuch as most textbooks are in appalling shape and have endured years of damage. Some have a few blank pages and sometimes teachers are compelled to make copies. Data further indicated that in some instances, many learners are grouped to share textbooks. The availability of resources appears to play a pivotal role in student performance. This view is shared by Munda, Tanui and Kaberia [37] who observe that the availability of and quality of textbooks in a secondary school is strongly related to achievement among children from lower-income families especially those in rural boarding schools. According to Mbugua et al. [18], textbooks are a major input for performance in examinations. This view is shared by Kariuki, Kibet, Muthaa and Reche, [18] who observe that the availability of and quality of textbooks in a secondary school is strongly related to achievement among children from lower income families, especially those in rural boarding schools. The availability of textbooks in schools, however, is ultimately what determines students' outcomes in mathematics. Brown et al. [32], from a theoretical perspective, argues that adopting constructivist approaches to teaching and learning requires practice-based models, which demand adequate resources.

4.5 Teacher related factors

Data from interviews indicated that poor performance than intended was generally due to insufficient guidance, mathematics difficulty, and the subject's expectations. On the other hand, data showed that learners' performance was impacted by teachers' reluctance to assume responsibility for teaching Mathematics in Grade 12. Hence Bed [38] states that a positively motivated teacher can assist students in reducing their Mathematics anxiety and go above and beyond to assist learners in getting past their learning challenges. In the same vein Pereira [17], affirms that the language of instruction often influenced the performance of learners in all subjects during schooling. Particularly among rural learners or those who have been subjected for long periods to tuition using a different language, performance was poor. Poor teaching and inappropriate strategies from teachers affected learning [14]. In lay terms, there is consensus that more experienced or better-qualified employees and particularly a combination of both tend to perform better than their peers do. As identified, allocation of Grade 12 Mathematics classes to under-qualified teachers, student teachers and the reluctance to accept responsibility and accountability by the appropriate teachers have largely compromised results in Mathematics. This was further argued by Mensah et al. [21] that, even in the presence of adequate physical resources, poorly equipped teachers could affect learners negatively.

4.6 Learner personal factors

Data showed a variety of learner-factors that are important in influencing how well learners perform in Mathematics. These included gender, anxiety, economic status and attitudes of learners. According to Bed [38], Mathematics anxiety is one of the key factors affecting students’ ability to successfully learn Mathematics. Mathematics anxiety is a general negative feeling towards the process of learning the subject and affects the students learning negatively. This finding adds weight to Mensah et al. [21] who showed that the attitude presented by learners towards attaining knowledge in Mathematics was vital in determining the learners’ outcomes in the subject. Additionally, Mkhize [27] states that many students struggle with Mathematics at some point. They frequently lament that Mathematics is hard and that they hate it. They also readily quit when they do not understand anything. A negative mindset like this can quickly turn into cycles of low confidence, less motivation, and poor performance [27].

5. Conclusion

The outcomes from the study provided a clear picture of the nature of the major problems driving poor academic performances among learners studying Grade 12 Mathematics in the Chris Hani District. The consistent and perennial underperformance of learners is a creation of the combination of the various issues discussed above.

6. Recommendations

It is recommended that capacity development techniques targeted at enhancing and upgrading teachers' subject-matter expertise and all-around skills be a requirement in the contemporary educational system. Regular and consistent workshops, frequent reorientation, and seminars addressing the various skill shortages and upgrades should be conducted.

Regarding the points made here, it is suggested that perhaps future research should take into account not only the voices of educators and learners but also the opinions of parents in an effort to improve the poor performance of learners.