Teaching and learning mathematics in South Africa (SA) is characterised by serious challenges because the pass rate in Mathematics is always below the expected level. The introduction of the Curriculum Assessment Policy Statement (CAPS) ushered in new hope that the situation would improve. However, teachers still encounter challenges when they use…

Introducing new concepts to learners in an order of increasing complexity appears to be beneficial for learning, but typically introduction of concepts does not always adhere to this principle. We examined whether introducing new algebra concepts in a contrasted manner or in an order of increasing complexity instead of a different more typical…

This study was framed within a quantitative research methodology to develop a concise measure of calculus self-efficacy with high psychometric properties. A survey research design was adopted in which 234 engineering and economics students rated their confidence in solving year-one calculus tasks on a 15-item inventory. The results of a series of…

The changes in our society in recent years and the consequent idiosyncrasy of young people demand new teaching methodologies. The methodology known as flip teaching, in which pupils study the subject before the class experience, using the material given by the teacher, makes it possible to turn the classroom into a place to solve different…

Increasing and decreasing functions can be combined into a quadratic to explore the competing demands of number of sales, price points and profit (or loss). An interesting application of taxation rates is also explored.

In this article, the authors present the use of digital tape diagrams--implemented using GeoGebra (2001) dynamic mathematics software--as a support to static diagrams to pose and solve proportional reasoning tasks. They show how dynamic sketches can allow students to explore standard tasks in proportional reasoning in ways that emphasise…

This informal essay is based on a presentation James Tanton gave at the Australian Association of Mathematics Teachers (AAMT) 'Why Maths?' Conference in 2019. It begins by offering two first steps to problem-solving that Tanton believes are key for finding success--and joy--in doing mathematics: (1) Be human! Have an emotional reaction to the…

Many university and high school introductory physics courses include a laboratory portion where students follow a manual to conduct "cookbook" experiments. Here, we present an authentic research project for introductory physics students that focuses on kinematics that can be done outside a formal laboratory space. This experiment can be…

MathCheck is a relatively new online tool that gives students feedback on their solutions to elementary university mathematics and theoretical computer science exercises. MathCheck was designed with constructivism learning theory in mind and it differs from other online tools as it checks the solutions step by step and shows a counter-example if…

When teaching through problem solving, effective mathematics teachers need to lead discussions that assist students in making connections between different solution strategies. However, while teaching a methods course for preservice teachers (PSTs), we noticed that after solving a problem and presenting various solution strategies, many PSTs…

Many pre-service mathematics teachers in South Africa are apprehensive about the content of Euclidean geometry, because they did not study Euclidean geometry in high school but will be expected to teach the content when they start their teaching career. This article reports on a study that explored the role of semiotic representations in…

Mathematical reasoning requires perseverance to overcome the cognitive and affective difficulties encountered whilst pursuing a reasoned line of enquiry. The aims of the study were: to understand how children's perseverance in mathematical reasoning (PiMR) manifests in reasoning activities, and to examine how PiMR can be facilitated through a…

The teaching of Mathematics in the context of the Mathematical Olympiads in Brazil constitutes a context of research still little considered, with particular interest in the teaching and the learning phenomena. In Brazil, we identified a large number of teachers and students who do not participate in official math competitions, such as the…

This study aimed to develop mathematics teaching anxiety scale for prospective primary school teachers. It was designed based on survey method and conducted with four sampling group consisting of 956 prospective primary school teachers at Education Faculties in Turkey. First sampling group was consisted of 404 prospective primary school teachers…

Self-efficacy, the belief in one's ability to succeed in learning tasks, predicts learning and success in education broadly and physics specifically. While self-efficacy increases for students in most introductory science and mathematics courses, self-efficacy consistently decreases for women in physics courses. This study used the experience…