School of Mathematics, Statistics & Computer Science

Dr Mthobisi Ntuli’s research focused on understanding why students struggle with mathematics. He is pictured celebrating his graduation with his family.

Understanding Why Students Struggle with Maths

‘In the realm of first-year university mathematics, students often face challenges in applying critical evaluation and analysis skills to solve mathematical problems,’ says newly capped applied mathematician, Dr Mthobisi Ntuli.

‘Despite the significance of Higher Order Thinking Skills (HOTS) in problem-solving, there is a gap in understanding how to develop and assess these skills effectively among first-year calculus students. Existing research indicates a deficiency in students’ basic knowledge and skills, hindering their ability to tackle university-level calculus concepts.’

Ntuli’s PhD research sort to address this gap by utilising HOTS to enhance first-year students’ problem-solving abilities in mathematics.

His motivation stemmed from the recognition of varying student performances and the importance of understanding why certain students struggle while others excel.

‘By focusing on developing the necessary skills to overcome threshold concepts, such as understanding limits, my study aimed to empower students to navigate complex mathematical problems effectively,’ he said.

Ntuli explained the motivation for his research: ‘Generally, in a class or group of students, you can find students who perform exceptionally well and others who perform poorly. This may be because of students’ prior education or lack of basic knowledge and skills to understand concepts of first-year university mathematics.

‘Research has shown that two students can perform the same in a task up to a specific mathematical point and then one student takes a further step while the other cannot. As a researcher, it is very important to get an understanding why one student lagged, and which skills the other student used to go further. Understanding this will empower researchers to produce methods of how to help the student who lagged to develop the necessary skills to be able to take that further step.’

Ntuli’s study focused specifically on improving problem-solving abilities in first-year calculus students by developing HOTS. His primary objective was therefore to create purposeful assessment questions aligned with module content to foster the development of HOTS.

‘In order to effectively develop HOTS through assessment, it was crucial to formulate assessments with well-structured formats featuring relevant questions and tasks,’ he explained. ‘Those assessments not only promoted HOTS development, but also offered insights into students’ higher-order thinking abilities.’

Ntuli said that an analysis of written responses and interviews revealed a lack in critical thinking and problem-solving skills. For example, students struggled to identify applications of mathematics and establish linkages between derivatives of a function and trigonometry, exposing shortcomings in their higher-order thinking.

Ntuli’s findings are significant as they contribute to understanding how well-designed assessment questions could be used to evaluate the development of HOTS among first-year calculus students. By refining assessment strategies, educators could foster higher-order thinking skills in their students, promoting a more comprehensive understanding of the subject matter.

Having started at UKZN as an undergraduate in the BSc Augmented Programme, and now with his PhD successfully behind him, Ntuli hopes to pursue a career as an academic and researcher.

For more insights, Dr. Ntuli discussed his research in an interview with ENCA, which you can watch here. Additionally, you can read more about his work in this news coverage by IOL here.

In his spare time, he is an avid runner, participating in full and half marathons on a regular basis. He thanked his family and church for their support, as well as his supervisor, Professor Anesh Maharaj for his unwavering support, invaluable contributions and mentorship.

Words: Sally Frost

Photograph: Sethu Dlamini