Uh-oh, it's got algebra in it

Richard Cohen get's a zero, cause he doesn't need any of this. My 6th grader got 10 of 10, because he will need algebra to get into a good college.

I got 9/10. I didn't know what the mode of the series of data was. I guessed between mode or standard deviation and guessed wrong. I had a 50/50 chance and blew it.
But then again I don't recall ever seeing this covered. I still have my school textbooks(Since the 5th grade I always stole an extra copy of my school books from the classroom spares so I could keep one at school and one at home. Nobody ever caught me so what the hell?)
I'm not going to go through the 50+ odd books I've had all the way from 5th-12th grade to find it but I honestly don't think the mode of a series of numbers was ever covered at any grade level when I was still in the grades.

MYOB'
.

I got a 9/10, and I'm a math idiot.

How can you see what question(s) you got wrong? I suspect it was the mode/standard deviation question because that was total guesswork.

I think this topic and the original post on Cohen column are an example of what's wrong with math education in the US -- and I say this being one of the lucky few with a gift for math and a love of the subject.

I've spent a lot of time tutoring people in math, regular people and otherwise good students who for want of a decent teacher and moderately enlighted teaching methods struggled with the work and the humilation of failure. Making them feel even worse -- even if possible -- is not the answer. Changing the way it is taught and the way schools are run is, if I may be so bold, the obvious solution.

10/10

According to Richard Cohen, that means I cannot construct a readable English sentence.

In grad school, the instructor of our statistics courses noted a well known entertainer was going to visit campus that weekend. I can't recall who, say Dolly Parton, just to have a name. He said he'd really love to meet her. We started kidding him about it.

"Whatever would you two have in common to talk about?" we chided.

"Why," he replied, "bimodal distributions, of course."

MYOB and Mnemosyne, the mode of a series of numbers is the number that appears the most times in that series. So in the series {2,2,3,4,5}, 2 would be the mode because it appears two times while all the other numbers appear only once.

Robert Reys, a former high school mathematics teacher, now a professor of mathematics education at the University of Missouri-Columbia writes:

...most US schools are still mired in a 19th-century course sequence of Algebra I, Geometry, and Algebra II.

Do you think that's the case because it works so well?

Algorithms and tedious procedures were demonstrated with little or no explanation of why they work. Sensemaking and understanding were not a part of my experience of learning mathematics. Students left class thinking that math consisted only of dull procedures and rules to memorize.

That fits with my experience until I got to advanced math courses in college.

Dr. Alfred S. Posamentier, Dean, School of Education, and Professor of Mathematics Education at City College of NewYork writes:

Our current dilemma is facing off those who successfully learned mathematics with those who feel that there must be a better way to learn mathematics, since so few learn it successfully and then develop a love for the subject. We are obviously not doing this task as well as we should, or else there wouldn't be so many people ready to admit (and be proud of it) that they were never good in mathematics. Would we have this math teacher shortage today if we had taught mathematics better at the lower grades?

Much of what I've seen in the Cohen posts and their comments looks like remarks from the "those who successfully learned mathematics" group -- and those who admire them. What I haven't seen are comments from anyone who actually knows something about math ed.

Posamentier continues:

We thought that all we had to do as teachers was to explain concepts and procedures clearly, have learners practice, and then give them reinforcement and feedback. Now with technology, we have been studying the brain and how meaning develops. Neurobiologists have shown that algorithms are performed on a different side of the brain than the side used for mathematical thinking and that focusing on the practice of algorithms in the early years actually can impede the development of mathematical reasoning. Cognitive developmental researchers have also proven repeatedly over the last fifty years that meaning develops progressively. Mathematics cannot just be explained or transmitted. The brain chunks information in order to organize it and make sense of it, and thus new ideas are connected to prior conceptions.

George Polya (1887-1985) a distinguished mathematician and professor at Stanford University who made important contributions to probability theory, number theory, the theory of functions, and the calculus of variations wrote in 1969:

Therefore the schools, especially the primary schools, are today in an evolution. A sizable fraction, ten to twenty percent, already have the new method of teaching which can be characterized in the following way in comparison with the old method of teaching. The old method is authoritative and teacher-centered. The new method is permissive and student-centered. In the old time the teacher was in the center of the class or in front of the class. Everybody looked at him and what he said. Today the individual students should be in the center of the class, and they should be allowed to do whatever good idea comes to their mind. They should be allowed to pursue it in their own way, each by himself or in small groups. If a student has a good idea in class discussion then the teacher changes his plans and enters into the good idea and now the class follows this idea.

That was written 37 years ago. Everybody here who was taught math in this "new" way raise their hand.

Phew, I was a little nervous to actually take it but it all worked out.

I was also surprised to see the 'mode' question on there. I don't recall covering any statistical concepts beyond the mean in K-12, but then again I'm frankly a bit hazy about a good chunk of my childhood.

Maybe that speaks to more stats training in school nowadays, which would be a good thing.

I always thought the mode was that lump of vanilla ice cream that arrives with your apple pie.

The one that made me pause was the "-7" one. Was stuck for a while wondering if it was a prime number. Couldn't recall ever hearing of a negative prime, though it didn't seem an unreasonable idea, but in the end decided it was just an integer.

Crap, 8/10. I always forget what defines irrational numbers and other mathematical deifnitions.

But I'm sure I got all the actual problems correct. That test was extremely easy. I would be a very upset parent if my son or daughter could not pass that.

Has anyone here emailed this to Mr. Cohen for his response? ;)

MYOB and Mnemosyne, the mode of a series of numbers is the number that appears the most times in that series. So in the series {2,2,3,4,5}, 2 would be the mode because it appears two times while all the other numbers appear only once.

Ah. In that case, that was definitely the one I got wrong, then. I guessed it was the standard deviation.

And I have to agree with AndyS -- math is VERY poorly taught in this country. I probably would have had fewer problems with math if I hadn't been put in the stupid group of math students in 5th grade.

Why was I there? Because the teacher couldn't explain to me why I couldn't subtract a larger number from a smaller number during long division when I knew perfectly well that negative numbers existed. It turned into a whole, "Because I said so, that's why!" situation, which is the situation in which I learn least well.

In fact, most math seems to be taught that way. Not, "Here's one way to solve this problem," but "This is the only PROPER way to solve this problem."

10/10, philosophy and political science geek. I guess I should get a job with the scientificians!

There's always a fifth answer for the ID/creationist students: God knows/Goddidit and that's good enough for me.

I gave up after 5 of the questions; considering I last took a math class 30 years ago, a class which I hated, that's not surprising

Truly, would someone explain to me the relevance of any of those questions in my day to day life (I'm a secretary by profession). I'm not trying to be provocative, I want to know. Please note: "Because it promotes logic" or "It will make you a smarter human being" or any variation on those won't fly.

Mnemosyne, you've copped to the cruel way of talking about tracking in schools with the line, "I probably would have had fewer problems with math if I hadn't been put in the stupid group of math students in 5th grade." I'm not pointing a finger at you; this is how most everyone talks about it. Kids learn early on they come in three varieties â smart, regular, and stupid â and math class is often the determining factor. While there are people who have real difficulties with math that might be traced to genetic endowment, I'm convinced that most people who really struggle with it are victims of bad teachers and bad teaching methods.

