Why Study Algebra?
 

Not in college, but in middle school/high school. Son is struggling in algebra right now, and part of his struggle comes from not liking math (really not liking math) and not seeing the point of algebra. He's the kind of kid for whom motivation typically comes either from being interested in a subject or at least seeing some value in it or reason to learn it. He's positive that he won't want to do the kind of job that will involve lots of math (though we remind him that could change, or he might surprised how math is used in some jobs). So we get "why do I need to know this?" from him. And frankly, I'm having trouble coming up with answers.

Why am I having trouble coming up with answers for him? Well, because I too hated algebra and all other forms of advanced math, and because I've rarely needed it in real life either -- I've never needed to know how to work linear equations or to know what polynomials are. (This, of course, means I'm useless at helping him with his homework.)

In fact, I've said for decades that I thought one of the real failings in my math education (algebra, algebra II, trigonometry) was that it was all presented so abstractly. It was always "this is the theory, this is the rule, here's how to solve the equation." No one ever said "and here's why it matters" or "and here's how you would use this outside a math classroom."

So what I have for him is:

• It's teaching you a logical, problem-solving oriented way of thinking that can apply in all kinds of non-math situations; and
• The Powers-That-Be have decreed that if you want to be on a college track, you need to pass algebra, geometry and algebra II.

That second reason was enough to motivate me, but it seems not to be enough for him. So, does anyone have suggestions for answering a middle schooler's "why do I need to know algebra?"

I work at a market research company, so statistics is a daily thing, but we have statisticians to deal with the heavy stuff. Things like this made me wonder why I needed all of the advanced math classes.

"Once I finish Math 101, 102, and 103, I won't have to take math anymore" was my motivation.

Perhaps the argument that the logical thinking you learn for how to solve the problems can be used in all aspects of life.

Exactly -- that is the other motivation I forgot to mention, but that I've tried with him: "Because once you finish it, you won't have to take it again. Otherwise, you'll keep taking it over and over." (Oh, and I've also tried that this is an opportunity to learn how to get jobs you dislike done, because there's always going to be some part of your job you'd rather not have to do.)

And to be clear, obviously I know there are many professions and occupations where you would need to know higher forms of math. But I think he's like me: I knew I disliked math enough that any career that required lots of it was automatically excluded from consideration. I guess what I'm looking for are examples from anyone not in a math-oriented field as to how they've used what they learned in algebra.

The only time I ever use it is solving word problems: If I leave Nashville at 6:30 PM and travel to Atlanta going 70 MPH, what time will I arrive? Convert your answer to the correct time zone.

I'll also cross multiply to get a percentage.

And that's it.

I struggled with it, and became a Journalism major to avoid algebra in college.

Algebra, I loved it! Geometry, on the other hand...ugh. Just, UGH.

Try equating Algebra to a "puzzle" or "mystery" that he needs to solve. ("something's missing...")

Use of visuals could be helpful (I'm thinking of a modified form of comic strip conversations), since visuals worked for me in understanding "how to solve for X". AAMOF, visuals work for me for just about everything. Don't tell me! Don't talk at me! SHOW me. (no I wasn't born in MO).

I think I use algebra quite frequently. Though I never write it out equation style, because I learned the principles, I can do this in my head without having to think about it. I don't like math and always say I'm terrible at it, but it becomes intuitive. I never took calculus and avoided it like the plague in higher Ed. Passed physics and am board certified in radiation physics without calculus. Algebra, though, is very necessary.

My thoughts on this may not be helpful at all because I really enjoyed math. I treated algebra problems like puzzles (like AzTheta), and I've always been a fan of puzzles/games. I am a philosophy teacher. While I rarely use math-proper in my daily professional life, I certainly benefit from the logic skills I learned in math. Doing algebra problems (and later, geometry and trig) forced my brain to practice applying specific rules in specific situations. I know that having a solid background in math strengthened my ability to understand symbolic logic, and I certainly use symbolic logic professionally.

Yeah, but that's basic math, not algebra: Distance divided by mph = travel time.

