Researchers agree that both domain-general skills and domain-specific skills contribute to mathematics knowledge, but questions arise as to which skills can and should be trained to improve children's learning outcomes. In this article, we synthesize research on training three domain-general constructs in early childhood (patterning skills,…

Generalizing patterns is an important feature of algebraic reasoning that is accessible to students across grade-levels because it connects their numerical reasoning to algebraic reasoning. In this article, the authors describe how teachers can use the game Crack the Code to introduce generalizing to their students or can extend students'…

Cross-sectional and longitudinal data from students as they advance through the middle school years (grades 6-8) reveal insights into the development of students' pattern generalization abilities. As expected, students show a preference for lower-level tasks such as "reading the data," over more distant predictions and generation of abstractions.…

After stating that almost any topic could be generalized, the author was challenged to generalize the topic of polyominoes. His response is presented in this article. (SD)

Relationships between the linear dimensions, surface area, and volume of parallelepipeds are examined. (SD)

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)