Reviews an alternative patterning approach and highlights the difficulties it can present when students lack the requisite skills and knowledge of processes. Describes how this approach can be used to introduce elementary algebraic ideas and offers recommendations for establishing these important understandings. (ASK)

A method for helping students to find formulas involving symmetry under various conditions is explained. Necklace symmetries, orbit counting, tetrahedra and cubes, relationship patterns, and finding patterns are discussed. (CW)

Illustrates where several unexpected patterns of antiderivatives can be realized during calculus instruction via the application of integration by parts to the exploration of particular members of families of functions. (JJK)

Reports unique solutions given to five problems from individual students in mathematics courses for prospective elementary school teachers oriented toward problem solving. Concludes that such courses are feasible, promote problem-solving abilities and strategies, and develop appreciation and confidence in preservice teachers. (MDH)

Discussed are ways in which students can generalize both quadratic or cubic situations. Generalizations are produced using the factor method, repeated linear generalizations, means of the mean, and through the use of differences. (KR)

Chess experts remember meaningful knowledge in the form of networks or patterns. Applied to mathematics instruction, effective classroom approaches can use investigation to identify patterns or rules. Described are a class activity and a small-group activity to investigate addition of signed numbers and linear relationships. (MDH)