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Richard Cohen on Algebra, "Meh".

Dylab

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There is a somewhat widely circulated column out by Richard Cohen on the L.A. school district's requirement for students to have a year of algebra and a year of geometry. http://www.washingtonpost.com/wp-dyn/content/blog/2006/02/15/BL2006021501989.html

Cohen discusses the story of Gabriela Ocampo who dropped out of highschool after failing algebra six times. I'm sympathetic although I'm not without my suspicions. In a unparalled level of stupidity Cohen derides the requirements in part by saying,

Here's the thing, Gabriela: You will never need to know algebra. I have never once used it and never once even rued that I could not use it. You will never need to know -- never mind want to know -- how many boys it will take to mow a lawn if one of them quits halfway and two more show up later -- or something like that. Most of math can now be done by a computer or a calculator.
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I don't think it is neccesary to explain why this comment is dumb. (Here at least.) I'm curious what your thoughts on the whole situation is.

Here are a couple blog links.
http://scienceblogs.com/pharyngula/2006/02/richard_cohen_advocate_for_ign.php <PZ Myers attacking the comment

http://scienceblogs.com/ethicsandscience/2006/02/algebrahating_and_societal_pro.php <Speculative diagnosis on the issue.
 
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So this guy doesn't do his own taxes? He doesn't know how to figure out how many miles per gallon his car gets? There's no way he can understand a credit card application, or figure out loan payments.



I am not anti-algebra. It has its uses, I suppose, and I think it should be available for people who want to take it.
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That's one of the dumbest things I've ever heard. Just mind-boggling. How does this guy think the world works? Who programs those computers? Who teaches him how to use his calculator?

As for his examples of algebra-savvy students who couldn't write, I'd like to point out to him that most scientists (who usually take math up through Calc II at the least) have more publications in peer-reviewed journals than he does with all his typing skills.
 
To add:

In the fall of 2004, 48,000 ninth-graders took beginning algebra; 44% flunked, nearly twice the failure rate as in English. Seventeen percent finished with Ds.
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From an LA times article. Which mentioned that 2004 was the first year that students were requried to pass algebra and geometry before graduating. Why were we graduating students before 2003 who couldn't pass basic math classes? Oh, it can't just be LA. I have in front of me 20 labs from first-year engineering students, showing appalling algebra skills, no calculus whatsoever (although it was a requirement for this course), and, at times, poor writing and communication skills.

Sometimes I wonder if I went to the only high school in the nation with expectations of it's graduates beyond the ability to walk across the stage and successfully intercept a piece of paper.
 
How the bloody do they teach algebra to get such a high failure rate? High school algebra ain't rocket science...
 
There is nothing more infuriating than the ignorant preaching the value of their ignorance.

It may be true that you can get by in life without needing to know algebra. But you can also live without knowing how to read. The real question is - does the effort required to learn algebra have a sufficiently good payoff?

In my opinion, the answer is yes, for many reasons:

a) Learning anything exercises the brain, which in turn allows you to learn more easily.

b) No knowledge is useless.

c) Those who possess knowledge will constantly see applications for it; those who lack knowledge may deny that these applications are valid.

Note that none of the above is algebra specific, of course. Here's some specific reasons:

i) Engineering and science disciplines are math-based. They are also well paid, desirable, and prestigious professions. Therefore, learning higher mathematics (I'd really include calculus here as well) is a portal to a better job and a higher standard of living. This is the "pragmatic" reason - regardless of whether computers can solve all mathematical algebraic problems or not, universities offering engineering or science degrees will want you to be able to demonstrate mathematical proficiency. As a computer programmer, I am highly skeptical of this claim - certainly packages like Mathematica are very good, but I don't see an algebra-novice making head nor tails of such programs - you still need to know what an equation is in order to get a computer to solve it.

ii) Algebra is useful for all forms of finance. It is a boon when budgeting; it helps to figure out where the bargains are when you're shopping; it will let you know how much time you'll save on paying off your mortgage if you make a lump sum payment.

iii) Algebra can save you money. Yes, you might be able to buy computer programs that will help with the options in ii, but if you understand algebra you can figure it out yourself.

iv) Algebra - and mathematics in general - is just plain fun. For those who disagree, I'm wondering if there might be a way to improve the teaching of it so that you would come around.

