This study explored students' mathematics-related beliefs and the relationship between the beliefs and their strategies for solving non-routine mathematical problems. The study was guided by Daskalogianni and Simpson's 2001 belief systems categories and strategies for non-routine mathematical problems. The participants were 625 grade 11 students…

A relevant aim of research in education is to find and study the reasoning lines that students deploy when dealing with problematic situations. This can be done through an analysis of the answers students give to a questionnaire. In this paper, we discuss some methodological aspects involved in the quantitative analysis of a questionnaire by means…

This article reports on using open-response questions to reveal the level of, and change in, conceptual understanding of a small sample of Grade 11 learners of trigonometry in a South African high school. The investigation used learner response sheets in a regular classroom with the teacher as researcher. Combining the idea of concept image and…

Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

In general, mathematical representations such as formulae, numbers, and graphs are the inseparable components in science used to better describe or explain scientific phenomena or knowledge. Regardless of their necessity and benefit, science seems to be difficult for some students, as a result of the mathematical representations and problem…

We present a summary of a study carried out with students of the first year of Bachillerato (the first of two pre-university non-obligatory secondary education courses in Spain) to determine and analyse some of their errors and difficulties in learning inequalities with the aim of improving the teaching-learning process of this topic. The study…