The purpose of this study is to examine how the categorization skills of the 6th grade students in fractions are distributed and to determine the classification errors made by the students, along with the procedural errors of the students in fractions. The descriptive survey model, one of the quantitative research methods, was used in the study.…

Fractions are core content of elementary school mathematics, and conceptual knowledge of fractions is essential when developing a comprehensive understanding of fractions. Previous research, however, has indicated limitations in student teachers' fraction knowledge. This study investigated 57 Swedish elementary school student teachers' conceptions…

The aim of this study was to develop an instrument for assessing sixth-grade students' number sense skills in fractions and decimals. This study was conducted on 452 sixth graders (10-11 years old) from the western region of Turkey. The construct validity of the number sense test (NST) was examined via exploratory factor analysis (EFA) and…

Diagrams and in general the use of visualization and manipulative material play an important role in mathematics teaching and learning processes. Although several authors warn that mathematics objects should be distinguished from their possible material representations, the relations between these objects are still conflictive both from an…

This article models how to plan and facilitate implementing the same task in two sixth-grade classrooms with two different learning goals using the Five Practices structure.

Preservice teachers commonly struggle with topics related to fractions, ratio, and proportion. The use of double number lines can facilitate the teaching in these areas and provide autonomy and flexibility in mathematical thinking. Moreover, double number lines support many topics in the curriculum, including unit rate, convenience scaling, and…

In this study, it is aimed to comparatively examine practice questions and sample solved questions about the multiplication of fractions in mathematics textbooks in Turkey and Singapore. In this direction, document analysis was used as a research method. Descriptive analysis was used in the analysis and the questions in the books were examined in…

We explore the responses of 26 prospective elementary-school teachers to the claim "1/6.5 is not a fraction" asserted by a hypothetical classroom student. The data comprise scripted dialogues that depict how the participants envisioned a classroom discussion of this claim to evolve, as well as an accompanying commentary where they…

The teaching of fractions is often identified as the point in primary school instruction when the "wheels tend to fall off". While there could be many reasons for this, the overuse of one 'preferred' resource at the expense of a range of representations will often create gaps in understanding at best, and misconceptions at its worst. In…

In this article, the authors introduce and illustrate a new activity that involves "follow-up equations," which are equations that follow up on ideas children have already expressed when solving fraction story problems. Specifically, teachers pose story problems and purposely attend to fraction ideas that arise in children's strategies…

This research aims to 1) develop an effective Active Learning plan combined with skill practice according to the 70/70 criterion, 2) study the learning achievement index through Active Learning combined with skill practice, and 3) investigate the satisfaction towards Active Learning combined with skill practice. The sample group consisted of 27…

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…

Since mathematics scores have not improved appreciably in the last 20 years, a need exists to improve fraction instruction for preservice teachers (PSTs), so future elementary students are more successful with fractions (NCES, 2019). Unfortunately, it appears that many future teachers have not mastered fractions to the point they can teach…

It is well known that fraction knowledge is relevant for later success in mathematics. However, many students still face difficulties when dealing with fractions. Predictors of fraction knowledge have been widely examined. Systematizing "mathematical" predictors, whether their predictive contributions are direct or indirectly mediated…

Learning fractions poses a challenge for many elementary school students, including applying fraction knowledge in novel contexts. For instance, there are substantial individual differences in students' tendency of spontaneous focusing on quantitative relations (SFOR), which is related to the development of rational number knowledge. In this…