In Pre-Calculus courses, students are taught the composition and combination of functions to model physical applications. However, when combining two or more functions into a single more complicated one, students may lose sight of the physical picture which they are attempting to model. A block diagram, or flow chart, in which each block…

This classroom note is presented as a suggested exercise--not to have the class prove or disprove Goldbach's Conjecture, but to stimulate student discussions in the classroom regarding proof, as well as necessary, sufficient, satisfied, and unsatisfied conditions. Goldbach's Conjecture is one of the oldest unsolved problems in the field of number…

A steady stream of research has shown that many elementary school teachers have weak mathematical knowledge in some areas, including place value and fractions. Since a teacher's mathematical knowledge affects their students' performance, improving elementary school teachers' knowledge is critical. A better understanding of the mathematical…

Described is an experience in assigning mathematics problems that have been purposefully selected from professional journals to assist upper level college mathematics students in developing confidence in their ability to contribute published solutions. Several examples are included. (JJK)

Timing stoplights and trying to determine the best way to allocate cycle time to the two directions is discussed. The simple case and improving the model are both considered. (MNS)

Some misconceptions about learning are discussed and specific suggestions for helping students in a college developmental mathematics class learn how to learn mathematics are presented. Extensive footnotes are appended. (MNS)

Two topics are discussed that can be presented in a discussion of the annual percentage rate (APR): difference equations and fixed-point iteration. A program in BASIC using the iteration procedure is included. (MNS)

In this article, the author takes up the special trinomial (1 + x + x[squared])[superscript n] and shows that the coefficients of its expansion are entries of a Pascal-like triangle. He also shows how to calculate these entries recursively and explicitly. This article could be used in the classroom for enrichment. (Contains 1 table.)

Presented is an activity where students determine the multiplication tables of groups of small order. How this can be used to help develop an understanding of the concept of group isomorphism is explained. (KR)

The author discusses the definition of the ordinary points and the regular singular points of a homogeneous linear ordinary differential equation (ODE). The material of this note can find classroom use as enrichment material in courses on ODEs, in particular, to reinforce the unit on the Existence-Uniqueness Theorem for solutions of initial value…

Presented is a way to provide students with a review and an appreciation of the versatility of pointers in data structures by improvising with binary trees. Examples are described using the Pascal programing language. (KR)

Various ways in which computers can be used in the classroom depending on the subject, students' background, and individual teaching style are discussed. A way to evaluate professional software packages for use in the classroom is included. (KR)

The programing language PROLOG is compared to LOGO in terms of its ability to handle mathematical ideas. This is demonstrated by using PROLOG in solving a geometric theorem and two lemmas. The listings of the computer programs used to solve the problems are included. (KR)

Four techniques used to incorporate writing and active learning into mathematics classrooms are described. They include summary sheets, short focused writing, medium length writing, and student presentations. Examples of how each technique can be used are included. (KR)

"Gedankensimulation" is a term adapted from Einstein's "thought experiments" to indicate mentally created simulations that can help conceptualize ideas. Presents seven examples of simulations that can be utilized to solve problems or illustrate concepts in probability and statistics. Problem contexts include games of chance,…