In three experiments, three normal preschoolers were presented with sorting tasks ordinarily insoluble for four-year-olds. Found that, although the subjects had difficulty correctly sorting the pictures when told what criterion to sort by, they could provide correct answers when asked what they were looking for. This self-instructional effect was…

Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)

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)

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)