The very nature of algebra concerns the generalization of patterns (Lee 1996). Patterning activities that are geometric in nature can serve as powerful contexts that engage students in algebraic thinking and visually support them in constructing a variety of generalizations and justifications (e.g., Healy and Hoyles 1999; Lannin 2005). In this…

Mathematics education practitioners and researchers have long debated best pedagogical practices for introducing new concepts. Our design-based research project evaluated a heuristic framework, whereby students first develop acontextual sensorimotor schemes and only then extend these schemes to incorporate both concrete narratives (grounding) and…

In two experiments, an adult presented 2-year-olds with an unfamiliar solid object, either rigid or flexible, and performed an action that emphasized the object's shape or material. Children were then asked to choose an object that matched the one shown. As hypothesized, the adult's action information alone directed children to attend to relevant…

Presents an activity in which students develop their own theorem involving the relationship between the triangles determined by the squares constructed on the sides of any triangle. Provides a set of four reproducible worksheets, directions on their use, worksheet answers, and suggestions for follow-up activities. (MDH)