Research about the optimal methodologies for guiding the training of primary school instructors in the instruction of early algebra remains in the process of determination. This manuscript delineates the methodology involved in developing and validating an assessment tool to evaluate the mathematical acumen of prospective primary educators in the…

In this article we aim to deepen our understanding of the content and nature of the early childhood teacher's knowledge, focusing on those aspects which might promote students' algebraic thinking. Approaching arithmetic from the viewpoint of algebra as an advanced perspective and considering the analytical model "Mathematics Teachers'…

In order to promote the design of innovative instructional activities at the Linear Algebra, we perform a design-based research project to explore how to teach Linear Algebra at the university level. In this article, we present the results of three cycles of a teaching experiment that we carried out to design, try out, and improve a local…

The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…

Students' difficulty in learning and suitably understanding the concept of the algebraic variable has been studied with a number of tools and documented for several populations. Little research has been conducted, however, using the same tool to explore understanding of the notion among populations from different countries in an attempt to…

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…

The present study tries to identify the "picture in mind" that students' have about defining, proving and modelling. We access to it through external representations of their mental representations; in particular, from the way in which these representations are expressed in written form (sentences and situations). In the study we have…

This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr…

This volume of the 30th annual proceedings of the International Group for the Psychology of Mathematics Education conference presents: plenary panel papers; research forum papers; short oral communication papers; and poster presentation papers from the meeting. Information relating to discussion groups and working sessions is also provided.…