Here we give an example of a problem that could be beneficially investigated by AS/A level students. It is a geometry problem that they can profitably tackle by geometric (especially geometry software) and algebraic means. Such problems naturally lead students to the need for proof--an essential part of mathematics that is often lacking in current…

Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.

In this note we consider a type of integral that is usually presented as an example in any textbook discussion of integration by parts. Invariably this integral is determined by integrating by parts twice and solving. We will present an alternate approach to this integral which makes use of the linearity of the integral, i.e., the fact that…

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

The Chinese used the idea of generating equivalent expressions for solving problems where the problems from a historical Chinese text are studied to understand the ways in which the ideas can lead into algebraic calculations and help students to learn algebra. The texts unify algebraic problem solving through complex algebraic thought and afford…

This study investigated factors promoting the use of self-constructed diagrams by examining students' perceptions and daily class activities, and comparing Japanese (n = 291) and New Zealand (n = 323) students. Algebra word problems and a questionnaire were administered. The results revealed that the New Zealand students used diagrams more often…

Middle school teachers realize the value of students playing games in mathematics classes if those games emphasize problem-solving strategies, algebraic reasoning, or spatial sense. This article describes various versions of the traditional game of nim and shows how working backward can be used to find a winning strategy. The link is then made…

This article reports results from a study focused on teachers' knowledge of students' understanding of core algebraic concepts. In particular, the study examined middle school mathematics teachers' knowledge of students' understanding of the equal sign and variable, and students' success applying their understanding of these concepts. Interview…

Research indicates that students have great difficulty solving algebra word problems and that few high school seniors have mastered the fundamentals of algebra, let alone algebra problem-solving skills. Improving students' algebra problem solving skills is considered to be critically important by those who have worked on reforming mathematics…

The inequality involving the arithmetic and geometric means is a powerful tool in dealing with applications of mathematics. It is very important in geometric programming. The article discusses this inequality and demonstrates two real world applications accessible to secondary teachers and students. (Author/KM)

The author observes that the predictor functions determined geometrically by Ranucci (EJ 090 184) can be algebraically derived, and that capable students might enjoy verifying them. Algebraic formulations and derivations are provided. (SD)

Human information processing is analyzed in terms of eight fundamental concepts: procedures, operations on procedures, frames, planning language or meta-language, heuristics, knowledge in other forms, critics, and pointers. Examples of this processing are given. (MK)

This is unit eleven of a fifteen-unit SMSG secondary school text for high school students. The text is devoted almost entirely to mathematical concepts which all citizens should know in order to function satisfactorily in our society. Chapter topics include coordinate geometry and problem analysis. (MP)

THIS LEARNING ACTIVITY PACKAGE (LAP) IS DESIGNED TO GUIDE STUDENTS IN LEARNING HOW TO USE AXIOMS, IN WRITING PROBLEMS INTO EQUATION FORM, AND IN SOLVING EQUATIONS. IN ORDER TO ATTAIN THESE GOALS, THE STUDENT AT SOME POINT IN HIS PROGRAM MUST BE ABLE TO (1) WRITE A DEFINITION OF "AXIOM", (2) USE THE AXIOMS OF A FIELD IN SOLVING EQUATIONS, (3)…

This study investigated differences in problem-solving performance following instruction varying in the type of heuristic advice given. The subjects, 176 college students with two years of high school mathematics experience, were provided programed instruction over a three-week period in three topic areas: finite geometry, Boolean algebra, and…