Algebra-Real life applications???

I was once told by an accountant that she used algebra in her work. Maybe you could find a website that accountants visit and get some good help there. Past that, I’ve never met anybody who uses algebra. Of course, I don’t know many rocket scientists or nuclear physicists. Maybe they use algebra.

Years ago I used to teach history of American education courses. I taught my students as I had been taught by my own professor, that the inclusion of algebra in secondary education in America was a move largely engineered by a man named Charles Eliot, President of Harvard, and his “Committee of 10”. The Committee of 10 were the people who designed the curriculum for the then new invention that was the American high school.

Eliot’s belief was that algebra was a “gentleman’s pursuit” meaning it had no real use but was an exercise in logic for the mind of young gentleman who really would not need to go on a earn a living but rather live off their family’s accumulated wealth. Things like algebra, Greek, and Latin had long been part of the curriculum of “young gentlemen’s schools” and with the invention of the free American high school, Eliot felt that only the successful completion of algebra merited the awarding of a high school diploma to all the “lesser sort” that would now be receiving a higher education.

Eliot and his cronies didn’t include algebra because they thought it useful. They simply algebra as one of the hoops that young minds must jump through.

I don’t teach algebra but now that I teach Middle School I tell those students who complain about algebra they’ll need it to take the SATS. If you have very college-oriented students, they’ll quiet down when they hear that. If you don’t, tell them to blame it on Charles Eliot.

Greetings Lonnie,

Here are some excerpts about algebra from the book Homeschool Your Child For Free by LauraMaery Gold and Joan M. Zielinkski:

“Why learn algebra? For one thing, it’s the basis for all higher math.”

“Algebra is a brain tool. It is a series of skills that increases one’s ability to reason and to think logically.” HS math teacher

“I use algebra every day in my classroom, my kitchen, my car, my study, and on my computer. Algebra (and all math concepts) allows us to function in the real world. I travel on occasion, and, being a teacher, I cannot afford to waste money or time on the road. I use the formula for distance (d=rt) to make sure I use the most efficient means of transportation.” 8th-grade algebra & pre-algebra teacher

“The truth of the matter is that we all use algebra everyday in our lives without calling it by that distateful name. Did you ever budget your spending for the week or month? plan which bills will be paid out this week’s paycheck and which will be paid from next week’s? determine the area of the walls in a house so you could buy the right amount of paint? decide which size of a certain product in a store was the better buy? calculate how much herbicide, pesticide, or fertilizer you would need to treat your yard, a flower bed, or a field on a farm? figure out, at a theater or game, which candies or drinks you could afford after you had paid for the tickets? purchase a certain amount of material to make an article of clothing and base the amount on the dress size you wear and the money in your budget? plan how much you could place on layaway for a gift according to the amount of disposable income you had left in your household budget or allowance? arrived at a solution after using numbers in any way? If you said yes to any of these or to similar situations, then you have used algebra in the real world. The actual study of algebra formalizes these procedures and puts them in a logical sequence.” HS math teacher

“I use the basic I=PRT formula to budget and to find the status of my investments. I use algebra for shopping, when I use the ratio and proportion to determine which item is cheapest. There are many other ways to apply algebra. It can actually save you thousands of dollars a year if you use it right, maybe even more. I’m glad there’s algebra.” College Junior

Hope this helps!

Blessings, momo

Finding real life applications for algebra concepts is kind of like finding real life applications for phonics- if you know phonics, you use it every time you read and write, and if you don’t know phonics, you figure out some other way to muddle through, but in real life nobody every asks you “what are the spelling patterns for the long a sound?” If you actually learn algebra, you use it all the time- calculate the appropriate dosage of medication for the patient (doctor, nurse, veterinarian), manage vectors for flight plans (pilots, air traffic controllers), statistics (actuaries, any scientific research), accounting, computer programming and systems management, any type of engineering, etc. Heck, I even used trigonometry to figure out how to construct the Star of Bethlehem for the children’s christmas play. I could have used trial and error, or some other approach, but since I know trig (it was buried pretty deep, but it’s still there), that was the easiest way for me to tackle the problem.

“Real life” math usually involves skills beyond beginning algebra, just as real life reading involves more than basic phonics. Here are some quotes from people who actually use math in real life (and they aren’t rocket scientists). You can find more info at this site
http://www.maa.org/careers/index.html

“But, all formulas aside, my mathematics education has trained me to solve problems logically, and I use that skill in every project I take on. Every day, I use logic to reason precisely, distinguish contradiction from complexity, and determine whether or not a given conclusion has really been proven. Even when no equations are involved, mathematics is an essential part of my job. “
A Consultant for Price Waterhouse

“All of my work has been well grounded because of my initial studies in mathematics. The ability to think logically and to analyze problems and situations clearly has been invaluable. Mathematics also teaches one to be precise, which is key in research as well as in clinical medicine. In medicine, it is not as important to be brilliant as it is to be thorough and precise in our thinking. Currently, I am the Co-Director of the Cancer Program at the Graduate Hospital. I feel I have been extremely fortunate to be able to work in an area which is intellectually and academically stimulating and also is of service to mankind. “
A Clinical Associate at the Univ of Penn School of Medicine