Think of it â and help me out here PZ since this is directly related to human biology â why do we structure schools such that everyone is expected to progress, year-by-year in every subject along with other people of the same age? Just off hand that seems preposterous, yet it is the basic organizing principle of all K-12 education in the USA. Is there anything in developmental biology that suggests this is a good idea? I'm thinking here of the vast variation demonstrated among the general population along most every dimension that one can measure.

Couple that notion with the oddity of saying to a 13 year old that math, for example, is to be learned in 9 month units broken into 50 minute chucks starting 2 o'clock, 5 days a week, in a room full off of 20 to 35 students of the same age and one teacher with a white/black-board at the front of the room. In math in particular it's quite possible if you fail to learn a certain idea a couple of weeks into the course everything subsequent to that will become a blackhole sucking in any perseverance and self-esteem you might have left â to say nothing of killing off all joy in the subject. This is the reoccurring theme in the people I've worked with.

Now put a bad teacher in the picture, one who takes the easy out and teaches only to the top 10% of the class. I can't think of a better way to ruin the mathematical experience for the vast majority of students.

Personal experience: I took at grad course in computational theory (entirely about math and proofs) at the U of Michigan. Of the more than 60 students who started the course less than 20 of us passed. Yep, I had that intense rush when looking at my grade at the end of the semester. I was way cool, I survived, I must be really smart. But what does it say about the teaching method? You couldn't get in to the engineering grad school if you didn't have some pretty impressive qualifications. Sure, a fancy grad school has some slack with stuff like this, but a similar thing happens to many people much earlier in their educational life. It's an absurd approach to what should be one of the most joyous aspects of living: learning.

Truly, would someone explain to me the relevance of any of those questions in my day to day life (I'm a secretary by profession).

Someday you might want to be something other than a secretary. I think it's fair to want children to have as many options open as possible (even past grade 8!) and this material is not all that difficult for most kids.

Whether or not you need or remember it now is not relevant to whether or not our kids should know enough to be able to decide between a multitude of fulfilling vocations. You have your niche and are satisfied with it, but we can't afford to have our high schools turn out too many secretaries. We'll need some other jobs filled too.

They never taught "mode" in my arduous climb up through Diff E way back when, either, but I've seen it a lot on the 7th/8th grade homework I've been helping my wife grade recently. Maybe its the Venn Diagram for the new millenium - that was red hot when one of my kids was in school and seems to be passe now.

Henry Holland: that exact sort of basic algebra would absolutely do wonders for many of the people I work with and for. They have a terrible time figuring out that 100 parts per million is 1/10 gallon per thousand gallons, or that this translates to 1.26 gallons of chemical per pay in a well that makes 300 barrels of fluid per day. And these folks aren't dumb: they just didn't get properly taught or didn't pay attention in junior high school.

But hell, it keeps my phone ringing...

:Day." Not "pay." I wish I'd passed typing back in high school.

Henry, you ask

Truly, would someone explain to me the relevance of any of those questions in my day to day life (I'm a secretary by profession). I'm not trying to be provocative, I want to know.

I think that's a brave and â in a good sense â provocative question. I'm eager to hear the answers others here might give you. Here's mine:

The relevance of those questions to your day-to-day life is, IMO, near zero (this is from someone very into math with a lifelong love of the subject, as I've said before). The reason it is only near and not actually zero is that some facility with algebra might help protect you from getting ripped off by a life insurance salesman or loan provider. However, there are many laws and regulations to protect you from those sorts of things.

Also, it might help your self-image when people say things like You have your niche and are satisfied with it, but we can't afford to have our high schools turn out too many secretaries. Doesn't get much more condescending than that, does it? Those sorts of comments are so typical of the math-enabled.

I see math ability as having a similar function to language competency. If you are fluent in, say, French as well as English you can talk to French people. If you are familiar with computer jargon you can talk to computer geeks like me about computers regarding both practical uses and their affect on society. Being more able in the language of mathematics means you can talk to others with that fluency. There is little relevance to your day-to-day life. Knowing how to sing and dance would have more impact on your happiness.

Why am I a math lover? Because it gives me entry into a vast intellectual environment with its own unique rewards. There is little in the sciences (both hard and soft), business, and economics that is not permeated with mathematics. Engineering is all about math. Even music has an aspect that deeply mathematical. Modern cryptography which is more and more significant in business and our personal lives is rooted in abstract algebra, a subject dear to my heart. All this and the innate beauty of pure math comes from a knowledge of mathematics.

What many math bigots don't seem to acknowledge is the wonderful variation among human beings. Some of us love math, others sing and dance or play softball, some especially gifted people seem to do it all. There's no reason to hold up math, beyond basic arithmetic, as especially important to the good life.

"How can you see what question(s) you got wrong? I suspect it was the mode/standard deviation question because that was total guesswork."

Backspace and change one of the answers you think you got wrong. Only do one at a time. If your score worsens then you had it right originally and move on to the next one. That is what I did. I went back and selected Mode rather than the other one and got 10/10.

MYOB'
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it's not related, but nonetheless, i have a hope, a dream, that one day fundamentalism and religiously-inspired ignorance will be looked down upon by a scientifically-enlightened society as disease...
perhaps then we could be at peace.

Someday you might want to be something other than a secretary. I think it's fair to want children to have as many options open as possible (even past grade 8!) and this material is not all that difficult for most kids.

No, I'm perfectly content to be a secretary. I know, it's hard to imagine, but there it is. And, as is obvious, I meant "How is it relevant to ME", nowhere did I even hint the opportunity to learn it should be denied others. Kids should be taught basic math (+, -, /, %) and if they want to pursue anything beyond that, it should be an elective.

I bitterly resented having to take two years of algebra in jr./high school when all I wanted to take was music and art classes but instead had to sit through that rubbish. And guess what? Not once, not even close, could a teacher answer my question and trust me, I asked. The standard answer: "Because". Oh how I laughed when the math/science geeks would ask the same question I posed in my original post in my beloved music and art classes. I sympathized and felt that they shouldn't have to be there if they didn't want to, all their evident antipathy did was take instruction time away from me and my musician/artist friends.

They have a terrible time figuring out that 100 parts per million is 1/10 gallon per thousand gallons, or that this translates to 1.26 gallons of chemical per pay in a well that makes 300 barrels of fluid per day.

Finally, some relevance! But I would say that's simple fractions and division and so on. Erm, OK, I guess you'd need the formula for figuring that out but instead of the 2x-/4-(y1453) stuff, why not something like this to convert kilometers per hour > mph: divide the km/h speed limit by 8 and multiply by 5. I wonder if that poor girl that Cohen wrote about had this stuff presented like that? Mode/standard deviation? Pointless in this context.

The reason it is only near and not actually zero is that some facility with algebra might help protect you from getting ripped off by a life insurance salesman or loan provider

Again, simple fractions, percentages and so on that are taught in basic math classes (which I had no problem with).

Even music has an aspect that deeply mathematical.

