This qualitative semi-structured interview study investigated how the opportunity to learn with productive struggle emerges in a teacher's beliefs, anticipation, planning, teaching, and response to struggle in learning mathematics. In this study, the experiences of student struggle in the teaching and learning of fractions was investigated through…

Developing an understanding of fractions is critical, as it is the first connection of whole-number properties to rational numbers within a single framework. The unique properties of fractions necessitate solution processes that are distinctive and often more complicated than whole-number processes, resulting in many students struggling with…

The goal of this research was to examine fifth graders' understanding of fractions on the number line. This case-study design focused on the various ways that students represented fractions on number lines. Students responded to task-based interview questions by identifying fractions as a number on the number line as well as equivalency and…

Developing an understanding of fractions is critical and is an educational focus, as reflected in national standards and principles. This study conducted a quantitative synthesis of 22 experimental studies to investigate the overall efficacy of previously conducted fraction interventions compared to standard instruction. Instruction type and…

Students require knowledge of fraction, arithmetic and integer to tell the time. The purpose of the current study is to discover the conceptual knowledge related to hours, how the students read the clock and use half and quarter concepts to read the time in Turkey. A qualitative research method with a case study approach was used for this…

In this study, the middle school mathematics teachers' knowledge of division of fractions was investigated through the strategies that they proposed and the problems that they posed for division of fractions. The data was collected from 22 middle school mathematics teachers through the task and semi-structured interviews. The data of this case…

When a student struggles with a mathematics task, adults may rephrase or expand initial task instructions to clarify instructions or scaffold problem solving. Yet expanded instructions may not benefit all children, especially children with a mathematics learning disability (MLD). Here, we explore whether expanded instructions differentially affect…

Mixed numbers and fraction in general have been a problem for students not only in understanding the concept of itself, but also in understanding the operation of it, such as addition. Thus, supporting students in learning addition of mixed numbers is needed. The aim of this study is to develop a local instructional theory and materials related to…

Background: Prior research with adults and children suggests that inhibitory control may have a role to play in learning counterintuitive fractions and decimals that are inconsistent with whole number knowledge. However, there is little research to date with primary school-aged children at the early stages of fraction and decimal instruction that…

In this article, the author describes how to help develop students' conceptual understanding of fractions through the tactical card-based game Nearest to One. Nearest to One promotes number-sense based strategies for comparing fractions, such as benchmarking (e.g., Is the fraction greater or less than one-half?) and building to the next whole,…

The present study, conducted from the perspective of cultural history (Certeau, 1982; Chartier, 1990; Chervel, 1990; Julia 2001)), aims to investigate guidelines for the use of teaching materials to teach fractions in the primary school, present in pedagogical manuals of the period from 1930 to 1970. The research is based in references such as…

To test the hypothesis that a higher tendency to "s"pontaneously "f"ocus "o"n "m"ultiplicative "r"elations (SFOR) leads to improvements in rational number knowledge via more exact estimation of fractional quantities, we presented sixth graders (n = 112) with fraction number line estimations and a…

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…

Mathematics instruction can work to open or constrain children's opportunities to learn, and the busy, interactive nature of instruction makes it challenging for researchers to identify patterns in high-quality opportunities to learn. While researchers have documented how whole-group discussions and small-group work can contribute to such…

This research aimed to develop a valid and reliable test to be used to detect sixth grade students' misconceptions and errors regarding the subject of fractions. A misconception diagnostic test has been developed that includes the concept of fractions, different representations of fractions, ordering and comparing fractions, equivalence of…