Why does algebra work

The idea in real life is to solve problems however you can. Algebraic manipulations -- particularly standard cookbook manipulations -- are just one way to solve certain kinds of problems. Feynman himself seemed to hold that the algorithmic or cookbook types of rules one learns in algebra class are really just rules for people to follow who don't really understand mathematical thinking. I wouldn't go quite that far, but I would say that following such rules is only one way to solve many apparently mathematical problems.

Return to text. They are attempts at giving you some practice in solving problems the way they supposedly appear in real life, since real life problems don't appear already set up in formulas or equations. However, unfortunately, real life problems also don't appear formulated as structured as word problems do; and they don't appear at the end of a unit so that you get an arbitrary, circumstantial, clue to what is expected.

Languages are "conventions" because what words or phrases or marks on paper mean is what people decide they mean or what they happen to grow to mean. There are private conventions, such as secret codes, and public conventions such as ordinary languages. There are also private conventions for individuals. For example, if you are measuring and sawing wood, you might mark the length of the wood to be cut by putting your mark even with the end of your measuring tape, or you might put the mark just outside the measuring tape.

Either way is fine, as long as you know when you go to cut the wood, which way you chose to make the mark. If you made your mark even with the end of the measuring tape but cut the wood inside of that mark because you thought you had made the mark on the outer edge of the tape, your wood will be a fraction shorter than you intended. So it is important to remember what your mark really means. You can do this by remembering how you do things each time you do them, even if you do them differently each time.

Or, usually easier, you choose a way to do it every time and then do it that way each time, and there is less to remember. You have developed a convention for yourself. In math and science, ambiguities of ordinary verbal language such as in the "Green Ham and Eggs" case are tried to be eliminated by developing and improving as necessary, precise symbols that have very specific meanings.

This is intended to prevent confusion in communicating to others what you are doing. But it also helps you keep straight yourself what you are doing, by not having to remember each time what you meant by using a specific symbol.

Conventions have something of an arbitrary nature, however, though once developed they might have some sort of logic or psychological sense of appropriateness or seeming reasonableness of their own. They are arbitrary in that we could have used any symbol to designate what we want to designate.

And in some cases how we use them is arbitrary. But if there were no such convention, someone might take it to be equivalent to 27, because they thought it meant 3 times the sum of eight and one, which would be 3 times 9. In algebra, sometimes they state conventions in ways that make it sound like they are a conclusion to some sort of logic rather than merely an arbitrary convention or choice that was once made. This confuses students who are trying to understand "why" something is the way it is when, in fact, there is no logical reason, because it is simply a convention.

For example, using the "x" below to mean simply the multiplication symbol not an unknown variable some teachers at the beginning of algebra will ask students what the answer is to something like. But conventions, once established, also have a resulting logic that is not arbitrary.

For example, because the English drive on the left side of the road, and Americans drive on the right side of the road, the way they each have to make right or left turns from two-way streets onto two-way streets in their own countries is different.

When Americans turn right, they stay near the curb. When they turn left, they have to "swing wide" to get to the right side of the street onto which they are turning. The English have to do just the opposite, hugging the curb lane to make left turns and swinging wide to the outside lane to make right turns.

That is a logical result of choosing which side of the road to drive on, even though the choice itself had no logic but was simply a matter of convention. Moreover, there is another logical result of the convention. Although we are taught to look both ways before crossing a street, we tend to look one way, toward the traffic approaching on the curb side, as we step off the curb; and we look the other way as we get to the center of the street.

In America, one generally then looks left before stepping off the curb, and right once one gets to the middle of the street. In England, that can put you in front of a bus, because the traffic next to the curb is coming from your right, not your left; and the traffic on the far side of the center line is coming from your left not your right. The English have the same problem in reverse when they are in America.

That is a very difficult habit to overcome when visiting the other country and walking across streets. But the reason you have to look the way you do as you cross a street is a logical result of the side of the road the country chose to have drivers use. So conventions which are arbitrary, nevertheless can have consequences that logically depend on them. This work is available here free , so that those who cannot afford it can still have access to it, and so that no one has to pay before they read something that might not be what they really are seeking.

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The Purpose The difficult part is to figure out which changes to make to both sides that will be useful and helpful for you to figure out what the variables or "unknown quantities" or "unknowns" are. Typically students are taught a number of principles and manipulations that seem to many of them to have nothing to do with anything.

