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…

In the body of knowledge in mathematics education research, fractions are one of the researchers' concerns. The reason is because fractions are very difficult for students to understand. This study explores elementary school students' knowledge and obstacles in dealing with the multiplication of fractions. This study employs descriptive…

This paper presents findings from a study that examined the strategies that children, who had only been taught the part-whole fraction sub-construct at school, used for finding the fraction associated with solving varied partitive quotient problems. A qualitative, microgenetic research design was used involving nine year 5 (aged 9-10) children…

The present study tests two predictions stemming from the hypothesis that a source of difficulty with rational numbers is interference from whole number magnitude knowledge. First, inhibitory control should be an independent predictor of fraction understanding, even after controlling for working memory. Second, if the source of interference is…

This article explores three attributes of teachers' understanding of fraction magnitude: the accuracy and reasonableness of teachers' estimations in response to fraction arithmetic tasks as well as the alignment of the estimation strategies they used with the concept of fraction magnitude. The data were collected from a national sample of…

This research aims to explore students' learning obstacles in solving fraction problems in elementary school. This qualitative research used a case study method. The research subjects involved 30 third-grade elementary school students from two different schools in Bandung City, Indonesia. The instruments utilized were test and non-test. The test…

We examined the development of numerical magnitude representations of fractions and decimals from fourth to 12th grade. In Experiment 1, we assessed the rational number magnitude knowledge of 200 Chinese fourth, fifth, sixth, eighth, and 12th graders (92 girls and 108 boys) by presenting fraction and decimal magnitude comparison tasks as well as…

Attending to the whole unit that a number refers to in a mathematical problem situation and showing flexibility in coordinating different units are foundational for mathematical understanding. In this study, we explored teachers' attention to and flexibility with referent units in situations involving fractions and fraction multiplication. Using…

Students enrolled in post-secondary developmental mathematics courses hold mathematical misunderstandings that begin before their college careers. Specifically, these students struggle with conceptual understanding of fractions, ratios, and proportions. The Common Core State Standards in Mathematics outline standards for K-12 mathematics…

We present the evolving fraction conceptions of two elementary school children with mathematics learning disabilities (MLD). We use qualitative analyses to capture the mathematical knowledge and experiences of each child and show how teaching was used to support advancement of their fractional reasoning. Results illustrate two viable pathways of…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

Fractions are highly important. Therefore, it is crucial to understand the developmental trajectory of fraction knowledge and its main predictors and consequences. Our research team has proposed that we have a neurocognitive architecture dedicated to processing nonsymbolic ratios, which serves as a startup tool for fractions: the Ratio Processing…

A formative pilot study of a fractions intervention was conducted to address the intervention's potential for improving fifth-grade struggling students' knowledge of fractions, and to identify any logistical or instructional design issues, before scaling up for a randomized control trial. In the first section, we provide details of the formative…

In this study, we investigated which teacher characteristics influence student proficiency development regarding fractions in Grade 5 of Dutch primary education. At least three domains of research (i.e. perspectives) on effective teaching can be distinguished: studies focusing on teachers' background characteristics, on their knowledge and…

Making sense of fractions is critical for building the mathematical competence of upper elementary students with and at-risk for a mathematics learning disability. The primary aim of this study was to investigate the effectiveness of teaching students with and at-risk for learning disabilities an intervention in which they learned to construct…