What instructional materials and practices will help students make sense of probability<br>notions? Li (11 years) participated in an interview-based implementation of a design for the binomial. The<br>design was centered around an innovative urn-like random generator, creating opportunities to reconcile two<br>mental constructions of anticipated outcome distributions: (a) holistic perceptual judgments based in tacit<br>knowledge of population-to-sample relations and implicitly couched in terms of the aggregate events with no<br>attention to permutations on these combinations; and (b) classicist-probability analytic treatment of ratios<br>between the subset of favorable to all elemental events with attention to the permutations. We argue that<br>constructivist and sociocultural perspectives on mathematics learning can be reconciled by revealing<br>interactions of intuitive and formal resources in individual development of deep conceptual understanding.<br>Learning is the guided process of blending two constructions of problematized situations: the<br>phenomenologically immediate and the semiotically mediated.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education