## Promoting Arithmetic and Algebra By Example 158 158

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)."*
## an example where algebra is useful? (Score:5, Insightful)

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.

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most people would probably just prefer to google

Most people wouldn't think to do that. And how many paint ads will you suffer through before you find software that gives a good enough answer for you?

## Re:an example where algebra is useful? (Score:5, Interesting)

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? (Score:4, Informative)

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? (Score:4, Informative)

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: (Score:2)

Which alternative would you prefer?

One that's easy for everyday people to visualize in their heads.

Like "millimeters".

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As I said, millimeters is exactly the same as liters per square meter.

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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 "bigg

## Re: (Score:3)

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.

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tehcnically L/m^2 is the correct unit

Um, that's the whole point. "Technically correct"

isn'twhat the public should be fed.What the public needs is something they can visualize in their heads, and more importantly, compare with other things. This is why MPG fails, and why L/m^2 is a bad choice (whats wrong with "millimeters"?)

"bigger is better!"

a) People usually want to know which model consumes less.

b) Is a car which consumes 20MPG twice as bad as a car which consumes 10MPG? No? So how much worse is it, exactly?

(Try answering (b) without a calculator...then ask the same question for a car which does 10GPM vs. a car which does 20GPM)

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Start by using GPM as a metric.

MPG and GPM have the same information content. So no reason to switch. And MPG has the "bigger is better" thing going for it.

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

Nothing bad about it. The real dimensions are liters of fluid per square meter of land. That doesn't translate easily into a single unit "millimeters", but average height of a pool of fluid in millimeters, assuming the land were flat and the fluid didn't run off".

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Why not actually use millimetres?

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Why not just say "millimeters"?

## The Fallacy of Utility (Score:5, Insightful)

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: (Score:2)

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 requir

## Re: (Score:2)

always uses the Math-Makes-you-Logical fallacy.

It's not a fallacy, if it's true. And you should be saying "More-Logical" instead since no one is claiming that knowledge of math somehow magically makes your quirks, psychoses, and personal relationships smooth out.

## Re: (Score:2)

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: (Score:2)

It's the "(of equal or lesser value)" part. For example if you buy one priced at $1.00 and another normally priced at $.60, then you get the second at $.30 on sale for a total of $1.30, which is an 18.75% discount. The crossover point is 2/3 of a dollar. Anything less than that for the second item and the discount is less than 20% on the whole thing. Any more than 2/3 of a dollar and the whole thing is greater than a 20% discount up to a maximum discount of 25%.

## Re: (Score:2)

First Item is $100.

Second Item is $30 (you pay $15)

Total savings is 100*(1-(115 / 130)) = 11.5% savings

If you had 20% off on all ... you would be well ahead.

Break even point is if Item 2 is $66.67

Any less and 20% is the better deal

Any more and buy one, get half off is the better deal

Solved that with Algemebra

'cause I am SMRT (doh!)

## Re: (Score:2)

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: (Score:2)

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: (Score:2)

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.

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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

## Re: (Score:2)

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: (Score:2)

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.

While math can vary wildly in character and complexity, it's worth noting that humans already do a lot of complex math. They just aren't aware of it. Basic math can get you the paint you need. A better awareness of math can get you the paint you need, when you change your mind, without having to rethink the problem from scratch.

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I used some trig yesterday for the first time in years. I had a piece of wood I needed to cut at an angle, and I didn't have a protractor.

It was sad - I had to look up which of the basic trig functions was opposite/adjacent (tangent, of course). And it's been less than a decade since I took college trig.

(It was pointless, though. My dumb ass used 6" as the opposite side rather than 5 1/2" for a 1x6 plank, so the angle came out wrong. It was my derp for the week.)

## Woops (Score:2)

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: (Score:2)

If you thought your keyboard was dirty now...

## Re:Woops (Score:4, Funny)

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

## Re: (Score:2)

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...

yes, all the time. I have a netbook that is my kitchen computer. I look up recipes, etc. It's not dirty, because I don't have it in the same part of the kitchen that I'm measuring ingredients in.

## My Brave Suggestion (Score:2, Insightful)

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: (Score:2)

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: (Score:3)

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: (Score:3)

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

## Re: (Score:2)

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?

## Re: (Score:2)

"I don't need to know the math of bilinear interpolation to use it."

No, but you need to know what it is regardless to understand why such interpolation modes have the effect they do and hence what mode you need to get the effects you desire. If you hadn't studied maths you wouldn't even know what bilinear interpolation even was, so how would you know to look for it or that it was what you were looking for in API docs etc.?

You may not need to do matrix manipulation thanks to libraries, but you need to know h

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No, they're only partly imaginary.

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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 (Score:4, Insightful)

(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: (Score:2)

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

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Why is it bad? It unquestionably means you're an intellectual!

Congratulations on your official designation.

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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: (Score:2)

http://en.wikipedia.org/wiki/Brave_New_World [wikipedia.org]

Considered by some to be one one of the top ten English-language novels of the 20th century.

## Re: (Score:2)

Clearly we need a few intellectuals.

