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…

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…

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…

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…

In this study, it was aimed to determine the errors and misunderstandings of 5th and 6th grade middle school students in fractions and operations with fractions. For this purpose, the case study model, which is a qualitative research design, was used in the research. In the study, maximum diversity sampling, which is a purposeful sampling method,…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, 2017) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments examining…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…

This study examined discussions centered on precise mathematical language use in two fifth grade classrooms. Drawing on episodes from lessons in which teachers focused on encouraging mathematics reasoning, our analysis examines the relationship between precise language use and mathematical justifying. We present three classroom episodes that…

In the Hypothesis-Experiment-Instruction (HEI) method students are presented with a problem with three or four answer alternatives, which leads them later to recognize the distribution of choices, discuss a variety of ideas among them, and integrate distributed pieces of information. This study examined the effects of presenting a problem with or…

This study was concerned with the verification of a learning hierarchy for the mathematical task of adding fractions, when group learning procedures involving teacher-student interaction were used. Through a task analysis procedure a hierarchy of 13 subordinate skills was hypothesized, behavioral objectives were specified, and a curriculum…

Following the Migrant Student Record Transfer System skills list, this checklist, designed for non-English speaking students, is a system for rapidly evaluating a student's skill level and for keeping track of the student's mastery of suggested objectives at the fifth and sixth grade levels. Objectives to be mastered with 100% accuracy include:…