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Yishay Mor, Maths Lunch, IOE, Dec. 2008 A Narrative Epistemology for Mathematics;  Genetic, Normative and Imperative
Agenda ,[object Object],[object Object],[object Object]
A possible path from experience to knowledge
Narrative ::  something  happened to  someone  in some  circumstances
Narrative has.. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],My focus is on narrative as a cognitive / social epistemic vehicle: A means for making sense of the world.
From body to story Perception Attention Selection Sequencing
Linguistic & Neuro-cognitive evidence ,[object Object],[object Object],[object Object],[object Object],[object Object],Zwaan & Radvansky, 98; Mar, 04
Translated ,[object Object],[object Object]
Brain metaphors..
Fusing Narratives My Swan Your Swan Swancept
Genre transposition Paradigmatic Imaginative  I saw a white swan I saw a white swan Swans are white
Ok, but what has this got to do with learning mathematics?
Learning = creating knowledge ,[object Object],[object Object],[object Object]
Epistemology ,[object Object],[object Object],[object Object]
Three Epistemologies ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example: genetic I predict that when I add up the totals they will start at 0.5 and increase by smaller and smaller amounts without getting to 1. I think this because the first number in my sequence is 0.5. This takes me half way to 1. To get to 1 I would need to add this again but I only add half of this, 0.25. This means that each time I only add half of what is necessary to get to 1 so I will never get there. I think the line of the graph will look like the graph above upside down or the one underneath but not so wobbly!
Questions ,[object Object],[object Object],[object Object]
Example: normative
Design patterns [describe] a problem which occurs over and over again in our environment, and then describes the core of the solution to that problem, in such a way that you can use this solution a million times over, without ever doing it the same way twice (Alexander et al., 1977)‏ C o n t e x t Problem Solution
Tell me a story ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
The three hats ,[object Object],[object Object]
What do  you  see? After a case story is presented, ask the audience to identify the primary points from their perspective. What is the key message you take from this story?
Make it a pattern When, Where, Who Collision of forces Cookbook: ingredients, procedure, expected outcomes  C o n t e x t Problem Solution
Questions: normative ,[object Object],[object Object],[object Object]
Example: Imperative
Example design pattern: objects to talk with Learning activities involve the use or construction of artefacts. When providing tools for learners to discuss their experience ... allow them to include these artefacts in the scope of their discussion. [...] Whatever the nature of the objects, the medium should support a visual (graphical, symbolic, animated or simulated) 1:1 representation of these objects.
Questions: imperative ,[object Object],[object Object],[object Object],[object Object]
http://xkcd.com/55/

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Narrative Epistemology for Mathematics

  • 1. Yishay Mor, Maths Lunch, IOE, Dec. 2008 A Narrative Epistemology for Mathematics; Genetic, Normative and Imperative
  • 2.
  • 3. A possible path from experience to knowledge
  • 4. Narrative :: something happened to someone in some circumstances
  • 5.
  • 6. From body to story Perception Attention Selection Sequencing
  • 7.
  • 8.
  • 10. Fusing Narratives My Swan Your Swan Swancept
  • 11. Genre transposition Paradigmatic Imaginative I saw a white swan I saw a white swan Swans are white
  • 12. Ok, but what has this got to do with learning mathematics?
  • 13.
  • 14.
  • 15.
  • 16. Example: genetic I predict that when I add up the totals they will start at 0.5 and increase by smaller and smaller amounts without getting to 1. I think this because the first number in my sequence is 0.5. This takes me half way to 1. To get to 1 I would need to add this again but I only add half of this, 0.25. This means that each time I only add half of what is necessary to get to 1 so I will never get there. I think the line of the graph will look like the graph above upside down or the one underneath but not so wobbly!
  • 17.
  • 19. Design patterns [describe] a problem which occurs over and over again in our environment, and then describes the core of the solution to that problem, in such a way that you can use this solution a million times over, without ever doing it the same way twice (Alexander et al., 1977)‏ C o n t e x t Problem Solution
  • 20.
  • 21.
  • 22. What do you see? After a case story is presented, ask the audience to identify the primary points from their perspective. What is the key message you take from this story?
  • 23. Make it a pattern When, Where, Who Collision of forces Cookbook: ingredients, procedure, expected outcomes C o n t e x t Problem Solution
  • 24.
  • 26. Example design pattern: objects to talk with Learning activities involve the use or construction of artefacts. When providing tools for learners to discuss their experience ... allow them to include these artefacts in the scope of their discussion. [...] Whatever the nature of the objects, the medium should support a visual (graphical, symbolic, animated or simulated) 1:1 representation of these objects.
  • 27.