I'm a hobbyist musician that can read and understand some of the most complex opera scores ever written (hello Reimann's Lear and Zimmerman's Die Soldaten, how ya doin'?) and know exactly what's going on. That involves.....wait for it....be patient.....wait.....simple division and multiplication. Not a scintilla of algebra is involved. I learned how to read music in 15 minutes (thank you to Bobby, an old drummer boyfriend of my sister!) when I was 9.

Look, I'm ashamed of myself that I even agree .001% with anything Richard Cohen has ever said, but when I read that screed of his, I was all "YES! Finally! Someone is writing what I've felt for 30 years". Of course, a second reading revealed that he's basically an idiot, but that has nothing to do with his dislike of algebra.

The prime reason for learning algebra is an increased ability at pattern recognition.

Is it necessary? No. Most of the time. For some people.

Is it helpful? Certainly.

The one that made me pause was the "-7" one. Was stuck for a while wondering if it was a prime number. ...

It is. The test incorrectly marks that answer as wrong.

There is a very general definition of prime number which applies to all number systems, but which is beyond the scope of ordinary school mathematics. However, it turns out that prime integers are precisely those which are evenly divisible only by themselves, their own negatives, +1 and -1. For pedagogical purposes at the elementary level, this, or some equivalent, can (and should) be taken as the definition.

The test also unfairly offers "whole number" as one of the alternatives, and incorrectly marks that answer as wrong too.

How about we talk about the real uses of algebra, where and when they crop up?

The point of algebra is simple. It allows you to work with more complicated mathematical situations in a simpler way.

If you can keep several separate numbers in your head at once, your need for algebra may be less - but that doesn't mean it wouldn't help.

It also allows you to learn general rules for getting answers to certain types of questions that you COULD just learn the special rules for ... but then, you have to learn more rules.

For instance: If you intend to work out a good budget ... algebra is very helpful. It's not necessary... but it simplifies what you need to do, and can do so significantly.

Or, for an example that will motivate children rather more than adult secretaries... if you have five dollars, and want to get as much candy (each of which has different prices) as you can, you can use algebra to work that out - and again, you could use simple arithmatic, but algebra simplifies it.

Calculus, now, that one's hard to apply to day-to-day life. ;) (But it's very useful if you ever want to do physics. ... which is why I'm a computer scientist, not a physicist.)

wow. I passed.
I have been a math illiterate since about 8th grade, so I'm surprised. I have a mental block when it comes to math. I've always figured it had something to do with my mom sleeping with my 7th grade math teacher and him talking about it in front of the whole class (I'm not kidding.)

I did get one wrong, but it WASN'T the "mode" one, so I am a little perplexed by that.

"The test also unfairly offers "whole number" as one of the alternatives, and incorrectly marks that answer as wrong too."

aha! That means I got 10/10! :)

Henry, think of it was like being forced to eat broccoli - its good for you.
Change algebra to music classes - what percentage of students are ever going to go into music for a living? Maybe 1 percent at most? Yet music classes up until 9th grade were NOT an elective, everyone had to take them. Then, in my school system, budget cuts in the 70's changed that.

I think overall school is a pretty crappy way to learn things, but its the only way we have to take masses of kids and pound some knowledge into them and hope at least some of it sticks.

If in 8th grade you hate algebra and your plans are to be a rock star, you might find yourself with a different set of priorities when you're in your second year of college, and you might then be glad you learned the math you didn't want to learn. Or, you might be glad you were "forced" to take the music classes you once hated.

Schools have to strive to give kids a rounded education that does as much as it can to cover all of the later possibilities in their lives - and in doing that, they will inevitably be forcing "useless" material on kids... the only alternative to that is to expect kids to choose their lives paths at age 12. That used to work, and even worked better 20 years ago than it works now. These days, nobody has one career their whole life. Well, almost nobody.

I got 9/10, and I haven't had any math instruction in 10 years (apart from day-to-day stuff we all utilize except, of course, Richard Cohen). I'm pretty proud of that, because math was always my worst subject (closest I ever came to getting a C was in college trig). Of course, I've spent most of that time as a journalist (recovering, nowadays), so I'm all screwed up. And for what it's worth, I hated the music and art classes I had in school. Can't draw a straight line to save my life and my first music teacher told us that blues, soul and country music "were not real music" and the music ap guy I had in college said the above three were too "common" to "have any real beauty".

... However, it turns out that prime integers are precisely those which are evenly divisible only by themselves, their own negatives, +1 and -1. ...

Oops. I just realised I have committed the common blunder of failing to exempt +1 and -1 (which are not primes) from the definition. The correct definition is:

Prime integers are precisely those, with the exception of +1 and -1, which are evenly divisible only by themselves, their own negatives, and +1 and -1.

Truly, would someone explain to me the relevance of any of those questions in my day to day life (I'm a secretary by profession). I'm not trying to be provocative, I want to know. Please note: "Because it promotes logic" or "It will make you a smarter human being" or any variation on those won't fly.

I'm surprised at no-one else (having looked through the replies) apparently providing specific instances of the usefulness of algebra.

Henry, I doubt any of those specific questions would come up in your everyday life. However, I don't suppose you were really intending to be as restrictive as that. There certainly are issues which arise in normal life and are best solved by algebra and higher mathematics of various sorts.

For example, some digibox users (ie a TV interface) had found they couldn't access certain pages of the BBC website. The situation was very complex (many variables) and they weren't very good at submitting coherent bug reports! Suddenly, one page which used to be visible suddenly stopped working for them. That was an important clue because the page itself hadn't changed. Just the number of conversations attached to it had. That meant the number of links (rather than graphics or any of the other variable factors elsewhere) was the culprit. I knew I could provide another way to look at the page, but adjusting one number meant that there were more of some links but fewer of others - changing at different rates. I had to quantify those rates with algebra and then differentiate to find the minimum point and solve back. When I posted the new link for them to use, it worked. They would probably have become annoyed and given up if I'd experimented on them with lot of different links in a trial and error method instead.

Perhaps as a secretary you don't do much viewing of websites with inferior equipment. However, you almost certainly do other things where you need to establish a balance (depending on how much responsibility you have). Eg Ordering in bulk might save on packaging and delivery but cause storage or cash flow problems. You could work out lots of separate guesses and then pick one, or you could find the "right" answer straight away.

#7 is a trick question too: The second alternative is "none of the above", but the only "above" answer is 40%, which is wrong. As to whether -7 is a prime number, well it is a prime element in the ring Z of integers, but the term "prime number" usually applies only to numbers greater than 1. -7 is also a Gaussian prime, but we can hardly expect the average 8th grader to know that. 8-)

Henry,
I admire your confidence at age 14, about your chosen career path. Most kids have no idea at that stage, and not teaching them math is shutting down their career options not only in the exact sciences, but social sciences as well.

Also, as Sagan said once, furniture factories are being shut down for lack of personnel able to perform simple math unaided by machines.

Algebra also provides one with the ability to perform algorithmic tasks, which is no trivial matter.

