Research findings concerning student learning difficulties in algebra are discussed. A teaching approach which takes into consideration these findings is suggested. Encouraging students to see patterns and to develop flexibility in their thinking are stressed. (CW)

Described is a way to illustrate cyclic and dihedral groups through symmetry using corporate logos and hubcaps. Examples of the different kinds of symmetry groups are explained in terms of Leonardo's Theorem. (KR)

Presented is a way of extending the list of rotation groups to include all finite subgroups of symmetries of the sphere, up to conjugation in its full group. Included is Klein's method for enumeration of the finite subgroups. (KR)

Described is an approach to teaching algebra in a meaningful context by using problem solving to motivate students and increase their retention. Examples of this approach are given. (CW)

Investigates the development of understanding of multiplication from the early school years through to the top primary age group. Identifies the children's difficulties and analyzes their solution strategies. Reports that progressive abstraction is related to the children's developing understanding of number and to their procedures for addition.…

Summarizes the interview and observation of mathematics teachers on their classroom teaching of problem solving. Discusses the related issues that teachers should consider as they plan and teach problem solving lessons. (YP)

Encourages classroom teachers to improve their students' reading and reasoning skills by helping them to interpret math problems correctly. (RAE)

A fairly traditional precalculus problem is modified to address some common concerns with the teaching of problem solving. Areas of problem solving which are illustrated include: posing the problem; modeling the problem; transforming the data; and examining the solution. (PK)

The Hawaii Algebra Learning Project (HALP) developed a curriculum that intertwines algebraic content, instructional methods, and assessment techniques with a problem-solving focus. (MKR)

Presents four investigations involving geometric sequences and series: folding a sheet of paper in half 8 times, stacking pieces of paper cut in half 50 times, snapping your fingers at intervals doubled in length for 1 year, and summing time intervals continuously cut in half. (MDH)

Presents results of a study to determine the effect of type-size on the mathematical problem-solving achievement of first, second, and third graders (n=259). Analysis of variance indicated that no significant differences in achievement existed. Concludes that textbooks can utilize smaller type sizes on word problems. (MDH)

Presents the mathematical proof, based on elementary number theory, for a card trick seen by students on television. Provides sources for other mathematical magic tricks that serve as motivational devices. (MDH)

Presents a series of challenges, problems, and examples to demonstrate the principle of mathematical induction and illustrate the many situations to which it can be applied. Applications relate to Fibonacci sequences, graph theory, and functions. (MDH)

The purpose of this study was to compare the achievement for the operations of multiplication and division on whole numbers of elementary grade students who were taught functional diagnostic strategies with a randomly selected group who were not taught the informal diagnostic strategies. Included are the methodology, results, and discussion. (KR)

Number sequences are useful complements to traditional drill and practice. Described is an activity in which the basic rule, add the tens digit to five times the ones digit, is used to generate a sequence of numbers. The dialogue between teacher and student discussing characteristics of emerging patterns is given. (MDH)