Many dance artists in their first encounters with improvisational dance making begin not only to learn how to compose spontaneously, but also to gain skills for coping with the uncertainties inherent in the form. This article suggests helpful dance scores for beginning students of physical improvisation and those who teach improvisational…

Multi-touch technology is increasingly being used to support collaborative learning activities. However, to know how this technology can be used most effectively, we need to understand if collaborative interactions differ when groups are using multi-touch technology compared with other tools. In this paper, we compare the interactions of groups of…

Most students can follow this simple procedure for division of fractions: "Ours is not to reason why, just invert and multiply." But how many really understand what division of fractions means--especially fraction division with respect to the meaning of the remainder. The purpose of this article is to provide an instructional method as a…

The article details how school counselors can use principles of positive psychology to promote students' career development by facilitating students' pursuit of purpose and meaning. Specifically, the publication identifies how school counselors can actively employ with their students five constructs of positive psychology--namely strengths,…

From a Marxian/Vygotskian perspective, learning is social in origin and it happens in the presence of others that are more knowledgeable. Extending this view to the learning of mathematics, such learning also becomes inseparable from the presence of others (people and artefacts). Researchers over decades have studied different interactions to see…

Why might it be (at least sometimes) beneficial for adults to process fractions componentially? Recent research has shown that college-educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study…

Fractions are an important mathematical concept; however, fractions are also a struggle for many students with disabilities. This study explored a new framework adapted from the evidence-based concrete-representational-abstract framework: the virtual-representational-abstract (VRA) framework. The VRA framework involves teaching students to solve…

Long before the release of the Common Core State Standards (CCSSI 2010), the Mathematical Tug-of-War was engaging students in the type of reasoning and problem solving described by the Standards for Mathematical Practice (SMP). In this updated version of a Marilyn Burns task, students use algebraic reasoning to determine the outcome of a contest…

The classical "brachistochrone" problem asks for the path on which a mobile point M just driven by its own gravity will travel in the shortest possible time between two given points "A" and "B." The resulting curve, the cycloid, will also be the "tautochrone" curve, i.e. the travelling time of the mobile…

For many teachers, the term "scaffolding" has come to mean providing just the right amount of help when a student encounters difficulty. However, there is another facet of scaffolding that has been largely ignored, and that is making decisions about what to focus on to help the student. In this article, new research findings are shared…

Decision-problem structuring is conceptualized to be a process comprising activities characterized by the students. The activities are cognitive efforts of a group coming to an understanding and determining the representation of the decision-problem and of what knowledge is relevant to the decision-problem. Cognitive effort refers to the fraction…

As part of the recent history of the mathematics curriculum, reasoning and argument have been emphasized throughout mathematics curriculum standards. Specifically, as part of the Common Core State Standards for Mathematics, the Standards for Mathematical Practice were presented, which included the expectation that students develop arguments and…

Clients face many different obstacles within healthcare and education settings. Professionals in health and education fields are in a position to be a problem-solving resource to clients, students, and patients. The subset of professionals being examined are problem-solving professionals, who work with clients/students/patients, within the health…

In this study, we explore thirty-two second graders' performance on integer addition problems before and after analyzing contrasting cases involving integers. The students, as part of a larger study, completed a pretest, were randomly assigned to one of three intervention groups, and participated in two small-group sessions, one short whole-class…

This study focused on investigating the ability of 58 pre-service mathematics teachers' (PSMTs) to construct-evaluate mathematical conjectures-proofs in a mathematics course. The combined construction-evaluation activity of conjectures-and-proofs helps illuminate pre-service mathematics teachers' understanding of proof. The result of the study…