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Promoting Arithmetic and Algebra By Example

timothy posted about 2 years ago | from the how-many-trains-can-2-boys-paint-if-both-are-moving? dept.

Education 158

Capt.Albatross writes "A couple of months ago, the New York Times published political scientist Andrew Hacker's opinion that teaching algebra is harmful. Today, it has followed up with an article that is clearly intended to indicate the usefulness of basic mathematics by suggesting useful exercises in a variety of 'real-world' topics. While the starter questions in each topic involve formula evaluation rather than symbolic manipulation, the follow-up questions invite readers to delve more deeply. The value of mathematics education has been a (recurring issue on Slashdot)."

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an example where algebra is useful? (4, Insightful)

wierd_w (1375923) | about 2 years ago | (#41468121)

Aside from the obvious ones in engineering, where few kids will participate...

There is the issue of "how much paint will I need to paint my house?"

Doing the math will save you money.

Re:an example where algebra is useful? (2)

Lumpio- (986581) | about 2 years ago | (#41468441)

...but most people would probably just prefer to google for "how much paint needed", enter some parameters and have software do the hard lifting (multiplication) for them.

Re:an example where algebra is useful? (4, Interesting)

DanTheStone (1212500) | about 2 years ago | (#41468535)

Figuring out how much money a better-MPG car will save you.
Figuring out which size of an item at the supermarket is a better deal. (Especially if one has a Bonus 25% More For Free! so the label doesn't tell you the correct price-per-amount.)
Converting measurements for cooking/baking. (If I need 1/3 cup of sugar, and all I have is 1/2 cup measuring device, how full should I fill it?)
Knowing whether the store's ripping you off by not giving you the full discount listed. (The thing says it's 40% off, why did it ring up 30% off?)

Understanding which deals aren't good deals. You wouldn't believe how many people don't understand that "Buy One Get One 50% Off (of equal or lesser value)" is worse than a 30% discount. Or that it's worse than a 20% discount in many cases.

It's true that all those things can be done without algebra, but anyone who doesn't understand algebra will have a really hard time figuring them out. Failing to understand algebra means you'll have a problem with real-world problem solving, and will probably waste your money.

Re:an example where algebra is useful? (3, Informative)

Joce640k (829181) | about 2 years ago | (#41468757)

Figuring out how much money a better-MPG car will save you.

Start by using GPM as a metric.

You'd think engineers'd know that 1/x is a curve, but nooooo...

Still it's not as bad as measuring rainfall in liters per square meter like we do here in Spain.

Bottom line: Getting the basic math right would mean the public wouldn't have to. Or at least, not so much.

Re:an example where algebra is useful? (1)

Anonymous Coward | about 2 years ago | (#41468889)

What's wrong with using liters per square meter (also known as milimeters) as a way to measure rainfall?

Re:an example where algebra is useful? (4, Informative)

vrt3 (62368) | about 2 years ago | (#41468931)

Still it's not as bad as measuring rainfall in liters per square meter like we do here in Spain.

I'm wondering, what exactly is the problem with that unit? Which alternative would you prefer?

Because if it's mm that you prefer, you're maybe interested to know that liter per square meter is exactly the same as mm:

liter / m^2 = dm^3 / m^2 = (10^-1 m)^3 / m^2 = 10^-3 m^3 / m^2 = 10^-3 m = mm

Re:an example where algebra is useful? (2)

tlhIngan (30335) | about 2 years ago | (#41469459)

Start by using GPM as a metric.

You'd think engineers'd know that 1/x is a curve, but nooooo...

Still it's not as bad as measuring rainfall in liters per square meter like we do here in Spain.

Bottom line: Getting the basic math right would mean the public wouldn't have to. Or at least, not so much.

You do realize the metric equivalent ot MPG is... L/100km! Which is just a minor variation on GPM.

Engineers do use the right units. It's just that MPG is a much nicer "more intuitive" unit for shoppers - as in "bigger is better!" while if you use the standard L/100km, it's "smaller is better". (Note we're still using "people sized" units, using L/m is more correct SI, but turns the numbers meaningless

And L/m^2 is a valid unit - it tells you how much liquid fell per unit area. We normally use mm (or inches for imperial folk), but tehcnically L/m^2 is the correct unit (even though it simplifies down to mm in the end).

It's just like how we use kWh for our electrical meters, when the correct unit is J (it simplifies down to that - a watt is J/s, so you have time on top and time on the bottom which cancel through a conversion). Or AH/WH for battery capacity. We could use the correct units, but the alternative units do make it easier to intuitively grasp the concept.

Re:an example where algebra is useful? (2)

imnotanumber (1712006) | about 2 years ago | (#41469717)

You do realize the metric equivalent ot MPG is... L/100km! Which is just a minor variation on GPM.

Sorry, while the rest of your post is correct, the metric equivalent of MPG (or better Miles/Gallon) would be Meters/Liter (distance/volume). L/100km (Volume/Distance), which is used in Europe is the "inverse" of MPG.

Re:an example where algebra is useful? (1)

Antipater (2053064) | about 2 years ago | (#41470109)

Yeah, you know, in his whole long-winded post where he talked about how one unit was "bigger is better" and one was "smaller is better", I don't think he realized that he was talking about inverses. Thanks, though, I don't think the rest of us realized either that the metric equivalent of a mile isn't a liter.

Re:an example where algebra is useful? (1)

Garridan (597129) | about 2 years ago | (#41470119)

I'm sorry... did you say that not using SI prefixes is "more correct"? That is simply ridiculous. The whole point of SI is to make bringing things into scale easier. People get the weirdest ideas sometimes...

