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,…

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.…

Fractions are among the most problematic concepts that children encounter in their primary school years because of the many different conceptions of fractions. Textbook analyses have tried to provide insights into how fractions are introduced, focusing on the different concepts and representations of fractions. In this paper, we contribute to…

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…

Conceptual and procedural instruction order may affect students' learning and generalization of math skills. This study compared two instruction sequences, concepts-first and iterative, and their effect on fraction performance through a class-wide intervention. Fourth-grade students (N = 114) were randomly assigned to the concepts-first,…

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…

Purpose: The purpose of this paper is to explore whether and how principles from variation theory can contribute to the planning of teaching and learning beyond learning study. Design/methodology/approach: We study whether and how principles from variation theory contributed to a group of teachers' planning of teaching and learning about decimal…

Understanding of fractions is difficult for Indonesian students. This often leads to misinterpretation in solving fractional problems. In this study, a task aiming at identifying students' struggles in understanding the basic concept of part-whole relationships in fractions was developed and tested with six 4th-grade students. The task uses…

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…

This qualitative document analysis study reports on opportunities to learn provided by textbooks for mathematics content courses for pre-service elementary teachers. Specifically, the study examined opportunities to engage in problem posing and quantitative reasoning, in the context of fractions, provided by six textbooks commonly used in the…

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…

For students to develop adequate conceptual understanding about fractions, they require experiences that afford them opportunities to think flexibly about multiple interpretations of fractions. This article presents a sequence of lessons designed to offer such experiences for students in Years 3 and Year 4. The lessons adopt a challenging tasks…

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…