LOL. I hear so many people say this. My experience (and my wife's), on the other hand, was the exact opposite. I never had any problem with geometry, and it made perfect sense. I can see a circle, a sphere, a cone . . . . I can easily see how it applies to everyday life -- "How much carpet do I need to redo the downstairs? How much sand do I need to fill this sandbox?"

To me, geometry was concrete, and its relation to real life was obvious. Algebra, on the other hand, was totally abstract, and its relation to real life was completely lost on me.

As for visual helps, I think I'm about to order this book, which we've heard good things about: Algebra Survival Guide: A Conversational Guide for the Thoroughly Befuddled.

http://i43.tower.com/images/mm101535...-cover-art.jpg

I thought I would never need math in my career (in fact, I hated statistics so much in grad school) and now I work with statistics almost exclusively, and even if I don't do much of the heavy lifting, understanding where it comes from and why is very helpful.

Sometimes things just have a way of shaking out that you need this stuff. I was a foreign language major to avoid math. Now I'm here.

For Algebra, the puzzle piece of it is great if he likes puzzles. Also, game designers use math A LOT, and A LOT of algebra - so if he likes video games, that might be a way to relate. People who write computer programs use all sorts of math, including algebra.

Something as simple as figuring out what you need to tip (total times .2 equals x) is a good example of algebra. Plus you need algebra to understand the equations for geometry, which he might like better.

Also, baking! How do you double or halve a recipe?

I hated math. I just never did well in it. In High School, I took Algebra 1 & 2, Geometry, Trigonometry, Analysis, and Pre-Calculus. I took Calculus twice in college - the first time, I just couldn't get it and dropped the class, then retook it at my second college - the professor definitely made the difference in my ability to understand the concepts.

Often, during algebra, I would get the correct answer but not by following the rules of theorems or equations (see, I can't even remember the correct verbiage). I can do math in my head, but kind of do it backwards. I can't explain it any better than that.

But as an English/Journalism major whose career went from the Newsroom to the Advertising industry to Product Management in a world-leading internet company, and now as a housewife, I can say with absolute certainty that math happens in every day life.

From figuring out tips (divide by ten then add half to get to 15%), to using geometry to figure out angles for household projects with the hubby, to adjusting recipes for fewer or more servings than the original calls for, to estimating project timelines, to figuring out how far it is from point A to point B, or reading a "to scale" map, I absolutely use math on a regular basis.

I don't know if any of that helps.

I love love love puzzles, and I am glad that math has allowed me to solve things in my heead very quickly, but the way that it's taught in college kills me.

It's great to get the principles down in MS/HS so that you understand when to use certain functions. I was a working professional in college, though, so when a professor tells me "In the real world, you can't use a calculator," I find it hard to take him/her seriously.

LOL yeah - I don't use a calculator. I use an excel sheet.

But you have to understand the concepts to put it in your calculator (or excel sheet) correctly.

Also, if he ever gets a part time job he'll use it to figure out how much he makes a week, or to figure out an hourly rate for overtime, anything that takes more than one step.

And if he ever uses a budget. Or makes investments. Or pays his taxes. Anything that's not simple arithmetic or uses algebraic concepts in some way.

Right, which is why I think it's helpful to "show your work" in MS/HS.

If I told my boss to hold on while I showed my work to figure out the future valaue of an investment, he's spit on me and then fire me. The "scare tactics" that professors tried to give us (since many of the students were full-time students with no jobs) were BS and that turned me off to many of the assignments.

I'm thinking of a million ways I use it now.

Figuring out the percentage of my income I spend on health insurance is a big one (since it's open enrollment right now).

These are all very "adult" answers that might be lost on him, though. I'd stick to baking.

Very true. He loves video games, so his teacher tried this one. The answer he got was "I don't care how they come up with them. I just like to play them." Oy.

(Meanwhile, mom and I have added our own style of motivation. No video games at all on school days -- the "old" rule was no more than one hour of "screen time" on school days -- unless and until we, his teacher and his tutor see improvement. He doesn't have to start making As all of a sudden, but we have to see that he's trying his best.)


Right, but these are all basic math -- for the most part standard addition, subtraction, multiplication and division. He has that stuff down. He gets how he'll use that kind of math throughout his life. He doesn't get how he'll use algebra -- e.g., linear equations, to use what they're working on now -- in everyday life.


