The objective of this paper is to establish comparisons between the Linear Algebra (LA) approach practiced in Engineering courses offered by Chilean and Brazilian Higher Education Institutions and, for that, teachers from both countries were interviewed. From a methodological point of view, the research consists of two case studies. For the…

This large-scale study characterizes the algebraic learning of a cohort of nearly 800 French students during the last year of middle school (9th grade, 14-15 years old) and examines their evolution in relation to the composition of the classes to which the students belong. Based on the Anthropological Theory of the Didactic (ATD), the study is…

The research reported in this article sought to develop a taxonomy of grade 11 students' levels of understanding in algebraic problem-solving tasks. The student sample was from high schools in the province of Ontario in Canada. Problems from four areas in algebra namely, variables, expressions, equations and word problems were chosen to be…

This article aims to delve into the meaning of school mathematical concepts by their semantic analysis. Concretely, this paper aimed primarily to describe and characterize the meaning of derivative of a function at a point expressed by mathematics pre-service teachers. In order to achieve this goal, we use a semantic framework, in which the…

The aim of this study is to examine the ability of pre-service mathematics teachers to detect errors made in solving questions about matrices. The study particularly focused on revealing the internalization of the teachings such as the meanings and relational dimensions of concepts and operations about matrix. The study was conducted with 26…

The relation to operands (RO) principles describe the relation between operands and answers in arithmetic problems (e.g., the sum is always larger than its positive addends). Despite being a fundamental property of arithmetic, its empirical relation with arithmetic/algebraic problem solving has seldom been investigated. The current longitudinal…

This study diagnoses and explores year eight students' misconceptions and mistakes in algebra. An in-depth exploration of students' misconceptions were carried out by conducting interviews based on the students' work as outlined in a cognitive map. Based on the cognitive maps, it can be seen that the students emphasize procedural knowledge rather…

This study was performed to determine preservice elementary mathematics teachers' solution performance of systems of linear equations using geometric representation, algebraic representation and transition from geometric representation to the algebraic representation and the predictive role of preservice elementary mathematics teachers'…

This paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

This study aimed to examine whether a computational thinking (CT) intervention related to (a) number knowledge and arithmetic (b) algebra, and (c) geometry impacts students' learning performance in primary schools. To this end, a quasi-experimental, nonequivalent group design was employed, with 61 students assigned to the experimental group and 47…

This paper sought to explore the Knowledge of Algebra for Teaching and the algebra difficulties of In-field and Out-of-field Junior High School mathematics teachers using the expanded KAT framework. The study employed the descriptive survey design and involved the participation of 374 mathematics teachers using an achievement test instrument. The…

This research is motivated by a linear equations system, which is the basis for studying necessary linear algebra materials, such as rank, range, linear independent/dependent, linear transformations, characteristic values and vectors. There are still prospective mathematics teachers who have difficulty solving linear equations system and…

The study examines the impact of APOS theory on students' achievement in Elementary Linear Algebra (ELA) in accordance with their adequate prior knowledge (APK) and inadequate prior knowledge (IAPK). The mixed methods were used to determine the problem-solving test in ELA. Data were obtained from 65 industrial engineering students at Andalas…

The aim of this study is to question freshmen's conceptual knowledge on function. In this context, after the teaching of the function, students' skills of defining the concept of function, interpreting the definition and multirepresentation for the function were examined. In the study, qualitative research approach was adopted and was an example…

This study was conducted to assess the students' level of abilities in solving algebraic word problems which is a main component in Science, Technology, Engineering and Mathematics (STEM). It also aims to determine the students' difficulties in solving these problems by using Newman's Model of Error Analysis (NMEA). Furthermore, this study was…