Fraction and decimal arithmetic pose large difficulties for many children and adults. This is a serious problem, because proficiency with these skills is crucial for learning more advanced mathematics and science and for success in many occupations. This review identifies two main classes of difficulties that underlie poor understanding of…

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…

Many fraction activities rely on the use of area models for developing partitioning skills. These models, however, are limited in their ability to assist students to visualise a fraction of an object when the whole changes. This article describes a fraction modelling activity that requires the transfer of water from one container to another. The…

To be able to provide better support for collaborative learning in Intelligent Tutoring Systems, it is important to understand how collaboration patterns change. Prior work has looked at the interdependencies between utterances and the change of dialogue over time, but it has not addressed how dialogue changes during a lesson, an analysis that…

In this quasiexperimental study, the authors investigated the effects of university within school partnership model, within which faculty members acted as teacher-researchers to improve fractional knowledge among middle school (Grades 5-8) students. Students in nine Grade 6 mathematics classes from two public middle schools in Turkey were assigned…

Mr. Buxton is a perplexed elementary mathematics teacher. He co-teaches a second-grade classroom, with Ms. Snyder. In their classroom they have 25 students; five are identified as academically at risk, and three receive special education services. In the past Mr. Buxton successfully used an instructional approach consisting of (a) modeling, (b)…

The efficacy of a research-based fraction sense intervention for sixth graders with or at risk for mathematics difficulties (N = 52) was examined. The intervention aimed to build understanding of fraction magnitudes on the number line. Key concepts were taught with a narrow range of denominators to develop deep understanding. The intervention was…

This article offers a reflection on the findings of three PhD studies, in the domains of, respectively, subtraction under 100, fractions, and algebra, which independently of each other showed that Dutch students' proficiency fell short of what might be expected of reform in mathematics education aiming at conceptual understanding. In all three…

This article describes how to teach fraction and percentage word problems using a model-drawing strategy. This cognitive strategy places emphasis on explicitly teaching students how to draw a schematic diagram to represent the qualitative relations described in the problem, and how to formulate the solution based on the schematic diagram. The…

Mathematical task design has been a central focus of the mathematics education research community over the last few years. In this study, six university teacher educators from six different US institutions formed a community of practice to explore key aspects of task design (planning, implementing, reflecting, and modifying) in the context of…

In this exploratory study, we documented teachers' knowledge of children's mathematical thinking as they engaged in the task of anticipating children's strategies for an equal sharing fraction problem. To elicit an array of knowledge, 18 teachers were deliberately selected with a variety of numbers of years participating in professional…

This paper explores the use of animations as an approximation of practice to provide a transformational technology experience for elementary mathematics preservice teachers. Preservice teachers in mathematics methods courses at six universities (n = 126) engaged in a practice of decomposing and approximating components of a fraction lesson. Data…

The present study extends recent advances developing and applying measures of mathematical content knowledge for teaching. Recent research has demonstrated that the Diagnosing Teachers' Multiplicative Reasoning Fractions survey provides information about distinct but related components necessary for reasoning in terms of quantities when solving…

Researchers have argued that there are strong links between primary school students' competence with fraction concepts and operations and their algebraic readiness. This study involving 162 Years 5/6 students in three primary schools examined the strength of that relationship using a test based on familiar fraction tasks and a test of algebraic…

The purpose of this study is to explore how different game designs support students' learning and enjoyment of fractions, specifically, early learning of equivalence and ordering. Two sets of games were contrasted, one that was characterized as "exploratory and implicit," and a second that was characterized as "directive and…