Is Algebra Necessary?

New York Times ^ | July 28, 2012 | ANDREW HACKER

[reaganaut1]

A TYPICAL American school day finds some six million high school students and two million college freshmen struggling with algebra. In both high school and college, all too many students are expected to fail. Why do we subject American students to this ordeal? I’ve found myself moving toward the strong view that we shouldn’t.

My question extends beyond algebra and applies more broadly to the usual mathematics sequence, from geometry through calculus. State regents and legislators — and much of the public — take it as self-evident that every young person should be made to master polynomial functions and parametric equations.

There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic. (I’m not talking about quantitative skills, critical for informed citizenship and personal finance, but a very different ballgame.)

This debate matters. Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.

The toll mathematics takes begins early. To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.

[JLS]

You are confusing capacity for abstract thinking with wanting to learn. When you have a class full of people who can learn everything about the operation of their smart phones, you have people who certainly have the capacity to learn algebra.

It is just a matter if they will put in the effort to learn algebra that the put into learning how to use their smart phone or how to play a particular video game. Part of teaching is to give exams that motivate them to learn enough so that they can move on. One of the things education does is separate out those who are willing to do what is necessary to have a better life from those who do not care enough.

[Vigilantcitizen]

My best friend of almost 40 years is a carpenter and owns his own contracting business, raking in around 3oo g’s a year with his 10th grade education.

There is no need to teach him to use geometry to find C when he can do so much faster with a framing square. Algebra isn’t needed to figure square footage or payroll.

[GladesGuru]

“Elementary algebraic topology would be a good substitute.”

Why not require the following as an alternative?
“Analytic and algebraic topology of locally Euclidean parameterization of infinitely differentiable Riemannian manifold”. Offer it in two semesters, as courses 101 and 102.

[Chewbarkah]

Dumbing down requirements until no one fails is a pathetic plan and just avoids reality.

The US refuses to “track” students who display no aptitude for “intellectual education” into vocational or technical training, or anything that might make them employable. It is a fact of life that half the population has an IQ on the down side of 100, but many children who are not geniuses have valuable lives, skills, talents and a great deal to offer. Why can’t we spend resources on training that is relevant to their aptitudes and lives? We are too proud and too PC to admit the obvious, much to the detriment of public school students and the nation.

That said, most children can learn basic mathematics if the subject is taught competently, and as others have written, learning math is mostly a matter of discipline over time. (Even computer math-learning software works if used properly). The US is far behind many “Third World” countries in math and science education, mostly because we set low standards and have too many incompetent teachers. Most, though not all, decent paying jobs seem to be in fields that do require math skills. Too many adults in America can’t even do their own tax returns, understand the falsified unemployment stats, etc.

[lonestar]

I still don’t know how to diagram a sentence. Completely useless, even to those who have plans to write as a career.

I couldn't diagram a sentence today...but I could when I was a 6th grader.

One method of teaching lauguage to the deaf is basically the same as diagramming sentences. They learn words as nouns, pronouns, verbs, adverbs, etc.

Diagramming a sentence would be useless in today's rap society.

Spll-chck is uslss to mst ppl!

[SpaceBar]

It is not necessary to know that the contour integral about a function analytic in the plane except for a finite number of isolated singularities is two pi i times the sum of the enclosed residues to flip a burger. To design a decent digital filter yes, to flip a burger no.

[Reily]

chess champion — then you used algebra (and higher mathematics!) and didn’t know it!

[Chode]

guess i don't understand the question

i know how to solve problems but guess i don't necessarily know when i am using algebra...

trig is mostly plugging in values into SOHCAHTOA

stats is, well, stats

and physics has the required formulas perfected where the hardest part is knowing which one to use and then plugging in the variables

for the things i used them for anyway...

i passed algebra one and two but like i said, i guess i just don't know when i'm actually using it since it never looks in real life like it did in class

[ladyjane]

How can you understand statistics if you don’t use algebra? Sure, you can plug numbers into formulae but to really understand what you’re doing it seems you’d need at least some basic algebra.

[Blagden Alley]

I came to the conclusion fairly early that it is the rigor of what is taught, and how well the assigned math is taught that is most important.

I had rigorous Algerbra, Trig, Physics, and so on in high school. No calculus, but tough problems. Hit a college in NYC where half my math year was Regis Prep School grads. Epsilon and Delta day one. Fit right in.

Did grad school until Uncle Sam gave me chance to join the Air Force, and remembered that in my last semester I sat next an 18-year old from Brooklyn College whose goal in life was to solve a word problem. Fell in love with computers in the AF and stayed in it.

Love math, but like many other things, too. Probability knowledge is handy for calculating pot odds, though.

[central_va]

People who are good at math have strong deductive reasoning skills. They are natural conservatives and for the most part not intellectually lazy. That is why liberals hate mathematics. That’s it in a nutshell.

[rbg81]

My take is that people can major in whatever they want to. But, somewhere along the way, someone should counsel them on the probablility of making $X/year with degree Y. If, after that, they still want to pay the $$ for a meager return, its up to them.

