Misconceptions occur as a result of learners' wrong beliefs and experiences, and because subsequent learning is built on these misconceptions, they cause new concepts to be learned incorrectly. Studies show that students have problems in making sense of many mathematical concepts in mathematics teaching processes and this situation can be…

This research investigates errors and misconceptions among learners in algebraic education by utilizing Koch's error analysis method alongside the Structure of the Observed Learning Outcome (SOLO) taxonomy. The primary aim of the investigation is to discern the kinds of errors and cognitive stages demonstrated by Grade 9 students when engaged in…

South African learners' performance in mathematics, both locally and internationally, has raised significant concerns, particularly in the realm of algebra. To address this issue, a mixed-methods study was conducted to explore the effectiveness of using algebra tiles to teach algebraic expressions. The study aimed to investigate algebraic…

Our research with Grade 9 learners at a school in Soweto was conducted to explore learners' understanding of fundamental fraction concepts used in applications required at that level of schooling. The study was based on the theory of constructivism in a bid to understand whether learners' transition from whole numbers to rational numbers enabled…

Visualisation is an important part of the cognitive process in mathematics. Pedagogical-psychological theoretical frameworks concerning cognitive processes consider perception and visualisation as basic conditions for the creation of correct mental imagery. This study examined visualisation as a key factor in the development of geometric concepts…

How errors are dealt with in a mathematics classroom is important as it can either support or deny learner access to mathematical knowledge. This study examines how a teacher, who participated in a professional development programme that focused on learner errors, engaged with mathematical errors in her Grade 9 classroom. Data were collected over…

In many ways, algebra can be as challenging for teachers as it is for students. With so much emphasis placed on procedural knowledge and the manipulations of variables and symbols, it can be easy to lose sight of the key ideas that underlie algebraic thinking and the relevance algebra has to the real world. In the The Xs and Whys of Algebra: Key…

In this article, the author describes a week of "timely" open-ended lessons with a high ability Y9 group of boys. He gives lessons that would give the students some sense of purpose, as they try to generate a mathematical entity to represent something they used regularly. He states that understanding metric time is something his students…

Ninth-grade students' (n=90) responses to impromptu, in-class writing assignments were examined to evaluate students' understanding of mathematical concepts. Participating teachers benefited by seeing how students' writings may reveal misconceptions concerning mathematical concepts, skills, and generalizations. (MDH)

Over a period of about 3 years, 3204 students in Grades 4 to 10 completed 9862 tests to identify and track their interpretation of decimal notation. Analysis of the longitudinal data demonstrates that different misconceptions persist among students to different degrees and in different patterns across the grades. Estimating the prevalence of…