I wasn't terribly good at math at school, but I did enjoy it enough to get a reasonable pass at 'O'-level and take it at 'A'-level. But the teaching changed, or I changed, or something, and I could never grasp calculus. I learnt enough to answer some questions -- I barely scraped a pass -- but I could never get a handle on how to use it, and the teachers never bothered to explain what it was for, blithely rushing into what seems like now to be nearly two years of differential equations. It didn't help that I was in the less-able class (i.e. not likely to get into Oxford or Cambridge) and the teachers scarcely seemed to care about teaching us. At the end of the course, they briefly covered a new subject that wasn't differential equations (but I forget what it was) and decided we were too dumb to be taught statistics, since we couldn't grasp diff eq. Argh!

And that, oh best beloved, is how I became a graphic designer.

Henry: I'm not sure why you differentiate (no pun intended) between algebra and arithmetic. Algebra is a more formalised way of doing arithmetic.

For example, "what's two times five?" can be expressed as "2Ã5" or "x=2Ã5". The outcome is identical. Claiming to use arithmetic without algebra is disingenuous - you're merely creating an implicit variable in your head ("the answer is..."), and removing the explicit "x=".

Algebra allows us to make our unknown explicit, and then manipulate it in less obvious ways. We can split up our unknowns into "(x-a)(x-b)=0" and so on. But that's just the advanced applications of knowing the system. Knowing in the first place is just formalising what we already do in our heads.

It's the same thing with language. We learn syntax as small children: how to conjugate tenses (with exceptions, like "eat" to "ate", instead of "eated"). Once we've mastered that, is that any reason to deny ourselves the fuller understanding of high school english classes?

You know, I'm a little afraid to take the quiz. What if I don't get a 10/10? And it's totally for gendered reasons that I'm worried.

I was in advanced math from 6th grade on. I took math with students one year older than me through my junior year of high school, when I took AP Calc. There, the regular AP Calc teacher was ill and had to take the year off so we got an eighth grad math teacher. He ended up taking a lot of days off -- I think he was panicking about teaching calculus -- and we learned nothing. It was taught in a computer lab so we would surreptitiously turn on the computers and play with them. I was one of two women in the class, and the guys would monopolize class time, flamboyantly answer questions on the board, and otherwise imply they totally understood the material. They did manage to teach themselves somewhat, because the teacher did not. Though I had loved math up to this point, I ended up with a 1 on the AP Calc exam. Completely bombed it.

I could say more specifically about the gender issues in my class but won't bother. Won't be anything you all haven't heard/experienced before. I will say I re-took calculus in college and had a great, energetic instructor and it made me enjoy the material again. It was a bigger class where a few personalities couldn't dominate so the teacher dominated (in a very useful way).

What the hell happened to my multiplication symbols??

1,4,9,10 were to solve linear equations.
2,6 were about definitions.
5,7 were about estimation
8 was to evaluate a simple expression
3 was about setting up an algebraic expression based on a word problem.

Some areas, such as geometry, were not covered at all.
Here is a more extensive 8th grade test:
http://www.doe.mass.edu/mcas/2003/release/g8math.pdf

Just FYI, here is a grade X Indian Central Board of Secondary Education
math question paper:

http://www.cbse.nic.in/curric~1/Math06.pdf

What the hell happened to my multiplication symbols??

This page obviously doesn't support Unicode very well. Try using the HTML representation: × gives you ×.

I recently found someone asking why they would ever need to know how to factor polynomials. It's tough to describe an everyday situation for some of those easy parts of algebra all by themselves, but the real answer is that they're necessary prerequisites for all sorts of more directly useful things.

My explanation to this person was that factoring polynomials is one of the simplest kinds of "root finding." That's necessary if you can control one thing and you want another thing, which depends on it, to be a certain value. And when you get into calculus, and that dependent thing is a "derivative," you can use root finding to see what value of one thing makes another thing the lowest or highest that it can be. Basically, it allows you to figure out the best value for something, and anyone can see uses for that.

10/10. 8th grade is mine.

Here's some relevance that can really help the average person. I track all of my finances on linked spreadsheets. I write in the formulas that carry info between cells on excel. It's really pitifully simple to do, but you do need to have a basic understanding of symbolic representation to set up those pages.

Of course, you could just buy Quicken and let it do everything for you as well, so I guess it's not absolutely necessary...

I'm not sure if this would have counted as grade 8 math where I was. I remember a unit on geometry in my class. I also remember that mode, median, etc. were actually covered (at this sort of elementary level) in my grade 6 course, and there was some statistics in my grade 7 course. I can't for the life of me remember what it consisted of, either.

It turns out, you don't really need to know how to *read* either. I mean, most people got by just fine throughout most of human history without reading. And in more modern times, I can think of a few careers in which reading is completely unnecessary. There are quite a few more I would have thought reading wasn't useful for when I was actually learning to read, which is probably more relevant. And there are certainly people that have trouble learning to read so it's not as automatic as you might guess once you've been doing it for 30 years.

Yet, I doubt there's a person on the planet who can read now and would be willing to go back and relive their life without it.

Why learn anything? Because it changes you.

I got 9/10, but my 10-year-old daughter got 10/10. Who says evolution ain't progressive? ;)

This page obviously doesn't support Unicode very well. Try using the HTML representation: × gives you ×.

That's the problem, you see — I did use the HTML entity. However, I think my downfall was then hitting preview to see if it worked, and submitting from that. I think the preview function probably inserts the resultant glyph back into the form, instead of the entity that you write, and so when you finally hit 'post' it makes an ugly mess of things.

This is all guesswork at the moment. I shall hit preview now and see what it does to my em dash :)

PS. I was right about the preview box mangling things up. Are the devs paying attention to this thread?

PPS. Why does this thing never remember my personal info? Does it rely on javascript?

I'm not sure why you differentiate (no pun intended) between algebra and arithmetic. Algebra is a more formalised way of doing arithmetic.

Arithmetic is expressible as algebra. That doesn't mean that it *is* algebra, though--its relationship to algebra is not unique. Arithmetic could be expressible in other systems as well. Just because arithmetic is a subset of algebra, doesn't mean that we can't differentiate between them. We differentiate between subsets and supersets all the time. Arithmetic is useful on its own, without any knowledge of algebra.

The test also unfairly offers "whole number" as one of the alternatives, and incorrectly marks that answer as wrong too.

I don't think so. "Whole number" is usually used to refer to the set of positive integers--only reading that comment led me to find that it has ever been used as a synonym for integers. So you can only really say that this question is not very precise, not that it's wrong.

10/10! Woo! Artist can do math! (I remember my eighth grade math teacher telling me that if I became an artist, I'd use geometry all the time. This was a filthy lie. I do not doubt that some artists are constantly plagued by their need to determine the volume of a cylinder, but my sleep is yet untroubled by it.)

However, I will not say that I do not use complex math in my life, because I have used more of my math education playing D&D than I would ever have thought possible.

Just because arithmetic is a subset of algebra, doesn't mean that we can't differentiate between them. We differentiate between subsets and supersets all the time.

That's true, but I think subsets and supersets are the wrong way to picture about this. Algebra is more a tool of manipulation that applies to all mathematics and logic. Rhetorical algebra was used thousands of years before the standard notations and formalisations were created. This is the algebra which I refer to when I say "the answer" — this implicit way of remembering where the answer goes once we've performed the calculations.

