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@wolf480pl @jaseg @count @techokami I wish I’d learned a little linear algebra in high school, especially for solving systems of equations, when I eventually learned that in college I was pretty mad about leaving it out in high school. In high school I kept failing to solve systems, ending up showing useless things like x=x, which I now call “circular algebra”

@ShadSterling @jaseg @count @techokami
Thing is, not all things in math can be solved by following the algorithm.

Some problems require you to:
- be familiar with what transformations of a formula are valid
- be able to imagine the result of applying these transformations
- have an intuition for which formulas are better / simpler / closer to your goal
- apply the transformations that in your imagination result in better formulas, in hopes of eventually reaching a solution

1/

@ShadSterling @jaseg @count @techokami

And I think solving linear equations without using matrices is an early opportunity to learn that skill.

Like, sure, it's also useful in proofs and integrals, but those appear later. Solving equation systems is sth you can learn when you're 12 to get an early start on that mode of thinking.

Of course not everyone will need this in their lives, but at that stage you can't reliably tell who won't need it :/

@wolf480pl @jaseg @count @techokami yeah, I learned all that while I was getting a degree in math, tho when I was 12 my classmates were struggling to understand fractions. The thing that made me mad was that for those system there is an algorithm, and they just left it out - didn’t even say it exists! I wouldn’t start with it, maybe end with it, but not even mentioning it is another example of not giving the dots for interested students to connect

@ShadSterling @jaseg @count @techokami
yeah, "later on you will learn another way to do it called XYZ" is something teachers could say more often