How can children's natural perceptuo-motor skills be harnessed for teaching and learning mathematical structure? We address this question in the case of the integers. Existing research suggests that adult mental representations of integers recruit perceptuo-motor functionalities involving symmetry. Building on these findings, we designed a…

This study investigates children's metarepresentational competence with regard to listening to and making sense of simple sonic stimuli. Using diSessa's (2003) work on metarepresentational competence in mathematics and sciences as theoretical and empirical background, it aims to assess children's criteria for representational adequacy of graphical…

Used realistic models of turning situations to study second, fourth, and sixth graders' concepts of turning and bending. Found that young students viewed turning (knob, doll, and door) as a movement, and bending (road bends) as a configuration. Many did not spontaneously interpret turning as a configuration or bending as a movement. Explored…