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

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wishI was a beta. (I don't think my conditioning stuck all that well.)## The NYT's Missed the Reason for Algebra Altogether (Score:5, Insightful)

The reason

is notalgebra'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 tothink.## Re: (Score:3)

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: (Score:2)

I live in a world where a large portion of the population thinks the world is about 6k years old because an old book and most of the "leaders" they look up to told them so. Many of them also believe that "creation science" is a better explanation for the origin of humans than is evolution, or is at least an equivalent "theory".

If you want to live a happy life in a world like that it is best not to think too much, and by "too much" I mean "at all".

The human race is doomed. Our technology for damaging the e

## Re: (Score:2)

The human race is doomed. Our technology for damaging the earth and killing each other has exceeded our political ability to control it. It will destroy us, soon.

There's this thing called "follow through", that is, completing a motion. Getting as far as we have, and then declaring inevitable doom, is not good follow through.

## Re: (Score:2)

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.

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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.

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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 sc

## Re: (Score:3)

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: (Score:3)

>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

## Re: (Score:2)

onlylogic. 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## Re: (Score:3)

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>Given the philosopy classes I've taken

And yet you skipped right over that Logic course.

--

BMO

## Re: (Score:2)

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.

## The problem with this is... (Score:2)

... 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: (Score:2)

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.

## Re: (Score:2)

>All of those are heavy math examples

All of those are industries that use Algebra I and II. Subjects studied in HS, and the subject of this article.

How else do you measure the bottom of a powerline between two power poles without touching the stupid thing? Protip: It's a parabola. Shoot the bottom of it and the ends and figure it out. You can then figure out how much it's going to sag on a hot day, because of the coeffcient of expansion of copper or aluminum.

See? Practical example.

--

BMO

## Re: (Score:2)

http://en.wikipedia.org/wiki/Caternary [wikipedia.org]

Otherwise I agree with your comments in this thread completely.

## Re: (Score:2)

... 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

Australian math/science teacher.

Work in a staffroom of 10 people.

1st person - PhD, ex-researcher. Small-craft air-plane pilot. Left research for teaching to spend more time with his teenage children.

2nd person - microbiologist who used to work in a public hospital lab identifying nasty bugs. Left for teaching because believe it or not, was less stressful and more rewarding.

3rd person - teaches, but also runs his own restaurant.

4th person - teaches but also donates her weekends to a community group

## Recurring Issue (Score:3)

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

## Re: (Score:2)

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

## Missing the point (Score:5, Insightful)

Andrew Hacker and nearly everyone else is missing the point.

Taking an algebra class for many students is

notabout 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: (Score:2)

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?

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

## Re: (Score:2)

I don't want a nurse treating me who doesn't know how to think.

Being good at alegbra != "being able to think."

I could as easily say "I don't want a programmer writing code for me who can't compose a compelling essay" or "I don't want a guy working on my computer who doesn't know about the Martin Luther and the Reformation."

You can be a genius in one area and a complete retard in others. Everyone has his or her skills, and shortcomings.

## Re: (Score:2)

Yes, because I'm sure nurses are regularly (or, for that matter, EVER) doing manual dosage calculations by hand, using an algebraic ratio. No doubt this comes in handy when they're mixing the medication themselves with a mortar and pedestal.

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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: (Score:2)

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?

No, I'm saying that the gen ed requirements for mathematics are far in excess of the requirements in other fields. When otherwise good students in unrelated fields are being forced to take a class that many fail 3-4 times before passing, your requirements need adjusting. Imagine being a CS major and walking into a required business course where as much as 75% of the class (without a VERY STRONG knack for business) was going to fail. Now imagine kissing your 4.0 CS GPA goodbye as a consequence--because you'r

## Re: (Score:2)

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-

## Re: (Score:2)

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 o

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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?

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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.

## Uh huh (Score:2)

*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 ou

## Oblig XKCD (Score:3)

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

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.

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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

## Re: (Score:2)

"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 (Score:2)

xout ofyof you learn algebra and go on to earnsdollars a year,y-xof you will earns*mdollars a year, wherem<1.## Math is useless until you need to use it (Score:2)

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 w

## The amount of math used expands to ability (Score:3)

## The bottom-line is (Score:2)

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.

## A Political scientist comment on Maths? (Score:3)

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: (Score:2)

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

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

## Tried and failed (Score:2)

This has been tried in many europeean countries in the 80's and it has failed quite miserably. Pretty much all of them returned to the true an tried method, with a salt of the new method in the 90's.

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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 sa

## Re: (Score:2)

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.

I think the problem with complex numbers is the name,

imaginary. It makes them sound like fantasy numbers which doesn't really exist, they are after all the "opposite of real numbers". At some point in history however, negative numbers must have felt equally strange. You can't have "minus five" apples in your hand, such a thing just doesn't exist. But today most people have no problem to understand that negative numbers are a useful tool to describe things in our life and universe, such as the difference be## Re: (Score:3)

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

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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 int

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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: (Score:2)

Veal!