How min-max problems can be solved with trigonometry and without calculus is described. (MNS)

A discussion of the mathematics of rugby is related to an earlier article about mathematics and the physical world. (MP)

Details a lesson that utilizes trigonometric identities to determine the optimal angle between the atoms of covalent bonds. Generates a proof of the optimal angle for a molecule with four identical atoms bonded to a central atom that has a complete valence shell. (DDR)

The authors have attempted to implement "less is more" in a variety of educational contexts. The schools they have been part of include a pilot school in Boston, New Mission High School(New Mission), a charter school in Fitchburg, North Central Charter Essential School (NCCES), and a charter school in Devens, Francis W. Parker Charter…

A series of problems involving number theory, the law of cosines, and geometric interpretations of solutions to equations is discussed. (SD)

This is the final test for students in the twelfth-grade course Mathematics 30, offered in schools in Alberta, Canada. Intended for administration in January 1985, it contains 52 multiple-choice questions and five written-response problems, with two-and-one-half hours allowed for completion. Approved calculators may be used. Scoring is done by the…

This is the final test for students in the twelfth-grade course Mathematics 30, offered in schools in Alberta, Canada. Intended for administration in June 1985, it contains 52 multiple-choice questions and five written-response problems, with two-and-one-half hours allowed for completion. Approved calculators may be used. Scoring is done by the…

The problem of finding the area of a regular polygon is presented as a good example of a mathematical discovery that leads to a significant generalization. The problem of finding the number of sides which will maximize the area under certain conditions leads to several interesting results. (LS)

This book is a sequel to MATHEMATICAL CHALLENGES, which was published in 1965. In this sequel are 100 problems, together with their printed solutions. The problems range from those that are quite simple to those that will challenge even the most ardent problem solver, and they include examples from algebra, geometry, number theory, probability,…

The authors hypothesize that a means-end strategy places a load on cognitive processing capacity which retards knowledge acquisition. Three experiments using trigonometry problems with high school students were conducted in which the problem goal was modified to disrupt strategy used by novices. Results supported the authors' hypothesis.…

Ideas are presented regarding: (1) unique learning activities for students who have difficulty with operations with signed numbers; (2) a mathematical inspection of a unique card trick that can be expressed as an equation; and (3) sketching of graphs of composite trigonometric functions. (MP)

Presents a trigonometry problem concerning control of the entry of sunlight through a window. (ASK)

Compared tutoring episodes where tutoring did and did not cause learning in university physics students to inform design of intelligent tutoring systems. Found that when students were not at an impasse, learning was uncommon regardless of the tutorial explanations employed. When students were at an impasse, tutorial explanations were sometimes…

Uses a variation of Hansen's surveyor problem to illustrate how exploring students' assumptions can lead to interesting mathematical insights. Describes methods that utilize self-stick notes and overhead transparencies to adapt computer software to specific classroom needs. (MDH)