The purpose of this study was to understand children's operations on fragmenting schemes while they are engaged with three different visual models, including circle, rectangle, and length model. This study was a sequential explanatory mixed method, which included two phases that happened sequentially with the dominant use of the quantitative…

Introduction: The 2022 NAEP Mathematics Assessment reported the "largest score declines in NAEP mathematics at grades 4 and 8 since initial assessments in 1990" (NAEP, 2022). More disturbing is that those who could least afford to lose ground lost the most. Gaps based on race, gender, and disability remain virtually unchanged from year…

Decimals and the related areas of ratio and proportion are recognised as one of the most challenging and complex areas of mathematics for young children to learn. In this study, four dynamic digital representations were used by Year 4 (9-10 years old) students in a set of video-recorded, individual task-based interviews to explore key concepts of…

This study used traditional and holographic video, along with eye-tracking technology, to examine how preservice teachers' physical act of looking is associated with how they attend to and assess students' fraction reasoning. Findings revealed that, although viewing of holograms may have influenced more focus on students' work area, there was…

The goal of this research was to examine fifth graders' understanding of fractions on the number line. This case-study design focused on the various ways that students represented fractions on number lines. Students responded to task-based interview questions by identifying fractions as a number on the number line as well as equivalency and…

In grade 3, students are expected to be able to represent a fraction on a number line by first identifying the interval from 0 to 1 as the unit and by partitioning the unit as needed on the basis of the denominator. This task extends these grade 3 fraction goals stated in the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010)…

Number lines and area models are both used pervasively in teaching fractions. Prior studies found that second and third graders demonstrated better magnitude knowledge of proper fractions after a 15-minute training using the number line as compared to using the area model. The current study aimed to extend these findings to improper fractions. We…

Prior research shows that multiple representations can enhance learning, provided that students make connections among them. We hypothesized that support for connection making is most effective in enhancing learning of domain knowledge if it helps students both in making sense of these connections and in becoming perceptually fluent in making…

Prior research shows that multiple representations can enhance learning, provided that students make connections among them. We hypothesized that support for connection making is most effective in enhancing learning of domain knowledge if it helps students both in making sense of these connections and in becoming perceptually fluent in making…

This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally explaining how…

Prior research shows that representational competencies that enable students to use graphical representations to reason and solve tasks is key to learning in many science, technology, engineering, and mathematics (STEM) domains. We focus on two types of representational competencies: (1) "sense making" of connections by verbally…

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.

A method of teaching students how to recognize when zeros are necessary and when they may be omitted is presented. (MP)

Examines the use of a ratio table for developing students' conceptual understanding of rational number. The ratio table is an alternative to cross-multiplication and can utilize both additive and multiplicative strategies. It organizes numbers and keeps track of operations and results, which aids the teacher in assessment. (MLB)