Fractions are an integral part of the mathematics curriculum. Most students acquire proficiency with these concepts during the course of their elementary education and are usually able to perform basic fractions operations when reaching middle-school age. However, a considerable number of students require extra help to not fall further and further…

This paper presents findings from a study that examined the strategies that children, who had only been taught the part-whole fraction sub-construct at school, used for finding the fraction associated with solving varied partitive quotient problems. A qualitative, microgenetic research design was used involving nine year 5 (aged 9-10) children…

This study aims to investigate the effect of gamification on fifth-grade students' academic achievements and attitudes towards mathematics course. For this purpose, the teaching process of the "fractions" as a subject of the mathematics course is equipped with gamification elements. The quasi-experimental design is preferred as the…

Prior work on teachers' mathematical knowledge has contributed to our understanding of the important role of teachers' knowledge in teaching and learning. However, one aspect of teachers' mathematical knowledge has received little attention: "strategic competence for word problems." Adapting from one of the most comprehensive…

When, how, and why students use conceptual knowledge during math problem solving is not well understood. We propose that when solving routine problems, students are more likely to recruit conceptual knowledge if their procedural knowledge is weak than if it is strong, and that in this context, metacognitive processes, specifically feelings of…

Background: Many teachers for different reasons recognise the teaching of fraction as a challenge. This research explored the teaching of fraction in Grade 5 by three experienced teachers (Ben, Greg and Will) in KwaZulu-Natal province, South Africa. Aim: The purpose of this study was to investigate the impact of different approaches to the…

Understanding how environments influence learning requires attending not only to what is present but also to what is absent. In the context of mathematics learning, this means attending not only to problems that children encounter frequently in textbooks but also to ones that appear rarely. We present research in this article showing that students…

Understanding how environments influence learning requires attending not only to what is present but also to what is absent. In the context of mathematics learning, this means attending not only to problems that children encounter frequently in textbooks but also to ones that appear rarely. We present research in this article showing that students…

The purpose of this article is to share how one teacher implemented exploratory writing within a mathematics lesson to support her third graders in making sense of fractions and communicating their mathematical ideas. The author defines exploratory writing, then describes the teacher's lesson while also presenting a general overview about how to…

This research aims to determine second-year university students' understanding in interpreting and representing fractions. A set of fraction tests was given to students through two direct learning interventions. An unstructured interview was used as an instrument to obtain explanations and confirmations from the purposive participants. A total of…

Puzzles involving infinite networks of resistors are an engaging way for students to explore the idea of infinity and self-similarity in physics. Recently K Atkin has described one such puzzle, alongside a solution based on an equivalent finite network (2022 "Phys. Educ." 57 025015). Here we present a generalisation of this problem which…

Fractions are foundational for success in algebra and STEM, but they are notoriously difficult for students. In past work, two separate branches of research from psychology and math education have studied fractions knowledge using different, isolated approaches. In this dissertation, I synthesize research from both fields about proportional…

The ability to apply mathematical knowledge to solve real-life problems is often considered one of the fundamental educational goals. However, more attention in mathematics education has been given to the development of abstract mathematical computations in symbolic form. The current investigation aims to disclose whether there are different…

Despite the documented influence of motivation on mathematics learning for most students, we understand far less about this relation for students identified with learning disabilities. Based on Rogoff's three planes of analysis (i.e., personal, community, and interpersonal), we gathered survey, interview, and video data to understand the…

Across two experiments, we investigated how verbal labels impact the way young children attend to proportional information, well before the introduction of formal fraction education. Five- to seven-year-old children were introduced to equivalent non-symbolic proportions labeled in one of three ways: (a) a single, categorical label for multiple…