The actuarial profession is described to provide secondary school mathematics teachers insights into how actuaries use mathematics in solving real life problems. Examples are provided involving compound interest, the probability of dying, and inflation with computer modeling. (MDH)

An educational technique to calculate the lifetime of a comet using software-generated random numbers is introduced to undergraduate physiques and astronomy students. Discussed are the generation and eligibility of the required random numbers, background literature related to the problem, and the solution to the problem using random numbers.…

Undergraduate students in the physical sciences can benefit from widespread availability of microcomputers and their link with numerical methods. Presented are examples of evaluating various transcendental mathematical functions, using numerical methods that emphasize the development of critical thinking skills and practical numerical techniques…

Describes the development of a set of magnets that focus high-energy electron and positron beams causing them to collide, annihilate each other, and generate new particles. Explains how dipoles bend the beam, how quadrupoles focus the beam, how the focal length is calculated, and the superconducting final focus. (MDH)

Describes the method that Archimedes utilized to calculate the volumes of spheres and other solids. The method found the volume of a sphere by comparing the mass of parallel slices of a sphere and a cone with that of a cylinder of known mass. (MDH)

A Reuleaux triangle is constructed by drawing an arc connecting each pair of vertices of an equilateral triangle with radius equal to the side of the triangle. Investigates the application of drilling a square hole using a drill bit in the shape of a Reuleaux triangle. (MDH)

Questions some fundamental assumptions of historical methods of space guidelines in college facility planning, and offers an alternative approach to space projections based on a new benchmarking method. The method, currently in use at several institutions, uses space per faculty member as the basis for prediction of need and space allocation. (MSE)

Presents the Semantic Vector Space Model, a text representation and searching technique based on the combination of Vector Space Model with heuristic syntax parsing and distributed representation of semantic case structures. In this model, both documents and queries are represented as semantic matrices, and retrieval is achieved by computing…

Discusses the evaluation of search engines and uses neural networks in stochastic simulation of the number of rejected Web pages per search query. Topics include the iterative radial basis functions (RBF) neural network; precision; response time; coverage; Boolean logic; regression models; crawling algorithms; and implications for search engine…

Develops a new model for a process that generates Lotka's Law. Topics include measuring scientific productivity through the number of publications; rate of production; career duration; randomness; Poisson distribution; computer simulations; goodness-of-fit; theoretical support for the model; and future research. (Author/LRW)

This Brief Report describes a secondary analysis of the solutions written by 306 second-year algebra students to four constructed-response items representative of content at this level. The type of solution (symbolic, graphical, or numerical) used most frequently varied by item. Curriculum effects were observed. Students studying from the second…

The purpose of this article is to describe a middle school mathematics teacher's model of his students' responses to algebraic tasks involving equivalent expressions and the distributive property. The teacher engaged in two model-eliciting activities designed for teachers by creating a library of his students' work and an accompanying "Ways…

Triangular numbers are used to unravel a new sequence of natural numbers here-to-fore not appearing on the Encyclopedia of Integer Sequences website. Insight is provided on the construction of the sequence using "buildings" as a viewable model of the sequence entries. A step-by-step analysis of the sequence pattern reveals a method for generating…

This article focuses on the kinds of conceptual changes that occur when students have to deal with negative numbers in elementary algebraic operations. Interviews were carried out with twelve 8th-grade level students who were selected on the basis of their results in a test where they were required to reduce polynomials. The questions applied to…

In this issue's "Classroom Notes" section, the following papers are discussed: (1) "Constructing a line segment whose length is equal to the measure of a given angle" (W. Jacob and T. J. Osler); (2) "Generating functions for the powers of Fibonacci sequences" (D. Terrana and H. Chen); (3) "Evaluation of mean and variance integrals without…