## Mathematical Reasoning and Ambiguity

Principal Investigator: Dr. Ami Mamolo |
Paradoxes, ambiguities, and other uncertainties can offer playgrounds through which learners, explorers, enthusiasts can develop appreciation of the aesthetic, structural, and generative elements of mathematics. "Playing" with ambiguities in language, notation, context, or perception can invite the development of new ideas and knowledge, as well as foster skills in mathematical argumentation. Above all,
playing in the realm of mathematics is just like playing anywhere else -- imaginative, creative, and just plain good fun. |

## Paradoxes of Infinity

Mathematics is shot through with infinity -John MasonSo is mathematics education. New twists on familiar paradoxes that challenge intuitions of infinitely full, infinitely many, or infinitely long are fruitful playgrounds for learners, educators, and researchers. They can shed light on the inner nature of mathematics and mathematical thought. Highlighted Article: - Mamolo, A. (2014). Cardinality and cardinal number of an infinite set: A nuanced relationship. Proceedings of the 38th International conference for the Psychology of Mathematics Education, Vancouver, B.C.
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## Ambiguities & the Unconventional

By grappling with ambiguities and unconventional re-presentations and ideas, learners can develop structural, aesthetic, and advanced mathematical understandings. Researchers can leverage these engagements to shed light on deep mathematical thinking, reasoning, and sensibilities.
Highlighted Article: - Mamolo, A. & Zazkis, R. (2012). Stuck on convention: A story of derivative-relationships.
*Educational Studies in**Mathematics, 81*(2), 161 – 177.
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