I find a use for algebra, calculus, trigonometry, probability theory, and so forth frequently. If you understand these techniques, your eyes will be opened to applications for them. If you wilfully remain ignorant, then there are none so blind as those who will not see.
 
About ten years ago I tutored my mom through algebra. It was an uphill battle for both of us, me trying to get through to her that she was not, "stupid," and her to even do this stuff. We actually had a huge fight about this. I was still in high school and doing Calculus and she asked me, "Why do I need to know this?"

This woman used to give me her used Dell puzzle books after she was done. She ripped out the answer key and tossed them before starting them. In doing the logic problems and the "word arithmetic" (one "word" divided into another with each letter representing a digit), I got enough of an introduction to Algebra that it was pretty easy for me.

"The reasoning." I told her.

She still doesn't understand that that's what she was doing all those years. She can do her taxes, she can do her algebra classes now and get As without my help, but I don't think she's made the connection yet.

*sigh*

(1/2 of thoughts. It's bedtime.)
 
Well, neither of my parents can do algebra and they get along fine. The taxes get paid, the loan applications are understood, gas milage is calculated, etc. It's absolutely false that you need algebra to get by.

Now, as to why you might want to teach algebra, is because it increases your potential in life. My dad held a respected, responsible position in the town, but there was not way he could become, say, and engineer. That happened to align with his interests anyway, so it was no loss to him. Prior to this he worked as a carpenter, and there were a few times he came to me to solve a math problem for him, but again, there are a large number of rules-of-thumb that can be used to solve most problems without math. If I wasn't there, he could have gone to somebody else, or worked it out by trial and error. yes, in that case he would have been better off knowing it, but some people just don't 'get' math. It'd be unfortunate if my father didn't get a high school degree - as smart as he is (he's developed curriculum for the state, for example), I doubt he could have passed algebra.
 
Mathematics is problem solving. The numbers, the variables, the expressions - they are simply a way of formalizing the process.

It sounds as if your father did get math - he just didn't get the number/algebraic symbol part of it. I'm not a teacher, but I wouldn't be at all surprised if it wasn't possible to vary the teaching method to breach this apparent gap.

In any case, I'm not sure what the situation is in the US, but year 10 (the final compulsory schooling year) in Australia has always required algebra and geometry. In fact, I believe introductory calculus is now at a year 10 level. I don't believe this is because kids are getting fundamentally smarter - it's just that the advent of calculators means that you can, to some degree, cut out some of the drudgery problems and cover more of the harder stuff.
 
Perhaps. I do recall tutoring my mother when she was getting her GED (she dropped out in 8th grade), and was never able to teach her Algebra. I think my teaching skills were pretty good, as I was a student math tutor at the time. But it is telling that other countries have these requirements. Tell me, is it required to pass algebra and geometry to graduate, and, if so, is the grading 'lenient' down in the D range to help students get through if they don't get it? My uninformed opinion is that probably most anybody can squirm through a course with a D as long as they are trying hard. The end result is that they "pass", though it can't be said they understood the material. That reflects my high school experience - an A counted for something, a D meant you were trying, but not suceeding. F was reserved for people who absolutely didn't try to learn.
 
p.s. in general, calculus is reserved for 12th grade, and only for those who are in an advanced track. It is absurd, I taught myself calc in 10th grade, and was doing junior (college) level by 11-12 grade. I don't think that is anything special; I had a friend who came over here from France to major in math and said it wasn't until his Junior year in college before he started seeing stuff that hadn't been covered in his high school.

