Following on from a wonderful exercise in Engaging Minds and having read and heard about speed writing as a way of getting ideas I have engaged with the exercise below. I have re-adapted part of the writing task in Engaging Minds to begin to help me think about ways of drawing together the various ideas from an examination of the chapter that I am writing in my PhD.
Now that I am nearing the completion of this draft chapter I will need to bring the various threads and themes together.
Activity: Write freely for 5 minutes about the threads and themes that you think are emerging. There is no need to look back, correct, pause and worry about sentence structure.
Relax.
Don’t rush…but do not stop and edit.
There appear to be several emerging themes that I can connect with ideas of embodied mind and the development of mathematical understanding through metaphor and examples. Students, I believe are more likely to reach understanding by examples although Vinner stresses the need for a mix of example and definition. Which comes first the chicken or the egg…. the examples or the definition…how does the concept get formed…is there every such a thing as a concept being fully formed or does it simply evolve and change in our minds as we evolve and change as individuals. Certainly when I taught basic mathematics to students I saw things that I had never seen before, and learned a lot more about mathematics. When I went on to do research into mathematics education and interact with the mathematics community I learned anew and saw afresh and began to ask questions about the nature of mathematical knowledge, know how and ability.
The path schema emerges fairly strongly from the data…but several others also do so. I think of the nature of physical movement, and how this is represented within the graphs…the personal nature of it all.
(191 words in five minutes)
I will need to continue this tomorrow and hope that ideas will come from it. If you wish to interact please leave your comments. These could help stimulate my thoughts further.
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