Katherine Valdes sent us a link to this newspaper column by Richard Cohen, “Math courses don’t add up.” He begins with a sad story about a high-school student in L.A. who dropped out “after failing algebra six times in six semesters, trying it a seventh time and finally just despairing over ever getting it.” He continues,
The L.A. school district requires students to pass a year of algebra and a year of geometry in order to graduate. This is something recent for Los Angeles (although 17 states require it) and it is the sort of vaunted education reform that is supposed to close the science and math gap and make the U.S. more competitive. All it seems to do, though, is ruin the lives of countless kids. In L.A., more kids drop out because of algebra than any other subject.
. . .
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 math can now be done by a computer or a calculator. On the other hand, no computer can write a column or even a thank-you note – or reason even a little bit. If the school asked you for another year of English or, God forbid, history, so that you actually had to know something about your world, I would be on its side. But algebra? Please.
. . .
I am not anti-algebra. It has its uses, I suppose, and it should be available for people who want to take it, but it should not be a requirement for graduation.
My reactions:
1. I’m not really qualified to give an opinion on whether algebra should be required. I don’t have a sense of what else is required, or how such a decision is made. I mean, my immediate reaction is that they should require math, English, history, science, and a foreign language–but then you have to find people to teach all these things, and maybe I’m missing something important.
2. I appreciate that Cohen things that algebra “should be available for people who want to take it.”
3. I think Cohen’s making some sort of fallacy in that, just because many people don’t need algebra, there’s no need to learn it in school. The real point is that many people use algebra, or could use algebra, for example even something as straightforward as understanding business forecasts. I would think that high school could give some people an opportunity to learn some of this stuff, then see if they want to go further.
4. In grad school, a friend of mine once commented that he had never had occasion to use imaginary numbers. I reminded him of this recently and he said the comment still stands. He’s a respected statistician who does top work, and I believe him. I’ve used imaginary numbers myself (having done some work in time series and spatial statistics, also my Ph.D. thesis had some Fourier analysis) but I agree that they’re not really necessary for most people, even most Ph.D. statisticians.
A totally preposterous article from a pretentious, self-admitted math hater.
If one has a breadth of knowledge, then there is certainly going to be things that are not used. However, that is not an argument against having that depth. The opponents of breadth that is not directly and immediately applicable (e.g opponents against nontechnical elective courses in technical majors) ignore the transformation of the student by that knowledge. I don't need to run three miles a week; I have a car, thank you. Therefore, all exercise is pointless. By a similar logic, having calculators saves you from doing or learning any algebra.
The US already has the most lenient education system in the developed world, the rest of whom are just dumb for teaching their kids stuff they won't need. As philosophers and logicians beg to differ, writing that kind of drivel is not the highest form of reasoning.
So, we've mostly learned that a) mathematics instruction at the high school level largely sucks (no big surprise there) and b) nobody at this high school cared enough to find out WHY this poor girl couldn't make it out in 6 tries (Sadly, also not a surprise).
This really has nothing to do with teaching algebra in high school. It just happens to be glaringly obvious when you start to hit maths where rote memorization ceases to be important that the kids aren't actually learning anything. The same thing is probably happening in, say, English classes its just less obvious for some reason.
Call me crazy, but I suspect we'd all be a lot better off if it was less about instructional minutes and more about, you know, teaching things. It doesn't really matter what's on the list if nobody's learning it.
In Britain we do it differently. Pupils do the General Certificate in Secondary Education (GCSE) in each subject separately. Getting 5 pass grades (A-C) is the median achievement and is seen as a benchmark. Obviously, the maths GCSE is a crucial subject and algebra is a part of that. I'm not a teacher, but I assume you could pass maths GCSE if your overall score was good enough, even if your algebra was bad. Or you could fail maths and still have GCSEs in other subjects. So there are arguments to be made about the pros and cons of requiring pupils to meet an overall standard of educational 'roundedness' versus specific subject skills. But even here, when you go for a job and employees see that maths is not your list of GCSEs you are going to be looked at unfavourably compared to those who do. It's a deep question that goes to the heart of what the outputs of the education system are supposed to be. Cohen's treatment of it was very superficial. Of course most people don't need all the algebra they learn. Nor do they need the foreign languages, the history, the geography (we have maps, don't we?) and so on. English does teach you to reason, but it teaches you to reason qualitatively. We also need our pupils to be able to reason quantatively and to use empirical data to suppose our arguments. It's worth noting that Cohen's argument makes very limited use of empirical data. He simply mentions that 17 states make a year of algebra a requirement for graduation. I wonder, is low maths content a general feature of his articles? He says "more kids drop out because of algebra than any other subject". Is it a lot more than the #2 subject or is it only slightly more?
A quote from Arnold Toynbee:
"At about the age of sixteen, I was offered a choice which, in retrospect, I can see that I was not mature enough, at the time, to make wisely. This choice was between starting on the calculus and, alternately, giving up mathematics altogether and spending the time saved from it on reading Latin and Greek literature more widely.I chose to give up mathematics, and I have lived to regret this keenly after it has become too late to repair my mistake… The choice I made was the wrong one, yet it was natural that I should choose as I did. I was not good at mathematics; I did not like the stuff. Looking back, I feel sure that I ought not to have been offered the choice; the rudiments, at least, of the calculus ought to have been compulsory for me… I was going to live in the Western world… and the calculus, like the fulrigged sailing ship, is one of the characteristic expressions of the modern Western genius."
If a student cannot pass calculus class after the sixth attempt, there is something wrong with either the student or the teacher. There is nothing wrong with calculus. Schools should not try to hide their failings by pruning the curriculum.
I think that we should have high school student not only be proficient in Alegebra but also Calculus.
