Documenting how students with learning disabilities (LD) initially conceive of fractional quantities, and how their understandings may align with or differ from students with mathematics difficulties, is necessary to guide development of assessments and interventions that attach to unique ways of thinking or inherent difficulties these students…

The purpose of this set of analyses, conducted on a randomized control trial examining the effects of a fourth-grade fraction intervention, was to assess the initial academic deficit severity hypothesis. With this hypothesis, at-risk students with more severe initial academic deficits are expected to profit less from intervention than do students…

Find out how to use photographic images to support the conceptual development of proportional thinking. This paper provides insight into a sequenced activity that promotes student engagement and makes links to familiar and unfamiliar contexts.

This paper demonstrates the explanatory power of Kieren's framework for rational number knowing (1988, 1992, 1993, 1995), renamed here the four-three-four model, by describing the different approaches of Grade 6 students to a quotient context task (sharing three or seven custard tarts between five people) using Kieren's terminology of…

Although many students struggle with fractions, students with mathematical learning disabilities (MLDs) experience pervasive difficulties because of neurological differences in how they process numerical information. These students make errors that are qualitatively different than their typically achieving and low-achieving peers. This study…

The main purposes of this study were to test the effects of teaching at-risk 4th graders to provide explanations for their mathematics work and examine whether those effects occur by compensating for limitations in cognitive processes. We randomly assigned 212 children to 3 conditions: a control group and 2 variants of a multicomponent fraction…

Maree Skillen provides a practical guide to using the free, Skitch app to promote mathematical exploration and understanding. Five activities are provided, with links made to the Australian Curriculum: Mathematics.

Teaching and learning fraction concepts provides challenges in primary schools all over the world. In this article, Shelley Yearley and Catherine Bruce describe a fractions-based research project conducted in Ontario, Canada.

This study sought to review literature pertinent to difficulties encountered by students in the learning and usage of mathematical terminology. The need to carry out this study arose from the concern by the Kenya National Examinations Council, and the general public, over the poor annual results in mathematics. Therefore, the objective of this…

The struggle with fraction learning in kindergarten through Grade 12 in the United States is a persistent problem and one of the major stumbling blocks to succeeding in higher mathematics. Research into this problem has identified several areas where students commonly struggle with fractions. While there are many theories of fraction learning,…

Research on problem-based learning (PBL) has tended to focus on the graduate level of education, paying less attention to the primary school level and to what is involved for students during the implementation of PBL. In this paper we take a step towards addressing this need for research by reporting findings from a descriptive, explanatory case…

To learn from an error, students must correct the error by engaging in sense-making activities around the error. Past work has looked at how supporting collaboration around errors affects learning. This paper attempts to shed further light on the role that collaboration can play in the process of overcoming an error. We found that good…

Educational video games have the potential to be used as assessments of student understanding of complex concepts. However, the interpretation of the rich stream of complex data that results from the tracking of in-game actions is so difficult that it is one of the most serious blockades to the use of educational video games or simulations to…

Given the key role of conversions of representations for mathematical understanding, it is highly relevant to investigate in detail competencies regarding conversions of representations. In particular, a corresponding competence model should not only be developed theoretically, but also examined empirically. However, such empirical studies are…

This paper focuses on an implementation a sequence of instructional activities about addition of fractions that has been developed and implemented in grade four of primary school in Surabaya, Indonesia. The theory of Realistic Mathematics Education (RME) has been applied in the sequence, which aims to assist low attaining learners in supporting…