This article focuses on first-year university students' understanding of concepts related to third-degree polynomial and trigonometric functions that they encountered during their study of Grade 12 mathematics. In this study three online questions from two first-year mathematics quizzes at the University of KwaZulu-Natal were analysed. The first…

Achieving proficiency in fundamental differential calculus concepts remains a persistent challenge for grade 12 students, raising concerns among mathematics teachers and policymakers. Despite the widely acknowledged applications of differential calculus across diverse disciplines, global examination diagnostic reports consistently highlight…

This case study explored Grade 12 learners' misconceptions in limits of functions. The study aimed at understanding problems that learners face in learning the concepts of limit by analyzing misconceptions that learners have and identifying the possible sources of these misconceptions to take remedial action. An exploratory research design was…

Mathematics low achievement has undeniably been found in both national examinations and international assessments. An educator needs to be aware and determine the factors in students' achievement. However, there were no observable studies focusing on the mediating effect of students' attitudes toward career aspiration and academic achievement.…

In the State of Queensland in Australia, Years 11 and 12 students can opt to study calculus based or non-calculus based mathematics. Calculus based mathematics subjects are a prerequisite for Science, Technology, Engineering and Mathematics (STEM), which has been identified as critically important for current and future productivity by the…

Conceptual understanding of calculus is crucial in the fields of applied sciences, business, and engineering and technology subjects. However, the current status indicates that students possess only procedural knowledge developed from rote learning of procedures in calculus without insight of core ideas. Hence, this paper aims to assess students'…

Several studies have explored students' understanding of the relationships between definite integrals and areas under curve(s). So far, however, there has been less attention to students' understanding of the Fundamental Theorem of Calculus (FTC). In addition, students' metacognitive experiences and skills whilst solving FTC questions have not…

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures,…

The teaching of probability has changed a great deal since the end of the last century. The development of technologies is indeed part of this evolution. In France, continuous probability distributions began to be studied in 2002 by scientific 12th graders, but this subject was marginal and appeared only as an application of integral calculus.…

Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one…

This qualitative case study in a rural school in Umgungundlovu District in KwaZulu-Natal, South Africa, explored Grade 12 learners' mental constructions of mathematical knowledge during engagement with optimisation problems. Ten Grade 12 learners who do pure Mathemat-ics participated, and data were collected through structured activity sheets and…

In this paper, we explore an approach to understanding how multimodality works in a community of practice. Using a social learning framework, we show how a community of practice, involving a pair of high school students, engaged in perceptual, bodily, and imaginary experiences while discussing about calculus concepts in a dynamic geometry…

This paper provides a detailed analysis of the mathematical communication involving a pair of high school calculus students who are English language learners. The paper focuses on the word-use, gestures and dragging actions in the student-pair communication about calculus concepts when paper-based static and then touchscreen dynamic diagrams.…

Nowadays, many technological means are available to support teaching, such as the interactive whiteboard, class sets of laptop or netbook computers, and high speed internet access. For mathematics education there are advanced software packages for geometry, algebra, calculus, and statistics, which in many cases are available on line at no cost.…

The paper focuses on analysing grade 12 learner errors and the misconceptions in calculus at a secondary school in Limpopo Province, South Africa. As part of the analysis the paper outlines the nature of mathematics errors and misconceptions. Coding of learners' errors was done through the lens of a typological framework. The analysis showed that…