Constructing formal geometry proofs in is an important topic in the mathematics curriculum. But students' difficulties with proof are well documented. This article focuses on proofs that use triangle congruence postulates in US high school geometry. Examining students' proof reasoning in one-on-one task-based interviews, we analyzed students' oral…

Recent research on the phenomenon of improper proportional reasoning focused on students' understanding of elementary functions and their external representations. So far, the role of basic function properties in students' concept images of functions remained unclear. We add to this research line by investigating how accurate students are in…

It is well known that learner performance in mathematics in South Africa is poor. However, less is known about what learners actually do and the extent to which this changes as they move through secondary school mathematics. In this study a cohort of 250 learners was tracked from Grade 9 to Grade 11 to investigate changes in their performance on a…

The purpose of this research was to explore to what extent probing learners' errors on simplifying algebraic fractions would help them to reduce those errors. The study assumed that students' errors and misconceptions persist because they handle mathematical concepts as if they were isolated chunks of knowledge. A sample of 15 grade 10 girls took…

Little empirical data are available concerning the cognitive abilities of gifted individuals in general and especially those who excel in mathematics. We examined visual processing abilities distinguishing between general giftedness (G) and excellence in mathematics (EM). The research population consisted of 190 students from four groups of 10th-…

The paper describes a study that examined the impact of two teaching approaches "focus on correctness" and "discuss errors" on secondary students' solutions to algebraic inequalities. Two groups of 10th graders were taught by two experienced teachers, Corry and Era, who followed their different didactical beliefs about the use of errors in…

Background: Trigonometry is an area of mathematics that students believe to be particularly difficult and abstract compared with the other subjects of mathematics. Trigonometry is often introduced early in year 8 with most textbooks traditionally starting with naming sides of right-angled triangles. Students need to see and understand why their…

Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…