The importance of teaching mathematics as a body of strategies and methods of inquiry is stressed; examples of situations which emphasize skills in classification, generalization, using symbols, and proof are given. (DT)

Modular arithmetic is used to show that there is at least one Friday the 13th in every year. A case-by-case proof is outlined and a proof of the general case is given. (DT)

Student errors led to this exploration of the conditions under which log of x base a = x. The discussion requires only techniques contained in a first-year calculus course. (MP)

Discussed is the problem of finding the volume common to two intersecting right circular cylinders. (MP)

A technique is given for solving problems involving a balance scale and a number of coins which are to be sorted in a certain number of weighings. (MP)

Methods are suggested for encouraging high school students to write mathematics research papers. Sources for information are discussed, a general outline for the paper is given, grading procedures are described, and several topics for reports are listed. (DT)

Beginning with a construction problem admitting a classical solution, the authors provide other solutions based on algorithmic estimation and transformational geometry. The latter methods are generalized to suggest solutions to other problems; hints to these solutions are provided. Teacher-student discussion could lead in many directions. (SD)

Proliferation of mathematical knowledge prohibits individual reduplication of all results and causes mathematicians to accept much on faith. To convey the spirit of the mathematical community, and provide maximum content coverage, instruction should allow students to accept some theorems without proof. Students would then find mathematics less…