This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…

This study examined the influence of addition and subtraction practice embedded within a word-problem intervention for Grade 3 students experiencing word-problem difficulty. Students (N = 448) were randomly assigned to one of two variants of a word-problem intervention or a business-as-usual comparison condition. Within the word-problem…

Background/purpose: In modern mathematical education, it is important to develop students' ability to understand the fundamental properties of geometric objects deeply. This makes it relevant to study the additivity of the area of triangles as a property inherent in various kinds of quantities and ways of representing it methodologically in the…

As students develop understanding and fluency in single-digit operations such as addition, they develop sophisticated strategies and number sense (magnitude, number order, and composition). Deficits in number sense and reliance on inefficient approaches can lead to struggle in mathematics. Intervention research in this area reported effects on…

In this paper, we report how 5-year-olds' arithmetic skills developed through participation in an 8-month-long intervention. The intervention program aimed to enhance the children's ways of experiencing numbers' part-part-whole relations as a basis for arithmetic skills and was built on principles from the variation theory of learning. The report…

There is a growing awareness that many children are not developing fast and accurate retrieval-based strategies for solving single-digit addition problems. In this study we individually assessed 166 third and fourth grade children to identify a group of children (called accurate-min-counters) who frequently solved simple single-digit addition…

This study aims to investigate the effect of history-of-mathematics activities on the development of mental computation of middle-grade students and to determine the students' views on the history of mathematics. This study was carried out as an action research project. The participants of the study consisted of 19 seventh-grade students studying…

When two third-graders collaboratively manipulated a multi-modal, digital learning device called TouchTimes (hereafter, TT), that introduces multiplication through visual, tangible and symbolic means, their thinking about quantity shifted from being additive to being multiplicative. In this study, I examine the children's interactions around/with…

This article proposes a practical method of teaching the addition of unit fractions using a series of mirror equation experiments.

A single fact-focused number-string discussion is unlikely to result in all students adopting more flexible and efficient fact strategies; however, these authors have found that repeated engagement in such discussions over time does promote student reasoning about relationships, which in turn leads to increased fact fluency. By cultivating a…

This paper makes a proposal, from the perspective of a research mathematician interested in mathematics education, for broadening and deepening whole number arithmetic instruction, to make it more relevant for the twenty-first century, in particular, to enable students to deal with large numbers, arguably an essential skill for modern citizenship.…

The purpose of this study is to electrophysiologically assess the effect of an individualized education program supported with musical activities on the success of primary school students with computational difficulties. A mixed-methods design consisting of qualitative and quantitative methods was employed as the research model. The research group…

The relation between mathematical achievement in early childhood and future academic success is well established. However, the effect of instruction on mathematical performance is less well-documented and often reliant upon self-report instruction measures and standardized achievement measures. Therefore, this study seeks to use observational data…

Overall mathematics proficiency of fourth graders in the U.S. continues to be poor and students falling at or below the 25th percentile display declining performance (NCES, 2017), which suggests the need for schools to provide supplemental intervention supports as soon as skill gaps are observed. Unfortunately, there is a paucity of small group…

This article reflects critically on the guidance offered to South African teachers in two canonical texts: the Curriculum and Assessment Policy Statements (CAPS) and Mathematics teaching and learning framework for South Africa: Teaching mathematics for understanding (TMU). I make explicit my philosophical orientation, and how 'teaching mathematics…