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Learning math from a human in a classroom works because it forms a local culture that cares about math. Students have a chance to be motivated by what the teac
by tylerneylon 15y ago
Learning math from a human in a classroom works because it forms a local culture that cares about math. Students have a chance to be motivated by what the teacher cares about, and this is a very social phenomenon.
It is harder to express sqrt(3/4) on a computer in a meaningful way because there is no ubiquitous and intuitive interface for doing this -- the article has a good point here. But that doesn't mean it's a problem we can't address.
I like the idea of thinking of students in a classroom as young mathematicians, because it respects the students and inclines us to teach in alignment with real-world use cases -- it addresses the 'when will we ever use this' question. From that perspective, it would be a mistake to exclude technology based on its shortcomings. If it is genuinely useful for doing math, then it is worth learning.
I see a lot of concern about math education -- I think most of it misses the main problem, which is that there's zero motivation for people who are great at math to become teachers. If I have a PhD in math, and I become a math teacher, then (i) my math friends will think I will never publish a paper again, (ii) they'll think I am no longer good enough for serious math research, and (iii) I will take a huge pay cut vs typical math-PhD jobs. I might as well add (iv) I would suddenly be working with many people who don't respect or care about what I'm good at (students). I'm an optimist - I think all of these are addressable in the long run. Questions about the virtues of technology are secondary to the ecosystem and cultural perceptions around teachers.
- ghshephard 15y ago"It is harder to express sqrt(3/4) on a computer in a meaningful way" I'd argue that you just did. Wolfram Alpha certainly has no problem with your expression. Nor does Excel.
- jfarmer 15y agoFine. Express the homological proof of the Brouwer fixed-point theorem on a computer. Ideally in a way that is easily understood by both a computer and a mathematician. Bonus points if it can be used as a teaching tool, too, so that a (sufficiently mature) math student could read it and follow the proof. Assuming you agree the above is Really Hard™, then we've established there's an upper limit on how effective computerized math education can be (for now). This leads to a bunch of interesting questions. Where is that limit? Can we design a computerized version that satisfies the design requirements for that system? Do we have the technology to make it happen? Is it even a technology problem to begin with? Yabba dabba doo.
- deleted 15y ago[deleted]
- Retric 15y agoDitto Google: https://www.google.com/search?q=sqrt%283%2F4%29+&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a https://www.google.com/search?q=sqrt%283%2F4%29+&ie=utf-... Bing: http://www.bing.com/search?q=sqrt%283%2F4%29+&qs=n&form=QBLH&pq=sqrt%283%252F4%29%2520&sc=0-0&sp=-1&sk= http://www.bing.com/search?q=sqrt%283%2F4%29+&qs=n&f... Duck duck go: http://duckduckgo.com/?q=sqrt%283%2F4%29 http://duckduckgo.com/?q=sqrt%283%2F4%29 And Yahoo: http://search.yahoo.com/search;_ylt=AvTUYMAAOlorkQUnfaCGxPSbvZx4?p=sqrt%283%2F4%29&toggle=1&cop=mss&ei=UTF-8&fr=yfp-t-701 http://search.yahoo.com/search;_ylt=AvTUYMAAOlorkQUnfaCGxPSb...