Why is algebra important in High School to College?
In: 0
Algebra is used to model many normal things you need to think about. For example, let’s say you’re going to an amusement park. The fictional entrance fee is $50, and that gets you access to a basic set of activities, but there are premium activities that cost $10 each. Your budget for the excursion is $100. How many premium activities can you participate in? In algebra, that would be something like
total_budget = entrace_fee + premium_fee * premium_count
We also know that
total _budget = $100
entrance_fee = $50
premium_fee = $10
With these four equations, we can substitute and solve them using algebra and discover that we can go on 5 premium activities. This example is deliberately simple, but it is meant to show how algebra comes up normally.
Another examples might be: I have a certain amount of credit card debt, that accrues at a specific annual interest rate calculated monthly, and I can only pay this amount. How long will it take me to pay it off? How much will I end up paying to get rid of that balance?
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.
Algebra is used to model many normal things you need to think about. For example, let’s say you’re going to an amusement park. The fictional entrance fee is $50, and that gets you access to a basic set of activities, but there are premium activities that cost $10 each. Your budget for the excursion is $100. How many premium activities can you participate in? In algebra, that would be something like
total_budget = entrace_fee + premium_fee * premium_count
We also know that
total _budget = $100
entrance_fee = $50
premium_fee = $10
With these four equations, we can substitute and solve them using algebra and discover that we can go on 5 premium activities. This example is deliberately simple, but it is meant to show how algebra comes up normally.
Another examples might be: I have a certain amount of credit card debt, that accrues at a specific annual interest rate calculated monthly, and I can only pay this amount. How long will it take me to pay it off? How much will I end up paying to get rid of that balance?
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?
Math is really the only thing
Everything else is in service to math
Everything else is quantified by math making it the most important thing.
I would say everything you learn up to algebra is like the alphabet of math. Something you teach someone when you don’t expect them to actually understand how to form words into complex ideas, but you want to introduce them to the building blocks you’ll be using later on. Then you start taking English classes where you learn what a verb is, what tense is, parts of speech, rules of grammar, the exceptions and intricacies. The actual rules of English.
Algebra is the rules of math. Math is such a huge, enormous topic that you spend the first 8 years of your student life just learning the alphabet of math. It’s not until algebra that you really start digging into the rules of math. How to combine concepts. Stuff like that. You hit this stage where the strides you take each year are exponentially larger and larger. The math that you learn becomes more and more powerful.
If you are going into any major that requires math (basically anything in STEM) you will use algebra concepts every single day in at least one of your classes. Outside academia is a bit of a pot shoot. But even in my very paperwork-focused job, I use algebra every week. It’s woven into everything we do.
If you don’t get a math-heavy major and don’t go into a job that requires much or any math from you, then the exact topics may not be that useful to you. But Algebra is such a huge expansion in the logic that you can use and the tricks you need to rethink and reframe problems into a form you know how to solve. I truly think that these skills are going to be extremely helpful to anyone. The tools you have to develop to solve problems need to be very generic and apply to any number of different types of problems, so you will start learning how to solve problems outside of math as well. Critical thinking skills, thinking outside the box, approaching from multiple angles, sorting through what you know, what you do t know, and what’s required to traverse the gap between.
All studies used to be branches of philosophy. Math is what happened when logic grew so large that it split off from philosophy and became its own discipline. Math is what happens when you extend logic. Math is logic. If you can do basic logic, then you can do basic math. If you can do advanced math, advanced logic will be easier too.
I would say everything you learn up to algebra is like the alphabet of math. Something you teach someone when you don’t expect them to actually understand how to form words into complex ideas, but you want to introduce them to the building blocks you’ll be using later on. Then you start taking English classes where you learn what a verb is, what tense is, parts of speech, rules of grammar, the exceptions and intricacies. The actual rules of English.