There's some good food for thought here. Thanks, everyone and keep them coming.

Converting the standard system of measurement to the metric system?

Linear equations are the lead-in to geometry - but you have to understand how to solve it before you can move on to harder geometry concepts - which plays into figuring out square footage of houses, how much paint you'll need to paint all the walls in a room, how many tiles you need to tile a kitchen... just cook up some home improvement projects! I'd love to say "we need to re-floor the kitchen because our kid is studying linear equations."

http://www.thefutureschannel.com/algebra_real_world.php

http://www.google.com/#hl=en&source=...w=1229&bih=823

http://www.google.com/#hl=en&source=...w=1229&bih=823

He'll use a lot of linear equations in the future if he studies economics (some four year colleges require everyone to take at least one econ course). Understanding them now will help him.

Honestly he may never use the linear equations and so forth, but unfortunately, that's not the point.


The point of most of the classes you take is the process you use to learn the material and not the material itself.


Much like at least half the meetings I attend aren't directly relevant to my job, but because I am asked to be there, I go.

It's a life skill.

Really? I never studied economics in any form at all, and I don't get the sense that I'm unusual in that.

BTW, I had to take one math course in college. I picked the easiest one I could find.

Okay, I'll be honest here. I do all of these things all of the time, and I don't see any connection at all with linear equations (y=mx+b or the other forms). All I need to figure out square footage is a tape measure; I don't need to know the slope of the line or how it graphs on a plane.

Am I missing something? Are my pathetic understandings of algebra showing? :o


Yeah, I think that's the bottom-line answer. Unfortunately, for an Aspergian, that frequently isn't a good enough answer. It's a common Asperger's trait -- the need to understand and buy into the value of something before expending any energy on it.

Thanks for the links, k_s.

Econ's becoming more and more common. I had to take three for my major in undegrad, but every major had to take at least two. I had to take the additional International Economics. I also had to take three in grad school, and surprisingly enough, it was the same three I had to take in undergrad but at a higher level (Micro, Macro, International). My major in undergrad was Foreign Language (International Government) and my major in grad school was "Badass."

Since linear equations are a lead-in for geometry, that's where you're using it to get floor space. Plus, if he goes into construction, contractors use it all the time, especially for designing entrances to buildings, etc.

It sounds kindof random, but figuring out slope goes into things like handicap ramps, etc. - which you can point out to him every time he comes across one. If the slope is all jacked up, it's not of much use to a person in a wheelchair. Even stairs are designed using slope.

The graph on the plane is just to conceptualize the concept in a context where it's not immediately apparent. And for things like statistical analysis, economic understanding, etc. where it's ideas instead of physical space.

Also, I know respiratory therapists use things like linear equations to figure out how much of one treatment a person should get, and I believe there's an equivalent for radiologists. Which seems random but I've become intimately familiar with both a Rad Tech associate's degree and a Respiratory Care associates degree and they use/do a shit ton of graphing.

You also need it for graphic design careers.

At my alma mater, Econ was reserved for business students.

I've edited my statement. This is a first I've heard of folks with recent 4 year degrees that didn't have to take any econ (usually I see people say "I only had to take micro/macro/basic").

Is he planning on making money ever? Supply/demand

From my perspective, K-12 taught me how to learn (or at least fake it for tests), a liberal arts education taught me how to think more critically, and my on the job training helped me figure out where I belong. However, I had to figure it out by myself with a lot of luck and good grace on the part of others.

I never use complicated formulas, I do not particularly enjoy math, and my husband is an accountant (which means I get a free pass in the math world). However- the concepts of problem solving do come in handy. Whether they are math related or other things- solving for "X" is a good capability to master. Do you need a full year of algebra (plus geometry, trig, and maybe even calculus) for that? No. Are there better real world applications to learn that skill? Yes, but how to approach that would be a deeper discussion. Ultimately, I took math because they told me to and because I needed it to go to college. I didn't know why I needed to go to college yet at that point, I just knew it was what came after high school. If he had any idea what he wanted to do professionally, you could bring it in that way... but he's probably too young and hasn't seen enough of the world yet to know what's out there.