Then they are given practice in using those principles or performing those manipulations -- principles and manipulations which may or may not make any sense to them. They are taught the rules for "order of operations" and then given practice calculating expressions that are written without parentheses. Or they are taught you can do the same things to both sides of an equation, as long as you do the same thing to each side.

Then they are given equations to solve, which seem to use a bunch of those manipulations or principles. And finally they are given problems in words which seem to have something to do with equations and manipulations. So what students need to do in general in algebra courses is: 1 Learn the symbols and conventions of the language by memory and practice.

It gives me a headache. Who wants to sit there and figure out what y or g or a is. First of all why would you be given half of the information of something in the first place.

Maybe for measurements it can save you time and physical work but to not know how much sue gets payed a hour if she gets payed a week, basic division works just fine. I am a High School Math teacher and I strongly believe that most of the reasons for Algebra here are bogus. Furthermore, more students are polite and go along with it but do not really buy it. However, the reason I teach Algebra and stress to kids the importance of it is simply this. That means to be a dental hygenist or a cop in some districts , you will need to pass that Math class.

Many of their peers find out years later the roadblock that math becomes. It can either open doors or close doors. Why that is is a bigger question but that is a fact. And how many people become mathematicians? Not many. Yet still calculus and algebra are being taught to everyone!

Fascinating right? Key word is some. This is the form I am being taught. And going back to one of my main arguments, when will I need to know statistics and calculus or calculate the population growth of rabbits? Dear Aidan, Thank you so much for you thorough response. I am a mother of two exceptional students both who have dyslexia and one with ADHD and physical special needs. I am currently searching the internet for ways of trying to break through the current learning block especially for my youngest child who is struggling the greatest with Algebra and seeking a real life need.

He is Yes the school system is broken. I am sorry for that. I feel my generation has failed yours in so many ways but would like to again thank you for your addition to my search and the sharing of your thoughts and feelings on this topic. They are relevant, well written and should be a wake up call to the school system and how one size does not fit all and how your time could have been used wiser pursuing other forms of education to a greater advantage. Nice article. Not good in school why, the technical school had two options, career and advanced.

Career was all the shop things cars, plumbing, machine shop, woodshop, electronics, electricity. These would produce 4 years of apprentices or technical colleges. I did advanced, University or College bound. The only problem was the Teachers in the Music department thought it would be a good idea to hijack the student time in the band by having them come in 2 hours early and stay 2 hours late.

That makes for a long day and for what! I would have otherwise been doing my homework. Landed a. I go to college while working and take the non-math course…turn down other jobs that are tech-driven, and end up doing upgrades for high school courses to keep my brain active. I was doing math all the time and never knew I was making up for lost time and misdirection you can always change direction.

I take one book and fly through it a month and then the next repeating it all year long. I am 34 years old and I work as a part-time tutor and full time 5th grade teacher. Maths is naturally a cold, soulless pursuit. Sorry to disagree. I know the basics of math without Algebra. In my life I have done many jobs. I was a Corpsman in the Navy. That is the only job I had to use algebra and really it was just plug in numbers to calculate drip rate for an IV.

Only one formula and easy to use without having to know Algebra beyond that one formula. I have worked in the Broadcast Industry where I created video production. Writing script, shooting and editing video. No Algebra there. I have worked in sales. Basic math but again, no Algebra. I was rather excellent in sales. I have worked as a school teacher for 3rd and 4th grades. No Algebra with that job. And I currently work in psychology as a therapist. Thanks to Algebra, I have had a client or two who needed help with anxiety and depression caused by their college Algebra.

But no real use of Algebra for this job. I have traveled the world, done my budgeting, and done many things outside of work. Not once have I ever had to use Algebra. I obviously learned it to get my BA, but it has been useless for my life. Again, just my opinion. But an opinion based on a lifetime of not using or needing Algebra.

I was really bad at mathdoes matter fact I did not like it math teacher said we would never use algebra or calculus and now after reading this I understand a whole lot more than I ever have thank you.

I did eventually pass the algebra class required in order to acquire a degree. So many of us were so completely lost. There are 26 cats in the pet shop.

This is two more than three times the number of dogs. How many dogs are there in the pet shop? Alice and Bob have some candy. If Alice gives Bob a piece of candy, Bob has twice as much candy as her. If Bob gives Alice a piece of candy, they have the same number. How many pieces of candy do they each have? When getting your child to attempt these questions, always ask them to show their reasoning, as this is the essence of algebra and indeed of all mathematics!

