If a curriculum developer's goal is to create a single linear sequence of tasks that lead to the development of some important mathematical concept, then some researchers have suggested that these sequences should follow progressions similar to stages of development that have been identified in Piaget-like research on the relevant concept(s).…

In 3 experiments, the authors examined mathematical problem solving performance under pressure. In Experiment 1, pressure harmed performance on only unpracticed problems with heavy working memory demands. In Experiment 2, such high-demand problems were practiced until their answers were directly retrieved from memory. This eliminated choking under…

This research analyzed the composing processes of two high school students designing horse ranch plans for a course in equine management and production. The investigation focused on understanding the problems driving the design process, the tools through which the students inscribed and encoded meaning in their compositions, and the integration,…

A mother and daughter share their insights on what American schools can learn about cooperative, student-centered, problem-solving approaches to instruction from the Hogwarts School of Witchcraft and Wizardry in the Harry Potter books. (Contains 11 references.) (PKP)

As with natural numbers, a greatest common divisor of two Gaussian (complex) integers "a" and "b" is a Gaussian integer "d" that is a common divisor of both "a" and "b". This article explores an algorithm for such gcds that is easy to do by hand.

Although dogs seemingly follow the optimal path where they get to a ball thrown into the water, they certainly do not know the minimization function proposed in the calculus books. Trading the optimization problem for a related rates problem leads to a mathematically identical solution, which, it is argued here, is a more plausible model for the…

Using the problem of determining where a Flatland artist was standing, this article takes another look at perspective.

What may have been the birth of a new calculus problem took place when the author noticed that two coffee cups, one convex and one concave, fit nicely together, and he wondered which held more coffee. The fact that their volumes were about equal led to the topic of this article: complementary surfaces of revolution with equal volumes.

This article describes several creative solutions developed by calculus and modeling students to the classic optimization problem of testing in groups to find a small number of individuals who test positive in a large population.

Consider the series [image omitted] where the value of each a[subscript n] is determined by the flip of a coin: heads on the "n"th toss will mean that a[subscript n] =1 and tails that a[subscript n] = -1. Assuming that the coin is "fair," what is the probability that this "harmonic-like" series converges? After a moment's thought, many people…

This paper presents a visual representation of complex solutions of quadratic equations in the xy plane. Rather than moving to the complex plane, students are able to experience a geometric interpretation of the solutions in the xy plane. I am also working on these types of representations with higher order polynomials with some success.

The increase of multilingualism in both natural and formal contexts has provoked a number of studies which have concentrated on providing evidence of multilingual processing and finding out about the differences and similarities between second and third language learning. This paper deals with the use of metalanguage in multilingual students in an…

Career and technical education is already ahead of the curve, since automotive technology, electrical technology and electronics students across the nation have been actively engaged in learning about hybrid, electric and even solar-powered cars. Students in the Environmental Technologies Club at Central High School in Phoenix, Arizona, have built…

Using the power series solution of a differential equation and the computation of a parametric integral, two elementary proofs are given for the power series expansion of (arcsin x)[squared], as well as some applications of this expansion.

A simple problem relating to birds chasing each other gives rise to a homogeneous differential equation. The solution draws on student skills in differential equations and basic co-ordinate geometry.