Dor Abrahamson – PME - NA 2007 Handling Problems

Fifty 4 th -17 th -grade students participated in individual interviews oriented toward probabilistic intuition. Participants were given a boxful of equal numbers of green and blue marbles, mixed, and a device for scooping 4 ordered marbles and asked to predict the most common sample. Students replied that the outcome with the highest relative frequency would have 2 green and 2 blue marbles. Their verbal reasoning was accompanied by a deictic–metaphoric gesture to the left then right, as if they were separating the colors in the box. Gesture, I argue, bridges direct intuitive grasps of situations to conscious reflection, thus concretizing the prereflective, possibly grounding it in material form such that it emerges as conducive to further elaboration in mimetic symbolic form. Situated mathematical reasoning transpires largely as embodied negotiation among kinesthetic image schemas afforded by available material resources and epistemic forms.