Visualizing parts, meaning interpreting the views of an object which has been represented in a drawing, is a fundamental skill in engineering. However, learning deficiencies and difficulties have been observed among engineering undergraduates, and there is a high failure rate in drawing courses. In order to determine the origin of these…

The golden ratio appears in a classical mechanics coupled-oscillator problem that many undergraduates may not solve. Once the symmetry is broken in a more standard problem, the golden ratio appears. Several student exercises arise from the problem considered in this paper.

Seeking more effective mathematics instruction, this author decided to incorporate Cognitively Guided Instruction (CGI) into first-grade classroom lessons. Students in CGI mathematics classrooms are prompted to use their prior knowledge to solve new problems, establish cognitive structures to which new learning can be connected, and be driven by…

Identifying the approach used by those revision experts par excellence--that is, professional editors--should enable researchers to better grasp the revision process. To further explore this hypothesis, the author conducted research among professional editors, six of whom she filmed as they engaged in their practice. An analysis of their work…

This paper, the second of a two part article, expands on an idea that appeared in literature in the 1950s to show that by restricting the domain to those complex numbers that map onto real numbers, representations of functions other than the ones in the real plane are obtained. In other words, the well-known curves in the real plane only depict…

In this article, the author reflects on her session at the 2006 conference, including the learning styles and strategies she observed. In her session, they explored some of the more unusual aspects of convex polyhedra (with regular faces), including the notions of "valence" and "species". Although the session was about shape and space, there was…

Handling problems in schools is inevitable. Administrators often must make decisions on critical issues and incidents, such as determining disciplinary actions and consequences for student misbehavior, and confrontations with irate parents. In all such cases, they must be able to provide necessary assistance in solving problems while avoiding the…

In most mathematics textbooks, each set of practice problems is comprised almost entirely of problems corresponding to the immediately previous lesson. By contrast, in a small number of textbooks, the practice problems are systematically shuffled so that each practice set includes a variety of problems drawn from many previous lessons. The…

Increasing people's ability to solve complex problems is more and more often being seen as an integral part of vocational education. While there have been numerous empirically-based approaches to the didactic structuring of teaching and learning arrangements by which students' ability to solve problems can be increased, knowledge of how to…

A method called the Remainder Method is proposed for the calculation of sample quantiles of a given order, for example, quartiles, hexatiles, octatiles, deciles and percentiles assuming that all the observations are distinct. Proof is given for a special case of deciles. The criterion "equisegmentation" is proposed, namely that the number of…

This article presents a rich geometry problem and discusses its solution. A variety of mathematically correct justifications for this answer are provided. (Contains 2 figures.)

The purpose of this article is to present a collection of problems that allow students to investigate magic squares and Latin squares, formulate their own conjectures about these mathematical objects, look for arguments supporting or disproving their conjectures, and finally establish and prove mathematical assertions. Each problem is completed…

Moral development research has often focused on the development of moral reasoning without considering children's understanding of moral advisors. We investigated how children construe sources of moral advice by examining the characteristics that children deem necessary for reasoning about moral or scientific problems. In two experiments, children…

This article describes how to incorporate problem-solving investigations in a fourth-grade classroom within a structured and rigid mathematics program.

The Math Forum is an online resource center for pre-algebra, algebra, geometry and pre-calculus. Its Virtual Math Teams (VMT) service provides an integrated web-based environment for small teams of people to discuss math and to work collaboratively on math problems or explore interesting mathematical micro-worlds together. The VMT Project studies…