Urban school districts have seen low scores on NWEA Map math scores (Education Recovery Scoreboard, 2024). To foster and promote urban youths' capabilities to learn mathematics, a new method to teach, enhance, and remediate understanding of fractions was developed, Fractions and Signed Numbers Workshop (FracSi). It utilizes the approach of an…

Our research with Grade 9 learners at a school in Soweto was conducted to explore learners' understanding of fundamental fraction concepts used in applications required at that level of schooling. The study was based on the theory of constructivism in a bid to understand whether learners' transition from whole numbers to rational numbers enabled…

Background: Concerning students' difficulties with fractions, many explanatory approaches are based on the distinction between conceptual knowledge and procedural knowledge. For further research in this field, it is thus crucial to make these constructs accessible to valid measurement. Aims: In this study, we aim at developing a test instrument…

We constructed and calibrated an instrument targeting conceptual and procedural fraction knowledge. We used this instrument in a quantitative study with 126 secondary students (7th and 9th graders), testing the hypothesis that there are individual differences in the way students combine the two types of knowledge. Cluster analysis revealed four…

Originally written 30 years ago, this paper is an analysis of the central challenge of schooling--that of engaging fully the powers of students' minds in classroom learning. This challenge maintains its relevance today. The work of engaging what John Dewey referred to as students' "inner attention" becomes the focus of an investigation…

The aim of this article is to shift the notion of 'sites' as places of work peculiar to continuous professional development (CPD) to a theoretical level, independent of, yet intimately connected to, their physical meanings, for example universities and schools. Most CPD initiatives have to contend with at least one of these two sites, in which…

This article investigates the impact of research findings on the representation of proportional reasoning in two commonly used Swedish mathematics textbook series for grades 7-9. A research-based framework that identifies five learning goals for understanding of proportional reasoning was used to analyse the textbooks. The results brought to…

We present the results of an in-depth qualitative study that examined ninth graders' conceptual and procedural knowledge of fractions as well as their approach to mathematics learning, in particular fraction learning. We traced individual differences, even extreme, in the way that students combine the two kinds of knowledge. We also provide…

This study synthesized intervention studies focusing on instruction to improve fraction skills. Seventeen studies met the inclusion criteria: being published in English-language peer-reviewed journals or dissertations between 1975 and 2014, and targeting 3rd- through 12th-grade students struggling to learn mathematics. From the "Common Core…

This study investigates the effect of materials developed based on conceptual change approach on 9th grade students'achievement in the subject of fractions. With this aim, a worksheet, conceptual change text and a two-stage performance test on the subject of fractions were developed. Quasi-experimental research model was used in the study.…