A seemingly paradoxical situation is explained which tells of one baseball player having a higher batting average than a second player for two seasons, yet having a lower overall average. (MP)

A proof is given of a construction axiom, involving the use of a Mira used to construct a segment of a length cube root of K when segments of lengths 1 and k are given. (MP)

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)

Seven different views of geometry are identified, and for each of the views, guidelines for designing individualized curricula are developed. (DT)

Features of one particular kind of map, called a polar stereographic projection, are discussed in detail. (DT)

Partial converses are considered of the theorem stating that in an isosceles triangle, the bisector of the apex angle, the altitude to the base, and the median to the base all coincide. (DT)

Presents an activity related to probability in order to answer a question based on the English football league. The question is "What is the probability that the FA Cup Final will be between the same two teams that played in the previous tournament?". (ASK)

Discusses the importance of calculators in the teaching and learning of mathematics. Argues that affordable graphing calculators let all mathematics students use computer visualization on a regular basis for both in-class and out-of-class activities. (ASK)

Explores a workable definition of mathematical structure and a rationale for teaching mathematical structure in the secondary school. Continues with mathematical structure appropriate for secondary mathematics teachers and suggestions for teaching mathematical structure in the secondary school. Contains 11 references. (ASK)

Features an investigation in which students study the time of each bounce of a ball and the total time that the ball would bounce. (ASK)

Describes a course diary that documents events in the course during the year and supplies a record of overall student performance and expectations. Explains the benefits and contents of a course diary, as well as what can be done throughout the year to make writing the course diary an easy task. (ASK)

Examines the roles of experimental tasks in "Elementary Geometry" (1903) by Godfrey and Siddons, which is considered one of the most important geometry textbooks in the history of geometry teaching. Roles of experimental tasks included preparations for deductive geometry and, even though it is implicit, the verification of geometrical facts.…

Presents problem situations that support students when discovering the multiplication principle, permutations, combinations, Pascal's triangle, and relationships among those objects in a concrete context. (ASK)

This article provided a general framework for reviewing mathematics textbooks, including a set of quality considerations organized around three key dimensions--Mathematics Content Emphasis, Instructional Focus, and Teacher Support. The quality considerations are intended to stimulate discussion of issues surrounding textbook selection. (Contains 4…

Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…