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I firmly believe there should be two math subjects taught at school. One being "Calculating" where students do the boring calculations and all the stuff, calcu

by wirrbel 12y ago

I firmly believe there should be two math subjects taught at school. One being "Calculating" where students do the boring calculations and all the stuff, calculus, algebra, etc. and another one where the interesting and challening part of math is taught in an accessible and fun way. There are a lot of topics in math and related to math that could be explored in that second, new subject, probabilities, paradoxa, symmetries, basic set theory, even concepts of linear algebra/groups, etc. that are normally taught in university can be broken down to really great middle-school or high-school lessons. The only problem with that in normal math classes is, that the angry parent will quickly complain when that is talked about in a normal math class because they think that their kids should be bored to death by calculations that their smartphone does better already. I was recently talking to a retired high school teacher who had taught language classes (he was really not a maths guy). We started talking about password security and piece by piece we discussed how easy those passwords could be guessed and in the end he had a good understanding of the concept of probability/information/entropy. This really made me think, if a really non-maths person can enjoy and understand a topic that a lot of students who have gotten STEM degrees directly refuse (something like "I do not understand what entropy is, that is something about the my room being in order or not but I have given up .....") To repeat myself: There are great concepts and modern curricula available, sometimes for decades. However mathematicians, math teachers and parents are just not supportive in chaning anything substantially.

mathetic 12y ago
> One being "Calculating" where students do the boring calculations and all the stuff, calculus, algebra, etc. and another one where the interesting and challening part of math is taught in an accessible and fun way. Wow. That can start a flame war. I am a huge fan of set theory and probability but since when calculus and algebra are boring? Sure if all you do is evaluate bunch of integrals, it is but what if you are learning about Fourier Series/Transform? It requires vector algebra heavily as well as calculus and I think it is just as stimulating as anything else. Sure it involves "calculating" but it is not a bad thing, calculating is at the heart of the subject.
- sanderjd 12y ago
  Thanks for this! I wrote but didn't post a comment about how I hate that I'm starting to feel guilty for my lifelong interest in and enjoyment of a bunch of stuff that now seems to be scoffed at as "boring".
  - deleted 12y ago
    [deleted]
- steego 12y ago
  > Since when calculus and algebra are boring? After reading your post, it sounds like it's pretty boring until you start hitting differential equations. That's a long time for most people to be bored with calculating before they get to the good stuff. > Calculating is at the heart of the subject As long the emphasis is leaving students with an understanding why it works and giving them the tools to create new methods that they can prove work.
  - pbhjpbhj 12y ago
    I always found the symbolic manipulation to be somehow enjoyable; combining different elements, working up equations that were forgotten and tying it all together to answer a problem (abstract or otherwise). But then in day-to-day life I tend to find calm in mental arithmetic too. It's perhaps a little like practising piano - the syncopation and variance of a piece that is an accomplishment offers rewards in itself. But, nonetheless playing simple scales or arpeggios can be an almost meditative exercise.
- wirrbel 12y ago
  My point - and I could have expressed this more clearly, granted - was that you have one class for doing the numbers (the boring stuff), and one for doing more theory and explorative stuff. I did not want to imply that calculus and linear algebra are boring by themselves. In practice, linear algebra is not at all taught in school, people are just forced to train a few landmark calculations (gauss algorithm, etc.) as fast as they can. What I would very much like to see is that people get a good unterstanding of essential concepts, kernel, image, projections, etc. As you mention, calculating is important, and thats why I propose two classes, one being about calculating, one being about the theory, in practice with the focus on _results_ in school, the conceptual part is left behind.

by wirrbel 12y ago

mathetic 12y ago

> One being "Calculating" where students do the boring calculations and all the stuff, calculus, algebra, etc. and another one where the interesting and challening part of math is taught in an accessible and fun way. Wow. That can start a flame war. I am a huge fan of set theory and probability but since when calculus and algebra are boring? Sure if all you do is evaluate bunch of integrals, it is but what if you are learning about Fourier Series/Transform? It requires vector algebra heavily as well as calculus and I think it is just as stimulating as anything else. Sure it involves "calculating" but it is not a bad thing, calculating is at the heart of the subject.

sanderjd 12y ago
Thanks for this! I wrote but didn't post a comment about how I hate that I'm starting to feel guilty for my lifelong interest in and enjoyment of a bunch of stuff that now seems to be scoffed at as "boring".
- deleted 12y ago
  [deleted]
steego 12y ago
> Since when calculus and algebra are boring? After reading your post, it sounds like it's pretty boring until you start hitting differential equations. That's a long time for most people to be bored with calculating before they get to the good stuff. > Calculating is at the heart of the subject As long the emphasis is leaving students with an understanding why it works and giving them the tools to create new methods that they can prove work.
- pbhjpbhj 12y ago
  I always found the symbolic manipulation to be somehow enjoyable; combining different elements, working up equations that were forgotten and tying it all together to answer a problem (abstract or otherwise). But then in day-to-day life I tend to find calm in mental arithmetic too. It's perhaps a little like practising piano - the syncopation and variance of a piece that is an accomplishment offers rewards in itself. But, nonetheless playing simple scales or arpeggios can be an almost meditative exercise.
wirrbel 12y ago
My point - and I could have expressed this more clearly, granted - was that you have one class for doing the numbers (the boring stuff), and one for doing more theory and explorative stuff. I did not want to imply that calculus and linear algebra are boring by themselves. In practice, linear algebra is not at all taught in school, people are just forced to train a few landmark calculations (gauss algorithm, etc.) as fast as they can. What I would very much like to see is that people get a good unterstanding of essential concepts, kernel, image, projections, etc. As you mention, calculating is important, and thats why I propose two classes, one being about calculating, one being about the theory, in practice with the focus on _results_ in school, the conceptual part is left behind.