The challenges facing first-year mathematics students transitioning from high school
Transitioning from high school mathematics to university mathematics can be daunting for many first-year students, possibly leading to lower success rates.
These gaps and the challenges faced by first-year students were under discussion at the Community of Practice (CoP) for the Teaching and Learning of Mathematics (TLM) at their first sitting on 9 April.
Professor Moeketsi Mosia (left), Vice-Dean: Teaching and Learning, Associate Professor and ETDP-SETA Research Chair in Mathematics Education, Department of Mathematics, Natural Sciences and Technology Education at the University of the Free State, said that the transition from high school to university is critical for STEM (Science, Technology, Engineering, and Mathematics) students.
“We surveyed because we wanted to understand that transition and investigate student experiences to adjust our pedagogical strategies and approaches to teaching mathematics,” he explained.
“We know that high school mathematics is a cornerstone for higher education success, but acknowledge discrepancies in understanding its true impact. The specific mathematical skills predictive of university success remain unclear. This study sought to contribute to these debates.”
Professor Mosia and his team undertook a cross-sectional and correlational study to determine students’ experience with mathematics teaching in institutions of higher learning and how different it is from their high school mathematical experiences.
He said that it was interesting to note that learners from Quintile 5 schools start on a higher trajectory when they start at university, and that this drops. Those who come from lower quintiles, he said, start low and slowly go up. [The South African Government uses a quintile system to allocate funding to public schools, with quintiles 1-3 being the most needy and 4-5 being the least needy. Quintile 5 schools primarily serve families with higher incomes.]
“This links to problem-solving issues in mathematics. Therefore, we may need to engage on this topic with both Basic and Higher Education departments,” he said.
Students explained that teaching changed from being interactive and engaging in high school to less interactive at university. It was a major transition, and some felt their preparation was not comprehensive enough for university-level demands. However, many indicated that high school mathematics encourages some critical thinking and problem solving to some extent, which was beneficial when they moved to university.
Professor Mosia said those surveyed felt moderately confident in their mathematics skills when starting university.
“There is a tendency to seek additional support for university-level mathematics (Mean: 3.18, SD: 0.856), indicating that while some students feel prepared, others need further help.
“Students report that teaching methods used in their high school classes are not very similar to those in university courses (Mean: 2.25, SD: 1.192), reflecting a misalignment in pedagogy. The biggest issue is how teaching in basic and higher education is completely misaligned and there’s no continuity. Universities must examine how they teach first years to ensure a smooth transition,” he reiterated.
He also revealed that:
- Students feel less prepared for university-level assessments (Mean: 2.89, SD: 0.850) although universities provide layers of support for students’ access.
- Students frequently encounter difficulties understanding complex concepts in university mathematics (Mean: 3.87, SD: 0.965).
- Students said there is much less technology usage at schools compared to universities.
“All this suggests that while foundational knowledge may be strong, the transition to advanced topics remains challenging for many. Sometimes first-year classes are so big that one must find ways to be creative and interactive.”
He continued: “In my time (as a student), our lecturers, at least with undergraduate mathematics, would take us through the thinking process in detail and how they arrived at the solution. But I think there’s been a shift where lecturers rely heavily on prepared slides that we now walk students through.”
Professor Mosia unveiled the most significant challenges facing university mathematics students.
“They acknowledge a difficulty in keeping up with the curriculum pace. Nearly 49% of students identified this as the biggest challenge. Mathematics teaching at university is fast-paced compared to high school. Many students struggle to keep up. Meanwhile 23.3% of students struggle with understanding complex mathematical concepts.”
Dr Anita Campbell (right), a senior lecturer in mathematics and part of the Academic Support Programme for Engineering in the University of Cape Town’s Faculty of Engineering & the Built Environment (EBE) questioned the type of feedback high-school learners receive from their teachers.
“Is the interaction only with their teacher or interaction with each other as they have more time at school? Do they have more feedback opportunities in basic schooling, that are lacking at university? Is it perhaps that the high school work is more procedural, that they’re getting feedback, and it’s comfortable because it’s not really problem solving that they’re spending their time doing, whereas, when they come to university, it’s more about developing a way of thinking? And that’s where it is (probably) so different; because they can leave out 3 to 5% of matric exam questions on problem solving and still get 95%.”
Professor Mosia agreed that there were nuances around these interactions: “First-year students say they feel universities are all about teaching and more teaching! There is less collaborative work at university whereas in basic schooling, students often work together in groups and find ways to help one another. They feel that this barely happens at university.”
Ms Sandra Swanepoel, a Mathematics Lecturer from the Cape Peninsula University of Technology (CPUT), said it would be interesting to compare the lecturers’ experience and perspective.
Professor Mosia agreed that it would complement the students’ study. “Then you would have two sides of the story of both stakeholders in the learning process. There is (probably) misalignment because sometimes what students think is important is not what the academic thinks is important.”
Identifying problematic areas in the first year mathematics curriculum
Mr Sboniso Mzulwini (left), a lecturer in the Department of Mathematics at Nelson Mandela University (NMU), followed with a presentation which identified problematic areas in the first-year university mathematics curriculum as students made the transition and shared his experience of teaching first-year modules and focused on data he collected in 2023 and 2024.
He said he had broken his survey into two topics: the first focused on reading and writing mathematics and correctly using mathematical symbols, while the second involved techniques and problem-solving, which students find more challenging.
The average results increased when quizzes changed from handwritten in 2023 to multiple-choice assessments in 2024. The average results for Test 2 remained below 50%, an assessment mostly on limits. Key issues uncovered included students’ struggles with logic, mathematical statements and proofs as well as difficulty with sets, limits, differentiation and integration.
“Students struggle with logical connectives and mathematical arguments, a huge part of what they must master in mathematics. If a student doesn’t grasp this, it only gets harder as the work progresses,” he said. “They have to know why they answer the way they do (often correct), otherwise they don’t get the marks that they could.”
Dr Vuyani Matsha, a lecturer at NMU, asked how collaborations between the education and science faculties could help to find solutions to some of these problems.
“It is a complex issue,” said Mzulwini. “I think we need more data to see how students perform as they progress from first year to third year, to improve our teaching and learning. We need to collaborate with the education faculty in collecting and interpreting the data together, for a better learning experience.”
TLM chairperson Dr Jacob Maritz, Senior Lecturer of Mathematics at NMU, said one of the biggest challenges was getting students to study mathematics at first-year level. It was vital to find solutions and improve success rates once they are in the system.
Mathematics teacher education
Professor Judah Makonye (right), Head, Mathematics Education at the University of the Witwatersrand, was the last speaker who focused on mathematics teacher education in South Africa. He highlighted the need for teachers to have deep content knowledge (CK) and pedagogical content knowledge (PDK), supported by work-based learning. Makonye noted improvements in mathematical achievement but highlighted ongoing challenges, including multilingual classrooms and teacher quality.
His recommendations included:
- Strengthening content focus in Initial Teacher Education (ITE) and Continuing Professional Development (CPD).
- Fostering collaborative teacher learning communities.
- Scaling mentorship and induction for novice teachers.
- Using digital technology for teacher training.
- Embedding learner-centred, diagnostic teaching approaches.
- Aligning teacher education with curriculum demands and assessment practices.
“Teacher quality is a key lever for improving mathematics learning outcomes,” he emphasised.
Janine Greenleaf Walker is a contract writer for Universities South Africa.
