The purpose of this study was to explore the efficacy of fractions intervention with and without an embedded self-regulation (SR) component for third-grade students at risk for mathematics disabilities. Fractions intervention focused on magnitude understanding and word problems. Embedded SR was designed to support a growth mindset (fostering…

International comparisons of languages have shown how mathematical concepts can be expressed and conceptualised in different languages. For multilingual students, these findings raise the question of how the interplay of languages and conceptualisations shape multilingual learning processes. This paper presents an investigation of case studies of…

The aim of this article is to shift the notion of 'sites' as places of work peculiar to continuous professional development (CPD) to a theoretical level, independent of, yet intimately connected to, their physical meanings, for example universities and schools. Most CPD initiatives have to contend with at least one of these two sites, in which…

In this study, we investigated which teacher characteristics influence student proficiency development regarding fractions in Grade 5 of Dutch primary education. At least three domains of research (i.e. perspectives) on effective teaching can be distinguished: studies focusing on teachers' background characteristics, on their knowledge and…

Students must leave elementary school with a firm understanding of fractions and decimals in order to make satisfactory progress in advanced mathematics. Firm understanding includes manipulation of rational numbers using different models of representation such as area and length. Research has demonstrated that a graduated sequence such as…

The contribution investigates opportunities that an educational tool called Concept Cartoons can offer in future teachers' education, namely in comparison with word problems in standard written tests. The referred empirical study was conducted in two separated consecutive stages, with two groups of future primary school teachers (the first one…

Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and…

Students have difficulties in solving problems of fractions in almost all levels, and in problem posing. Problem posing skills influence the process of development of the behaviors observed at the level of comprehension. That is why it is very crucial for teachers to develop activities for student to have conceptual comprehension of fractions and…

In this preliminary study, to inform a larger study where Year 8 students create an online module for peers, I surveyed mathematics teachers (n = 30) on essential mathematics topics: (a) most critical for students' success, (b) most conceptually challenging for students, and (c) in which more fluency is needed, as well as (d) their likelihood of…

In working towards unraveling the mechanisms of productive collaborative learning, dual eye tracking is a potentially helpful methodology. Dual eye tracking is a method where eye-tracking data from people working on a task are analyzed jointly, for example to extract measures of joint visual attention. We explore how eye gaze relates to effective…

This study investigated 11 pre-service middle school teachers' solution strategies for exploring their knowledge of fraction division interpretations. Each participant solved six fraction division problems. The problems were organized into two sets: symbolic problems (involving numbers only) and contextual problems (involving measurement…

This article examines whether the 7 abilities found in a previous study carried out by the authors to constitute fraction understanding of sixth grade elementary school students determine hierarchical levels of fraction understanding. The 7 abilities were as follows: (a) fraction recognition, (b) definitions and mathematical explanations for…

In this article the authors describe a project during which they unpacked fraction standards, created rigorous tasks and lesson plans, and developed formative and summative assessments to analyze students' thinking about fraction multiplication. The purpose of this article is to (1) illustrate a process that can be replicated by educators…

Guessing, for Pólya, is an important way of getting an initial handle on a mathematical problem. An argument can be made to place guessing in any one of the first three steps of the four-step approach to problem solving as described in "How to Solve It" (Pólya 1945). It could be a part of understanding the problem, devising a plan, or…

Fractions are troublesome for many children, especially students with learning difficulties and disabilities in mathematics. To address this serious educational concern, this article recommends the use of number lines to build fraction sense. Math activities that center on the number line build fraction concepts as early as third grade. A number…