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Designing Powerful Digital Environments for Professional Development

Explore the concept of mathematizing and its implications for professional development in mathematics education. Learn about complexity theory, embodied cognition, community of discourse, and the role of context and discourse in learning. Discover strategies for facilitating mathematizing and assessing its facilitation.

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Designing Powerful Digital Environments for Professional Development

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  1. Designing Powerful Digital Environments for Professional DevelopmentCathy FosnotDR-K12, 2009

  2. Hans Freudenthal Mathematics should be thought of as a human activity of “mathematizing”—not as a discipline of structures to be transmitted, discovered, or even constructed—but as schematizing, structuring, and modeling the world mathematically.

  3. Cognition does not start with concepts, but rather the other way around: concepts are the results of cognitive processes… How often haven’t I been disappointed by mathematicians interested in education who narrowed mathematizing to its vertical component, as well as by educationalists turning to mathematics instruction who restricted it to the horizontal one.Hans Freudenthal

  4. Complexity Theory and Embodied Cognition • Learning is complex, not linear • Ideas and strategies evolve through discourse and interaction and appear on a landscape of learning as developmental landmarks • Emotions and social discourse are central to mathematical activity. What defines mathematics is a set of shared preferences, ways of reasoning, and truths accepted by the community • Importance of the “surround” (Maturana and Varela)

  5. Young Mathematicians at Work • Community of Discourse • Think Time • Questioning • Paraphrasing • Pair Talk • Inquiry • Gallery Walks and Congresses

  6. Math Lessons vs. Math Workshop • Doing activities and problems vs. allowing learners to go deeply into the topic using sequences of crafted, related investigations over a period of time • Role of Context • Learning in and from a community of mathematical discourse

  7. Didactics: Role of Context • Open to allow many entries • Developing understanding by staying in the context to help children realize what they are doing • Crafting further contexts with constraints to support development

  8. Role of Discourse • Dialogue Ball • Ideas and strategies emerge in the community as children discuss their own attempts at sense-making, work together, and try out one another’s ideas

  9. Assessment of the Facilitation of MathematizingCatherine Twomey Fosnot, Maarten Dolk, BetinaZolkower, SherrinHersch, and Herbert Seignoret

  10. Assessment of the Facilitation of MathematizingCatherine Twomey Fosnot, Maarten Dolk, BetinaZolkower, SherrinHersch, and Herbert Seignoret

  11. Assessment of the Facilitation of MathematizingCatherine Twomey Fosnot, Maarten Dolk, BetinaZolkower, SherrinHersch, and Herbert Seignoret

  12. Assessment of the Facilitation of MathematizingCatherine Twomey Fosnot, Maarten Dolk, BetinaZolkower, SherrinHersch, and Herbert Seignoret

  13. The Turkey Investigations, grade 3…

  14. “Mathematics is not a careful march down a well-cleared highway, but a journey…”W.S. Anglin

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