The author of the piece fails to communicate a material point. Individual failure does not consititute a reason why a class of people should not be exposed to a subject. Using this logic what about reading and writing?
technically speaking, wouldn't they ALL be imaginary numbers? I mean, have you ever seen a REAL number in the flesh?
seriously though, I think a big problem with the teaching of algebra and other higher math is how theoretical it tends to be. I'm not a mathematician or statistician or scientist, but I use some form of algebra every day. the example in cohen's piece was stupid, but what about this:
you need to buy a new shirt for work, but payday isn't until tomorrow and all you have is a $20 bill. if sales tax is 4.375%, how much can you spend on the shirt itself?
x=amount you can spend on the shirt.
x + .04375x = 20
1.04375x = 20
x = 20/1.04375
x = $19.16
BAM! algebra!
(ps – I have…)
I find it incredible that the US expects to compete with the rest of the world by watering down their educational system to this extent. How can you compete in an increasingly technology driven world when your graduates can't even do high school alegbra or calculus. Without these basic maths, how can you produce engineers, doctors and scientists. IT's no surprise that a recent survey by the OECD ranked the US behind the Czech Republic in math and science skills. There was no surprise the Korea and Japan topped the list. You only need so many newspaper columnists and journalists will not make the US more competitive.
Personally, I feel if a student isn't smart enough to do simple algebra, she/he doesn't deserve to graduate from high school.
The high school diploma should be held to a reasonable standard or else its already diminishing value will just plunge further.
I think both Algebra and basic math skils should be taught in High School. I never had the chance to take Algebra in High School because I was in Special Education. My case Manager wouldn't let me. I have been able to taught myself some those. I think is important Algebra is taught to all that can benefit even if you don't ever use it again life. I'm college right and I'm taking algebra which I'm sturggling in but I'm slowly starting to understand the stuff. I'm not going to let this stop from earning a degree even if it takes me longer to earn. I think is important for Kids to remember there basic math skills. As for someone that can't grasp Algebra, why are they being forced to take over and over six times. It is a waste of tax payer money. They are trying at the subject then let them graduate even if they don't pass the class. I never liked math before but I'm wanting to learn Algebra even if I don't ever use it or even a lot. I think my High school under judged my math ability. In the basic math I was point into I was getting A. I had the chance to a math Alive course which was problem solving and it might had some Algebra in it. I didn't though out of fear.
Algebra is stupid we will never use it in our lives unless we are going to have jobs that require it.
Honestly, nobody needs algebra except those who teach it and those who use extensive theoretical math in their professions (like astrophysicists). There are people out there who absolutely love staring at numbers and manipulating. Some could be great at it, but due to ineffective or insipid teachers, never actually learn it. In any case, nobody should be forced to fill so much of their time on something they will never use. Business majors need to use basic arithmetic like addition, subtraction, division, multiplication, ratios, and percents. Doctors need medical training, not quadratics. Artists, writers, non-math teachers, journalists, and several others will need LOGIC, not Algebra.
Teachers don't help. Some grade like machines, most teach using dead methods, and almost all of them lose their students' trust (due to power trips, frequent pop quizzes, etc).
Basically, high school math today could be great if you're Einstein and can sort through all the vocabulary, excessive homework, unnecessary stress, and confusing haze that surrounds the dread subject of Algebra.
And Calculus is absolutely useless for most people too.
To me I think Algebra should be required in every state in order to graduate High school. No matter what job you teach or what future carrer you are planing to have you still need to know Algebra. Just like Writting/typing.
School is school dont be lazy try your best and shine. Im only Fourteen and hate doing homework shoot that's the only reson im on the computer but doing homework is recommened and a rule in school so just take time and do it. If you don't understand just ask for help mom, dad, sister, brother, or even teachers anyone will love to help out. I have no one so i just go on online websites and they help out alot.
Algebra, English, Science, any classes are all the same it's not hard if you just pay attention. That's one of my own weakness but i try my best. Nothing is pointless in school they wouldn't waste our time because if they waste our time they wouldn't want to waste their own time either.
Sincerly,
The Fourteen Year Old Teen.
N O ;
we should'nt have algebra in hish school!
it's a comeplete waste of time. we could be learning about something that we are going to use later in life,instead of something were not going to use.
To compensate for both sides.
Basic math mandatory elementary to middle school.
When high school comes down to algebra,geometry,and calculus.The student has to take algebra mandatory but Is not required to graduate.The student will take algebra,intensive math all that stuff till they pass it and do not have to take it anymore or take it till they graduate.The student must show strength in other areas.
Now if a algebra teacher has to many failing students should be moved down to a lower class,bring in a new teacher.
My algebra did not give a flying **** if we learned or not,he gave the problems with minimal explanation.
My intensive math teacher taught the same algebra chapter,and I got it in a matter of minutes,as to being two hours in my algebra class.
God help you if you need an equation to figure this one out.Why do you not know that retailers sell clothing items for $18.97 or maybe $18.99 or possibly $19.00. If you have any basic math skills you at all, work smarter not harder.
Algebra is useful…up to a point. To any rational person that uses logic effectively in their life, the thought of an imaginary number line along with two negatives equaling a positive, when multiplied together, is preposterous. The fact that kids are dropping out of school because of this illogical nonsense is even more preposterous. Of course parts of Algebra are fine. I have no problem with the foil method. Nevertheless I would like to see schools go back to a more relevant form of math which used to be taught when my father was in school. My father is faster than any calculator known to man. He was taught this in school. He can multiply and divide three digit numbers in his head faster than a whiz kid can type them into a calculator. What is happening with this so called 'new math' is so ludicrous. Fortunately there are many people who are smart enough to rebel against it. We happen to be the ones who ask the math professer how and why!!!!