Arithmetic is useful on its own, without any knowledge of algebra.

I don't think it is — if we have no way of assigning meaning to an expression then the arithmetic is useless. Anyone can type 2×5 into a calculator and hit the enter button, but it takes algebra (in some form, no matter how simplified) to know that "the cost of five pies at two pounds each" is semantically the same as the above calculation; and consequently, will provide the answer that you want.

That's why, IMHO, people find the word-based maths questions on the back page of newspapers so challenging. Because the simple conversion of a problem into "knowns", "unknowns" and "relationships between" is beyond a lot of people. Anything more than a few values (the oft-quoted 7±2 items) and the human brain gets a bit overloaded; which is where falling back on notation and formalisms is so useful.

If we don't have that facility then our ability to use arithmetic is hampered: we can't get the answer if we can't correctly pose the question.

This is, of course, all just my little opinion. :)

10/10. The last question was tricky: "Now, please tell us what kind of code we should give you for your results" - Code? I don't want it in code. You gotta learn how to crack codes just to find out your answer?

Henry, you ask why you "need to know" algebra. And then you state you are a secretary and are satisfied with your job, as if those two statements have anything to do with your question. This reveals what you think education is for - that it is strictly mercenary, that it teaches you how to make money, that it has nothing whatever to do with you as a person.

I can only paraphrase to you from the Underground Grammarian:

Sweet are the uses of audacity. Henry may indeed be asking to provoke, and as a challenge, and without even suspecting that he truly does want an answer, or even that there is one, but all of that can be said of every true and important question. The important question is the one that no one can answer, as we can answer questions about the principal exports of Brazil and the capitals of the states. The important question calls not for that sort of answer, but for thoughtful consideration. It calls for that thinking of which Henry seems to have detected no trace in, of all things, the study of algebra! Why on earth would anybody teach this stuff to a whole bunch of children who will never again algebrate once they leave this place?

Here we can see the difference between the answering of a question and thoughtful consideration of a question. There surely is an answer, and an especially appropriate one in the case of Henry, who hasn't done any serious thinking about mathematics: Those who teach it can get some money from the taxpayers. While we would provide only an accidental occasion of education in stating this, we would have won Henry's praise for candor and good citizenship by the truth: "You have to take this course, Henry, since it is required by law; and I am teaching it in order to get paid for putting you through your term of enforced labor for the state. So shut up and mind your QED's." In his opinion, so far as we can tell, that is not only the truth, rare enough, but also the whole truth, rarer than rubies. But that truth, we suspect, Henry knew already. His question means: I know what's going on here, but I can't understand why such an unaccountable system should exist at all. Can you tell me, Mr. Teacher?

It's a fine question, and a fair one. It is also a question that Henry would probably not have had to ask at all had his teacher asked it first of himself and considered it. Had he done that, he would have been teaching in a way that would have led Henry out of darkness and into light.

A specter is haunting the schools. The dead hand of problem-solving rules them. They can find no other justification for the study of algebra than the hope that some of the students will be able to solve problems in algebra. Sometimes they do go a little further and claim that such studies as algebra are pushups for the mind, exercises for the strengthening of something or other. But even this slightly better idea they trivialize by supposing no other possible power of the mind than the same old problem-solving. Well, of course, Henry, we know that you will never again in your life have to solve problems in algebra, but you will have to be an "educated" consumer who can figure out unit prices in the supermarket, won't you, to say nothing of balancing your checkbook?

Such an argument is, of course, too puny, even for the school people, to preserve algebra as a "required course". It is also, typically, an argument from particulars rather than principles, and any Henry of our time could demolish it by whipping out his calculator. Here we can see the great mystery at the heart of the school mess. What is it with these people, that they scramble like demented trash-pickers after every newly noticed particular and never see the principles of which every particular is no more than an instance? AIDS comes along, and they need new programs, with funding. Cholesterol comes along, an old grandmother dying in a nursing home comes along, oat bran comes along, cocaine comes along, abortion, toxic waste, the fractional latchkey family... Particulars are always infinite. And they all need programs, and funding. But in principle, such things are never new; they are all local appearances of the permanent and universal.

Algebra is a world of principle, and a dramatic revelation of the power of principle. In fact, algebra, and even algebra alone, could provide a true and sufficient education out of which to understand the worth of living by principle in a life beset by a never-ending succession of nasty particulars, and at the same time provident of joy and goodness and thoughtfulness.

Listen, Henry, and be comforted. There is nothing wrong with your impatience and chagrin. Your very objection proves that you can see, if only from a great distance, an important truth. Algebra is a strange study indeed. It doesn't even exist, in the sense most ordinary to that word. There is no algebra our there; you will not find it under a rock or washed up on the beach. Never will a little child bring it to you, asking what it is. Algebra isn't even as "real" as a poem or a song, which can be picked up in the world even though the world could never make it.

Algebra has its dwelling place only in a mind. We can not even say, as we can of our power of language, that algebra exists in the mind. It can live only in a mind that creates it anew for itself. That's why no one can really teach you algebra, and why math teachers are, as you seem to have figured out, a bit of a fraud. But I can no more create something in your mind than I can take off a few of your pounds by watching my calories. I can show you some tricks, but you must do the teaching. And, no matter what they tell you in the slippery world of pliable convictions and values, you will have it in your mind that you can know something--truly know it, and not just believe it, or be informed of it--and maybe, since that is so, you can truly know something else. It's interesting to wonder what such a something else might be.

I think you should learn algebra, because I wish you well, as a teacher, even a bit of a fraud teacher, should, and not because I want you to solve algebra problems. You will find that algebra shows you some truths. The first great truth is that there can be something real, and complete, and harmonious, and even, in some strange way, absolutely perfect right in your own mind, and made by you alone. You will see that you have a wonderful freedom not mentioned in the Bill of Rights, the freedom to decide what your mind will contain and how it will work. You don't have to copy the rest of the world.

Algebra tells sad truths too. Where there is no balance, there is no truth. What is equal is equal, and between the equal and the unequal there is no conference table, no convenient compromise. In this terrible law there is a hinting question for all of life. Are there other things like that?

Algebra will show you the inexorable, the endless and permanent chain of consequence, the dark thread of necessity that brought you to a wrong answer because of a tiny little mistake back in the second line. I know how unfair that seems, and how scary that what seems unfair is nevertheless justice. Is life like that too, as all of nature seems to be? How then shall we live? What are the laws of the algebra of our living, and where do they exist, where created? Who can show us how to learn them?

No prudent teacher would ever say such things to Henry, of course; he is probably not ready to listen. It takes some serious living to see the truth hidden in algebra.

Enjoy the whole essay, "The Uses of Audacity", at: http://www.sourcetext.com/grammarian/newslettersv14/14.3.htm

Harald Hanche-Olsen wrote:

.. As to whether -7 is a prime number, well it is a prime element in the ring Z of integers, but the term "prime number" usually applies only to numbers greater than 1. ...