We seem to have horrendous levels of duplication in our lower levels. For example, we learned to multiply 3-4 digit numbers together in 3rd grade. 346*761, that sort of thing. Yet in 5 grade, I recall weeks spent on multiplying 3 digit numbers, then 4 digits, then 5, etc. Egads, if you can do 3 digits, you can go n digits. What a waste of time. We did learn more in 5th grade, but there is just a lot of repetition.
 
roger said:
Tell me, is it required to pass algebra and geometry to graduate, and, if so, is the grading 'lenient' down in the D range to help students get through if they don't get it? My uninformed opinion is that probably most anybody can squirm through a course with a D as long as they are trying hard. The end result is that they "pass", though it can't be said they understood the material. That reflects my high school experience - an A counted for something, a D meant you were trying, but not suceeding. F was reserved for people who absolutely didn't try to learn.
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That's a good question.

Without seeming to appear arrogant, I've never been a D student at anything, so I really couldn't say. In Australia, you can leave school at any time after your 15th birthday - there is no requirement to graduate, but if you don't, you will find some options curtailed (though of course we have adult education programs to allow people to go back later in life and graduate, or finish upper school).

If you want to go on to upper school (year 11 and 12), you probably need at least a passing grade in mathematics, science, english, and social studies (a catch all that lumps in a little geography, a little history, a little economics, and a little politics). Whether that is a D or a C, I couldn't say - and you also need to keep in mind that I'm 33 now, so my high school days are a fair while back (though I doubt things are any easier - quite possibly the requirements are a little more stringent now).

Kiless would be a better person to ask, as she's a high school teacher. I'm just the mug that married her. :)
 
roger said:
p.s. in general, calculus is reserved for 12th grade, and only for those who are in an advanced track. It is absurd, I taught myself calc in 10th grade, and was doing junior (college) level by 11-12 grade. I don't think that is anything special; I had a friend who came over here from France to major in math and said it wasn't until his Junior year in college before he started seeing stuff that hadn't been covered in his high school.
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Keeping in mind that it's been a while since I was at high school, as I recall we didn't do any calculus at year 10 or earlier. Year 11 and 12 we certainly did, but at that point you are technically able to avoid doing any mathematics whatsoever.

"Back when I were a lad", there were 3 levels of "upper school" mathematics. You could do Applied Mathematics, which I understand was basically just a revision of lower school stuff, perhaps with a little trigonometry thrown in. Then there was Maths I, which had differentiation, a little trigonometry, and some basic linear algebra. The highest level (which is what I did) was Maths II/III - a double unit, in effect. We covered calculus including differentiation, the fundamental theorem of calculus, and basic integration; trigonometry including some simple proofs; linear algebra (I think we were introduced to matrices, but I cannot be sure - certainly we never did anything with dot products, cross products, or determinants); and a fair few geometric proofs, algebraic equations for lines and surfaces, and "related rates". It wasn't until first year uni that we did Taylor series, vector spaces, or partial differentiation. I understand that the top mathematics units in upper school now touch on at least matrices and Taylor series - but again, it's been a fair whack since I was at high school.

We seem to have horrendous levels of duplication in our lower levels. For example, we learned to multiply 3-4 digit numbers together in 3rd grade. 346*761, that sort of thing. Yet in 5 grade, I recall weeks spent on multiplying 3 digit numbers, then 4 digits, then 5, etc. Egads, if you can do 3 digits, you can go n digits. What a waste of time. We did learn more in 5th grade, but there is just a lot of repetition.
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I'm certainly not trying to suggest that the Aussie system is better, or anything. Calculators are allowed into class at primary school level now (I wasn't allow a calculator for mathematics even in year 12, though we could use them for our final Physics and Chemistry exams). There are many Aussie teenagers that probably could not multiply two 3 digit numbers without a calculator, or perform long division. I feel this to be a bad thing, but I'm possibly being overly picky here.
 
Reliance on calculators is a bad thing - you don't know how to calculate anything if you don't have a calculator, and you don't develop the ability to do rough estimates in your head or be able to tell whether the result of a calculation is plausible.

Also, you don't develop an understanding of structure or meaning of a calculation or its operations.

I wouldn't allow a calculator in any math class from grade school through college.
 
Complexity said:
I wouldn't allow a calculator in any math class from grade school through college.
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We had $120 graphing calculators in my algebra classes. Learning to use them properly is also necessary. Those big buggers are complex--have you seen the instruction book? It's over an inch thick!

But if you couldn't do the equations on paper, you couldn't figure out how to do them on a calculator, or at least, that was my experience.

At any rate, we weren't allowed to use them on tests--any tests, including the big ones administered by ETS, like the Praxis I (general knowledge, including math and science). If you hadn't learned how to do the operations, you would be bugger-all on the test, where it really counts. So having a calculator in class wasn't the path to easy street one might imagine.

It depends on how the instructor uses them. Great for homework, but not at all used on tests. That seems about right to me.
 
Complexity said:
Reliance on calculators is a bad thing - you don't know how to calculate anything if you don't have a calculator, and you don't develop the ability to do rough estimates in your head or be able to tell whether the result of a calculation is plausible.

Also, you don't develop an understanding of structure or meaning of a calculation or its operations.

I wouldn't allow a calculator in any math class from grade school through college.
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I use a calculator all the time, I do in fact rely on it, but I can also do any of the calculations I use that calculator for on paper if I didn't have access to it. Someone can be aware of the method by which it works even if they are spoiled by a calculator. I'm talking a simple one though. I'm not sure how screwed up one could get doing higher math using a more advanced calculator than what is provided in Windows :D. As to how quickly I could do that math, well, I've never been good at memorizing numbers at all, so no, I have not memorized the various tables I was expected to in school. I'd be doing it all manually.
 
Its official Complexity isn't allowed to teach math, ever.

Just out of curosity what it is your education and job background?
 
On a similar note Ted Rall wrote in an op-ed piece related to the number of people from other countries that are filling engineering and science postions in the US. Ted went on degrading these technical fields essentially saying that the jobs were horrible anyhow, so let expats take them. (he gave some anecdotes about himself taking physics in college and a friend working in the defense industry)

I wrote him an email asking him to turn off all the technology designed by engineers and see how long he could survive, e.g. try turning off the electricity first. I then remarked that I could live without political commentary for a very, very long time. He never replied.

I do have alot of students that can't make rough estimates. Whatever value the calculator pops out, they put down. (missing a bracket on a TI calculator can really mess up the results) I rely on my calculator as well, but I can usually tell if I punched something wrong by the end result. Learning with a slide rule may have something to do with that.

Of course we have computers to do that stuff now, but someone has to know the design basis and someone has to program them.


glenn:boxedin:

We live in a society where it's considered okay for intelligent people to be scientifically illiterate.


<O:pLawrence M. Krauss</B>
 
Calculators are only good to speed up computing trig functions when the angles are given in degrees...

/what other uses could they have?
 
Dylab said:
Its official Complexity isn't allowed to teach math, ever.

Just out of curosity what it is your education and job background?
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Ph.D. in Computer Science, Northwestern University
M.S. in Computer Science, Northwestern University
B.S. in Computer Science, Mathematics minor, Northeastern Illinois University
B.A. in English Literature, Mathematics minor, University of Illinois at Urbana-Champaign

Three years as a Computer Science teaching assistant and instructor (one term) at Northwestern University
Five years teaching Computer Science at the university level after Northwestern.

The last two years of teaching were at a university whose math department was going through hell regarding calculators. They were nearly evenly split on the use of calculators in the classroom.

They eventually opted for allowing graphing calculators to be used in all math classes and on all tests. Students were allowed to use the calculators for derivation and integration - I am certain that few of them learned any calculus to speak of, regardless of test scores or grades.

For the record, I'm a damned good teacher. :)

I got out of teaching and have been developing software for the past ten years. I'm currently a rules systems architect at an insurance company.

Much of my spare time is spent developing algorithms for challenging problems.
 
Jorghnassen said:
Calculators are only good to speed up computing trig functions when the angles are given in degrees...
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Speeding up computing trig functions when the angles are given in radians? Or can you calculate the sine of six-tenths of a radian off the top of your head?
 
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