Is Algebra Necessary? by Andrew Hacker

[Dogpatch]

This topic reminds of a true-story humour line in Reader's Digest quite a few years ago.

This woman went to the cashier with her goods but the cash register broke down (for whatever reason).

Anyway, the young lady working the cash register looked at the woman and said, "I'll have to do this the old-fashioned way."

Now the woman thought the young cashier would take out pencil and paper and calculate the total in her head and on paper.

Nope - the young cashier brought out a calculator.

Apparently a true story

[Tory_canuck]

In high school, I passed math 20 Pure and Physics 20, but failed the 30 levels. In the place of math 30 pure, I took the math 30 applied so I could graduate.Math was never my strongest subject.I excelled in social 30 and English 30-1 though. Some people are stronger in other areas than others. Although Math is not my strong point, I still posses basic mathematical skills in trig, percentages, calculations, and such.quadratic equations are not used very often. Most of the math I have used involved calculating hose lengths or converting pounds to kilograms in a warehouse of heavy duty truck parts, or calculating post judgment interest in a lawsuit at a law firm.

[Number 6]

What we need is a return to education, and not lieberal indoctrination. The trivium and quadrivium need to be brought back in full force. Not everyone of course has the same gifts, talents, and skills, but with hard work and determination, is it that hard to rise above mediocrity? It is a matter of training the mind at an early age, along with discipline and all those things which the older generation (shall I say 40 plus) were still being taught?

I didnt care for math as a kid but I loved science. But my gifts were in the humanities more than hard and applied sciences. Thanks to a rigourous philosophical and theological education, (the development of critical thinking and logic) math and science became much easier to understand. I still enjoy physics, esp astronomy, and for other reasons, ballistics. (How much energy is produced by such and such a calibre with x amount of grains fired from y weapon, which will impart z on a target at distance d.)

Alas we have a generation of twitters and glued-to-phones/pods/pads who cannot count, make change, write properly or even speak properly. If I was given a tongue depressor for every time i heard the word "like" uttered incorrectly, usually by a vapid headed teenage of the female variety, build me a kwai over the river bridge I could. As for profanity, sweet fuddermudders, the stuff you hear these days my cod my son my halibut basket........

Is all people want panem et circenses? If so, I am cheering for the lions.

"Is that a pair of courderoys walking away from us? No, just a pair of regressive jeans."

[BlawBlaw]

I think the people having a field day in criticizing the OPEN article really need to read it again, and perhaps work on their own practical literacy skills. He specifically says he is not talking about basic numerancy or arithmetic skills but rather abstract algebraic manipulations that few people require in their daily lives, whether at work or at home.

Sure, society can always use more engineers (although you have to keep in mind that quantitative skills are also necessary for many parts of social sciences as well) it doesn't make sense to force students through courses that they have no aptitude for, to try and teach skills they will never use, and then derail them from pursuing studies and careers that they are rather handy with.

Not everyone needs their grade 12 course of study to be a "Hong Kong Six Pack" (three mathematics and three sciences). It behaves parents to instill discipline and drive their kids to reach their potential when basket weaving is easier than calculus, but the system shouldn't be designed to create failures. You can't make a silk purse out of a sow's ear so forcing it on everyone will not be productive in most cases.

One thing the author got wrong is with respect to the SAT scores. The actual skills required for the SAT are rather modest. Given time, anyone proficient with grade 7 math can work out the answers. However, time is what you don't have when you write the exam. It doesn't test your mathematical skills per second but rather the ability to perform the calculations quickly and accurately under pressure.

[The Gooch]

I sure hope the Engineer who builds the engines for the airplane I am flying in doesn't have their bar lowered. Just sayin'.

[RadicallyLiberal]

The problem being, without a competent introduction to algebra, you don't just level off current high tech & theoretical student numbers, you will heavily reduce them. Until children are introduced to them, you never know their aptitude.

I had teachers who obviously hated math and were incompetent in teaching it. I had to teach myself over a 15 month period between graduating Grade 8 and going into Grade 10. I had no teacher interested in my learning or even assisting me. I bought every math textbook for my age level and teachers guides that I could afford, from paper route money and mowing lawns. That is unrealistic for most kids and shouldn't have to happen.

Only reason I am in tech, is MY initiative, in spite of my public education.