Oops again. You're right---I should have checked my definitions before sounding my mouth off. Apologies for the misinformation and false accusation that the test's marking of that answer was incorrect.

I wrote:

The test also unfairly offers "whole number" as one of the alternatives, and incorrectly marks that answer as wrong too.

Skemono replied:

I don't think so. "Whole number" is usually used to refer to the set of positive integers--only reading that comment led me to find that it has ever been used as a synonym for integers. So you can only really say that this question is not very precise, not that it's wrong.

On this one I'm prepared to stick to my guns. The term "whole number", like the term "natural number", seems to be genuinely ambiguous. I have no problem with anyone choosing the definition they prefer and sticking to it. But for a test offered to such a wide audience as this one was, it seems unreasonable to me to mark an answer as wrong when, according to one reasonably widely accepted use of the terminology concerned, it is in fact correct.

Henry asks a legitimate question. Lots of people fail miserably at one topic or another. Languages, math, spelling, music, drawing, gym each have their victims. Knowledge or capability in each of those areas is good, but none of them is absolutely necessary for leading a long, productive, and happy life. So why make them absolute requirements for high school graduation?

1) An important reason to force students to master something they hate and can't do is to teach them that they can in fact do what they previously considered impossible. When this works, it's the best confidence-builder in the world, although it will backfire if the student keeps failing.

2) If you can do some math, you can disagree more confidently with people who are trying to push you around with math and statistics. (In retrospect, should people have trusted Bush with respect to social security, or should they have looked a little more carefully at his dismissal of 'fuzzy math'?)

3) Life isn't predictable, the fates throw curveballs at us. The secretary in my department was (I think) happy being a secretary, but then all the professors got computers and started doing their own typing. Also, state support for higher education dried up. To keep her job, our secretary had to start doing new stuff, including spreadsheets, which require algebraic formulas if you are going to do anything useful with them.

4) Here are two hypothetical story problems that might be relevant: A) Henry, suppose you've decided to start an amateur arts group to put on an opera, and it's going to cost $8,000 when all is said and done. (You had to do math to get the cost, but let's skip that.) You've got 75 prime seats that you might be able to charge around $15 for, 200 seats that you might be able to sell at $10, and you want to sell maybe 50 seats to kids at $5, and you also want offer a few seats as freebies for publicity. How many performances will you have to sell out to break even? How do slight variations in the pricing structure affect your budget? Algebraic formulas in a spreadsheet are the easiest way to figure this out.

B) Two salesmen are trying to sell you a photocopier. One copier costs $12000, and ink is $75 a cartridge, good for about 1000 pages, and they promise that parts will be available for 5 years. They'll let you buy it for $12000, or for $311.29 per month over 5 years. The other company offers to rent you one, and they'll provide ink, paper, and servicing, but they'll charge you $85 / month plus 4 cents per page. Your boss doesn't know math either. Which deal works best for you?

As someone said earlier, algebra (and, more generally, mathematics) teaches you how to arrange numbers in complicated word problems so that you can arrange things in logical ways and get answers according to general principals.

Henry,

In one of your comments above you say "that's just arithmetic" and go on to demonstrate that you can do simple algebra. I suspect that's true for many people. You have an intuitive grasp of at least some of the subject, apparently the parts you need in your day-to-day life. Good for you. Often we learn in spite of the school system.

When I mentioned that music can be seen as deeply mathematical you responded:

I'm a hobbyist musician that can read and understand some of the most complex opera scores ever written (hello Reimann's Lear and Zimmerman's Die Soldaten, how ya doin'?) and know exactly what's going on. That involves.....wait for it....be patient.....wait.....simple division and multiplication. Not a scintilla of algebra is involved.

Oh, there is a rich world out there, involving many scintilla's of algebra, trig, and other parts of math. Just google "mathematics and music" and check out a few of the links.

Math Anxiety, Lousy Textbooks and the Fun of Autodidact Algebra.

I was one of those folks with a blinding math anxiety, in which the numbers and symbols become inscrutable runes of a language I do not know. At all.

I got 9/10 on this silly test. What gives?

Algebra in high school was a course I dropped because I was failing, but I stole the book and happily did the whole thing over the summer on my own. For fun. (I still have the book and it beats today's typical HS Algebra book by far.)

It may have been the way it was taught in class or simply that class is a public place and for years I could not seem to do math of any kind in classrooms. Or anywhere when someone was looking. Alone, I could do the math and even enjoyed it, but if someone so much as watched me subtract the last check in my checkbook, I could not make sense of the numbers.

Still I did algebra on my own for fun. It was a secret, though, because if anyone knew, I would have to prove it, and I knew I could not do that because if my smart siblings (who always aced all the maths) were to watch me, the math aphasia would hit.

I used to blame the six-foot tall scary nun, Sr. Barnard, who taught 4th grade. We had these timed drills of the multiplication tables, and when you were finished you would slap your paper down on your desk and go stand up by the board. Public, competitive, terrifying. That's when my beloved math turned to babble before my eyes. I even got tunnel vision and damn near passed out during those drills. I would practice at home, feverishly, and do fine, and still Tuesday mornings were so scary to me that I regularly had "a tummyache mommy I think I am going to throw up I can't go to school".

I dropped out of college (to take a theatre job that allowed me to travel all over the North America) and it was thirteen years before I went back. The first math course I took ("College Math for Nontrad Dummies" or whatever it was called) was taught by the head of the department (I went to one of the Vermont state colleges), a guy who somehow convinced us that no one need to have math anxiety. He was also one of the most calm yet enthusiastic guys I have known.

I aced the course and ended up tutoring other nursing students in every subject, even the math bits. (As a non-trad, I did all those little money makers: peer tutor, drive the shuttle bus to the hospital, sell my kid's meds to the college kids...okay, I didn't do the last one)

Years later, when my kids took math and algebra, I watched how it was taught. It has worsened, IMO. Maybe some of us will always be situational math aphasics, and that is what self-paced computer-based courses can help resolve, perhaps.

But the books I have seen over the last couple decades have sucked. In an attempt to make algebra "relevant" or something, and heaven forbid they should intimidate students with volume, the books are full of pictures and graphs and stories. But what happened to all the pages of problems? Now there are ten or twenty to solve before you go to the next concept. There used to be 100-150! By the time you were through these (or the odd numbered ones as many teachers assigned), you usually grokked it. Boring? Sometimes. But also mesmerizing, immersive, meditative, and rewarding.

I have no idea how common my tale may be. I meet an alarming number of Humanities tribespeople who are proud of despising math and algebra. WTF? For all the movie-inspired common stereotypes of scientists, I have not actually met many geeks without poetic sensibilities, but I have met lots of poseur lit sillies who talk obscurantist drivel and think muddy means profound...

Skeptyk

However, I think my downfall was then hitting preview to see if it worked, and submitting from that. I think the preview function probably inserts the resultant glyph back into the form, instead of the entity that you write, and so when you finally hit 'post' it makes an ugly mess of things.

This is all guesswork at the moment. I shall hit preview now and see what it does to my em dash :)

PS. I was right about the preview box mangling things up. Are the devs paying attention to this thread?