In the last example, they may solve the problem through trial and error. Algebra becomes really powerful when it gives us systematic methods that can be applied to a flexible range of problems. Math-Whizz, the multi-award-winning online math tutor from Whizz Education, can help! With just 60 minutes of access to the Math-Whizz Tutor each week, your child can expect to increase their math learning by 18 months in their first year of use. It can truly help!

We're glad you explored this Wonder, Isaac! Speaking of bedtimes, you might enjoy exploring Wonder next! Hey there, Hunter!

To become an engineer, you'll be required to take a lot of math classes. It will take a lot of practice and studying to master math subjects, but we know you can do it!

We believe in you! It may not be as obvious, but even salespeople and staff at shelters need to use algebra in their daily lives.

In fact, no matter the job, we bet there are times everyone needs to do algebra. Take a look at this webpage from IPracticeMath. This page lists just a few situations any person could encounter that involves algebraic math. Check it out and let us know what you think! Thank you for showing me this website. Now I realize that salespeople can use algebra in prices and people in shelters use it to split things evenly among the animals.

We really do use algebra in iour daily lives! Thank you for introducing this topic :. You're welcome, Nolan! Sometimes the reasons we learn certain things in school aren't explained very well. We're glad that you now know some real-life examples of why algebra is important! Hey there, Karter! We hope this Wonder helped explain why math and specifically algebra is important! Thanks for your suggestion, Lily. Have you ever researched events that happened on your birthday? Take a look by clicking here!

Sometimes math becomes a lot more enjoyable when you get a thorough explanation of why equations work the way they do. If there's something that confuses you, Karter, be sure to ask your teacher for more help. Hey there, LOL! Sometimes you might feel that you don't need to learn algebra, and that's OK. We hope this Wonder helped you understand some of the reasons why algebra is important. Thanks for being our 50th commenter on Wonder , Jack. We hope you enjoyed this Wonder! Algebra can certainly be challenging to learn but it's so important, Lily!

Don't be afraid to ask for help when something confuses you! Hi, Jomol! It's so great that you visited Wonderopolis. We encourage you to research Kpop a musical genre from South Korea online to determine if it's safe for your child. Welcome, Brooke! Thanks for sharing your opinion about homework! We like algebra, too. We're glad you're having fun exploring Wonderopolis! We agree, Carol! We're glad you liked this Wonder and enjoy math! Thanks for joining the discussion and sharing your opinion, Jaimalyn!

We hope you learned more about why algebra is so important from reading this Wonder! Great question, Shantal and Shannah! We encourage you to read the Wonder closely to learn more. You can also talk with your family, friends, and teachers to see what they think! You're very welcome, Ryan! We're glad it was helpful. It's always nice to know why you're learning something! Thanks for joining the conversation, Antoinae! Math is all around us Welcome, Aarav!

We're glad you like math. You're right, it is very useful in life and very important! That's a great question!

Think of math as an umbrella that covers algebra, geometry, calculus and other types of mathematical subjects. They all have aspects that make them unique, but they all have certain things in common, like using numbers and equations, that make them all math.

Hi, Bobby! It is so important. That's right, Douglas! We're glad you learned something new from today's Wonder. Thanks for your comment! Great to hear, Douglas! We do, too! Math is all around is if you think about. How many places do you see math? Algebra is a type of math, just like geometry and calculus! We are undergoing some spring clearing site maintenance and need to temporarily disable the commenting feature.

Thanks for your patience. Drag a word to its definition. You have answered 0 of 3 questions correctly and your score is:. Want to add a little wonder to your website? Help spread the wonder of families learning together. We sent you SMS, for complete subscription please reply. Follow Twitter Instagram Facebook. Why do I need to learn algebra? What is algebra? How long has algebra been around? Wonder What's Next? Try It Out We hope you're ready to dive deeper into the world of algebra!

Check out the following activities with a friend or family member: Think about all the types of things you do on a daily, weekly, and monthly basis. How many of those things involve math of any kind? For example, do you ever go shopping and have to count money or add up the cost of items?

Make a list of all the things you can think of that you do in real life that involve math and share it with a friend or family member.

Can they think of other examples? Do You Speak Algebra? Use this simple activity to learn more about the "language" of algebra and how to speak it.