Bringing together the research of leading international scholars in the field of digital learning, "Designing Effective Digital Learning Environments" discusses cutting-edge advancements in digital technology and presents an evidence-informed summary of best practices for effective design principles and implementation within educational…

There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This…

Modern technology has enhanced many aspects of life, including classroom education. By offering virtual learning experiences, educational systems can become more efficient and effective at teaching the student population. The "Handbook of Research on Collaborative Teaching Practice in Virtual Learning Environments" highlights program…

Visualization of mathematical relationships enables students to formulate conjectures as well as to search for mathematical arguments to support these conjectures. In this project students are asked to discover the sufficient and necessary condition so that two circles form the circumscribed and inscribed circle of a triangle and investigate how…

"It's All Connected" provides teachers of mathematics the support they need to improve their instruction. This in-demand collection of lessons for grades 6-8 explores proportionality, proportional relationships, and proportional reasoning, acknowledging that the ability to reason proportionally is crucial in the middle school mathematics…

The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at…

First-year university students design and play their own games, including board, computer, and other kinds of games, to learn mathematical concepts and practice procedures for their pre-calculus and calculus courses. (Contains 2 tables and 8 figures.)

The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…

Middle and High school students of the twenty-first century possess surprising powers of spatial reasoning. They are assisted by technologies not available to earlier generations. Both of these assertions are demonstrated by students who are challenged with George Polya's classic Five Planes Problem. (Contains 5 figures.)

Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…

This booklet is intended to help students do their best on the ACT. It summarizes general test-taking strategies, describes the content of each test, provides specific tips for each, and lets students know what they can expect on test day. Included in this booklet are complete practice tests--"retired" ACT questions that were administered to…