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)

Presents activities to create designs with different arrangements of square tiles, which gives students an opportunity to make conjectures about perimeter and to make convincing arguments to justify those conjectures. Includes worksheets. (MKR)

Examined the problem-solving strategies of above average students (n=42) in grades 2-4 on problems involving forgotten or new material while practicing arithmetic with a computer. Identified the different problem-solving strategies used, sorted them into categories, and illustrated them with examples from students' protocols. Made suggestions for…