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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

by 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.

mathetic 12y ago
In that case fair enough. The problem would be that understanding higher level concepts one way or another requires the underlying mathematical rigour and mental agility to do the "boring" stuff. So it would not be dividing existing curriculum into to but doubling the amount of lessons. I would have loved that when I was in school but I know that that course despite all of its beauty would be extremely boring to most other people.
- wirrbel 12y ago
  I think there are many topics in math that are left out because students have to train a few numerical algorithms. For example I was not at all exposed to logic in my math classes (if I was, it was very informal and only on a side note). However people would greatly benefit from this, probably even more than sucessfully calculating the shortest distanc between a line and a given point. The additional class would have room for some algorithms as well, some graph algorithms maybe (DFS, Djikstra), maybe also Binary Search, etc. A lot of those concepts do not require extreme amounts of calculation skills but they train the mathematical mind. We expose students in calsses on literature, geography, biology with various concepts, yet we limit contact to math on a narrow subset (roundabout requirements of an engineering college class for college-preparing courses). If you do not end up in STEM or CS, you will probably only use the rule-of-three after having left high school for 5 years. Just discussing questions like: "You have a scale and 12 billiard balls. One is lighter than the others. How many times do you have to weigh balls until you find the lighter ball?" would be inherently beneficial to students. Students afraid of equations can work on this as well and even have fun.

by wirrbel 12y ago

mathetic 12y ago

In that case fair enough. The problem would be that understanding higher level concepts one way or another requires the underlying mathematical rigour and mental agility to do the "boring" stuff. So it would not be dividing existing curriculum into to but doubling the amount of lessons. I would have loved that when I was in school but I know that that course despite all of its beauty would be extremely boring to most other people.

wirrbel 12y ago
I think there are many topics in math that are left out because students have to train a few numerical algorithms. For example I was not at all exposed to logic in my math classes (if I was, it was very informal and only on a side note). However people would greatly benefit from this, probably even more than sucessfully calculating the shortest distanc between a line and a given point. The additional class would have room for some algorithms as well, some graph algorithms maybe (DFS, Djikstra), maybe also Binary Search, etc. A lot of those concepts do not require extreme amounts of calculation skills but they train the mathematical mind. We expose students in calsses on literature, geography, biology with various concepts, yet we limit contact to math on a narrow subset (roundabout requirements of an engineering college class for college-preparing courses). If you do not end up in STEM or CS, you will probably only use the rule-of-three after having left high school for 5 years. Just discussing questions like: "You have a scale and 12 billiard balls. One is lighter than the others. How many times do you have to weigh balls until you find the lighter ball?" would be inherently beneficial to students. Students afraid of equations can work on this as well and even have fun.