The Fallacy of Utility (5, Insightful)

catchblue22 (1004569) | about 2 years ago | (#41469483)

I suspect that algebra has value beyond its immediate application and utility. I think this is often overlooked in debates like this. When learning algebra, you are in effect modifying your brain in a particular way. You are training yourself to think a certain way. You can gain a feeling of mastery if you learn it well. And implicitly, you are taught the value of reason and logic. The very fact that you are asked to learn algebra carries the message that logic and rational thinking are valuable skills, and that people who are good at such things are particularly valuable to society. The pursuit of a topic like algebra encourages discipline and structure in the way you think about many other things.

To focus only on the immediate applications of algebra is small minded and unwise, in my opinion.

Re:The Fallacy of Utility (0)

Anonymous Coward | about 2 years ago | (#41469971)

Post basic arithmetic math becomes problem solving in new and wonderful ways, closer to philosophy than counting.

It's about taking a problem, breaking it down into the basic bits and then seeing what you can do with those basic bits to create a solution.

Anytime I've ran across someone with problems to beginning algebra all I've had to do is let them know that the basics of algebra is to break down the problem into smaller parts and then solve those, once they understand that the rest is usually a breeze.

Re:The Fallacy of Utility (1)

styrotech (136124) | about 2 years ago | (#41471123)

I have to agree. It's not just the logical and rational aspect though - it is also the abstract nature of algebra.

Being able to think in both an abstract way and a concrete way is important.
When kids move on from plain old arithmetic to algebra, they need to wrap their heads around thinking about solving problems in a more abstract way. There is another similar step up when learning calculus.

eg dealing with a boss that can't think in abstract terms at all reinforces this to me. Every description of a requirement or proposed solution to a problem is a concrete special case rather than a more abstract general case that could be used to pre-emptively solve a host of similar problems or requirements in the future.

Re:an example where algebra is useful? (1)

chrismcb (983081) | about 2 years ago | (#41471077)

You wouldn't believe how many people don't understand that "Buy One Get One 50% Off (of equal or lesser value)" is worse than a 30% discount. Or that it's worse than a 20% discount in many cases.

Could you elaborate in which cases is 20% discount better? Assuming you want two items?

Re:an example where algebra is useful? (1)

bmo (77928) | about 2 years ago | (#41468557)

A word problem:

If you have 20 cows in a barn, and they leave an open gate at 1 per hour, after 1 hour, how many cows will be in the barn?

Math teacher's answer: 19.
Dairy farmer's answer: None.

--
BMO

Re:an example where algebra is useful? (1)

fahrbot-bot (874524) | about 2 years ago | (#41469543)

If you have 20 cows in a barn, and they leave an open gate

"They leave an open gate?" Dude. If your cows are controlling the gate, you've got other problems than Math.

Re:an example where algebra is useful? (0)

Anonymous Coward | about 2 years ago | (#41471663)

And the math teachers answer is wrong in any case. It should be 18. Open the gate, cow leaves. 60 minutes later another cow leaves. So after one hour there would only be 18 cows (although in reality the dairy farmer is correct, 0 cows left).

Re:an example where algebra is useful? (1)

crazyjj (2598719) | about 2 years ago | (#41468723)

If you need a fucking algebraic formula to figure out how much paint you need to paint your house, you're probably too stupid to use either algebra or paint.

Re:an example where algebra is useful? (2)

wierd_w (1375923) | about 2 years ago | (#41469191)

A formula is more useful, given the innate variability with paint.

The thickness of the film varies between brands and types of paint, so the coverage in square meters/liter will be variable.

A formula that incorporates these variables, and how many coats you need for the desired effect will tell you *exactly* how much paint you need, regardless of paint type, as long as you plug in the values.

Contrary to your opinion, algebra can save you a considerable amount of time finding such answers, and save you money in terms of wasted gas driving to and from the hardware store, and in cans of unused mixed paint.

Likewise, you can use it to determine how many 2x4s you will need to build that deck, and how many nails it will take. How many cans of water sealer you will need. A whole host of things.

Or, you could just be a troll, plug your ears and go "nuh uh! You iz dumbz if you use algebra for that! Derp!" Like you are now. Let me know how that turns out for you whe you need to build something.

Re:an example where algebra is useful? (1)

Golddess (1361003) | about 2 years ago | (#41471237)

Or, you could just be a troll, plug your ears and go "nuh uh! You iz dumbz if you use algebra for that! Derp!" Like you are now. Let me know how that turns out for you whe you need to build something.

Not the OP, but I thought their point was "you don't need complex mathematics for all that, just a basic understanding of math". For example..

you can use it to determine how many 2x4s you will need to build that deck, and how many nails it will take.

I find it hard to believe that anything higher than a basic understanding of math (how to add/subtract/multiply/divide) is needed for such tasks.

Unless... did you mean so that you can figure out how to not over-engineer the deck?

Re:an example where algebra is useful? (1)

History's Coming To (1059484) | about 2 years ago | (#41470495)

Zombies. Seriously, zombies. A few simple rules like "if a zombie catches you there is a 60% chance you will be infected, 20% chance you will be eaten, and a 20% chance you will escape" and you've suddenly got some equations that work nicely, and can be graphed to show different "what if?" zombie survival scenarios. Then you show them the tedious painting-a-house example to show how it can be used in different applications, but make sure there are zombies in the first bit they learn.

Re:an example where algebra is useful? (0)

Anonymous Coward | about 2 years ago | (#41471377)

Algebra wouldn't answer that question for this house [eikongraphia.com] . Only Calculus [math.info] would help here.

Woops (1)

ddt (14627) | about 2 years ago | (#41468171)

Unfortunately for the counter-argument, every one of those examples can be replaced by simply visiting a website online that does the math for you.

Re:Woops (1)

Antipater (2053064) | about 2 years ago | (#41468453)

Wasn't one of those examples related to recipes? Have you ever tried to surf the web while cooking?

If you thought your keyboard was dirty now...

Re:Woops (4, Funny)

Anonymous Coward | about 2 years ago | (#41468487)

"Siri, how much is 400 grams in some fucked up imperial measurement?

My Brave Suggestion (1, Insightful)

MyLongNickName (822545) | about 2 years ago | (#41468185)

I must bravely agree with the author completely. We must prepare our children for the future. Clearly we need a few intellectuals. But these folks all wear grey and work far too hard. The semi-intellectuals are about the same. Let's have our school system produce more of us, the ones who have the truly best balance in our work. We are smarter than the manual labor groups but don't have to work or study as hard as the elites.

Re:My Brave Suggestion (1)

dgatwood (11270) | about 2 years ago | (#41468305)

How beauteous mankind is!

In all seriousness, though, even working in software, I can count the number of times I've used algebra on one hand... maybe two hands if I count in unary. That said, I still think that it is good to understand higher-order math, if only because every once in a while, I do need it, and not knowing it would require a lot more work.

Re:My Brave Suggestion (2)

pieisgood (841871) | about 2 years ago | (#41468399)

Then that is your particular FIELD. In graphics, we use it all the time. It helps to understand differential geometry and Brownian motion when working with real time and ray tracing applications respectively. I mean, all higher order analysis works on concepts of stochastic processes, so really we do need people to understand algebra (At the very very least).

Re:My Brave Suggestion (2)

dgatwood (11270) | about 2 years ago | (#41469667)

Even people doing graphics and audio manipulation mostly just use APIs written by other people who do the hardcore math for them. If I want to perform an FFT and use the resulting data set, I don't need to know how an FFT is computed; I just call a function in an FFT library. If I want to render a 3D scene, unless I'm actually writing software for use in some specialized field, chances are I'm just going to throw a spline model at OpenGL and tell it to wrap a texture around it. I don't need to know the math of bilinear interpolation to use it. I just need to know how to set the interpolation mode for the vertex in question. And so on.

I'm guessing that probably no more than one or two percent of programmers will do any significant amount of algebra or calculus or trig during their careers, and that most of the people who do either write low-level graphics or audio code, work for NASA or the aerospace industry, or work in a handful of other highly specialized fields where exacting precision is required. The vast majority of computer programmers will never need to use math above a middle school level, even though much of the software they write will do so routinely. And this is the beauty of code reuse. It means that I can do higher-order math without having to crack open a textbook and remember how all that stuff works, because somebody else already did the heavy lifting. :-)

Re:My Brave Suggestion (1)

pieisgood (841871) | about 2 years ago | (#41470805)

My simple retort would be, who writes the API? Do you have the time to wait for someone to do something for you? For most "mathematically difficult" problems? The trend, in graphics at least, has been to put more programmability in the hands of the user rather than restriction to specific API calls. Shader based work flow has fully replaced API functions that would have normally done these operations for you. Another thing is, how do you expect to be competitive if you're not implementing current research? I guess it depends though.

Re:My Brave Suggestion (2)

AK Marc (707885) | about 2 years ago | (#41468661)

I'm in IT and use math daily. I've gotten promotions because I was the only person that could do complex math easily.

Re:My Brave Suggestion (1)

Anonymous Coward | about 2 years ago | (#41469165)

I always thought that people who could do complex mathematics were imaginary!

Re:My Brave Suggestion (1)

Joce640k (829181) | about 2 years ago | (#41468813)

even working in software, I can count the number of times I've used algebra on one hand.

How do you factorize code without algebra?

Re:My Brave Suggestion (3, Insightful)

styrotech (136124) | about 2 years ago | (#41471243)

In all seriousness, though, even working in software, I can count the number of times I've used algebra on one hand...

(At the risk of repeating one of my other comments)

Do you think the abstract problem solving you practised while learning algebra (or eg calculus later on) has subconsciously helped your programming?

I'm of the opinion that the primary benefit of learning algebra and calculus etc isn't the specific techniques you learn but the ability to think in a much more abstract way when required. Even after most of the actual techniques have faded from memory, you still have the subconscious rewiring left behind by abstract problem solving.

And it is very important for a programmer to think abstractly.

Re:My Brave Suggestion (0)

Anonymous Coward | about 2 years ago | (#41468319)

"I'm so glad I'm a Beta."

Re:My Brave Suggestion (1)

sandytaru (1158959) | about 2 years ago | (#41468793)

Sometimes I wish I was a beta. (I don't think my conditioning stuck all that well.)

Re:My Brave Suggestion (1)

jellomizer (103300) | about 2 years ago | (#41468525)

Man, what a bad day for me to have my Gray Shirt and Gray tie, and black(dark gray) Pants shoes, and sockes.

Re:My Brave Suggestion (1)

catchblue22 (1004569) | about 2 years ago | (#41469523)

I must bravely agree with the author completely. We must prepare our children for the future. Clearly we need a few intellectuals. But these folks all wear grey and work far too hard.

What future is that? The Decline and Fall of Western Civilization?

Re:My Brave Suggestion (1)

fahrbot-bot (874524) | about 2 years ago | (#41469597)

Clearly we need a few intellectuals.

I'm thinking that 640K ought to be enough intellectuals for anyone ....

Ever closer to Idiocracy (1)

AmazinglySmooth (1668735) | about 2 years ago | (#41468261)

Every story like this reminds me of the movie Idiocracy. Maybe we should just encourage people to have lots of kids. We could even use the useless ones as food!

Re:Ever closer to Idiocracy (0)

Anonymous Coward | about 2 years ago | (#41468405)

But it's got electrolytes!

Re:Ever closer to Idiocracy (1)

Jeng (926980) | about 2 years ago | (#41469821)

We could even use the useless ones as food!

That would be hugely inefficient. The amount of meat you get out of a human body vs the food that goes in is a horrible ratio.

You might get a week or two worth of meat from a body, but that body needs tons of food throughout its lifetime to create that little bit of meat.

Re:Ever closer to Idiocracy (1)

NatasRevol (731260) | about 2 years ago | (#41470063)

Veal!

payroll and cash flow math (1)

Anonymous Coward | about 2 years ago | (#41468309)

Try doing something as mundane as payroll or cash flow estimates without algebra, and you will know why. Even better, try to explain it to someone who DOESN'T understand basic algebra, and you will lament why they don't know algebra. Well, unless you have no plans on ever employing or managing people, because you will be a political scientist all your life.

Re:payroll and cash flow math (2)

shaitand (626655) | about 2 years ago | (#41469001)

You don't need to know basic algebra to perform basic algebra. Basic math combined with the properties of real numbers (mostly intuitive themselves) makes basic algebra intuitive. Building these problems out as traditional equations involves a bunch of extra steps that serves no purpose except to satisfy a teacher who wants you to show your work. It's sort of like unit conversion. They give lessons on this and show frustrating slow processes where you put numbers over other numbers and toss in a conversion factor. But nobody would actually go through that garbage to convert a unit you added a bunch of extra crap to the problem just to cancel it out later.

A foot is 12 inches. If you have 36 inches how many feet do you have?

Anyone who understands multiplication and division can solve this problem without being taught a formal unit conversion process. If writing this down they would write 36/12 = 3.

http://www.math.com/school/subject2/lessons/S2U2L1GL.html [math.com]

Re:payroll and cash flow math (1)

fermion (181285) | about 2 years ago | (#41470469)

Algebra is the way we introduce critical abstract thinking in the US. Thre are other ways, but when I hear people object to algebra I often see it as an objection to the teaching of critical thinking, the ability to objectively assess validity based on fundamentally verifiable assumptions, or as verifiable as possible.

It is interesting you mentioned cash flow. It was what I did as a young adult. Interesting it did not involve great complexities of algebra, but my ability to put the words of my boss into a model and then assess that model for validity proved very profitable for me. The later was what was important. Assessing the model. To often people just put code in a machine, or just use canned models, with no ability to understand if the output is valid. They think they don't have to think because the machine does it for them. The machine is useful because it allows some to do work they could not otherwise do, and other to amplify thier work, but it does not think. A computer can enforce rules, free us up to do more profitable work,, but it cannot validate. So we have a case where a lot of bad stuff is floating around just because it comes out of a machine and few people are wise enough to understand that it is bad.

Example (0)

Anonymous Coward | about 2 years ago | (#41468337)

I, for one, encourage natural selection to take it's course.

The NYT's Missed the Reason for Algebra Altogether (5, Insightful)

zbobet2012 (1025836) | about 2 years ago | (#41468343)

The reason is not algebra's application to daily life. The reason you teach algebra is because algebra teaches symbolic manipulation. Learning math teaches you not just how to add two numbers. Addition is almost unnecessary in daily life (we do have calculators). Learning algebra is critical because it teaches us to think in terms of abstractions, of models. We do not teach mathematics to teach you how to add, we teach mathematics to teach you how to solve, to teach you how to think.

Re:The NYT's Missed the Reason for Algebra Altoget (2)

mark_reh (2015546) | about 2 years ago | (#41468489)

But teaching kids how to think is not desirable in an economy that can't provide any jobs where they need to think. Thinking leads to people not doing everything their "superiors" tell them to do, and that leads to unhappiness. You kids to grow up to be happy, obedient adults, don't you.

Re:The NYT's Missed the Reason for Algebra Altoget (0)

Anonymous Coward | about 2 years ago | (#41468665)

In what world are you living? Last I checked, the job areas that are growing are the ones where people need to think. The ones where thinking is less helpful (e.g. assembly line manufacturing) are hiring fewer people. Heck, they're even automating things like the checkout lines at supermarkets.

It is true that there are some educational areas where even a doctorate won't guarantee you a good paying job. The problem is that these tend not to be areas with a great deal of application. If you major in English or psychology, you need to go out of major to find a job. We have too many graduates in those areas. STEM majors can find jobs with just a bachelor's.

Re:The NYT's Missed the Reason for Algebra Altoget (0)

bmo (77928) | about 2 years ago | (#41468515)

>We do not teach mathematics to teach you how to add, we teach mathematics to teach you how to solve, to teach you how to think.

Then you are using the wrong tool for the job.

The tool you should be using is symbolic and philosophical logic, and philosophy in general.

--
BMO

Re:The NYT's Missed the Reason for Algebra Altoget (2)

zbobet2012 (1025836) | about 2 years ago | (#41468597)

The reason you teach algebra is because algebra teaches symbolic manipulation

The tool you should be using is symbolic and philosophical logic

How do you propose to teach someone symbolic logic without teaching them what symbols are, and how to manipulate them?

Re:The NYT's Missed the Reason for Algebra Altoget (2)

bmo (77928) | about 2 years ago | (#41468939)

>How do you propose to teach someone symbolic logic without teaching them what symbols are, and how to manipulate them?

You are implying that algebra is the be-all and end-all of symbolic logic?

Let me introduce you to New Math. I was a "victim" of it.

It revolved around number theory, set theory, and logical operations - and, or, not. I knew venn diagrams and set notation before I knew how to find least common denominators.

New Math was widely derided by people who thought that arithmetic proficiency done through rote learning and timed tests (which was my third grade math) should be the goal of the early grades. The thing is though, when home computers showed up, I was able to teach myself programming, and a course in digital circuits wasn't as hard as it could have been, and all sorts of stuff including a summer course in Logic (with Irving M. Copi's book) that made one of my smart friends drop in a week.

My point being is that teaching philosophical logic as such is a better tool for teaching one how to think, because it's not just applicable to math. It's applicable to law and debate and other such things. It gives one an appreciation as to why, in a law, there is an "or" instead of an "and" linking clauses.

But hey, what do I know.

--
BMO

Re:The NYT's Missed the Reason for Algebra Altoget (1)

zbobet2012 (1025836) | about 2 years ago | (#41470353)

There is no such thing as "philosophical logic". There is only logic. Philosophy uses logic to reason about the world, but you can't reason in the first place without logic. And yes algebra is the, mathematically speaking, the foundation of logic. Algebra introduces the entire concept of a variable. Tell me exactly how one can make a philosophical argument of any merit without understanding the fundamental of abstraction. It is not the be all and end all of abstraction, and of symbolic manipulation, but it pretty close. Most children grasp the concept of metaphor and simile precisely the same time they grasp the basic concepts of algebra for a reason.

Re:The NYT's Missed the Reason for Algebra Altoget (2)

AK Marc (707885) | about 2 years ago | (#41468737)

You can't teach philosophy to children. Given the philosophy classes I've taken, you shouldn't teach it to adults. It's a class in mental masturbation. The old philosophers were the Original Internet Trolls. The point of philosophy is to argue, not to learn, discover, or use. Sure, after a few millenia of arguing a truth may accidentally be stumbled upon, but that's a by product, like plastics from the space program.

Re:The NYT's Missed the Reason for Algebra Altoget (2)

bmo (77928) | about 2 years ago | (#41468991)

>Given the philosopy classes I've taken

And yet you skipped right over that Logic course.

--
BMO

Re:The NYT's Missed the Reason for Algebra Altoget (1)

lgw (121541) | about 2 years ago | (#41470425)

Most people find their first symbolic logic course to be quite hard. I've seen college students actually break down in tears over their first logic course - it is quite frustrating at first, and would be a reall turn-off to the 95% of people who don't enjoy such challanges.

Algebra is just an easier way to teach abstraction and abstract reasoning. It's much easier to relate the symbols to what they symbolize, and the manipulation is more intuitive.

Re:The NYT's Missed the Reason for Algebra Altoget (0)

Anonymous Coward | about 2 years ago | (#41468841)

Bingo!

Along the same line of thought but from a different perspective...
I studied engineering in college, and although math and science competency are critical, I realized that my high school English classes were also very helpful to doing well in school. My high school English teachers stressed the importance of clear, coherent, logical thinking when doing literary analysis. I will probably never write another term paper on a book, but I daily have a need for clear, coherent, and logical thought.

Re:The NYT's Missed the Reason for Algebra Altoget (1)

dkleinsc (563838) | about 2 years ago | (#41468945)

Addition is almost unnecessary in daily life (we do have calculators).

No it's not unnecessary. I have $5 - can I afford a $4 sandwich and a $1.50 drink? I'm not going to pull out a calculator for that.

Here's my argument for teaching algebra: The more advanced algebra courses teach exponential growth. That's exactly the kind of equation you would do well to understand if you were, say, taking out a loan to buy a home. Not that there have been any problems with people taking out mortgages they don't understand or can't pay back.

Re:The NYT's Missed the Reason for Algebra Altoget (1)

shaitand (626655) | about 2 years ago | (#41469133)

Why would you teach a symbolic manipulation system that nobody is going to use?

It doesn't make sense to have people go through algebra courses if the end goal is just to learn the concept of a variable, a formula, the properties of real numbers, basic logic, and a convoluted system in which we build giant equations to explain how to write down basic mental math most people find intuitive.

Re:The NYT's Missed the Reason for Algebra Altoget (1)

vlm (69642) | about 2 years ago | (#41469269)

Why would you teach a symbolic manipulation system that nobody is going to use?

Ugh. Its to teach that symbolic manipulation is possible and how to think symbolically, not the training task of how to factor equations.

A literary comparison is better.

As a training item were the original Tom Swift books excellent training for my job? No they're Fing useless as training manuals unless you're building an actual repellatron or a tri-phibian atomicar (real titles, BTW).

As an education tool were the original Tom Swift books great engineering tools? F no, they were pretty soft sci fi, use science in place of magic and you're there.

Were they a good way to teach me to read about 4 to 6 times as fast as a yankee can speak, hell yes.

Same analogy with algebra. You're going to learn how to manipulate symbols. Not just equations but symbols in general. Statements in a computer program? People? Who knows. But if you're doin' it right, your mind itself is actually different after you learn algebra.

The problem with this is... (1)

bmo (77928) | about 2 years ago | (#41468401)

... that most k-12 math teachers never left academia.

Most math teachers go directly from high school to university or a teaching college and go right back to k-12.

The ones that have seen the inside of a machine shop, the inside of a land-evidence vault, worked for a logistics firm, done bookeeping, been an actuary, or even looked through a theodolite, are few and far between. So even coming up with "real world scenarios" is next to impossible.

--
BMO

Re:The problem with this is... (1)

shaitand (626655) | about 2 years ago | (#41469155)

All of those are heavy math examples. Concepts from basic algebra are useful in daily life. Even simple things like figuring out how much to paypal someone if you want them to end up with $25 AFTER the fees.

Recurring Issue (2)

NEDHead (1651195) | about 2 years ago | (#41468465)

But is it recursive? And more interestingly, does it converge?

Re:Recurring Issue (0)

Anonymous Coward | about 2 years ago | (#41469145)

It folds into a hypercube...
http://dimensions-math.org - best math movie I've ever seen.

Re:Recurring Issue (1)

NatasRevol (731260) | about 2 years ago | (#41469589)

I wonder if the time cube is a hypercube...

Missing the point (5, Insightful)

n5yat (987446) | about 2 years ago | (#41468491)

Andrew Hacker and nearly everyone else is missing the point.

Taking an algebra class for many students is not about the algebra, it's about learning to think. Even if you never use algebra again, the process of learning algebra is mental exercise that improves the mind. Taking a foreign language, studying biology, learning economics, studying history - it doesn't matter what the subject is, merely the more you learn the better a learner you are, and the better thinker you are.

In sports we see athletes perform all kinds of exercises that help develop skills used in their sport, but are never used directly. Ever see footage of a football player stepping through tires? Ever see one do that during the game? Ever see footage of a quarterback or pitcher throwing the ball through a hanging tire? Ever see them do that in a game? Athletics is filled with examples of training exercises done to hone one's skills for a game, yet we have difficulty accepting that mental exercises hone skills we need for life.

Re:Missing the point (1)

crazyjj (2598719) | about 2 years ago | (#41468811)

Taking an algebra class for many students is not about the algebra, it's about learning to think.

Actually, for the vast majority, it's about passing a class...to jump through a hoop...to get a piece of paper. And it's unfair to make people jump through said hoop who will likely never use it again in their lives (or even remember it, in the unlikely even that they need to). Many a 4.0 GPA Nursing major has had his/her GPA destroyed by a College Algebra class that they had to repeat multiple times--and for what?

Re:Missing the point (1)

JakeBurn (2731457) | about 2 years ago | (#41469011)

I definitely agree. While an algebra class does great things for a student's ability to learn and use concepts in other ways, when its presented in a way that most students cannot relate to it does more harm than good. It almost seems like a throwback to decades past when that was the best way they had to get people to think outside the box. Seems like there must be better ways to get kids to think about problem solving that is more easily related to than a subject they have already convinced themselves they will never use again in their life.

Re:Missing the point (1)

Comrade Ogilvy (1719488) | about 2 years ago | (#41469811)

Seems like there must be better ways to get kids to think about problem solving that is more easily related to than a subject they have already convinced themselves they will never use again in their life.

Not likely. If they are in just for the grade, then learning to think will be staunchly resisted regardless of the topic on hand. Once you throw in the towel on teaching general principles that are widely applicable across the generations, you are left with a million losing battles on which factoids Johnny gets to veto because he decided they do not "feel relevant".

Numeracy and simple algebra is extremely useful for financial decision-making. If we cannot make a course that is compelling based on lucre-sweet-lucre then the problem really is the students who decided "they will never use [this] again". There is only so much we can do for people who will sign up to self-fulfilling prophecies in order to justify their own laziness.

Re:Missing the point (2)

vlm (69642) | about 2 years ago | (#41469299)

I don't want a nurse treating me who doesn't know how to think. I'm not seeing the problem here.

Re:Missing the point (1)

lgw (121541) | about 2 years ago | (#41470553)

So what you're saying is: universities should just sell students a piece of paper, without forcing them to do any of that difficult "learning" business? Wow, that's more cynical that my own outlook on school, and that's saying something.

Or were you confused and thinking that nursing isn't a complex technical subject? The only major I can think of that requires no actual thought or learning is an Education major.

Re:Missing the point (1)

DriedClexler (814907) | about 2 years ago | (#41469035)

I don't think your point generalizes like you claim, certainly not to history classes. The only skills you pick up in history classes are 1) memorizing factoids, and 2) predicting what form of BS your teacher wants to see in an essay.

Now, there are certainly real skills required to do historical research (eg, looking at different sources and inferring what actually happened). And there are good reasons to teach history even with these failings (eg, so students can put events and news in context, learn the origin of traditions). But history most certainly does not help you hone useful skills the way that algebra does -- unless you agree history is the "practice BSing" course.

Re:Missing the point (1)

NatasRevol (731260) | about 2 years ago | (#41469631)

You don't think predicting what form of BS your (teacher/boss/peer/reviewer/parent/spouse/child/opposite sex) wants to see isn't a real skill?

Re:Missing the point (1)

lgw (121541) | about 2 years ago | (#41470597)

There were once history classes that taught you how to be a leader: you'd read speeches given by real leaders in history in times of crisis that motivated real people to overcome real problems. You see what political ideas have been tried in the past, and what worked and what failed horribly. It all built towards critical thinking regarding politics. But since schools these days value political brainwashing over critical thought, that all fell by the wayside.

Re:Missing the point (0)

Anonymous Coward | about 2 years ago | (#41470635)

But Maths is different. It teaches you how think in a way which is fundamentally different to what you learn in language, biology, economics and history as you mentioned.

algebra isn't enough for given examples (0)

Anonymous Coward | about 2 years ago | (#41468499)

Unless they're VERY careful with the questions they ask for some of these examples, elementary algebra won't solve them. The interest and depreciation ones require simple ODE's - nothing you couldn't pick up in a week or so - but springing them on Algebra I students is a bit cruel.

Re:algebra isn't enough for given examples (1)

wierd_w (1375923) | about 2 years ago | (#41468803)

The understanding of the simple physics of simple machines would benefit greatly from basic algebra.

Eg, calculating torque to RPM change over an arbitrary gear ratio, or how much energy is needed to push a 1kg weight with a 1 meter lever.

Granted, these would only ever be interesting or useful to people who like to build things, but I can't begin to state how grateful I am to have been exposed to algebra.

I agree though, the typical scenarios created to sell algebra textbooks (rather, the problems shown in said books) are horrible, unnantural contrivances.

For some things, like "i", (sqrt of -1), I still haven't found a useful application outside of complex physics and formal mathematical proofs. It's a very unintuitive concept. Sure, if you want to calculate the mass of a tachyon its a fun thing, but seriously....

But simple algebra? If nothing else, it helps you disassociate your values, and see the raw algorithm. The numbers can change, but what gets done to them does not. That is a very useful piece of learning.

The reall issue here is not "math is hard yo, and nones o' dis shit gonna get used nohow teach." But rather "all students need to be treated the same."

Not all students are the same. How you teach students shouldn't be cookie cutter. Some would take to algebra like ducks to water. Denying them that is a crime against mankind. Others would rather perform a self-clitorectomy with broken glass. Forcing them to endure is also unreasonable.

As a cultue, we are so afraid of segregating our children's education, because some of us feel threatened by the percieved successes of others. (Not enough that I succeed, others must fail.) Rather than own up to our owm mediocrities, we denounce them, and enforce a fiction that causes real pathologies.

This is one of them.

Uh huh (2)

kiriath (2670145) | about 2 years ago | (#41468561)

*jokingtroll*
I'm so sick of all these nerdy math / science posts... we need more patent litigation and mobile device war posts
*/jokingtroll*

Seriously though, I think that straying away from the mathematical fundamentals will lead to straying from linguistic fundamentals and historical fundamentals. Eventually the bulk of the education system will be 'Can you read well enough to use a computer? Congratulations you are a high school graduate".

The ability to follow through an entire equation and achieve the outcome is very useful in life. Perhaps not in the form you learn in Algebra, but in one form or another.

But lets just let our kids get less smart and more dependent on the technology that will eventually stop evolving because nobody is smart enough continue the evolution.

Algebra is more than "how many apples" (1)

Anonymous Coward | about 2 years ago | (#41468699)

Learning mathematics is learning to solve problems. Moving math into symbology (algebra) teaches problem solving as a concept vs. a rote skill. Anyone who thinks math is a useless skill needs to seriously re-examine their thinking. Learning how to approach, analyze, and resolve a problem is a skill that many do not have and the country is worse for that lack.

It's Education, not Training (0)

Anonymous Coward | about 2 years ago | (#41468709)

Practical instruction is always contrasted against wrote memorization and algorithms like long division. What's missing in both is actually understanding the subject being taught.

Make It Practical (1)

Anonymous Coward | about 2 years ago | (#41468717)

While algebra is useful, how it is taught is counterproductive to certain learning styles. Many kids don't pass may because they don't see the point. I had that problem in school.

If they would make it practical, instead of teaching it through theory, it would be more enjoyable. Say for kids who like computers, give them a math class where you build a circuit board and use physics or something.

Re:Make It Practical (1)

oh_my_080980980 (773867) | about 2 years ago | (#41468775)

You remember those word problems...those were practical. Sometimes you need to try.

Algebra isn't critical - it's pleasure (5, Interesting)

claytongulick (725397) | about 2 years ago | (#41468797)

I've been a developer for about 16 years, and have had a pretty spotty math education. I've generally taught myself what I need to know as I needed to know it - 3D programming? What's a matrix? How do I rotate things with it? Developing animate graphical charts? How do I scale from business coords to pixel coords, and animate? Draw box an whiskers charts etc...

Recently, I've decided to stop doing the corporate developer gig and to go to school. As part of that, I've needed to take math a lot more seriously, so I've bought some books and been going through a more rigorous program.

One thing I've discovered through this process is that I *really enjoy it*. I'm not being pressured to learn something for a test, I'm not worried about a grade. Instead, I take my books to a coffee shop and relax and think about fascinating things, like trying to visualize the complex plane, and what the value for i really is, and what dividing by zero really means.

Instead of memorizing the quadratic equation, I spent some time learning how to derive it from basic principals. Instead of memorizing that the vertex of a parabola can be found by -b/2a, I noodled around and tried to visualize the determinant (sqrt(b^2 -4ac)), it's effect on an equation, and what happens if you zero it out.

I spend a leisurely afternoon coming up with a visual proof of the Pythagorean theorem, and was pretty excited when I finally had it, and was even more excited when I googled it and saw the same basic proof has been derived by students for a really long time - I loved the notion that I was connected back through time with a whole bunch of other people who were going through the same mental steps.

This stuff is great! And I'm only scratching the surface. I'm in baby algebra - and I'm excited to keep going.

My point is - we go about this stuff all wrong. Forcing kids to memorize equations so they can pass an exam is absolutely pointless, if not masochistic. Exploring really interesting concepts about numbers, and what they mean - this stuff should be recreation. It's great!

I see my older son struggling through his algebra course, and he hates it. He doesn't care, and hates doing the homework. But when I get excited about some math problem I'm studying, he'll come over to look over my shoulder to see what I'm doing, and we'll puzzle it out together. He forgets that we're doing math, instead we're talking about concepts and challenging each other. We'll spend an hour or two going over something that's really cool, and we both have a great time.

Ask him about math, however, and he immediately relates it to school, and he'll tell you how much he hates it.

Re:Algebra isn't critical - it's pleasure (1)

ralphbecket (225429) | about 2 years ago | (#41470799)

Bingo! Like any well taught subject, mathematics should be fascinating fun. I can't find the link, but some maths professor turned high-school teacher wrote a scathing article about contemporary maths education saying it would be hard to come up with a better way to ensure students have any latent interest in the subject thoroughly expunged. His point, like yours, was that maths should be taught the way music is taught: there's something beautiful here that isn't easy to be good at. Nobody teaches music as though it's likely to be useful.

I have the same complaint about school computing courses. By all means teach kids how to use Office or whatnot, but do it in a different class! Basic computer science stuff is interesting *and* useful (e.g., sorting, propositional logic, counting systems, regular expressions, basic graph theory results, etc.). I digress.

Re:Algebra isn't critical - it's pleasure (1)

Anonymous Coward | about 2 years ago | (#41470903)

I believe you were looking for this: http://www.maa.org/devlin/lockhartslament.pdf [maa.org]

Re:Algebra isn't critical - it's pleasure (2)

Idetuxs (2456206) | about 2 years ago | (#41471211)

"It is a miracle that curiosity survives formal education." Einstein.

It's tough when you need to graduate and you don't have time to have fun.

It's easy (1)

wonkey_monkey (2592601) | about 2 years ago | (#41468845)

Look kids, if x out of y of you learn algebra and go on to earn s dollars a year, y-x of you will earn s*m dollars a year, where m<1.

Math is useless until you need to use it (1)

TheSkepticalOptimist (898384) | about 2 years ago | (#41469105)

The idea that people must know more math is ridiculous. Just because you know more math does not make you smarter, nor does it generally improve that quality of life, including ability to get jobs or perform daily tasks.

In the "google" era of instant information, knowing that you need to use some math principal to perform a task and being able to retrieve information on how and where to use it is more important than expecting to memorize hundreds of examples or theories about math.

However I will say that while in school learning math is important to developing problem solving skills. I may have forgotten 90% of the math concepts I learned in High School and definitely most of the crap forced on my in University, but I know that my problem solving skills were honed learning to solve meaningless mathematical problems and theories. Math courses should focus more on the how of math then the why of it.

Learning math is not useless, but knowing specific math knowledge that you generally do not apply to day to day situations is useless, period. Its like regurgitating random facts at a party, nobody cares. If you feel the problem you are trying to solve can be achieve through math, Google it.

All about Equality (1)

Anonymous Coward | about 2 years ago | (#41469171)

The way public schools in the USofA teach algebra is a crime against common sense. Algebra should be introduced with the simple concept of equality.

      =

No matter what This Side or That Side look like, they are the same. From there follows the idea of equivalent operations and it is all gravy from there. I taught my wife's little brother more algebra in an afternoon then his teacher did in a semester. They tried to disqualify his final exam because he didn't show all his work (unnecessary steps, imho). We fought it and they eventually caved.

His teacher was a physical educator and didn't understand the concept that there was only 1 right answer in math but multiple ways to get the right answer.

I have to dumb down explaining math to my 2nd grader cause the teachers want them to use boxes and visual crap. Sad.

The amount of math used expands to ability (2)

DMUTPeregrine (612791) | about 2 years ago | (#41469253)

The amount of math used expands to fill the user's ability. The more math I learn the more uses for that math I find.

The bottom-line is (2)

Anonymous Coward | about 2 years ago | (#41469333)

Being skilled in math makes your brain a far more capable information processing system, even if you're not aware that you're using math in your day to day life.

The need for logic? (1)

Anonymous Coward | about 2 years ago | (#41469407)

Maths is the only logic that many people really come across in life. I'd expect most of the readers here to understand the if -> then sort of logic, but that is actually a mathematical concept. Day to day I just quietly shake my head at the lack of logical rigor people apply in their ordinary lives, but then I remember that at best they have management degrees and have never really had to think. Then, and more importantly, I am frequently disappointed in the logical processes of qualified engineers and scientists, but then many of those people never have gone past second year tertiary mathematics education, if they did any at all!

My point is that maths is as pure a form of applied logic as you are going to find. You can't BS or fudge maths, the mistake will always come back to haunt you. If you then apply that level of reasoning to other areas of life, then at the least you understand the limitations of your reasoning and stop saying such stupid things all the time.

I completely conceded to the argument that mathematics is so often taught terribly.

You are a life-long what? (1)

NikeHerc (694644) | about 2 years ago | (#41469701)

If you made an effort to learn some math, IMHO you are more likely to be a life-long learner.

If the only effort you made toward math was avoiding it, IMHO you are more like to be a life-long idiot.

Math (0)

Anonymous Coward | about 2 years ago | (#41470143)

Find a formula that results in me getting consistently laid by a super model and I will learn math.

Won't work. (0)

Anonymous Coward | about 2 years ago | (#41470195)

Most people are too illogical to understand math. We wouldn't have the TSA, the Patriot Act, free speech zones, etc. otherwise.

Algebra is mandatory right now. It clearly isn't making people more logical (or at least not in any noticeable way).

A Political scientist comment on Maths? (2)

Kittenman (971447) | about 2 years ago | (#41470675)

Bear in mind the TFA is from a Political Scientist. That's just below an economist in my book. I'm sure we'd all welcome comments from maths teachers about Political Science (btw, why the hell is Political Science a science?)

Re:A Political scientist comment on Maths? (1)

dcollins (135727) | about 2 years ago | (#41470883)

"(btw, why the hell is Political Science a science?)"

Because, strategically, they knew that was better than calling their discipline "Professional Bullshit Artist".

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