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.

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.

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.

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".

> 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.

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.