Discusses (in 10 sections) some problem-solving techniques that are typically encountered in a first course in discrete mathematics. Sections (which include exercises) are titled: draw a figure; search for a pattern; mathematical induction; one-to-one correspondence; recurrence relations; generating functions; calculus; finite differences; and…

Mathematical observations are made about some continuous curves, called transitions, encountered in well-known experiences. The transition parabola, the transition spiral, and the sidestep maneuver are presented. (MNS)

Use of the computer program "Integrate Using Definition" can help students develop understanding of integral. Several applications of the program are discussed. (MNS)

Appreciating the power and beauty of mathematical thought should be an integral component of a student's mathematical education. The meaning of aesthetics in the realm of mathematical reasoning, the relationship of aesthetics to problem solving, the results of two studies, and recommendations for developing aesthetics are included. (MNS)

A possible method of derivation of prescriptions for solving problems, found in Babylonian cuneiform texts, is presented. It is a kind of "geometric algebra" based mainly on one figure and the manipulation of or within various areas and segments. (MNS)

Provides examples in which graphs are used in the statements of problems or in their solutions as a means of testing understanding of mathematical concepts. Examples (appropriate for a beginning course in calculus and analytic geometry) include slopes of lines and curves, quadratic formula, properties of the definite integral, and others. (JN)

An approach to polynomial approximations that leads the student to stumble on Taylor's theorem and its proof is presented, with a generalization. (MNS)

A proof for a limit is given, with a recommended presentation consisting of three lemmas followed by the theorem. (MNS)

Results obtained when a procedure for assessing the questions on uniersity mathematics examinations to see what skills were needed for their solution are given for a sample of 1400 questions set during 1976 in 10 British universities. The method is a way of focusing rational argument. (MNS)

Decimal expansions of fractions are considered. Theorems and corollaries for some properties and for prime and composite denominators are presented. It is suggested that students write computer programs to deliver decimal expansions. (MNS)

The authors draw together a variety of facts concerning a nonlinear differential equation and compare the exact solution with approximate solutions. Then they provide an expository introduction to the elliptic sine function suitable for presentation in undergraduate courses on differential equations. (MNS)

This paper presents some ideas on how to utilize TI-83 Plus calculators to perform division of one polynomial (the divided) by another polynomial (the divisor) and how that procedure might be incorporated into a college algebra lesson. Four ways to obtain the quotient and remainder when dividing a polynomial by a first-degree polynomial are…

Reasons why mathematics teachers should teach writing are discussed. Getting started by including an essay question on a test is proposed and suggestions on giving feedback are noted. (MNS)

Suggestions are given on how to help students in developmental mathematics courses develop appropriate study skills. Ideas concerning reading, using the testbook, and taking tests and notes are included. (MNS)

The Mathematics Learning Center at Cerritos Community College in Norwalk, California is described. Discussed are how it is organized, financed, staffed, and operated. Pitfalls to avoid and helpful hints are included. (MNS)