Government schools, indeed. Breeding ignorance and mediocrity, one student at a time.

[BlawBlaw]

The problem being, without a competent introduction to algebra, you don't just level off current high tech & theoretical student numbers, you will heavily reduce them. Until children are introduced to them, you never know their aptitude.

I agree with that generally, but the same logic can apply to many fields of study while at grade 12 you have six that are considered for university entrance and maybe 8 or 10 that you can finish in one regular school year. Grade 11 science should have introduced students to chemistry, physics and biology such that they know their strengths and weaknesses before their final year; same with math (although it seems to be broken down differently than when I graduated: calculus, algebra, relations & functions).

[RedDog]

I sure hope the Engineer who builds the engines for the airplane I am flying in doesn't have their bar lowered. Just sayin'.

Similar ballpark - Remember Air Canada and Gimli? Mathematical conversion error. Oops. That one could have gone a lot worse. Firstly the pilot was an experienced glider pilot, requiring techniques not generally used by commercial pilots; and he had served in the military at that former base and both knew of it in the first place and knew the former landing strip, if still there, was aligned the desired direction for his silent approach.

http://en.wikipedia.org/wiki/Gimli_Glider

[Kate Shaw]

No, they are multiplication. No XY/CD = (2X)(4)-Y squared involved.

Multiplication is a subset of algebra.

For example the 20% discount, that means multiply the price by 4/5. How do you think I know that?

I suppose there's no need to know that, you can ask your iphone.

I don't have an iPhone, and why bring fractions into it? (Fractions are not algebra either.) Move the decimal point one place to the left and multiply by 2. What's hard about that?

Calculators, incidentally, do not help math dunces do math. They merely make it possible for us to be stupid much more quickly. If I am trying to multiply 36 x 12 on a calculator and my answer is 327, how do I know if that's right or wrong? (It's wrong, actually.) It is entirely possible and in fact, usual, for me to multiply two numbers five times and get five different answers. Often none of these answers is correct. And I could swear I'm punching the buttons exactly the same way each time. Ditto adding more than two numbers of more than two digits. The calculator does only what I tell it to do, not what I want it to do. Unlike Google, which when I type Frx Neqs, it asks "Did you mean FOX NEWS?" Invent a calculator that does that, and I'm saved.

P.S. Teachers have already decreed that spelling, punctuation and grammar are unnecessary and should be suborned to "creativity" and "self expression". Good luck with that.

[DA_Champion]

I think the people having a field day in criticizing the OPEN article really need to read it again, and perhaps work on their own practical literacy skills. He specifically says he is not talking about basic numerancy or arithmetic skills but rather abstract algebraic manipulations that few people require in their daily lives, whether at work or at home.

Sure, society can always use more engineers (although you have to keep in mind that quantitative skills are also necessary for many parts of social sciences as well) it doesn't make sense to force students through courses that they have no aptitude for, to try and teach skills they will never use, and then derail them from pursuing studies and careers that they are rather handy with.

Not everyone needs their grade 12 course of study to be a "Hong Kong Six Pack" (three mathematics and three sciences). It behaves parents to instill discipline and drive their kids to reach their potential when basket weaving is easier than calculus, but the system shouldn't be designed to create failures. You can't make a silk purse out of a sow's ear so forcing it on everyone will not be productive in most cases.

One thing the author got wrong is with respect to the SAT scores. The actual skills required for the SAT are rather modest. Given time, anyone proficient with grade 7 math can work out the answers. However, time is what you don't have when you write the exam. It doesn't test your mathematical skills per second but rather the ability to perform the calculations quickly and accurately under pressure.

I remember taking the SAT... it's only been a decade. They use the exact same algebra that the author is decrying in the article, for example, I found this via google images:





The skills the author is decrying in the article are basic math skills, high school level math skills like those in the above two questions. It's important to realize that at that age kids don't know what they want to do, so you can't start closing doors. When I was 14 I wanted to become a politician or historian. Kids need time to find out what they're good at.

A large part of the reason that economists, biologists and sociologists don't use math that is as advanced is simply that they are less competent at math. If their abilities improved, they would use more math and the achievements in those disciplines would rise. That's apparently been the trend in biology recently.

[DA_Champion]

I don't have an iPhone, and why bring fractions into it? (Fractions are not algebra either.) Move the decimal point one place to the left and multiply by 2. What's hard about that?

