Since its first notable appearance in the "Second Handbook of Research on Mathematics Teaching and Learning," the phrase productive struggle has garnered support from a few, yet very influential, educational researchers. However, since the phrase was popularized by Hiroko Warshauer in 2011, examinations of the productive struggle have…

In many scientific contexts, students need to be able to use mathematical knowledge in order to engage in scientific reasoning and problem-solving, and their understanding of scientific concepts relies heavily on their ability to understand and use mathematics in often new or unfamiliar contexts. Not only do science students need high levels of…

Technology is a means that makes work or tasks easy, efficient, and operative. A more encompassing definition refers to it "as the tools created by human knowledge of how to combine resources to produce desired products, to solve problems, fulfill needs, or satisfy wants" (Koehler and Mishra. 2008:5). It can either be contrivances of tradition or…

I. Klugkist, O. Laudy, and H. Hoijtink (2005) presented a Bayesian approach to analysis of variance models with inequality constraints. Constraints may play 2 distinct roles in data analysis. They may represent prior information that allows more precise inferences regarding parameter values, or they may describe a theory to be judged against the…

Included are the description, operating characteristics, uses, and future plans for the Topological Panorama Camera, which is an experimental, robotic photographic device capable of producing visual renderings of the mathematical characteristics of an equation in terms of position changes of an object or in terms of the shape of the space…

Two microcomputer-based laboratories, the motion detector and the sound detector, are discussed in terms of their affects upon the facilitation of an understanding of graphs and their ability to aid in the development of conceptual understanding from graphical analysis. The author relates experiences in using these labs with high school students…

The history of education is made up in part of accounts of various subjects which have developed into courses of study. Mathematics of some kind has always been included in such courses. In the American colonies, arithmetic was an important subject for practical reasons. It was needed for trade and commerce. Sailing vessels plying between Europe…

The paper argues that a relationship between visualization and mathematical problem solving ability exists. Research suggests that visual imagery leads to increased understanding of mathematical concepts at both the primary and secondary levels. Mathematical potential is not necessarily "born." Potential can be created in the least likely students…

This is volume 3 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. This volume presents a detailed and careful technical analysis of the constituent aspects underlying spatial thinking as well as interesting reports of…

This is volume 4 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. The introduction to this English language translation highlights the fact that significant advances have been made in the understanding of both the…