Mathematical representations are 'visible productions' that embody mathematical ideas. The author guides teachers with suggestions for the use of representations in mathematical problem solving with students. Representations can be used to help make abstract mathematical ideas accessible, allowing teachers and students to interpret, communicate,…

Learners in general struggle when working with word problems. South African learners in particular have an added barrier owing to the many official languages that have been legislated. The South African Department of Basic Education, through its curriculum statements, envisages that problem solving will play a fundamental part in mathematics…

Although student covariation reasoning has been explored in depth to improve understanding of the correspondence between variables, research has focused on studying existing reasoning about variables in Cartesian representations. The working method had a qualitative approach, with a descriptive exploratory scope, the spontaneous representations…

Drawing bar diagrams has been shown to improve performance on mathematical word problems wherein the relational keyword is consistent with the required arithmetic operation. This study extends this by testing the effectiveness of bar diagram drawing for word problems with an inconsistent keyword-arithmetic operation mapping. Seventy-five fifth…

Dyscalculia presenting 3 to 6.5% of all those who need remediation in mathematics to enhance their ability of solving word problem. The study aimed to use sketchnote and working memory-based intervention to enhance word problem solving ability of students with dyscalculia. Thus, the study examined the role of integrated intervention involving both…

This paper aims to discuss the use of Brousseau's Theory of Didactical Situations in mathematics (TDS) for eighth-graders to explore the concept of triangle inequality in Euclidean geometry. Data sources included observation notes, video recordings of lessons, and students' written work. Data analysis was done through a deductive content analysis…

The cognition processes of students with autism spectrum disorder (ASD) in solving mathematical problems is still rarely studied in depth, although the prevalence of the students is increasing. The purpose of this research was to describe the cognition processes of students with ASD in solving mathematical problems. The subjects in this research…

This article is about the systematization and representation young children spontaneously use when they are working on a combinatorial task. In this article, documentations from 123 children working on the same task are analysed. The question asked is if there are any connections between the systematizations and representations used in the…

This study explores first-year university students' reasoning as they learn to draw Lewis structures. We also present a theoretical account of the formal procedure commonly taught for drawing these structures. Students' discussions during problem-solving activities were video recorded and detailed analyses of the discussions were made through the…

Previous research on problem diagrams suggested that including a supportive diagram, one that does not provide necessary problem solving information, may bring little, or even negative, benefit to students' problem solving success. We tested the usefulness of problem diagrams on 12 different physics problems (6A/B experiments) in our massive open…

In this study we investigated how two different approaches to drawing free body diagrams influence the development of students' understanding of Newton's laws, including their ability to identify real forces. For this purpose we developed a 12-item two-tier multiple choice survey and conducted a quasiexperiment. This experiment included two groups…

This paper describes the use of diagrams as self-explanatory tools. It considers the use of diagrams, in general, and more specifically, examines research that is currently being undertaken in the broad field of visualisation. The research participants referred to in this article were Advanced Certificate of Education students and the paper…

The use of pictures created by students as aids in the learning of mathematical concepts and the problem solving process is promoted. (MP)

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces…