Why Study Algebra?

[BraveMaroon]

Originally Posted by MysticCat

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.

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.

[MysticCat]

Originally Posted by KSig RC

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.

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. ) 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.

Originally Posted by DeltaBetaBaby

As for linear algebra, is he into sports at all?

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

Originally Posted by agzg

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.

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.

[DeltaBetaBaby]

Originally Posted by MysticCat

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

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

[AZTheta]

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.

[Munchkin03]

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.

[KSUViolet06]

This is sort of my lane-ish (I'm taking Teaching Math in SPED right now.)

You use algebra anytime you try to calculate an unknown based on other info you have.

Ex: Modifying a recipe is an algebraic function.

Everyone ahead of me pretty much stated what I was going to say. Apply it to what he likes and see if that changes anything. Good luck. He seems like a very bright boy. Remember that he's no less bright because he is struggling with math (you know that, as a dad but not every parent does.)

[MysticCat]

Originally Posted by DeltaBetaBaby

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

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.)

Originally Posted by Munchkin03

We had to take a semester of calc and a semester of physics for architecture but that was the extent of my college math.

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.

Originally Posted by AzTheta

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.

Thanks!

Originally Posted by KSUViolet06

You use algebra anytime you try to calculate an unknown based on other info you have.

Ex: Modifying a recipe is an algebraic function.

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.

Everyone ahead of me pretty much stated what I was going to say. Apply it to what he likes and see if that changes anything. Good luck. He seems like a very bright boy. Remember that he's no less bright because he is struggling with math (you know that, as a dad but not every parent does.)

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.

[Munchkin03]

Originally Posted by MysticCat

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.

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.

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?

[Psi U MC Vito]

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

[agzg]

Originally Posted by Munchkin03

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

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.

[KSig RC]

Originally Posted by MysticCat

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.)

From the video game angle ... a lot of the problem-solving in video games is figuring out the pattern or the unknown from a series of known "variables". For example, you know that there are 5 pieces to the puzzle, and 5 caves to explore - if you don't find that puzzle piece in Cave C, you can be pretty sure you missed something, so you backtrack, find what you missed, fill in the gaps, etc.

Even in something like a first-person shooter, you're constantly examining where you know people are, and what you don't know, to see if you can figure out what's going on from the context clues.

What kinds of games does he like? He may be using related critical thinking without even realizing, and that might be your hook.

[AlwaysSAI]

I haven't read every post of the entire thread, so excuse me if I say something that has already been said.

I currently teach Algebra I in the same state you live, MC, and in a county not very far away. Let me know if you decide you want an algebra tutor. (;

Originally Posted by MysticCat

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.

This is very true and in the state you live, it is a result of standardized testing. There are "more creative" things that can be done with Algebra but because Algebra I is and always will be an EOC class, teachers are less likely to do more fun things. Their goal is to teach it exactly how it will look on the EOC so that the students can pass it. (As an special ed teacher teaching Algebra, my approach is a bit different, but gets the same result.)

Originally Posted by KSUViolet06

(I'm taking Teaching Math in SPED right now.)

Nothing can truly prepare anyone to teach Algebra I to students with IQs of 50 and below. Teaching Algebra to EC kids is a very, very difficult job.

[KSUViolet06]

Originally Posted by AlwaysSAI

Nothing can truly prepare anyone to teach Algebra I to students with IQs of 50 and below. Teaching Algebra to EC kids is a very, very difficult job.

.

Fun fact: The math course at my university includes tutoring local SPED elementary school students. However, our kid's IQ ranges are slightly higher (think mild learning disabilities and some behavioral issues, my lowest IQ is probably in the mid 60s.) As such, my math experiences are a LOT diff than yours (my kids are younger so we're doing basics right now.)

I'd love to hear about some of the strategies you use for that age/ability level, though. If you feel like sharing of course. Especially since it looks as though I will be math tutoring part-time (elementary and middle SPED) next semester (which is, I might add, my first ever non-preschool education related job for real money!)

[psusue]

Originally Posted by MysticCat

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.

