Seeing Chance: Fostering Student Implicit Knowledge Towards Fluency in the Domain of Probability and Statistics

Dor Abrahamson

Leading mathematics education authorities have identified student understanding of probability and statistics as “essential [for being] an informed citizen, employee, and consumer.” Yet, national reports currently paint a bleak picture of students’ understanding of this subject. Student performance is especially disconcerting given that very young students already have rich everyday experiences with chance. If students can generally make sense of addition and subtraction on the basis of understanding simple situations, why can they not leverage their implicit understanding of probability towards formalizing this understanding mathematically? Perhaps prevalent classroom learning supports do not engage these implicit understandings. I propose to identify, typify, and tap students’ early notions for this domain and explore potential learning paths towards mastery of the central ideas of probability and statistics. To do so, I will work closely with elementary and middle-school students to observe their strengths and challenges in negotiating between their unarticulated intuitions and a set of objects and computer-based activities I have been creating. The proposed methodology is ‘design research’: through cycles of implementation, analysis, and modification, I will home in on concrete and virtual forms that enable students to express their knowledge and link it to formal mathematical notations. The learning-and-facilitation tools are designed for students to ground, within a coordination of combinatorial analysis and simulations of probability experiments, an appreciation and understanding of the ineluctable determinism of emergent distributions of stochastic events. One direction of the planned research is to explore the temporal–spatial and additive–multiplicative relations inherent in various visual representations of stochasm. That is, I will investigate: (a) learners’ resources that enable them to understand outcomes of probability experiments that are experienced dynamically yet represented statically; (b) learning issues of students’ additive vs. multiplicative reasoning; and (c) design issues, e.g., how implicit visual cues enable or constrain spatial–temporal and additive–multiplicative coordination.

About Dor Abrahamson

The third son of Jack, a professor of surgery, and Gila, a musician and translator, Dor was born in 1965 in Haifa, Israel. Dor earned an undergraduate degree in music performance (cello) at the Jerusalem Academy of Music and then studied at Tel Aviv University, where he achieved a Masters in cognitive psychology (magna cum laude). At Northwestern University, Evanston, IL, Dor joined the School of Education and Social Policy, where he completed the Learning Sciences doctoral program under the supervision of Dr. Karen C. Fuson. In his doctoral dissertation, Keeping Meaning in Proportion: The Multiplication Table as a Case of Pedagogical Bridging Tools, Dor developed insights from an implementation of an innovative unit on multiplicative reasoning that led to a model of student situated mathematical learning. Dor then pursued a postdoctoral position under the supervision of Dr. Uri Wilensky at the Center for Connected Learning and Computer-Based Modeling, where he did further design research on the topics of probability and basic statistics. Dor researches cognitive and social aspects of student mathematical learning and creates bridging tools designed to help students tap their perceptual judgments and basic mathematical skills in building procedural fluency with formal representations. These learning tools are also designed to bridge between students by stimulating collaboration and classroom discussion. Dor has recently accepted an Assistant Professor position at the University of California, Berkeley Graduate School of Education. Dor is married to Gabrielle and they have a baby daughter, Neomi.