The purpose of this research was to investigate students' mathematical understandings of fraction division with an ethnomathematics/STEM framework. A small group teaching study (Cobb et al., 2003) was conducted using design research methodology to examine how students interacted with the curriculum. The researcher served as interventionist and…

The number line is a powerful tool for supporting students' understanding of fraction magnitude. Fractions are a critical component of mathematics instruction in the elementary and intermediate grades. More specifically, understanding fraction magnitude is central to mathematical development. Yet, fractions are challenging for many students,…

This study's purpose was to examine the effects of the concrete-representational-abstract integrated (CRA-I) sequence on the performance of students who struggled with rational number concepts. Three students in southeastern U.S. fifth grade class participated in the study. The CRA-I intervention was grounded in the principles of explicit…

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 algorithm for fraction multiplication is relatively easy to memorize and implement with accuracy. The simplicity of the algorithm masks the conceptual complexity involved in making sense of what fraction multiplication means in quantitative situations. One important interpretation of fraction multiplication involves fraction composition,…

This study investigated how three fifth-grade students' understanding of fraction and decimal magnitude evolved over the course of a five-week teaching experiment. Students participated in teaching and learning sessions focused on developing concepts of fraction and decimal magnitude. The following questions guided this study: (1) How do fifth…

Learning progressions can reflect students' continuous in-depth thinking development paths, and their establishment is an iterative process from the construction of hypothetical learning progressions to the verification of that hypotheses. Considering the limitations of the existing verification method of learning progressions based on a rule…

This pilot study examined the feasibility of using worked examples as a mechanism to improve verbal explanations of fractions concepts among Grade 5 students with mathematics difficulties in a small-scale randomized controlled trial (RCT) before scaling up to a large-scale RCT. Students (N = 49) were randomly assigned to a business-as-usual (BAU)…

This study aims to examine the effect of problem posing-based active learning activities on students' problem-posing skills and problem-solving achievement. To this aim, an experimental design with pre-test post-test control group was employed. The participants consisted of two groups of sixth graders, one experimental group (N=23) and one control…

This study investigated children's knowledge of the addition of fractions with unlike denominators. It focussed on the strategies used by children to add fractions with unlike denominators. A cross-sectional survey of Grade 8 children in schools in two districts in Ghana was used. A test on the addition of fractions with unlike denominators was…

The current study investigated the effects of the concrete-representational-abstract integrated sequence (CRA-I) for teaching fifth grade students receiving tier two interventions within a multi-tiered system of support (MTSS). The research questions addressed the following: the extent to which students' rational number skills changed as a result…

The purpose of this study was to investigate the effects of the concrete-representational-abstract--integrated (CRA-I) sequence on students with learning disabilities' performance when learning fraction and decimal concepts. Three elementary-level students in Grades 4 and 6 participated in a single-case multiple probe across behaviors study. The…

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…

PS-I learning approaches with an initial problem-solving phase (PS) followed by an instruction phase (I) can be optimised by providing adaptive (individualised) instruction that builds on students' problem-solving products. A computer-based implementation of both phases offers the possibility of adaptivity at the transition from the…

The intention of the study was to examine the effects of a fraction intervention in a whole-class environment. The intervention aimed to enhance students' conceptual fraction knowledge, with a major focus on fraction magnitude understanding. This study included 120 fifth-grade students in standard classroom settings. Utilizing a cluster randomized…