Ambiguity of language can form a barrier to understanding mathematical concepts. The word 'capacity' is problematic as it holds a variety of meanings and might not be understood in school mathematics, to be an aspect of volume. We investigated pre-service primary school teachers' interpretations of 'capacity' when given the definitions of 'volume'…

The aim of this study is to examine the concept images of mathematics educators and pre-service elementary mathematics teachers regarding the relationships between the concepts of slope, rate of change and derivative. Four mathematics educators working in different state universities and responsible for Analysis courses, three pre-service…

This article draws from Hiroko Kawaguchi Warshauer's conceptualisation of productive struggle, which capitalises on experiences that elicit struggle, that is, those that require students to 'expend intellectual effort' and that are productive, in the sense that they seek to 'advance thinking and deepen' understanding of mathematical concepts and…

This pilot study examined the feasibility of using worked examples as a mechanism to improve verbal explanations of fractions concepts among Grade 5 students with mathematics difficulties in a small-scale randomized controlled trial (RCT) before scaling up to a large-scale RCT. Students (N = 49) were randomly assigned to a business-as-usual (BAU)…

This 5-year longitudinal study examined whether high mathematics achievers in primary school had cognitive advantages before entering formal education. High mathematics achievement was defined as performing above Pc 90 in Grades 1 and 3. The predominantly White sample (M[subscript age] in preschool: 64 months) included 31 high achievers (12 girls)…

Special tasks for pre-service teachers (PSTs) in university mathematics courses ("interface tasks") are a common innovation in recent years to overcome the second discontinuity. By this, we mean tasks that are situated by typical everyday challenges of mathematics teaching and in which PSTs must use their mathematical knowledge and…

Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

This study aims to analyze and to describe, in terms of information processing theory, the thinking processes of junior high school students as they solved problems involving direct and inverse proportions. This study design is qualitative and exploratory-descriptive in nature. 26 students in the seventh grade of SMP Negeri 1 Kota Ternate were…

Technological mediums such as dynamic environments with drag-and-drop features have been considered promising agents in helping students explore and generate conjectures about mathematical concepts. This study investigated the dragging modalities sixth and seventh-grade students use in solving proportional problems in a dynamic geometry…

This case study investigated the relationship between five undergraduate interior design students' reasoning with numerical units and reasoning about length and area. The multiplicative concepts frame participants' coordination of numerical units. Differences were found between participants' reasoning about length and area, based on their…

Over the course of the introductory calculus-based physics course, students are often expected to build conceptual understanding and develop and refine skills in problem solving and qualitative inferential reasoning. Many of the research-based materials developed over the past 30 years by the physics education research community use sequences of…

This paper explores magical realism as a theoretical lens for analysing mathematics classrooms. Traditional frameworks often overlook the complexities of teaching and learning, focusing solely on measurable aspects. Inspired by magical realism -- a literary genre blending the fantastical and the everyday -- I propose a new perspective on how…

This study examines the impact of the linguistic transition from Arabic to French on the comprehension of mathematical concepts among first-year middle school students in Morocco. Utilizing a mixed-methods approach, the research analyzes student performance in identifying quadrilaterals and calculating their area and perimeter in both languages.…

In 2020, the COVID-19 pandemic urged authorities to share quantitative information such as infection and death rates. One way of disseminating was through graphs, maps, and diagrams. Such data visualizations communicate numeric data in compact ways, but also require a particular mathematical literacy from readers. We conceptualized this particular…

The importance of mathematical connections in teaching mathematics is broadly acknowledged in the literature. Nevertheless, more research is needed to clarify how different types of mathematical connections manifest in classroom interactions and how they can support student learning. This article uses the commognitive framework to analyse 15…