Tangent: I wish that when schools or teachers or parents or whomever talked about potential career paths, there was a way to focus on how to identify each child's strengths and capitalize on them. That way they could also explore the lesser known fields/positions. The personality tests we took in school always had the same 50 or so professions: doctor, lawyer, accountant, actor, mechanic, etc.

As an example, I was the annoying child that always asked why. Why does this happen that way, why does it work like that, why does this word come before that one, why is this person shy and that one's a bully, how do they know when to turn the lights red/yellow/green... and so on. My strength? Pure, unfiltered curiosity about the world and people around me. If I had more of a mind for math (or perhaps if I had learned it in a different method), I could have been well suited to be an engineer. However, I somehow wound up being essentially a business owner of an application used by call center agents. My job is to ask why constantly. Why do you need this feature, why do you need the agent to enter this information, what are you going to do with the information collected, how will this impact the agent's overall experience, etc. It's a great fit. Did I ever hear about this type of role in school? No. Had I ever heard of Six Sigma (and the Five Whys :))? No. Is this the right profession for me, at least for now? Absolutely.

As a parent of two kids who excell in math, I've kept the sentiment to myself, but I also wonder why higher level math is needed to the degree it's taught in school.

After all, I've never written a check for $200 over X. :rolleyes:

MC, you may not use by-rote algebra every day, but I'm certain you use the same sort of logic every day - it's very much related to the "lawyer brain" (solving for unknowns/inconsistencies).

Essentially, any time you're solving for an unknown, you're using algebraic thinking - and that's a skill he will want to have, even if it's just wondering how much he can spend on two different items while still making budget for the month, or how to determine his 401(k) match sweet spot.

These aren't sexy reasons, but they do show that the reason why algebra is hard (it requires you to attack a problem in reverse, essentially) is the same as its benefit: an angle to attack problems that you didn't have before.

I just found out that most business majors don't have to take calculus, and I am still digesting this new information. I can't really understand how you'd take econ without it.
\hijack


As for linear algebra, is he into sports at all? The guys who make predictions (and take bets!) use algebra. Virtually any forecasting application builds on algebra, so is there something that interests him, and lends itself to that type of demo?

Also, virtually all of the best-paying college majors these days require math to at least integral calculus, so that's something to keep in mind.

ETA: link

My school had "business algebra" and "business calculus," but if you took the regular ones, they sufficed.

Ok, yeah - I get that completely, and that's not just an Asperger's trait. Most of us dig in our heels on things we don't want to expend effort on.

Yeah, this gets at the main reason I have been able to come up with for him -- that it teaches a way of thinking and problem solving. But to his Aspergian brain, that's not good enough. The connection he wants to see is the specific one: I need to know how to do this kind of equation because I will use this kind of equation when I am doing this real-life task. And it's not enough to point to the kinds of jobs where you'd need to know how to do particular calculations; the fact that there are jobs where one would use, say, linear equations is irrelevant to him if it's a job he doesn't see himself doing (and if his attitude is that the job would be ruled out if it required much math). Of course, it doesn't help that he doesn't know what he wants to do. He just has the list of jobs that are out of consideration. (And yes, lawyer is out of consideration for him. :D) That leaves us reminding him that he wants to keep all his options open.

Non-trigonometrical tangent: He did tell me a few nights ago that one reason he dislikes math is because "it doesn't require any thinking." That is to say, in his view, it is mechanical or (his words), "nothing but method." You learn the formula, you plug in numbers, you solve the equation. There's nothing "creative" (again, his word) about it; nothing that requires you to think about it in the same way as, for example, you think about the effects of a historical event or the meaning of a story (or the application of a case). This lack of "creativity" makes it very, very boring to him. I'm trying to work through how this fits in to helping him approach algebra.


Not at all, unfortunately. Doesn't like to play them, doesn't like to watch them.

Perhaps this is what throws me. (Or again, maybe my own algebraic inadequacies are showing). I can see needing to know slope to figure out stairs or ramps (though I still don't see how linear equations come into using a tape measure to measure dimensions and multiply for area). And I know how to calculate the proper dimensions for stairs, though I've never had to do it. From his view, this makes it useless knowledge for me -- why do I bother knowing how if I don't need to use that information. That's the mindset we're dealing with.

