Professional Development

Education as Negotiation: The Case of Basic Probability

This video advances a view of teaching and learning mathematical ideas as equitable dialogue between individuals holding different perceptions of a shared sensory display.

For example, in the context of an introductory probability lesson on compound events, two people analyzing a random generator might “see” a collection of colored squares either as a combination (e.g., 2 Heads and 2 Tails in any order) or a permutation (e.g., Heads, Tails, Tails, Heads). They share a referent but hold different senses for that referent, where each contingent inference is equally valid, as predicated on what the person is or is not attending to. Often this is the case because the pupil is not yet sensitized to a figural dimension or features of the display in question that bear little importance to productive naturalistic judgment but are nevertheless critical for advancing mathematical analysis, here the order of singleton events within the compound event. An empowering pedagogical approach, it is suggested, is to surface the pupil’s inference as predicated on what figural properties of the display in question they are or are not attending to, highlighting under what perceptual construal that inference is indeed mathematically sound, while supporting the pupil in appreciating how attending to certain “hidden" properties leads to a different inference which is complementary and even enhancing of the pupil’s capacity to logically warrant their initial intuitive inference. That process of coming to perceive a formal analytic display as a model of a situation in question, that is, as warranting informal inference regarding particular properties or behaviors of the situation, is the cognitive achievement of grounded mathematics learning.

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About Professor Dor Abrahamson

Dor Abrahamson (PhD, Learning Sciences, Northwestern University, 2004) is a Professor at the Graduate School of Education, University of California Berkeley, where he runs the Embodied Design Research Laboratory.

Abrahamson is a design-based researcher who invents pedagogical technologies for teaching and learning mathematics. He analyzes data gathered in evaluating these products to develop theoretical models of cognitive and social process leading to insight and fluency. Abrahamson is particularly interested in relations between learning to move in new ways and learning mathematics concepts. His research has been funded by federal agencies and private foundations. Otherwise, Dor enjoys playing the cello, hiking, biking, reading, and spending time with his family and pets.

Age: Primary, Secondary