In this article, we examine how 10th graders make use of different intertwined representations when solving algebraic word problems. It is structured in a quantitative phase, with 61 students and a subsequent follow-up case study with nine pairs of students. We found that drawings and tables, used as auxiliary representations within variants of…

To improve students' mathematics achievement, their errors should be treated as an opportunity to stimulate conceptual and procedural understanding. Using a teaching scenario, this study investigated 40 high school teachers' analyses of and responses to a student error(s) in solving a quadratic equation by using the factoring method. The teachers'…

When translating word problems into equations, a common error consists of using the same letter to refer to two different quantities. This error, called multiple referents for the unknown, can be connected to the existence of deictic or indexical expressions within the problem statement. This paper aims to analyse the influence of indexical…

In this article, we present the results of a research study that explores secondary students' capacity to perform translations of algebraic statements between the verbal and symbolic representation systems through the lens of errors. We classify and compare the errors made by 2 groups of students: 1 at the beginning of their studies in school…

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…