High school learners underprepared for critical foundational university mathematics courses
There is a significant gap between high school and university mathematics for science and engineering students in South Africa with learners entering institutions of higher education unprepared.
This was one of the crucial findings of a research study presented at the first meeting in 2023, of Universities South Africa’s Teaching and Learning of Mathematics Community of Practice (TLM CoP).
Titled Exploring the Challenges When Transitioning from High School Mathematics to University Mathematics, the study focused on calculus and trigonometry. Lead Researcher, Dr Frikkie George (left) from the Cape Peninsula University of Technology (CPUT), explained that while the Mathematics Further Education and Training Phase covers ten content areas, (including Algebra, Geometry, and Statistics), trigonometry and differential calculus were chosen because they form the foundation for university mathematics and science courses.
The brief was to “explore the current South African high school mathematics curriculum and the National Senior Certificate (NSC) examination reports of the past five years to contribute to the existing literature on school-to-university transition.” Dr George was working with Ms Ekaterina Rzyankina (CPUT), a qualitative data analyst.
Another objective, according to Dr Pragashni Padayachee, Chairperson of the TLM CoP and Senior Lecturer: Mathematics within the Academic Support Programme for Engineering (ASPECT) at the University of Cape Town, was “to inform university mathematics support programmes (tutorial programmes and bridging courses) so that these interventions can be more effective in addressing the school-to-university transition challenges confronting mathematics and science students.”
The researchers have completed Phase One of the study.
Problem statement: High failure rate in first year
Dr George said that while Calculus & Trigonometry are being taught across the grades in the Further Education and Training Phase, it was found that in certain topics, the concepts and skills were similar but differed in the level of difficulty. The research showed that the under preparedness of learners resulted in a high failure rate for first-year university mathematics students enrolled in engineering and science programmes across universities in South Africa.
Said Ms Ekaterina Rzyankina (right): “There is a lot of literature showing that Mathematics is a critical subject in South Africa and that it is difficult for students to cope with high school mathematics. Many high school learners aspire to pursue mathematics-related courses at university, but transitioning from high school mathematics to university mathematics can be challenging.”
This transition, the literature stated, remains unresolved with the gap getting wider. Notwithstanding that the Class of 2022 was the ninth cohort to be exposed to the Curriculum Assessment Policy Statements (CAPS), Rzyankina said they had learnt from existing literature that “there is still a curriculum gap between high school and university mathematics which makes the transition from high school to university difficult. This results in high failure and attrition rates, and low throughputs at universities.”
Dire consequences
This had a range of dire consequences, she said. “If many students take longer to graduate, it means we are spending more to produce one graduate which leaves no room to admit new students into mathematics programmes. Worse still, when students drop out of university, the money invested will never be recovered.”
She added that low throughput rates suggest that the country will continue to have a scarcity of qualified personnel in the critical skills areas of the economy (4IR and 5IR). It also adds to unemployment.
Preliminary findings
Dr George said data gathering in this desktop study had entailed exploring the National Senior Certificate (NSC) examination reports, looking at the performance of matriculants over the past four years. “The questions based on calculus and trigonometry were the ones in which candidates performed worst. They did well in the low-order questions, but lack high-order thinking skills.”
The findings:
- Overall, the matriculants’ responses suggested a general lack of reading and comprehension skills.
- Many candidates did not understand the vocabulary used in the questions.
- A significant percentage of the 2022 candidates responded adequately to questions that required lower-order thinking skills but performed poorly in questions that demanded analytical, evaluative, and problem-solving skills.
Dr George said these findings necessitate that high school teachers use dialogical argumentation in the mathematics classroom. Teachers are urged to use technology, visual demonstrations, practical activities and visualisation to improve learners’ understanding of the subject matter. They are also encouraged to make use of online learning platforms such as YouTube, that offer visual presentations to explain challenging topics.
“These and other intervention strategies should be integrated to improve the conceptual understanding of mathematics topics, a concern pointed out in the NSC diagnostic report,” he told the CoP members, mostly mathematics lecturers.
Conclusions and Recommendations
The literature examined in this desktop study showed that while the current high school mathematics curriculum, based on CAPS, appears to cover a wide range of content areas, it lacks depth in critical content areas of mathematics. The conclusion was that this, therefore, does not adequately prepare students for university-level mathematics.
Said Dr George: “The findings of Phase I of this study indicate that many core aspects of algebra and calculus (i.e. complex numbers, vectors, matrices, proof by mathematical induction, integration, and differential equations) are excluded or covered vaguely in high school mathematics.
“To narrow the gap between high school and university mathematics, we recommend deepening the core aspects of calculus and trigonometry to specialise in minimal subjects directly linked to their intended fields of study at university.” Additionally, students needed to be informed of their lack of understanding through formative assessments that gave immediate feedback (such as the use of audience response systems).
Dr George said the next phase (Phase II) of this study would survey lecturers and students, to gain a better understanding of their teaching and learning experiences, respectively. This phase would seek lecturers’ and students’ opinions regarding the mathematics curriculum. These would be used to analyse mathematics tests — particularly calculus and trigonometry questions administered in the first semester of first year, to gain a deeper understanding of the challenges faced by students and how they can be addressed.
“The goal of this study is to provide evidence-based recommendations for addressing the school-to-university transition problem in mathematics education, so that all students can have the opportunity to succeed in these critical fields.”
The researchers are waiting for ethical clearance before they can begin Phase II of the research.
Charmain Naidoo is a contract writer for Universities South Africa.
