This paper analyses learners' common errors in simplifying algebraic problems. 102 Grade 10 learners from three rural schools in South Africa participated in the study. Following a quantitative approach, content analysis of learners' responses to algebraic tests revealed that while learners commit several errors in algebraic problems, encoding and…

This article considers the rise of generative Artificial Intelligence (GenAI) in the context of secondary mathematics education, focusing on its responses to cognitively demanding tasks and the pedagogical implications of these interactions. Using tools such as ChatGPT (OpenAI) and Gemini (Google), we investigate how GenAI engages in complex…

The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…

This qualitative review aims to describe the current status of problem-based learning (PBL) implementation in mathematics and identify research gaps in the area of investigation. Literature was searched using the ERIC and Google Scholar search engines. The inclusion/exclusion criteria included: articles published in reputable journals in English…

This study focuses on equivalent transformations of equations in the context of secondary school education. Solving (determining the solution set of an equation), normalizing (transforming an equation to reach a certain form), and reorganizing equations (isolating variables in formulae) are discussed as different possible applications of these…

This article presents several mathematics problems on the same theme that can be used in class or for independent study. It is very difficult to show students how mathematics research is done by mathematicians, so the author first introduces a problem that can be tackled solely by arithmetic and then gives an idea of how a mathematician might…

Discrete mathematics and mathematical modelling, along with the educational discourse surrounding these, have many connections. However, ways that the educational discourse on discrete mathematics can benefit from the inclusion of examples of mathematical modelling and the accompanying discussion are currently under-researched. In this paper, we…

Much attention has been paid to computational thinking (CT) as a problem-solving approach across various curricula, particularly in mathematics. Most studies solely used a digital instrument or examined transfer of program solving ability, neglecting the mathematics knowledge domain or how the novel digital instrument functions alongside the…

In this article, we explored Grade 11 learners' algebraic and geometric connections when solving Euclidean geometry riders. A qualitative interpretive case study design was followed. Thirty Grade 11 learners from a non-fee-paying secondary school in the Capricorn North district of South Africa were conveniently sampled to participate in this…

Background/purpose: This research aimed to 1) Compare mathematical problem-solving skills and academic achievement before and after learning the topic of Basic Counting Principles of Grade 11 students who were taught by traditional learning methods and open learning approach. 2) to compare mathematical problem-solving skills and academic…

Two problems, both from Gaspar Nicolas' "Tratado da Prática d'Arismética", published in 1519 are considered in this study. The tasks were carried out using pencil, paper and students from Portuguese schools. The aim was to explore the following students' performances: 1. The students were able to recognize the "error",…

With the system changes made in 2012 in Turkey, the fifth grade was transferred from the primary school level to the secondary school level. For this reason, secondary school teachers were forced to teach mathematics courses to a group of students they had never met before. Fifth-grade students do not deal with algebra and cannot use equations to…

For over a decade, Which One Doesn't Belong? (WODB; Danielson, 2016) has been a beloved classroom routine that invites students to engage in mathematical decision-making and justification. In the WODB routine, four related figures are shown to students, and they are asked to decide which of them doesn't belong with the other three. The beauty of…

Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

Metacognition supports students in successfully working through struggle by equipping them with the tools to maintain an awareness of what they are doing and to change directions when needed to overcome obstacles. Thus, it is of little surprise that effective problem solvers spend a significant amount of time analyzing tasks relative to the amount…