All holding hands as a torus; Total YES and the lack of it
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Maria Droujkova
Oct 26, 2011, 7:29:21 AM10/26/11
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Hello,
We had a good trek overall, yesterday, at the farmers market. We found a lot of disks, circles and things formed out of them - like cylinders, spheres and toruses. I am attaching the game sheet. At the very end, the atmosphere dropped, and the very last few minutes somewhat lacked energy and the sense of fun. I could not understand what happened and kept thinking about it. I woke up with the solution!
Total YES is the method of deep acceptance. With Total YES, you find ways to make whatever the other people suggest work, or at least try your best - sincerely best - to make it work. It is necessary for creative tasks, such as brainstorming. Playing the second Math Trek quest, when we make the math we find out of ourselves, is such a task.
When I asked kids what they would suggest for making a torus together, they first suggested something very fun - making "torus "eyeglasses" or other body additions out of their forefingers and thumbs. But I asked for more ideas, and several kids said they wanted to just hold hands to make a big circle out of themselves to represent a torus, others nodded - and for some reason, I flat out told them it would not work.
I tried to explain why I thought it would not work, too. But I now see a good way it does work! Arms are cylindrical, so the arm parts of our human circle would represent a big huge torus quite well. If we only tried, kids could point this out to me. The better response would be:
- Yes, let's try it!
- (Make a big circle holding hands)
- Can you help me see how it represents a torus?
It's much easier for kids to point out something they visualized, rather than to explain it in words - let alone argue with an adult about it, in words! Please convey my apologies to the kids.
We did implement Kim's excellent idea - holding our circled arms over our heads and standing in a circle. This really shows the torus as "a circle made out of circles." I was playing along, so I don't have a photo of this one - hopefully someone will email one to math...@posterous.com soon!
I had a long and rough morning yesterday with miscellaneous work-related ups and downs. All the more reason to practice Total YES more in the future! When we are tired or distracted, overlearned behaviors are still possible. High-responsibility professionals like surgeons or firefighters (or educators!) need to train their good practices all the time.
A picture of a human circle from our math club - see how arms can represent a torus?
Toruses out of fingers: fun fun! http://www.flickr.com/photos/26208371@N06/6282958944/
A circle made out of spokes (1D-->2D quest): http://www.flickr.com/photos/26208371@N06/6282439929/
Brenda Weiss
Oct 27, 2011, 12:33:59 AM10/27/11
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Maria,
Thank you for the reminder that much of teaching is encouraging students to take risks ... risks of trying, risks of being wrong, risks of sounding less intelligent than someone else, risks of coming up with something new and untried.
I find your reflections on your own teaching to be a challenge. I'm challenged to make learning fun and positive. I'm challenged to examine what I do and how it might be limiting someone else, to recognize that, and to open horizons, rather than stopping with what I can understand and come up with today.
We can learn more together, by talking, listening, imagining and creating, even when it means that my 8.8 y-o boys come up with something grotesque.
Thank you for being an encourager and sharing your journey.
Brenda
On Wed, Oct 26, 2011 at 4:29 AM, Maria Droujkova <drou...@gmail.com> wrote:
Total YES is the method of deep acceptance. With Total YES, you find ways to make whatever the other people suggest work, or at least try your best - sincerely best - to make it work. It is necessary for creative tasks, such as brainstorming.
... - and for some reason, I flat out told them it would not work.
Maria Droujkova
Oct 29, 2011, 8:28:31 PM10/29/11
to natur...@googlegroups.com, mathtrek...@googlegroups.com
Thank you for understanding, Brenda. Your mention of limiting reminded me of the discussion we had at Natural Math - I think you were a part of it - about divergent thinking. In one study, 98% of kids were geniuses at divergent thinking; later, almost every one of them loses that ability. Ken Robinson's presentation:
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