Noticed that myself a few days ago. Posted something which got eaten, tried to post again and previewed first, then finally just gave up entirely, but that was using &lt in an equation for getting a binary 0 or 1 result from it, to replace the use of an if-then.

Every forum/posting system has one of these damn glitches, so I chalked it up as yet another strange f-up on them, which like others will probably never get fixed. :p

Sorry if this is a bit redundant--haven't caught up on the thread yet. I'll be testing nested blockquotes now.

"Arithmetic is useful on its own, without any knowledge of algebra."

"I don't think it is--if we have no way of assigning meaning to an expression then the arithmetic is useless. Anyone can type 2.5 into a calculator and hit the enter button, but it takes algebra (in some form, no matter how simplified) to know that "the cost of five pies at two pounds each" is semantically the same as the above calculation; and consequently, will provide the answer that you want."

But, but! We do have a way--intuition. It's intuitively obvious that 2 + 2 = 4 corresponds to "if you have two apples and two oranges, how many pieces of fruit do you have?" You don't need to know any algebra to see that, because it's more or less built into our heads. You can't really formalize it without algebra, perhaps, (and I'm not sure about that,) but formalizing it isn't what we're really talking about here, just understanding the problem. So when you say "but it takes algebra (in some form, no matter how simplified)" you're really talking about formalizing it, not how people actually understand it.

And I agree that the formalization is worthwhile if one ever needs to deal with complicated problems, and I'll even conceed that good practice with the formalizations (something not all math classes teach well) can sharpen and expand your intuitions about math.

I actually think that people intuitively reason about math using their intuitions about material objects. I view an exponent in a polynomial function as applying a "bending force" to the graph of the function. By using these metaphors, we can take advantage of built-in brain processing to find regularities we wouldn't have noticed, and to solve things much more quickly and see more aspects of things. Being good at math is knowing the right metaphors to map to the formalisms you're working with. But absent the formalisms, those intuitions can still be present, operative, and useful.

9/10

Curse you, whole numbers! And the people who adhere to alternative definitions of them!

I'm rather proud of myself for getting the 'mode' question correct. That's the question that I missed on the SATs.

I suppose that schools will improve about the same time evangelical rightwing Christians decide Pharyngula is the most enlightening thing in the blogosphere.

N.Wells writes:

An important reason to force students to master something they hate and can't do is to teach them that they can in fact do what they previously considered impossible. When this works, it's the best confidence-builder in the world, although it will backfire if the student keeps failing.

I disagree profoundly. Force has no place in education; it's a surefire way to extinguish the love of a subject and the innate joy of learning. You might consider why a kid hates the material at hand. It will have nothing to do with the subject itself and everything to do with being asked to do something they don't understand and the feedback they get when they do something "wrong."

This is a blog about science and reason. Collectively we know a lot about human biology, sociology, and psychology. Be damn nice to see that knowledge applied to one area which has a chance of making a massive transformation in our quality of life: the education of children.

Where the hell are the knowledgable, leftwing idealists when you need them?

First, great blog.

I like the concrete example of the copiers, but hey, let's go from hypothetical to honest to goodness actual: suppose you are a glass beadmaker, commissioned to make 300 glass beads (same design) 12mm hole to hole plus or minus 1mm. You make samples to confirm that this size of bead does in fact require about 1 inch of a standard diameter rod (roughly 7mm).

Given that the typical soft-glass rod is about 13'' long, and there are 20-21 rods per pound, how much glass do you buy to complete this commission? I did the math, which came out to roughly a pound. It didn't seem possible, so I went ahead and bought 3 pounds of transparent dark aquamarine. That was back in 2002. I'm just now using up the extra:)

I could afford to screw around like this because this particular type of glass runs about $7/lb. However, you may be certain that if I'd had to make those beads out of borosilicate color, which at that time often ran $50/lb, I would've double-checked my results, and probably measured the *precise* diameter of the rod, using that fun little volume of a cylinder formula someone mentioned upthread that no artist would ever need to calculate more closely the exact amount of glass I needed.

In fact, back when I just sold beads I used to use algebra all the time to calculate how many metal beads (14k in particular is expensive) the customer would need to complete a regular, repeating design. The constants would be how much a small metal trim bead would slip inside the hole of a larger stone bead---you couldn't just add 3mm 14k plus (4x 10mm black onyx) to get the answer, you had to substract out some amount to compensate for how the not perfectly spherical beads lay against each other. And then there's that stringer's bugaboo, compensating for the diameter of beads in bracelets: as they get larger, the axis of the bracelet stands out further from the wrist, so that means a piece with bigger diameter beads needs to be longer.

Don't get me wrong: sometimes approximation works just as well.

But sometimes that math stuff really comes in handy---and I'm no genius with math---never really did `get' caclulus. And I wish I understood set theory(?) better---it would make designing kumihimo (a form of three dimensional weaving) color patterns so much easier.

So, yes, math is handy. Even for artsie-fartsies like myself;)

(whew! setting xemacs to 512 col width mostly works...so I [re]learned something new today: neither computers nor math come easy...)

for henry .. you mention that you only wanted to take music and art classes .. well, then you surely are acutely aware of the relevance of math to music! in fact, music is, in my opinion, a rather appealing form of mathematical expression.

10/10 I was unsure of the mode question, but since it couldn't have been the mean or average (someting like 16/5) or s.d. I just chose default.

Henry, think of it was like being forced to eat broccoli - its good for you.

Hahaha. It's no surprise that I hate broccoli--don't even get me started on brussel sprouts! :-)

Change algebra to music classes - what percentage of students are ever going to go into music for a living? Maybe 1 percent at most? Yet music classes up until 9th grade were NOT an elective, everyone had to take them. Then, in my school system, budget cuts in the 70's changed that.

Yes, I was one of the last load of school kids here in California that were educated in the pre-Prop 13 days, before the public schools were evicerated by that awful thing. And I still maintain that those kids in those music classes, that along with the art classes, were the only reason I showed up at all (well, OK, my parents and the law had some say!) were dragged down by the kids who didn't want to be there. I know all about the "well rounded citizen" argument, but dammit, you people that can't sing on pitch to save their lives, go away! :-)

BTW, I knew I wanted to be a musician when I was 8--hearing Hendrix and Cream in 1968 did my head in. When I quit music as a full time thing so that I didn't end up like Joplin/Hendrix/Morrison/Cobain--I was on that path, for sure--and went to the local JC to learn office administration, at no point, none whatsoever, was my D- in Algebra a hinderance to that. Yes, I realize that I was lucky about when I got in to this, but still.

This reveals what you think education is for - that it is strictly mercenary, that it teaches you how to make money, that it has nothing whatever to do with you as a person

Yes, that is *exactly* what I think public education up to the 12th grade should be about. Anything beyond (ie college, if people choose), well that fits in the purview of your paragraphs after that, all that "life of the mind" stuff. To be blunt, I find a lot of what you wrote hideously patronizing. Like, um, this:

No prudent teacher would ever say such things to Henry, of course; he is probably not ready to listen. It takes some serious living to see the truth hidden in algebra.

