Compares traditional mathematical models with computer simulations. Shows the strengths and flexibility of algorithmic computational simulations through a program designed to investigate and extend understanding in one of the most enduring questions in social choice research. Discusses solutions to this problem from each approach--analytic and…

Discusses two students' discovery that both of their answers to a computation for E in a chemical reaction in electrochemistry were correct, that there was not a unique answer, and that the textbook had presented only one of the possible answers to the problem. (MKR)

In this article, the authors describe their efforts to assess prospective K-8 teachers' knowledge of proportional reasoning. Based upon their analysis of prospective K-8 teachers' work on a mathematics performance task, they discuss the implications for preparing prospective teachers to teach proportional reasoning to their students. In general,…

Most of the research on academics and attention deficit hyperactivity disorder (ADHD) has focused on reading disorders in children with ADHD rather than difficulties in mathematics. In this article, we provide a comprehensive review of studies focusing on students with attention deficit disorders with or without hyperactivity and 1 area of…

Preschool children are often good at counting things but seem slow to learn that there is more to counting than simply finding out how many are in a single set. Counting is useful when comparing sets and when creating new sets to match existing ones. This is part of the numerical understanding that educators wish to foster in schools. In two…

A one-credit seminar course for junior-senior mathematics majors is described. The topic for the seminar is continued fractions, taught by a modified Moore Method, where the focus is on students creating their own mathematics. The students make conjectures after completing computational problems, then work on refining the needed hypotheses,…

The normal equations discussed in this paper for a least-squares parabolic fit have a unique solution if and only if there are at least three different x-values in the observations. This requirement is satisfied by most real sets of quantitative observations. For particular data sets, the appropriateness of parabolic fits should be assessed with…

In the seventh century, around 650 A.D., the Indian mathematician Brahmagupta came up with a remarkable formula expressing the area E of a cyclic quadrilateral in terms of the lengths a, b, c, d of its sides. In his formula E = [square root](s-a)(s-b)(s-c)(s-d), s stands for the semiperimeter 1/2(a+b+c+d). The fact that Brahmagupta's formula is…

At the start of a freshman calculus course, many students conceive the classical definition of limit as the most problematic part of calculus. They not only find it difficult to understand, but also consider it of no use while solving most of the limit problems and therefore, skip it. This paper reformulates the rigorous definition of limit, which…

This document is a collection of activity-based mathematics lessons for grades K-4 from the "Ideas" department in "Arithmetic Teacher: Mathematics Education through the Middle Grades." Each lesson includes background information, objectives, directions, extensions, and student worksheets. A matrix is included which correlates…

In this study, children (ages 7-12) of average intelligence who had learning disabilities (LD) (n=29) and typical children (n=30) were individually tested in a task that investigated the development of proportional structures of thought. In addition, mathematical knowledge was assessed on the Woodcock-Johnson Tests of Achievement-Revised (WJTA-R).…

These materials were developed in response to the Utah State Board of Education's new high school graduation requirements, particularly as they relate to the identification, teaching, and assessment of certain basic functional competencies. The document has been compiled as a guide and aid to mathematics teachers. Thirty competencies have been…

One difficulty that mathematically naive subjects encounter in solving arithmetic word problems involves the limitation on short term memory (STM) capacity. It is hypothesized that naive subjects, not having access to formal problem solving strategies, may find visualization useful in reducing strain on STM. Two experiments are reported. The…

Several examples are given of a variety of nonstandard problems, not ordinarily found in texts or courses, now accessible to students who have programmable calculators. These include: (1) finding limits; (2) evaluating infinite series; (3) calculating finite series; (4) computing variable length products; (5) solving equations; (6) searching for…

The purpose of this investigation was to determine the relationship between the acquisition of conservation skills and achievement in mathematics. The conservation skills measured were numbered, mass, area and volume. Mathematics achievement was measured by the Computation, Concepts, Problem-Solving and Total Mathematics scores on the Metropolitan…