Why is algebra important in High School to College?
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I will ignore the use case where people need to understand algebra for technical work (accountants, engineers, etc.) I’ll talk about the common man.
High school Algebra focuses on a really core idea in math: If you have an invariant, manipulations that don’t change the invariant are special.
And this is a really really instinctive thing to do.
Lets say you know that you change t-shirts once a day. Then if you want 7 days till laundry day you’ll need at least 7 t-shirts. What if you have to change t-shirts twice? Well then you’ll need 14 t-shirts.
You have kids and need to get them to school at 8am. Breakfast takes 15 min to make, and the kids take 10 minutes to get to school. You want 10 minutes of buffer time. You’ll have to make sure they get up by 7:25am.
You know your living situation costs 1500 a month. You know you spend around 200 dollars on food a week. You make about 3000 a month. Well then you have about 1800 a month to freely spend on other stuff.
So if this is so instinctive, why do we have a formal class? Practice, generalization, and abstraction
You need to practice this, because without practice your skills are trash.
You want to be able to generalize this, because sometimes you have more complex problems
You should learn how to abstract this because then you’ll realize that the important part of problems have nothing to do with the context of the problem, but instead are related to the problem itself.
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