Abrahamson, D., & Cendak, R. M. (2006). The odds of understanding the law of large numbers: A design for grounding intuitive probability in combinatorial analysis.

In J. Novotná, H. Moraová, M. Krátká, & N. Stehlíková (Ed.), Proceedings of the Thirtieth Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 1 – 8). Prague, Czech Republic: Charles University.


Twenty-eight Grade 4 – 6 students participated in 1 hr. clinical interviews in a design-based study that investigated: (a) probability-related intuitions; (b) the affordances of a set of innovative mixed-media learning tools for articulating these intuitions; and (c) the utility of the learning-axes-and-bridging-tools framework supporting diagnosis, design, and data-analysis. Students intuited qualitative predictions of mean and variance, yet only through grounding computer-based simulations of probability experiments in discrete–scalar, non-uniform, multiplicative transformations on a special combinatorial space, the combinations tower, could students articulate their intuitions. We focus on a key learning axis, students’ confusing likelihoods of unique events with those of classes of events.