Determining what students know and understand, as well as what misconceptions they have, is essential to planning and providing targeted intervention and support. In this article, a teacher uses formative assessment interviews to uncover evidence of students' understandings and to plan targeted instruction in a mathematics intervention class. The…

In this article, I use the Vygotskian concept of the Zone of Proximal Development (ZPD) to examine the learning experience of two grade seven pupils as they attempted to solve an addition of fractions problem using fraction strips. The aim is to highlight how tools can facilitate the enactment of a ZPD, within which the tool provides the guidance.…

This research is an exploratory study with a qualitative approach, which is based on interviews with a task-based the purpose of this study is to describe the understanding of elementary school students in interpreting sub concept fractions in changing of the object is given to fractions with limit intervention. While intervention on problems…

Learners in lower primary and even some in upper primary grades grapple to perform mathematical operations which involve fractions. Failure to solve these mathematical operations creates a gap in the teaching and learning processes of mathematics. We opine that this is attributed to use of traditional mathematical approaches of teaching and…

To understand relationships between students' quantitative reasoning with fractions and their algebraic reasoning, a clinical interview study was conducted with 18 middle and high school students. The study included six students with each of three different multiplicative concepts, which are based on how students create and coordinate composite…

We analyze the results of a study conducted for the purpose of assessing the viability of an alternative starting point for teaching fractions. The alternative is based on Freudenthal's insights about fraction as comparison. It involves portraying the entities that unit fractions quantify as always being apart from the reference unit, instead of…

This study examined the extent to which the iPad app, Spatial Temporal Mathematics (ST Math), diminished college remedial mathematics students' natural number bias and deepened their fraction conceptual understanding. In this quasi-experimental study one class played the ST Math fraction games for 8 weeks, and they were compared to a control class…

In this study, we considered how middle school teachers understood the relationship between fractions and ratios. We used two instruments to collect data from 11 teachers and relied on Knowledge in Pieces as a lens for considering understandings teachers have and how coherent those understandings are. From our analysis, we developed three main…

In this study it was aimed to determine pre-service primary teachers' knowledge structures of fraction through problem posing activities. A total of 90 pre-service primary teachers participated in this study. A problem posing test consisting of two questions was used and the participants were asked to generate as many as problems based on the…

Fractions are a well-researched area; yet, student learning of fractions remains problematic. We outline a novel path to initial fraction learning and document its promise. Building on Freudenthal's analysis of the fraction concept, we regard "comparing," rather than "fracturing," as the primary activity from which students are…

Mathematical knowledge and skills are crucial to success in academics and the workplace. The Common Core State Standards emphasizes fraction teaching and learning in elementary school. This mixed-method study explores fraction concept understanding among 14 deaf and hard of hearing participants between the ages of 8 and 16, as quantitatively…

The purpose of this study was to investigate future teachers' experiences and perceptions of using a virtual reality game for elementary math education. The virtual reality game was designed and developed to integrate a musical activity (beat-making) into the math learning of fractions. Five math education major students participated in this…

The purpose of this study was to examine and elaborate upon elementary prospective teachers' (PSTs) conceptions of partitive division with fractions. We examined the degree to which PSTs' conceptions were connected (i.e., capable of translating between representations correctly; aware that partitive division generates a unit rate for its quotient)…

This exploratory study examined the design issues related to a virtual-reality-based, gamelike learning environment (VRGLE) developed via OpenSimulator, an open-source virtual reality server. The researchers collected qualitative data to examine the VRGLE's usability, playability, and content integration for math learning. They found it important…

While previous work in the domain of proportional reasoning has primarily focused on the coordination of integer quantities, this study investigates how students coordinate fractional quantities. Fine-grained analysis of two seventh graders' responses to a set of systematically designed proportional tasks, shows how their knowledge of…