I’m a computer science professor, and I constantly see kids leaving the major for “easier” ones (like Elementary Education). For some, it’s a good decision because they can’t hack CS. For others, it’s sad because they can do the work, but just don’t want to.

Even a history major CAN learn skills that can help them in any number of jobs—the most important being how to think critically and communicate. Unfortunately, too many degrees have become dumbed down vehicles for political indoctrination.

[Carriage Hill]

Nowadays, too many kids are being raised by “A Village”, instead of ***Parents***.

[Dr. Sivana]

"Algebra is not impossible. We need to come up with more creative, practical ways to teach it."

You sound like a smart person. Do you really believe you can teach it over the IQ range 75-95?

That wasn't my quotation. But, I would say a motivatd low intelligence person can still learn to graph y=x, y=x*2, y=1/x with suitable effort. If not, maybe that person shouldn't be granted a high school degree. When degrees are handed out for compliant behaviour rather than academic achievement, the nature of the institution and the value of the degree is degraded for all.

[Reily]

All algebra is, is the manipulation of symbols to an end goal subject to a grammar (a body of logically consistent rules!). If you write computer programs you use an algebra. I argue also if you write grammatical sentences in a natural language you use an algebra. (Yes arithmetic is an "algebra"!)

You actually don't have to physically write anything down to do algebra, does Stephan Hawking write anything down? (Yes he uses algebra, the high school version as well as the other more abstract algebras.) I am sure he does some mental “algebra” to check his ideas before he communicates to his assistants.

[dsrtsage]

Algebra is easy and I can prove it. There are two reasons for student troubles, one is bad teachers, and the other is mental blocks (the “math is hard” meme).

Story #1 (bad teaching), my friends kid was in town (from a supposedly very good school system). He is fairly good at math, but was absolutely cratering in one area in his algebra two. This was in graphing rational equations (basicaly stuff like (X-2)/(x^2 + 2x +1) kind of stuff. Granted, I had done nothing of the sort in over 25 years, so I thought about it for a few, and came up with a plan to show him. I first asked him how the teacher explained how to do it. He rattled off the most ridiculously overly complicated list of nonsense I have ever heard. I then show him...first solve both the numerator and the denominator for x...where the numerator is zero that is where it crosses the Y axis, where the denominator is zero, that is where it approaches infinity. Then on either side of zero and infinity determine whether the whole function is positive or negative, and draw accordingly. After one or two examples of this he looked at me and said “It’s this easy, really”, I said “yes, really”, he said “My teacher spent weeks and weeks unable to explain what you taught me in 5 minutes”...I made him do all of the problems, which he had no problem with...then to make sure he had it I created a few and had him do them the next day...then I instructed him to teach his buddies who were also having trouble when he got home. Having him teach it, would cement it for him. Needless to say, he aced it when he got home.

Story #2 (Mental Blocks), I used to tutor all levels of university math when I was in school for extra money. One of my students was a very very stereotypical blonde sorority girl who was absolutely failing college algebra and was completely desperate. For the first two weeks it was pure hell. I tried in every way to make her understand even the simplest concepts to no avail, sometimes she would get so frustrated, that tears would come to her eyes. From my perspective it seemed to me that she was willfully not understanding it, and I was getting very frustrated (but could not show my frustration). I was convinced she was so hung up on math being hard that even if she was understanding it, she refused to believe it because she knew that math was hard, therefore, even if she thinks she is understanding it, it can’t be true. There was some point at some time that after attempt number 1067 of rewording my explanation, that I could see the lights suddenly fire up in her eyes, and a virtual earthquake went through every one of her synapses simultaneously. She looked down at the book, then looked up at me, and said...”What? Is that it? Is it really that easy?”. With that one question, the years of mental blocks came tumbling down, and from then on all new material was easy for her (with just a little explanation)..she ended up with a B as her final grade.

[ladyrustic]

Wow. Thank you for posting that link! Excellent article that should be required reading for every math teacher and high school student in the country.

[BlatherNaut]

The US refuses to “track” students who display no aptitude for “intellectual education” into vocational or technical training, or anything that might make them employable. It is a fact of life that half the population has an IQ on the down side of 100, but many children who are not geniuses have valuable lives, skills, talents and a great deal to offer. Why can’t we spend resources on training that is relevant to their aptitudes and lives? We are too proud and too PC to admit the obvious, much to the detriment of public school students and the nation.

Well said.

The cookie cutter approach to education ignores individual strengths and weaknesses.

Why not allow liberal arts majors to concentrate on their area of ability and interest, and those who wish to pursue a technical career to put their time and energy into furthering their academic goals, rather than wasting time on irrelevant courses? Why attempt to force a square peg into a round hole?

[stormer]

A room is 12x20 feet with a 10 foot ceiling. A gallon of paint covers 350 square feet. How many gallons do I need to complete the job?

I'm hiring a crew for a temporary job. Should I hire 10 less experienced people at $12/hr or should I hire 8 more experienced people who are 20% more productive at $15/hr?

My work truck gets 20 mpg. Along with insurance and depreciation, how much should I charge per mile for work related travel? How much should I charge if the price of fuel increases by 3%?

I could go on...

[Carriage Hill]

Excellent read, sp. Thanks.