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This article reports on a study which used the APOS (Action‐Process‐Object‐Schema) theory framework to investigate university students’ understanding of limits of functions. The relevant limit concepts were taught to undergraduate science students at a university in Kwazulu‐Natal in South Africa. This paper reports on the analysis of students’ responses to four types of questions on limits of functions. The findings of this study confirmed that the limit concept is one that students find difficult to understand, and suggests that this is possibly the result of many students not having appropriate mental structures at the process, object and schema levels.

Geometry and culture are interrelated, making school geometry closely connected to the environment as well as culture in which it is taught. With regard to this connectedness, the Zimbabwean mathematics syllabus indicates that geometry should be connected to the learners' environment and culture. This article explores teacherrelated challenges to the integration of ethnomathematics approaches into the teaching of geometry. Findings are based on feedback received from questionnaires and focus-group discussions in which 40 in-service mathematics teachers expressed their views on the challenges that affect the integration of ethnomathematics approaches into the teaching of geometry. Major challenges included lack of knowledge on ethnomathematics approaches and how to integrate these approaches into the teaching of geometry; teachers' lack of geometry content knowledge, teachers' views of geometry taught in schools, teachers' competence in teaching geometry, teaching and professional experience as well as resistance to change by teachers. The study recommends that teacher training institutions need to redesign their curricula to include ethnomathematics approaches and that there is need for in-service training on ethnomathematics approaches.

In this paper, we employ the Karmarkar condition to model a spherically symmetric radiating star undergoing dissipative gravitational collapse within the framework of classical general relativity. The collapse ensues from an initial static core satisfying the Karmarkar condition in isotropic coordinates and proceeds nonadiabatically by emitting energy in the form of a radial heat flux to the exterior Vaidya spacetime. We show that the dynamical nature of the collapse is sensitive to the initial static configuration that inherently links the embedding to the final remnant. Our model considered several physical tests on how an initially static stellar structure onset to a radiative collapse.

We describe an approach to develop higher-order thinking skills (HOTS) among first-year calculus students. The ideas formulated by Brookhart to develop HOTS were used to identify from the literature three core abilities that should be targeted. Then eight expected learning outcomes for the development of HOTS were documented, in the context of the study of first-year university calculus. Those expected outcomes were used to formulate sample tasks that were designed to target the development of the eight abilities. A pilot study was done to determine whether the tasks had the high mathematical demand envisaged. It was found that about 37% of the participants did not give any response to the tasks. Further it was found that about 31% of the participants were able to critically evaluate a given possible solution to a problem and make a value judgement. It is recommended that to promote HOTS among students, the formulation of tasks should focus on developing the following abilities: interpreting a general definition or statement in the context of a given model; translating a worded or graphically represented situation to relevant mathematical formalisms; identifying possible applications of mathematics in their surroundings; identifying linkages between groups of concepts and interpreting these linkages in the context of a model; working systematically through cases in an exhaustive way; critically evaluating one’s and others’ presented solutions to a problem; interpreting and extending solutions of problems; and using with reasonable skill available tools for mathematical exploration.