Many U.S. students possess only a weak knowledge of fraction arithmetic. I hypothesize that textbooks are a critical reason for students' poor performance on fraction arithmetic. This is not because of what textbooks contain but rather because of what they lack. Distributions of fraction arithmetic problems in textbooks are imbalanced, with…

Background: Digital game-based learning is gaining increased attention from both researchers and educators for improving mathematics instruction. However, the evidence for game-based learning is mixed and research with rigorous research design and analyses are limited. Objective: Here, in a pre-registered randomized controlled study, we…

This study examines the collective mathematical reasoning when students and teachers in grades 3, 4, and 5 explore fractions derived from length comparisons, in a task inspired by the Elkonin and Davydov curriculum. The analysis showed that the mathematical reasoning was mainly anchored in mathematical properties related to fractional or algebraic…

This study investigates the use of manipulatives by elementary students working on a fraction task. Extending previous work on the role played by the manipulatives in students' activity, we aim at describing how the choices made for the task design disrupt students' activity, creating opportunities to learn. The theoretical underpinnings allow…

Cignition delivers virtual tutoring in math and ELA, led by experienced educators. Their approach focuses on data-informed instruction and collaborative learning that encourages student-to-student interaction to build students' conceptual understanding. After a 2020 efficacy study of its 1:1 math tutoring offering, Cignition developed a group…

This study explored the design and implementation of the Cover-up and Un-cover games, two manipulative-based fraction games, in 14 fifth-grade classrooms. We examined how the fraction concepts were integrated into the game design and explored the nature of teacher-student interactions during games using lesson videos. Our examination showed that…

Many students' knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process and under…

Many students' knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's integrated magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process…

Benchmarking is an important strategy for comparing the size of fractions. In addition, knowing whether a given fraction is greater or less than a particular benchmark (e.g., one-half) can support students with accurately locating the fraction on a number line. This article offers a game-based activity that engages students in discussions around…

All students should have opportunities to develop their ability to reason mathematically. Gersten and Chard (1999) support this stance with respect to students with learning disabilities: "Even if students are not automatic with basic facts, they still should be engaged in activities that promote the development of number sense and…

This "Math Snacks" intervention measured 741 fifth grade students' gains in conceptual understanding of core math concepts after game-based learning activities. Teachers integrated four "Math Snacks" games and related activities into instruction on ratios, coordinate plane, number systems, fractions and decimals. Using a…

Collaborative and individual learning are both frequently used in classrooms to support learning. However, little research has investigated the benefits of combining individual and collaborative learning, as compared to learning only individually or only collaboratively. With our study, we address this research gap. We compared a combined…

Intelligent Tutoring Systems (ITSs) are beneficial for individual students learning in several domains, including mathematics where they have been used to support both secondary and elementary students. Collaborative learning may be beneficial to include in ITSs, particularly for conceptual knowledge. There is little work on collaborative ITSs,…

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 literature seems limited in what is known about conceptual processes that underlie evolution of students with learning disabilities (SLD) conceptions of fractions. This exploratory study examines how a foundational scheme of unit fractions (1/n) may evolve through the mathematical activity of two fifth grade girls. We analyze data segments…