Paradoxes and Ambiguities
Research Objectives |
Paradoxes, ambiguities, and other uncertainties can offer playgrounds through which learners, explorers, enthusiasts can develop appreciation of the aesthetic, structural, and generative elements in 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. |
This research focuses on the nuances of reasoning about, and with, mathematical infinities, paradoxes, and other ambiguities. At its core, this research is an exploration of techniques and abilities to cope cognitively with abstract mathematics. It seeks to offer a refined understanding of the tacit ideas and philosophies which can influence individuals' understanding infinity and resolution of ambiguities and paradoxical situations.
Curious?Mamolo, A. (2014). How to act? A question of encapsulating infinity. Canadian Journal of Science,
Mathematics, and Technology Education, 14(1), 1-22. 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. Mamolo, A. & Zazkis, R. (2014). Contextual considerations in probabilistic situations: an aid or a hindrance? In (Eds.) E. Chernoff & B. Srirman, Probabilistic thinking: presenting plural perspectives (PT: PPP), (pp.641- 656). Dordrechet: Springer Mamolo, A. (2010). Glimpses of Infinity: Intuition, Paradoxes, and Cognitive Leaps. Saarbrücken, Germany: VDM Verlag. Mamolo, A. (2010). Polysemy of symbols: Signs of ambiguity. The Montana Mathematics Enthusiast, 7 (2), 247-262. Zazkis, R.,& Mamolo, A. (2009). Sean vs. Cantor: Using mathematical knowledge in ‘experience of disturbance’. For the Learning of Mathematics, 29(3), 53 – 56. Mamolo, A. (2009). Intuitions of ‘infinite numbers’: Infinite magnitude vs. infinite representation. The Montana Mathematics Enthusiast, 6(3), 305-330. Mamolo, A., & Zazkis, R. (2008). Paradoxes as a window to infinity. Research in Mathematics Education, 10(2), 167–182. Math Explorations: Wijeratne, C., Mamolo, A., & Zazkis, R. (2014). Hilbert’s Grand Hotel with a Series Twist. International Journal of Mathematical Education in Science and Technology. Mamolo, A.& Bogart, T. (2011). Riffs on the infinite ping-pong ball conundrum. International Journal of Mathematical Education in Science and Technology, 42(5), 615 – 623. Chernoff, E., Knoll, E., & Mamolo, A. (2010). Noticing and engaging the mathematicians in our classrooms. Proceedings of the 34rd Annual Meeting of the Canadian Mathematics Education Study Group. Burnaby, British Columbia. |