” I enjoy being a mathematician/modeler/programmer in agricultural research. It requires creativity and problem-solving skills; there are all kinds of things to be discovered and endless challenging questions waiting for solutions. In applying mathematics to the “real world”, we observe and measure the world in such detail that we are able to see its simplicity and then communicate its process mathematically.”
A Mathematician with USDA

Also, see this page for a discussion of “why” the study of math is more than another hoop to jump through.
http://www.fordham.edu/mathematics/whatmath.html

Jean

This thread has given you many good quotes mostly from those who use algebra in their work although mostly they’re mathematicians (mathematicians using algebra should though be a no-brainer even to middle schoolers just beginning algebra)

. I don’t use algebra in my life. I found algebra taught in a way that did not connect it to life in any way. If all algebra is is finding a missing number,it shouldn’t take up two years of secondary curriculum so I’ve got to assume there’s much more to algebra than finding missing numbers.

Like Dorothy, you might be wearing the red shoes already that have the power to take you where you want. As most of the quotes you’ve been given were from mathematicians, perhaps it might be helpful to you to ask yourself how you use algebra in your life.

Keep a notebook from the moment you get up one day till you go to asleep. Write down every instance of how you used algebra in your day or your week.

Sara: According to this logic, we should not ask high school students to read Shakespeare, to learn chemistry or biology, to write essays, or to do anything else that requitres any modicum of higher-order thinking skills. After all, most of us spend a large amount of our time washing floors and doing dishes and caring for babies, or in an office pushing papers from place to place and unclogging the photocopier, and so on.

This logic leads to an “It’s good enough for the peasants” public school. I have attempted to teach in several of these. They are nice, well-meaning, caring institutions designed to gently prepare peasants to accept their lot in life. One is frequently reminded of George Orwell’s “Gee, I’m glad I’m a Beta”.

I remember one head of math at such a high school telling me his recipe of how to teach math — this was for Grade 12 advanced algebra, university preparation course: “Don’t give them any of the C questions; in fact, don’t give them any of the B questions. Just stick to the A questions.” (The text clearly stated that the C questions should be manageable by a good student, the B questions by an average student, and the A questions were intended as warmups for oral review in class.) He continued “Now, you see all the questions are in pairs, 1a and 1b, or 1 and 2, and so on. Each pair is the same question just with the numbers changed. Now, you do 1a in class and send them home to do 1b just the same way, and so on. And don’t bother with any long-winded explanations, don’t read the book in class, and don’t ask them to read the book; just show them how to do the questions.” Surprise, surprise — this school district was one of the lowest-performing in the country. These students graduated from Grade 12 with honours but couldn’t get into decent colleges, or failed miserably when they got there. Yet this teacher thought he was doing his students a service by breaking the work down and making it “easy” for them, and leaving out all the “hard” parts like actually reading the book and doing the average-level problems.

Personally, I get bored stiff and frustrated in classes that just repeat stuff I already know and give me an A for more or less showing up. (Hate education classes!!) High school and college classes SHOULD be mentally challenging. They SHOULD take us beyond our daily round. If not, why do we bother?

Algebra has a huge multitude of practical uses. In fact, that’s all real algebra is, a tool for solving problems. It’s used in physics, chemistry, biology, nursing, computer science, statistics (including in particular education statistics, something everyone here should learn to read critically), crime and social science statistics, the stock market, construction, ….. The comparison with phonics is very apt — algebra is a tool for use, something that leads you to new places, not something you do on its own for its own sake.

Higher-order thinking skills are the whole reason we have high schools and colleges, and math (*beyond* memorized arithmetic) is one of the vital tools of training thinking skills and logical processes and problem-solving beyond one simple step.

Mathematics as part of a liberal arts education was not invented by Eliot, far from it; it’s been a tradition for 2500 years (Let no one enter these halls without a knowledge of geometry, ca 500 BC) Many traditions stick around for a few decades or even centuries out of habit and inertia, but everything that has managed to last for a couple of thousand years through massive social changes has some merit to it.

First, we’d be in pleasant disagreement that algebra is the same thing as biology and chemistry. Math is a tool invented and intended to serve other disciplines. Without math, we couldn’t do physics as you point out. But algebra - when taught - is not taught rooted in its use. It’s isolated out from that and taught as a complete abstraction making it for some far more difficult to learn than biology or chemistry. There are also labs that go along with bio and chem offering hands-on interaction. Where are the labs for algebra as the curriculum is now? The modern understanding of math is that math is another langauge. Algebra is then a dialect of that other language but many students don’t know why they’re being taught to speak it. That very question - from an algebra teacher - started this thread. I can’t see any comparison between algebra and biology and chemistry in the way they’re taught at all or in the intention of their inclusion in the curriculum.

