Why is algebra important in High School to College?
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The consistent problem solving practice that comes with algebra is to your brain as a consistent weightlifting regimen is to your muscular growth.
Algebra is the study of functions/graphing with variables, Cartesian planes and such, it’s very important to learn because a lot of things in life can be represented using algebraic relationships.
The consistent problem solving practice that comes with algebra is to your brain as a consistent weightlifting regimen is to your muscular growth.
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.
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.
I never understood the question of “why are we learning X in school if we don’t use in real life?”. Well what about training your brain to do something more than driving a car and making toast? That’s like saying “I don’t know why I’m lifting weights in football practice if there’s no weights in the field”.
I never understood the question of “why are we learning X in school if we don’t use in real life?”. Well what about training your brain to do something more than driving a car and making toast? That’s like saying “I don’t know why I’m lifting weights in football practice if there’s no weights in the field”.
Algebra is the study of functions/graphing with variables, Cartesian planes and such, it’s very important to learn because a lot of things in life can be represented using algebraic relationships.
Without a solid foundation in algebra calculus will be an impenetrable learning curve. The most challenging part of calculus, IMHO, is the algebra and trig. Ideally we would teach two levels of geometry in High School in addition to algebra, that would be the best preparation for college level calculus.
When I say algebra, I don’t mean 8th grade algebra, I mean algebra 1, 2, and the pre-calc algebra that starts introducing students to linear algebra concepts.
Modern algebra was invented in the 9th century, before that when you studied a math it was mainly geometry. Using geometry to solve problems got really complicated really quickly. Using Arabic numerals and algebra greatly simplified complicated math. Rene Descartes (from cogito ergo sum) developed the idea of ‘analytical geometry’, or using a coordinate plane and algebra to analyze geometric problems. So when you graph stuff you can blame Rene. Those techniques lowered the entrance bar to abstract mathematics.
As many others have said, we use algebra all time. I have 3 kids, they need two slices of bread each for a sandwich. How many slices of bread do I take out of the bag?
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