Your truth is not my truth, my algebra teacher's truth is not my truth, full stop. Yikes, if the pomposity and condescension in your post could be distilled in to a form of energy, we'd be out of Iraq in a week.

You will see that you have a wonderful freedom not mentioned in the Bill of Rights, the freedom to decide what your mind will contain and how it will work. You don't have to copy the rest of the world.

Or I could take a good hit of LSD or peyote and find out the same thing, AND have a zillion times more fun doing so. Woo hoo! 1983...A Merman I Should Be while blazing! Taking LSD and listening to Genesis' The Lamb Lies Down on Broadway on a pair of kick-ass Sennheiser headphones taught me more about my life and the world I live in and my place in it than all the math and science classes (beyond basic math) that I've ever taken combined. This is not a joke.

Just google "mathematics and music" and check out a few of the links.

OK, here's one: http://tinyurl.com/brvgr

No where on that page or in any of the links is there anything that I, as a musician or as a listener of modern operas, would use. It's all interesting, the algorithims of non-tempered tuning and all that, but then so is "What do the numbers on LOST mean"? I wrote some short 12-tone piano pieces years ago and math had nothing to do with it. It's a technique--put the 12 notes of the chromatic scale in any order ("the row"), number that order sequentially, then come up with tricks to combine them (1 + 5 + 8 + 9; 2 + 7 + 11; etc.), go forwards with the note order, invert it starting from the last note etc. etc. to generate harmonies and contrapuntal lines. It's no different from harmonizing a Bach figured bass, yet the music + math guy jumps all over retorgrade inversions of the row to show.....I can't tell, actually!

I disagree profoundly. Force has no place in education; it's a surefire way to extinguish the love of a subject and the innate joy of learning.

As the kids today might say: Word! Wordy word McWord!

for henry .. you mention that you only wanted to take music and art classes .. well, then you surely are acutely aware of the relevance of math to music! in fact, music is, in my opinion, a rather appealing form of mathematical expression.

Once again *sigh* math and music are not bound, apart from learning multiplication and division. If you want to study The Golden Mean as used in Bartok's glorious string quartets, fine, but to write uber-complex music and play it--or to write a 12-bar blues--math is totally, utterly irrelevant. If I know that playing Em7 scale works with a D major chord, there is no math involved in learning that, my ear tells me that, just as playing an Ab+9 scale tells me its not not correct. Jeebus, enough with the "music and math" stuff already.

OK, I fibbed a little yesterday. I was trying to be a bit provocative. There's been some good examples of the use of algebra in every day life (I especially liked the "If your arts center wants to put on an opera--it made me feel all Mickey and Judy putting on a show in the barn!) and I've had to use that stuff in my job.

I suppose what my beef is is how kids are taught. I hated school--I mean, with the fire of all the suns in all the known universe, plus the other 10 or 11 string dimensions--and that's colored my attitude, duh.

In my ideal world, I guess, I would like to see these basics taught: basic math, reading, a smattering of history, civics and some science, maybe to an 8th grade level. Everything past that should be elective. If little Johnny knows he wants to make a ton of money as a CEO and hates art, then he shouldn't be forced to take an art class but through guidance be directed towards business oriented things. If someone is 15 and has no clue, *then* give them a plethora of options, i.e. "OK, Janey, how about you take some biology, some English lit, some this and that, and at the start of your senior year, we'll evaluate where you're at personally and make some adjustments".

Yes, yes, not a lot of people were as certain as me about their direction at such a young age, and yes, I had to do a full 360 career wise in my late 20's lest I end up like Keith Moon, but see, the thing is, by having that JC available to me, I was able to get the education I needed, when I wanted it. I think middle school and high school are horrible in their current formations, they actually *stifle* learning. I'll end by quoting these lyrics from one of my favorite bands:

But who can unlearn all the facts that I've learned
As I sat in their chairs and my synapses burned
And the torture of chalk dust collects on my tongue
Thoughts follow my vision and dance in the sun
All my vasoconstrictors they come slowly undone
Can't this wait till I'm old? Can't I live while I'm young?

Henry:

I suppose what my beef is is how kids are taught. I hated school—I mean, with the fire of all the suns in all the known universe, plus the other 10 or 11 string dimensions—and that's colored my attitude, duh.

I feel the same way, in fact music was my haven from 9th to 12th grades – and not because I had any natural talent. I was just enthralled and willing to work hard so I could enjoy being part of all the musical groups and make music. If I did have a natural talent it was in math and science, but I hated those classes – often mindnumbing and frequently taught by guys with egos bigger than the ocean.

On the music and math connection: I wasn't saying you needed math to do music or appreciate it, only that math can open up music to a different kind of understanding and creativity if you are interested in that sort of thing. You don't need much math to appreciate economics or biology either, but the more of it you know the more those subject have to offer. I, for one, would like to trade some of my math skill for the ability to sing harmony.

If children were so interested in learning, as some folks think, then they'd learn despite the bad teaching.

Does the average eighth-grader know what he or she will need to know? I think not.

Arun,

If children were so interested in learning, as some folks think, then they'd learn despite the bad teaching.

Forgive me, I have no idea what you are proposing but on the face of it this seems to be an ignorant remark. Please say more.

Yes, I could (and did...a long time ago). 10/10 for me.

I'm a legal secretary and I got a ten out of ten.

10 of 10, and I teach English! It was awfully easy (even if you didn't know the answers, it was simple to eliminate two choices).

If children were so interested in learning, as some folks think, then they'd learn despite the bad teaching.

It's hard to learn while you're being tortured.

That had better be 8th grade as in pre-algebra, not 8th grade as in Algebra 1 (which is required in 8th grade in an increasing number of schools). Because if those questions are supposed to represent the level of a typical Algebra 1 course these days, we're in even worse trouble than I realized.

Henry:

Is it better to buy or lease a car? How do you know? What's the difference between a stated and an effective interest rate? Which amortization terms should you choose for your mortgage and why?

If you have to choose between two different investments, how do you know which one will earn you more money?

What does it mean, practically, that the odds of winning a lottery are only 1 in 14 million?

Those are day-to-day examples of a minimum level of mathematical literacy which allows an artist to escape being taken to the cleaners.

Financial math, as a domain, doesn't require much more than 8th or 9th grade algebra but you can't do the math without the math, if you catch my meaning. And you can't understand even more complicated ideas without at least a basic appreciation of the underlying concepts.

I got the last one wrong. For some reason it just threw me. I have visual processing problems though, and too many "y" and "()" and "1/3" make some problems more difficult than they are.

Henry, if my words upset you, that was not their intent. If you laughed at them, it's okay. They laughed at Einstein and Bozo the Clown too. If all you want to do is to make children into things that make money, excuse me but I would rather poison you and all that agree with you with cyanide before I let you anywhere near an education decision. Education is not mercenary.

Beckham 'can't do son's homework'

ENGLAND captain David Beckham has confessed he is befuddled by his six-year-old son Brooklyn's maths homework.
...

I was an English major and scored a ten out of ten and my last math class was prob. and stat. back in 1990. I'm ready to go back to junior high.

Of course, I should have deleted that first "and." Just bubbly, I guess.