Algebra is the rules of math. Math is such a huge, enormous topic that you spend the first 8 years of your student life just learning the alphabet of math. It’s not until algebra that you really start digging into the rules of math. How to combine concepts. Stuff like that. You hit this stage where the strides you take each year are exponentially larger and larger. The math that you learn becomes more and more powerful.
If you are going into any major that requires math (basically anything in STEM) you will use algebra concepts every single day in at least one of your classes. Outside academia is a bit of a pot shoot. But even in my very paperwork-focused job, I use algebra every week. It’s woven into everything we do.
If you don’t get a math-heavy major and don’t go into a job that requires much or any math from you, then the exact topics may not be that useful to you. But Algebra is such a huge expansion in the logic that you can use and the tricks you need to rethink and reframe problems into a form you know how to solve. I truly think that these skills are going to be extremely helpful to anyone. The tools you have to develop to solve problems need to be very generic and apply to any number of different types of problems, so you will start learning how to solve problems outside of math as well. Critical thinking skills, thinking outside the box, approaching from multiple angles, sorting through what you know, what you do t know, and what’s required to traverse the gap between.
All studies used to be branches of philosophy. Math is what happened when logic grew so large that it split off from philosophy and became its own discipline. Math is what happens when you extend logic. Math is logic. If you can do basic logic, then you can do basic math. If you can do advanced math, advanced logic will be easier too.
Math is really the only thing
Everything else is in service to math
Everything else is quantified by math making it the most important thing.
A lot of good answers have been given here.
I’ll just add that a big part of algebra is simplification. You start with a mix of known and unknown numbers which are related to each other in different ways. This relationship is described in writing using symbols which, by the time you’re in algebra class, you’re already quite familiar with; it’s just one level more complex. By following certain rules, you learn to make that descriptive “sentence” slightly simpler, and then even simpler, in steps, until you arrive at the values for the unknowns, thus solving what seemed like an unsolvable problem. Each sentence you made was still expressing essentially the same thing; you just followed a process to break it down and express it in a new way each time, leading to a solution.
Teachers have already done this for you many times in school, breaking down complex topics into simpler chunks and repeating the same information in different ways. Algebra gives you a very structured way to practice building that problem-solving skill, yourself. It also is a very necessary foundation for all the higher levels of math.
Also, there are similarities between algebra, human language, and computer programming languages. You may find you improve your language and computer skills if you work on math skills at the same time, and vice-versa.
After algebra, you might ask what’s geometry for… and one answer is that in that class, as you visualize how numbers are related and learn about “proofs”, you also learn formal logic, which is the next level of problem-solving skills you’ll be really glad to have a solid foundation with, instead of whatever analysis skills you’ve cobbled together on your own so far. Algebra gets you started with that, but geometry really solidifies it.
A lot of good answers have been given here.
I’ll just add that a big part of algebra is simplification. You start with a mix of known and unknown numbers which are related to each other in different ways. This relationship is described in writing using symbols which, by the time you’re in algebra class, you’re already quite familiar with; it’s just one level more complex. By following certain rules, you learn to make that descriptive “sentence” slightly simpler, and then even simpler, in steps, until you arrive at the values for the unknowns, thus solving what seemed like an unsolvable problem. Each sentence you made was still expressing essentially the same thing; you just followed a process to break it down and express it in a new way each time, leading to a solution.
Teachers have already done this for you many times in school, breaking down complex topics into simpler chunks and repeating the same information in different ways. Algebra gives you a very structured way to practice building that problem-solving skill, yourself. It also is a very necessary foundation for all the higher levels of math.
Also, there are similarities between algebra, human language, and computer programming languages. You may find you improve your language and computer skills if you work on math skills at the same time, and vice-versa.
After algebra, you might ask what’s geometry for… and one answer is that in that class, as you visualize how numbers are related and learn about “proofs”, you also learn formal logic, which is the next level of problem-solving skills you’ll be really glad to have a solid foundation with, instead of whatever analysis skills you’ve cobbled together on your own so far. Algebra gets you started with that, but geometry really solidifies it.
Latest Answers