Topology is typically reserved for university students because of its abstract nature and the advanced mathematics it builds on. However, the visualizations and examples of topology are accessible to anyone. Topics like Knot theory, Combinatorial topology, and Topological Invariants have general concepts that are accessible even to a middle school student. I will be researching how these concepts Topology can be used as motivation for a grade school student and can provide them with an introduction of what it means to be a Mathematician. I think that this topic should be important to anyone who wants to find more ways to get young kids interested in math. I also think it is fun to learn about unique styles of teaching and different lessons that people have used. I am open to any ideas or topics anyone thinks might be relevant or helpful!
February 18, 2018
Topology and Education
5 Comments
Brent
February 19, 2018 — 21:58
I think that teaching students topology early is an exceptionally important endeavor. I have no references to back this up off hand, but much of our intuition develops in our “formative years” so as long as kids are not forming negative associations with the experience, early exposure will improve their ability to use math naturally. I really like that you are looking at grade school students instead of highschool and older. I know that on many many occasions I have been exposed to concepts in college and graduate school that made me wish I had seen them sooner. At that point the framework through which I see the world had been set and changing it really is quite a pain. I also think kids should learn programing starting in grade school, but that is a rant for another day.
gljohns3
February 19, 2018 — 21:42
This should be fun! I remember stumbling across groups and rings in high school but they didn’t strike me as interesting until I realized how nice they were in physics (sorry, yes I am a physicist), mainly because they make it easier to digest some things. But the ideas of abstraction and generalizing are pretty powerful when it comes to understanding math and physics. To me, that is math and physics. So it bothers me that when I tell people I have a degree in math they assume I know numbers well. That tells me that that is what they were taught math is. Something is a bit off there.
sroheda
February 19, 2018 — 21:06
This is a great idea. It would have been great to have some kind of an introduction to topology in school. I only now took up this subject as a graduate student, and realized that it could be very useful for my research !
jhmuelle
February 19, 2018 — 18:38
I look forward to hearing what you learn! Personally I strongly disliked math during middle school. If I had learned about something as interesting as Topology I’m sure I would have changed my mind. Especially because it is a kind of math that isn’t about numbers. Also it’s an interesting way to introduce proofs. Usually proofs are just well worded arguments, but in topology that can be comprised of almost only pictures. Fundamentally there are a lot of creative decisions about how a proof is constructed but these fun possibilities are over looked too often.
aliman
February 19, 2018 — 09:50
I like this idea. throughout middle school and high school, and even the first two years of college, I’d done fairly well in the mathematics courses that were presented to me. However, I had not heard or been presented with the topic of topology until early this year. I think an earlier exposure of topology could really help the younger generation to see that math can be abstract and not restricted by just numbers and/or greek letters, because when we look pass the epsilons and the deltas, things can get a little “knotty” sometimes. (I’m not sorry for the pun)