It's just good to use fractions as it is to multiple by 2 and move the decimal.

Kate, if you had been blind your whole life you wouldn't understand what the value of vision was, as you would have figured out how to get by without vision. People are resourceful and make do with what they have. If they have more they often do better.

Anybody who writes computer code has the same problem you have calculator. Invariably, if you write a semi-complex code, heck even a trivial code, there will be bugs in it when you first use it. It won't do exactly what you wanted to do. The only way you can identify those bugs is if you're thinking.

[Gerry T. Neal]

The importance of knowing fractions lies in the fact that not all fractions can be precisely converted into the decimal system. You have to round up or down when you divide something into a number of parts which cannot be converted into tenths or hundredths. Of course the fraction system has its limitations too, i.e., irrational numbers like pi, (the fraction 22/7 is to pi, what 1.67 is to 1 2/3) but the limitations are less than the decimal system, which does no better of a job with irrational numbers (3.14159265358979324 and on to infinity is hardly practical).

[Gerry T. Neal]

Re: the actual topic of the thread

The three r's used to be reading, writing and arithmetic. It has been almost a century since most schools eliminated Greek and Latin from reading and writing, then came the era of television and film which was not exactly beneficial to English reading skills, followed by the age of internet messaging and cell-phone texting which has done for English writing skills what films and TV did for English reading skills. The author of the article wants to eliminate algebra from the math curricula. The next step will be the elimination of basic arithmetic.

[BlawBlaw]

I remember taking the SAT... it's only been a decade. They use the exact same algebra that the author is decrying in the article, for example, I found this via google images:

I was just looking at practice exams and those sorts of questions are maybe one out of 10 questions.

It's important to realize that at that age kids don't know what they want to do, so you can't start closing doors. When I was 14 I wanted to become a politician or historian. Kids need time to find out what they're good at.

You are 14 in grade 9. By the time you have to pick your college entrance courses you have had three years to figure out what you are good at, with science, math and english all being mandatory.

A large part of the reason that economists, biologists and sociologists don't use math that is as advanced is simply that they are less competent at math. If their abilities improved, they would use more math and the achievements in those disciplines would rise. That's apparently been the trend in biology recently.

I don't know about biology but there are large swaths of economics and other social sciences are are math heavy, particularly in statistical analysis. Some people like Levitt - of Freakonomics fame - can get away with having weak quantitative skills, but if you read most economics papers in full, they get into the mathematical justification for their conclusions. Same same with other areas of social science research that use multiple regression analysis and related techniques to tease out the relationship between various factors (one that comes to mind is looking at the gender wage gap and the factors that influence it).

[DA_Champion]

I was just looking at practice exams and those sorts of questions are maybe one out of 10 questions.

Do you mean 1 out of 10 questions or 1 out of 10 non-geometry questions?
The original article said top schools required a 700/800, so you need to get some of those to get in.

You are 14 in grade 9. By the time you have to pick your college entrance courses you have had three years to figure out what you are good at, with science, math and english all being mandatory.

A lot of people switch majors in college. Possibly most.

I don't know about biology but there are large swaths of economics and other social sciences are are math heavy, particularly in statistical analysis. Some people like Levitt - of Freakonomics fame - can get away with having weak quantitative skills, but if you read most economics papers in full, they get into the mathematical justification for their conclusions. Same same with other areas of social science research that use multiple regression analysis and related techniques to tease out the relationship between various factors (one that comes to mind is looking at the gender wage gap and the factors that influence it).

I use multiple regressions. It's not that advanced -- a few lines of code. More precisely, people learn multiple regression in second year undergraduate courses.

Far harder than using multilinear regression is knowing which variables to pick, how to parameterize them (it's not always linear), how to deal with the errors, the correlations in the errors, and sample bias. What do you do when there are too many free parameters? That's when you're at risk. For that, you need to be able to visualize in your head.

In my experience there's no minimum bar for proficiency. If you know a little you do a mediocre job. If you know more you do better. Modelling is a skilled art. There's no floor or ceiling, and thus there is benefit to people being as proficient as possible.

It's like language skills. There's no floor to what language skills you'd like the next generation to have, nor is there a maximum beyond which nobody would benefit. We should be asking how best we can develop our youth's language skills. Similarly with mathematics.