Next, - algebra’s inclusion in the curriculum of American secondary education was invented by Eliot. Eliot didn’t invent algebra certainly but he did invent its use in public school. Prior to the 1890’s, few went on to high school in our country or any other. Those who did were from wealthy families and they took the traditional gentlemen’s curricula which, as you point out, had included algebra. When America’s middle class began to attend high school, and then America’s working class, Eliot had algebra there for them too.

I’d also disagree that the purpose of high school is to teach “higher order thinking skills.” If that were the purpose of our schools, why in heaven’s name did we design our schools as they are? How can higher order thinking skils be well taught or encouraged in large classes of 25, 30 and even 35? How can almost anything be taught when we put three thousand students in a huge and impersonal and out of date building as is the situation in my local public high school?

I sadly see algebra intended, as did Eliot, as an obstacle that he knew would prove difficult for many. Despite its use in certain professions, it is obtuse to many not yet in those professions. Rather than lift up those working class minds, Eliot wanted to weed them out. A philsoophy popular at the time was “social Darwinism” i.e. only the strong will survive and Eliot encouraged that thinking and that model in our then new American institutioon of high school. By placing obstacles in their path, Eliot hoped to insure that his college and others could continue to receive only America’s “better sort.” looking forward to algebra having weeded out those not of “fit mettle.” Eliot wanted to maintain the “purity” of Harvard and to work with the same class of young men that Harvard and other schools like it had always worked with.

I disagree philosophically that America’s schools and colleges should be about those who are privileged. I dislike that our high schools then and today serve our colleges more than they serve our children. They call me an idealist but in my world, all children would be successful and we would do the things that allow all of America’s children to feel successful. There is nothing sadder than the upper school next to the middle school where I teach as I watch my former students sorted out as they go through high school as my dear colleagues often unknowingly work - hand in hand- with colleges. We serve the colleges well. We tell them who will survive their curriculum based on who has survived ours.

Pursuant to this board, by the way, it deserves to be said that always among the first weeded out and made to feel like losers are the students with learning differences.

Clearly I believe algebra should be optional in a high school curriculum. I would see algebra able to be taken after college or in college by those who intend to enter those professions that use it.

But underlying that is certainly my belief that America’s schools should work for America’s children - not our colleges.

Sometimes there are not real direct answers to this question. It may be a students idea that i can’t think od a way that I’ll use this and therefore it is useless. The idea of uselessness is another way of saying I really don’t want to do this work and if I can convince the teacher that this really useless I don’t have to do it and therefore I get out of work that I don’t want to do. Well, I haven’t run into to many students that are dying to do factoring.

However, factoring is very usefull for two reasons.
1. It teaches the mind how to be more logical. The more they have to think about abstact things and come up with answers the more the mind can become more logical. The mind is not born logical it is learned. Do your part, make them become logical.

2. There many parts in algebra. We learn the parts separately. Factoring is a middle ground that has to be learned separately so we can go on to other things.
Factoring is one of the most important part of algebra and it is one thing that not only must be taught, but must be learned just so we can get on with other things.

your students are going to fight you on this, but what they hay your the boss and because your the boss you don’t have to explain everything. Just make them do it, it’s for their good in the long run. I know that this sounds dictatorial but that how life is. Life really is not a democracy in high school. And that is just too bad–-they have to learn and you job to make sure it gets done. Factoring isn’t fun either ––it’s pain plow work.

Here you go:

Cooking (ever double a recipe? or cook for an odd #, like 11?)

Your taxes (ever try to depreciate anything)

Your retirement / 401k / investments (making investments, figuring return, figuring how much stock you can get for $X)

Your car (miles per gallon; speeding tickets that are $Y for ever mph over speed limit Z)

Child support (w/ 1/3 of kids living in divorced households or out of wedlock, this may be the only math skill some people will ever need; and if you kids have different parents, the math fun is even greater)

United Way (if I get paid 24x/yr and how much do I give per pay period if I only want to give $500 per year)

School (if tuition is $200 per credit + $W per lab hour, etc.)

Mortgages (if I pay bi-monthly, how much interest do I save over the life of a mortgage; 15 year v. 30 year; how long will it take me to save a down payment; etc.)

Credit Cards (how long will it take me to pay them off)

Diet (if this burns Q calories per hour but I eat T calories per day)

Distance (how long to drive 300 miles)

More car things (if I can affort $400 / mo on a car payment what can I get if I lease or buy, which is a better deal if I drive H miles per year, what is the APR on a loan, etc. You can really get screwed if you don’t know math!)

The list is endless! I can’t believe you didn’t get lots of helpful responses from us non-math people.

Innumeracy is something we have at our peril, especially now that fewer companies offer full pensions and people have to take charge of their financial future.

The list could be endless but the sad fact is algebra isn’t taught this way. The chapters in the book are not entitled… How To Depreciate Your Taxes, How To Pay OFf Your Credit Cards. That would be a meaningful way to teach algebra in the context of its potential use.

Instead it’s taught operation by operation , never connecting it to real life in any way. Even though a non-math major you clearly the leap between the concept - algebra - and its real applications.

But you may have had the ability to make that leap on your own because unless you went to a very different school or had wonderfully different math teachers, nobody ever taught you to use algebra that way in an algebra class.