See I can totally get where he's coming from because in 8th grade when I took algebra I barely paid attention (because I hated math) and then didn't get it (which made me hate math) and that made me want to pay attention less (because I did not care about math!) It was super frustrating. One thing that I know now that I wish I knew then is that it doesn't end at algebra. If you don't work hard at algebra I, you will struggle with algebra II, and so forth. I wish I had the foresight at the time to just stick with it and tough it out. It made my life a living hell mathematically for two years as I was learning concepts later that built upon ones that I never got in the first place. I often wonder if I'd just worked harder then if my life would have gone differently later.

Originally Posted by MysticCat

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. ) That leaves us reminding him that he wants to keep all his options open.

The other point I have is that he has no idea yet what will truly interest him-- many of the topics that he may go on to love haven't yet been covered. For example, I HATED math with the burning passion of a thousand fiery suns, but when I learned about immunology and genetics, it sparked my interest in chemistry. And in chemistry you use linear equations to figure out things like rates of heating vs. cooling, etc. If my interest was sparked earlier, that could have changed things. Maybe try magazines like Popular Science or Popular Mechanics to show him how cool science and math can be?

Originally Posted by MysticCat

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.

This is true with algebra, but when you get past the basics math can be super creative. Math, in itself, is a language full of rules just like how grammar guides our rules. If you think about something as massive as the Golden Gate Bridge and how many things needed to be considered before it could be built; the wind, rain, other elements, fog, the weight of the cars, the smoothness of the surface, to make it cost effective, etc. Mathematical fields need critical thinkers and critical thinkers may need math to get to their end goal. Math is just a way to represent what would take a lot longer in words.

Originally Posted by MysticCat

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.

This may actually be your eventual selling point, because a lot of what has happened historically is described mathematically. Ex: If a town has a runoff problem from a local factory and the runoff in the water is found to have 20 parts per million of a toxin, how long has this been a problem and how much toxin is being released every minute? It may sound dumb, but if he wants to think critically about pressing issues he may have to truly understand mathematical concepts in order to 1. be a better, more informed citizen and 2. potentially work to make a difference with them. Say (as per the example) that the runoff is not immediately problematic at a certain level, but it is at the current level. How much of it would have to be stopped in order to get it to a safe level? What would be the impact over time (this is a direct linear equation if the level remains constant).

Other things that tie in mathematically are things like geography. National and state boundaries are figured out through triangulation. Things like population increases are statistical but rates of literacy, homelessness, people without healthcare, etc can be described and projected with algebra and statistics. Natural resources, gross domestic product, inflation, etc are all able to be described with math and may eventually be of great interest to him. And honestly he sounds like the kind of kid that once he gets something he'll take off with it (i.e. if he gets that eventually he can be very creative with math he might love it). So my suggestion would be to try to pique his interest with scientific/mathematical things and in the meantime maybe expose him to some statistics? He may like them, and those build on algebraic concepts. Hope this helps.

[southbymidwest]

Wow psusue, great post! To a non-algebrain like me (I was the geometry/trig/stats type), this makes a lot of sense.

MysticCat, I think your son has to look at this at a macro versus micro level also. School is about learning about all sorts of stuff, even that which you don't have an affinity for, or like. I'd bet big money that the vast majority of us took classes in something that we despised, and thought that they were "stupid" to take. I hated algebra and calculus. And I would rather stick knitting needles in my eyeballs than do a puzzle. My husband, the B.S. in math/2 masters degrees in math related areas, hated foreign languages-suffered through 4 years of French, including French literature. He, as a science/math/engineering dude, thought it was worthless, as he was not going to use it with his work. Was going to make SURE that he would never need it in any job he took. Ehh. At times we just have to suck it up and do it. That in itself is a life skill. We will always have situations where we don't want to do something, but we must do it anyways. And try our best to do so. Sorry, not much help. But I did like this blog that discusses algebra in high school, as it seems to be a much discussed subject all over the country. I also found the replies quite interesting also.

http://blogs.ajc.com/get-schooled-bl...ebra-ii-maybe/