Pharyngula

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'
.

Posted by: MYOB | February 25, 2006 8:04 PM

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.

Posted by: AndyS | February 25, 2006 8:34 PM

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."

Posted by: Bill Ware | February 25, 2006 8:47 PM

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.

Posted by: AndyS | February 25, 2006 9:14 PM

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

Posted by: Kieran | February 25, 2006 9:31 PM

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? ;)

Posted by: BlueIndependent | February 25, 2006 9:47 PM

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

Posted by: bmurray | February 25, 2006 10:44 PM

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.

Posted by: Henry Holland | February 25, 2006 10:55 PM

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.

Posted by: bmurray | February 25, 2006 11:01 PM

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...

Posted by: Coragyps | February 25, 2006 11:10 PM

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 – in a good sense – 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.

Posted by: AndyS | February 25, 2006 11:53 PM

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.

Posted by: benzene | February 26, 2006 12:14 AM

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.

Posted by: AoT | February 26, 2006 1:44 AM

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.)

Posted by: Michael "Sotek" Ralston | February 26, 2006 3:08 AM

"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! :)

Posted by: Anon4This | February 26, 2006 3:25 AM

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".

Posted by: Matt T. | February 26, 2006 4:04 AM

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.

Posted by: SEF | February 26, 2006 5:23 AM

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.

Posted by: ParanoidMarvin | February 26, 2006 5:51 AM

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 "2×5" or "x=2×5". 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?

Posted by: Ithika | February 26, 2006 7:17 AM

What the hell happened to my multiplication symbols??

Posted by: Ithika | February 26, 2006 7:40 AM

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

Posted by: Arun | February 26, 2006 7:49 AM

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.

Posted by: Troutnut | February 26, 2006 8:14 AM

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...

Posted by: rjb | February 26, 2006 8:34 AM

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.

Posted by: blah | February 26, 2006 8:46 AM

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?

Posted by: Ithika | February 26, 2006 9:19 AM

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.

Posted by: Skemono | February 26, 2006 10:07 AM

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. :)

Posted by: Ithika | February 26, 2006 10:19 AM

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

Posted by: Jason | February 26, 2006 10:32 AM

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.

Posted by: N.Wells | February 26, 2006 11:39 AM

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

Posted by: Skeptyk | February 26, 2006 12:03 PM