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…

Many problems and activities which can be worked with a calculator are contained in this booklet. The problems include: pattern recognition, combinations of operations, estimation, squares and square roots, rate problems, area, and volume. Chapter topics include: getting to know the calculator, single-step problems, using formulas, and…

A lawn-mowing problem is discussed in terms of clarifying the problem; making initial conjectures; experimenting; developing a solution; and supporting formulas, theorems, and corollaries. (MNS)

Presents transcripts of freshmen engineering majors solving elementary physics problems to examine some limitations of formula-centered approaches to problem solving. Although students use formulas successfully, the qualitative conception of the underlying physical situation is weak. Results from written tests indicate that this phenomenon may be…

Some appearances of pi in a wide variety of problems are presented. Sections focus on some history, the first analytical expressions for pi, Euler's summation formula, Euler and Bernoulli, approximations to pi, two and three series for the arctangent, more analytical expressions for pi, and arctangent formulas for calculating pi. (MNS)

Presents a hyperknowledge framework of decision support systems (DSS). This framework formalizes specifics about system functionality, representation of knowledge, navigation of the knowledge system, and user-interface traits as elements of a DSS environment that conforms closely to human cognitive processes in decision making. (Contains 52…

Presents a problem-solving activity in which students are asked to find the shortest distance from one vertex of a cube to the vertex diagonally opposite by moving along the surface of the cube. Extends the problem for any rectangular solid. (MDH)

Ritzville Pyramids are cone-shaped piles of wheat found near the community of Ritzville, Washington. Presents the practical problem of determining the volume and surface area of a Ritzville pyramid to help farmers solve cost-effectiveness questions related to selling the wheat. (MDH)

Discusses the problem of how the stars on the American flag would be arranged were another state added to the Union. Presents solutions using linear equations based on conditions given in the problem. (MDH)

In Experiments 1A and 1B, students read a concise booklet containing 653 words and 6 illustrations describing the formation, propagation, and dispersion of ocean waves (concise group) or an expanded booklet containing 327 additional words and 5 additional illustrations describing relevant mathematical formulas and computations interspersed…

Usiskin takes another look at fractions, years after writing the article "The Future of Fractions" for "Arithmetic Teacher".

In most mathematics problem solving work, students' motivation comes from trying to please their teachers or to earn a good grade. The questions students must tackle are almost never generated by their own interest. Seven open-ended college algebra-level problems are presented in which the solution of one question suggests other related questions.…

The consistency with which students apply procedural rules for solving signed-number operations across identical items presented in different orders was examined in a study involving 161 eighth graders. Inconsistent rule application was common among students who had not mastered signed-number arithmetic operations. (TJH)

Discusses solutions to the problem of maximizing the range of a projectile. Presents three references that solve the problem with and without the use of calculus. Offers a fourth solution suitable for introductory physics courses that relies more on trigonometry and the geometry of the problem. (MDH)

Illustrates various methods to determine the perimeter and area of triangles and polygons formed on the geoboard. Methods utilize algebraic techniques, trigonometry, geometric theorems, and analytic geometry to solve problems and connect a variety of mathematical concepts. (MDH)