This article presents a case study of two Grade 5 boys' argumentation concerning addition and subtraction of negative numbers while using an interactive tablet-based application simulating positive and negative tiles. We examine the properties of integers they conjectured, and the kinds of evidence and arguments they used to support their…

After years of noticing the challenge our students have with fraction operations, we decided to implement a scaffold approach that focuses on using benchmarks to better develop both students' understanding of a fraction as a quantity and their ability to think about fraction operations meaningfully. While we found this approach supported students…

The relation to operands (RO) principles describe the relation between operands and answers in arithmetic problems (e.g., the sum is always larger than its positive addends). Despite being a fundamental property of arithmetic, its empirical relation with arithmetic/algebraic problem solving has seldom been investigated. The current longitudinal…

It is critical that elementary students develop understanding of fractional numbers because understanding concepts such as fraction magnitude predict later mathematics success. Representing fractions in multiple ways assists students in developing a sense of fraction magnitude. A systematic approach to presenting multiple representations is the…

Studies on math learning programs are lacking that consider a wide set of outcome variables, and students' practice behavior. Therefore, we investigated whether an adaptive arithmetic learning program fosters students' math performance (addition and subtraction), math self-concept, and a reduction of math anxiety, and how practice behavior…

This study employed an alternating treatments design to compare the effects of two types of practice conditions on the subtraction fact fluency in a fifth-grade classroom. Eight, fifth-grade students participated in the study over a 5-week intervention period practicing addition and subtraction facts in a "fact families" condition (A +…

The number line and the neutralization model have been used very extensively in teaching integer additions and subtractions for decades. Despite their advantages, issues concerning subtractions on these models are still debatable. Therefore, the neutralization on an empty number line (NNL) model is proposed in this research to help students better…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

Developing textbooks of optimal quality is crucial for enriching the students' learning and understanding. This study examined fraction addition and subtraction problems in the U.S. and South Korean mathematics textbooks according to the types of denominators. In particular, we investigated Everyday Mathematics (EM) and South Korean mathematics…

Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…

Learning fractions is a critical step in children's mathematical development. However, many children struggle with learning fractions, especially fraction arithmetic. In this article, we propose a general framework for integrating understanding of individual fractions and fraction arithmetic, and we use the framework to generate interventions…

Many students fall below benchmarks in the area of fractions computation, particularly students with disabilities. Self-regulated strategy development (SRSD) is one strategy with proven effectiveness for improving outcomes for students with disabilities, although very few studies have applied SRSD to the area of mathematics. In this study, we used…

Writing and evaluating contextual problems is an important task in the work of teaching, and thus is part of the knowledge that prospective teachers must develop. In dealing with word problems posed both by children and themselves, prospective teachers will need to attend to the realism of the context and the consistency between the operation and…

In the current study we examined the effect of a self-regulated strategy development intervention on the fraction calculations of students with or at risk for disabilities using a multiple-baseline-across-sites, single-case design. Specifically, the intervention package addressed the following skills: adding and subtracting fractions with unlike…

The current study examines the mental computation performance owned by students at fifth grade. This study was carried out with 118 fifth graders (11-12-year-olds) studying at 3 randomly selected primary schools that served low and middle socio-economic areas in a city of Turkey. "Mental Computation Test (MCT)" has been used to reach how…