The focus of the present synthesis reflects the research on programs, practices, and policies intended to improve mathematics outcomes funded through the Institute of Education Sciences' (IES's) National Center for Education Research (NCER) and National Center for Special Education Research (NCSER). The authors were asked to review those published…

The goal of this paper is to promote computational thinking among mathematics, engineering, science and technology students, through hands-on computer experiments. These activities have the potential to empower students to learn, create and invent with technology, and they engage computational thinking through simulations, visualizations and data…

The purpose of this article is to examine one possible extension of greatest common divisor (or highest common factor) from elementary number properties. The article may be of interest to teachers and students of the "Australian Curriculum: Mathematics," beginning with Years 7 and 8, as described in the content descriptions for Number…

Understanding fractions remains problematic for many students. The use of the number line aids in this understanding, but requires students to recognise that a fraction represents the distance from zero to a dot or arrow marked on a number line which is a linear scale. This article continues the discussion from "Identifying Fractions on a…

In this article, we present some mathematical tasks designed to support pre-service teachers (PSTs) in obtaining a broader, more connected understanding of decimal numbers and quantities. We describe classroom scenarios from a content course in which PSTs experienced these cognitively demanding decimal tasks, enacted in ways that maintain high…

The ubiquitous practice of providing worked solutions to exercises in mathematics education has been under-researched. Little is known about what elements of a worked solution are valued by students. This exploratory study sought in-depth feedback from six undergraduate students who experienced a range of worked solutions designed to encourage…

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…

There are many continuous quantitative dimensions in the physical world. Philosophical, psychological and neural work has focused mostly on space and number. However, there are other important continuous dimensions (e.g., time, mass). Moreover, space can be broken down into more specific dimensions (e.g., length, area, density) and number can be…

This study examines if interdisciplinary teaching can be said to facilitate the learning and use of fractions by Swedish 12-year-old pupils. Home and Consumer Studies is well suited to interdisciplinary teaching, and young people can therefore find it interesting to study maths since the setting is relevant to them. Building on variation theory…

Thus far, it is unclear how students can learn most effectively from their own errors. In this study, reflections on the rationale behind self-made errors are assumed to enhance knowledge acquisition. In a field experiment with pre/post/follow-up design, the authors practiced fractions with 174 seventh- and eighth-grade students who were randomly…

With the recent emergence of online professional development (PD), such opportunities are increasingly available to educators. It is important, then, to assess whether and how such options can be valuable and effective for them. The goal of this study was to assess whether and how a Massive Open Online Course for Educators (MOOC-Ed) can serve as…

How should a wide variety of educational activities be sequenced to maximize student learning? Although some experimental studies have addressed this question, educational data mining methods may be able to evaluate a wider range of possibilities and better handle many simultaneous sequencing constraints. We introduce Sequencing Constraint…

In this proposal, I introduce a method for modeling the dynamics of a sixth-grade student's accommodation of his fractions scheme to include a disembedding operation (Steffe & Olive, 2010). I will describe a three-part approach consisting of a constructivist teaching experiment, retrospective analysis, and stochastic modeling of the student's…

When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…

While collaborative Intelligent Tutoring Systems (ITSs) have been designed for older students and have been shown to support sense-making behaviors, there has not been as much work on creating systems to support collaboration between elementary school students. We have developed and tested, with 84 students, individual and collaborative versions…