But I can promise you that in the dark ages when I took algebra, nobody ever suggested that the graph on the plane is just there to conceptualize the idea -- the graph was presented as the purpose and goal of doing the linear equation. In other words, the way it was presented to us left the impression that the reason for doing the linear equation is to be able to draw it on graph paper. I'm pretty willing to bet that's the impression he has as well. That goes back to what I said at the outset -- my experience was that my otherwise very good math teachers didn't give us any sense at all as to why anything beyond basic mathematics mattered outside the classroom.

This is a lot of good food for thought, everyone -- thanks.

Let's go the other way, then...what are his hobbies, and I will try to think of an application :-)

MC, I don't know where you live & it doesn't matter. I DO have a practical application, I think, that might make it visually "concrete". Got any steep hills anywhere that have those grade signs ("5% grade" with the wedge shaped piece to indicate the pitch of the road)? I was so excited to learn that I could apply algebra to figure out what exactly that meant.

At least, I think it was an algebra problem. It could not possibly be geometry, I have permanently deleted any geometry from my hard drive (brain). If it is geometry, I am going to be so disappointed. It can't be. You had to plot points on a line to figure it out.

I keep thinking "make it visual, make it visual". It's incredibly helpful when people with Asperger's can actually SEE what the rest of us are talking about. As I remind people constantly, "the speech stream is transitory and invisible. You can't see spoken words." The instant that things are put into a visual mode, watch the lights go on!

BTW I've sent out an SOS to my SLP friends to see if they have any useful resources for you. If I get any responses, I'll PM you. It may take a few days to hear from people; we're all crazy busy right now.

I think your reason #2 was the best one I could come up with since it's the only thing that ever got me motivated.

I'm in what's arguably a pretty math-heavy profession but I don't use much more than basic arithmetic. Very occasionally (like, once a year) I'll need some geometry but that's not really algebra-based. We had to take a semester of calc and a semester of physics for architecture but that was the extent of my college math. I think I used IB scores to get out of calc. I did enjoy stats, though.

He loves video games (though has made clear to us and to his teacher that he doesn't want to design them; I still wonder, though). He loves to read, he takes walks and runs (but we can't get him interested in track), and he takes karate, which he really enjoys. (It's the only sport-like physical activity we've been able to get him involved in.)

When I was my son's age I wanted to be an architect, and then I realized the math and physics that would be involved. Never liked math and never liked science. :o

Thanks!


I think I really must have an inadequate understanding of what differentiates algebra from other forms of math, because I would think of that as basic mathematics. That inadequate understanding on my part is probably not helping me help him.

Thanks. He is indeed a very bright boy. I think that has actually been part of his algebra problem -- aside from not enjoying math he's not used to things not coming easily, so there's a major frustration factor.

But get him started on things like the North Korean political system or the cult of Hitler, classical history, mythology, comparative politics or comparative religion (yes, he's been known to correct the teacher on things about religions other than ours, and yes the teacher looked it up and said "You're right") or many other topics, and he gets it a lot better than many adults.

The funny thing is, there's not that much math/physic involved! The most I do is arithmetic and a little geometry. I was talking with some co-workers at lunch today and we were saying how daunting older architects make the profession sound--perhaps so younger folks don't get into it?

But, maybe I have the same issue that you have--what I consider basic arithmetic (add/subtract/multiply/divide) is actually closer to algebra?

Maybe talk to him about Descartes and Newton. Both used math for philosophy. Not algebra, but algebra was a basis to what they used.

Well, arithmetic is part of algebra. Algebra is basically the concept of using one or more variables to stand for numbers, then solving for that variable. For example, when halving a recipe that yields 24 cookies, and for 24 you need 2 cups of sugar, how many cups of sugar do you use? If you were writing it out, you'd use "X" in the place of number of cups, and solve for it.

Plus, algebra is the application of rules(which is what seems makes it boring for MC Jr.), PEMDAS, FOIL, and so on.