This week’s introduction hinted at some fun and interesting mathematics, around imagining the infinite and infinitesimal. The article, Dancing Mathematics and the Mathematics of Dancing, by Sarah Belcastro and Karl Schaffer (2011), presented lots of interesting representations of mathematics. Both have Ph.D. 's in Mathematics and have created mathematical themed concerts. Sarah and Karl lay out the math that is in dance. Math such as, dividing music into counts, dance patterns arising from music rhythm, symmetry (of individual movements and movements of the people in a dance group). Symmetries include translations, mirror reflections, 180 degree rotations, and glide reflections.
My stop this week is the seemingly high level math that Sarah and Karl also present. Math such as graph theory and topology. These math topics can be symbolically daunting. However, stepping away from the symbolic representations, these topics can prove quite interesting and fun. I recall one professor saying a doughnut and coffee mug are topologically equal. This was not a topology class, just conversation that popped up. Essentially, pretend each is made of clay. Preserving all the holes or loops, could you mold one into the other? (The hand grip and doughnut hole)
(Image created by ChatGPT)
We could get students to “act out”, like in drama class, to make themselves topologically equivalent to other objects. We could extend this to making human clay figures that have the child’s pose. They could be molded to whatever the original object was.
In the image above the person (with arms making a loop), the coffee mug, and doughnut are all topologically equal. A biologist would have to ignore the fact the digestive system is an open loop, lol.
My question is what other objects could children make themselves topologically equal to? How would this look?
Activity - Rope Polygons (Regular)
Adapt the rope and knots to other math concepts:
Pythagorean triples. Example 3,4,5 Use the knots as a way to measure sides.
Three other ropes and knots could be used to make the squares of 3,4, and 5.
Circles - estimating the connection between diameter to circumference.
C = pi X d or circumference of any circle is a bit more than three times its diameter C - 3.14 x d. Let the distance between knots be a diameter then the circumference of the circle would
be three of these lengths plus about 15 percent of the way to the next knot.
Hi Shawn,
ReplyDeleteVery interesting food for thought (pun intended). This would be a good way to include more embodied learning into the math class. Examples would obviously vary by grade, but thinking about my grade 6 math class and our current unit on geometry, I'm going to now try to give the students multiple opportunities for assessment, rather than pencil and paper. They will be showing different types of triangles (scalene obtuse for example). One of the assessment opportunities could be for them to make the specific triangle with their bodies, alone (fingers maybe), or with a partner (joining arms). This type of varied assessment also includes the students choice, something that Amanda had touched on in her post this week.
Hi Shawn,
ReplyDeleteI am impressed with you integration of AI! As I was reading about the coffee and the doughnut I was imagining the image of them side by side in my mind and then scrolled to see the image you created. I think this serves as an opportunity (maybe something you are already doing and I should start doing) to use AI to generate images that show a topic being discussed visually. This connects with research related to the benefits of teaching using multiple modalities and the benefits of using visuals with ELLs.