ABSTRACT
Algebra and algebraic reasoning are proposed as a core constituent of a general mathematics education that extends throughout schooling. The conduct of the sequential design study suggests that spatial structure serves as a potentially important springboard to algebraic reasoning. This chapter suggests that synergies between algebraic and spatial reasoning, and opportunities to learn about them, may be far more important than distinctions based on age. Many classroom activities were designed to support developing meta-representational competence, to examine the connections between different senses. Conversely, algebraic description prompted rethinking the nature of space. Students originally perceived but several instances of similar figures. A large portion of the activities in the curriculum focused on providing opportunities to strengthen meta-representational competence by comparing the same action over multiple senses of similarity. At the end of the unit, the majority of students appeared to be able to fluidly coordinate relations among different systems of representation for describing geometric similarity for familiar, whole number dimensions.
