Students are indeed weak when it comes to understanding fractions and decimals. In line with the national curriculum, whole numbers and fractions are taught first before students start to learn decimals. By the time the students approach decimals, they should have acquired sufficient knowledge of whole numbers but limited knowledge of fractions.…

Building proficiency with fraction arithmetic poses a consistent challenge for students with learning difficulties or disabilities in mathematics. This article illustrates how teachers can use the number line model to support struggling learners in making sense of fraction arithmetic. Number lines are a powerful tool that can be used to help…

This study examines the presence of three conceptual metaphors for fractions -- The measuring stick metaphor, Arithmetic is motion along a path, and Arithmetic is object construction -- in four common and popular Swedish mathematics textbook series for years 1-3. I analyse the introduction of fractions and the kinds of tasks students are given in…

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…

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…

This study tested a novel approach to capitalizing on the benefits of play for informal math learning. Two experiments evaluated a platform called "Fraction Ball," that provides an embodied, playful, and physically active learning experience by modifying the lines on a basketball court to support rational number learning. In the Pilot…

Teachers' understanding of the concepts they teach affects the quality of instruction and students' learning. This study used a sample of 303 teachers from across the USA to examine elementary school mathematics teachers' knowledge of key concepts underlying fraction arithmetic. Teachers' explanations were coded based on the accuracy of their…

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction "x/y," children are often taught to use "partitioning": break the whole into "y" parts, and shade in "x" parts. Past research has shown that partitioning on number lines supports children's fraction…

Understanding fraction magnitudes is foundational for later math achievement. To represent a fraction x/y, children are often taught to use "partitioning": Break the whole into y parts and shade in x parts. Past research has shown that partitioning on number lines supports children's fraction magnitude knowledge more than partitioning on…

To explain children's difficulties learning fraction arithmetic, Braithwaite et al. (2017) proposed FARRA, a theory of fraction arithmetic implemented as a computational model. The present study tested predictions of the theory in a new domain, decimal arithmetic, and investigated children's use of conceptual knowledge in that domain. Sixth and…

Despite the research regarding the importance of peer review and feedback in pre-service special education teachers, there exists a gap in teaching complex mathematical concepts such as fractional operations. This study sought to address this gap by investigating how pre-service teachers can effectively appraise and revise peer-generated teaching…

We analyzed item responses provided by a nationwide sample of 990 in-service U.S. middle grades mathematics teachers to a novel survey focused on fraction arithmetic. The survey targeted four components of reasoning in terms of measured quantities: "Referent units," "Reversibility," "Partitioning and iterating," and…

The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of…

Students often show difficulties in understanding rational numbers. Often, these are related to the natural number bias, that is, the tendency to apply the properties of natural numbers to rational number tasks. Although this phenomenon has received a lot of research interest over the last two decades, research on the existence of qualitatively…

This document includes instructional tips on: (1) Building on students' informal understanding of sharing and proportionality to develop initial fraction concepts; (2) Helping students recognize that fractions are numbers that expand the number system beyond whole numbers, and using number lines to teach this and other fraction concepts; (3)…