Gifted Issues Discussion homepage Forums General Discussion Is Algebra Necessary?

The president of the National Council of Teachers of Mathematics (NCTM) may agree in spirit with Hacker, having written

http://www.nctm.org/about/content.aspx?id=28195
Endless Algebra—the Deadly Pathway from High School Mathematics to College Mathematics
by NCTM President J. Michael Shaughnessy
NCTM Summing Up, February 2011

...

The NCTM/MAA Mutual Concerns panel presented four concrete, relevant, alternative mathematical transition paths for high schools and colleges to consider. One path emphasizes quantifying uncertainty and analyzing numerical trends. Its mathematical foci include data analysis, combinatorics, probability, and the use of data collection devices, interactive statistical software, and spreadsheet analyses of numerical trends. A second transition path concentrates entirely on the development of students’ statistical thinking, beginning in high school and continuing into the first year of college. Statistical thinking involves understanding the need for data, the importance of data production, the omnipresence of variability, and decision making under uncertainty. This path differs both in purpose and approach from an AP statistics course. A third path recommends building a transition grounded in linear algebra. Linear algebra integrates algebra and geometry through powerful vector methods. It offers an arena in which students can work with important multivariable problems and provides students with general-purpose matrix methods that will serve them well in many fields, including mathematics, science, engineering, computer science, and economics. Finally, a fourth transition path incorporates a suggestion that an alternative to calculus can be found in calculus itself—but a vastly different calculus from the traditional calculus I. This path concentrates on multivariate applications of both calculus and statistics, because today’s application problems rarely involve single-variable calculus or univariate statistics. We live in a multivariate world. Therefore, students’ mathematics experience in preparation for their transition to college should emphasize multivariate functions, partial derivatives, multivariate data sets, and analyzing covariance.

**************************************

I wonder where these "alternative mathematical transition paths" have been fleshed out, and whether students who have trouble with the current algebra-to-calculus curriculum will fare better in them.

I found this statement in that article:


Hmm. Honestly, I think that if colleges want to claim that their students are getting a real college education, they should ensure that everyone understands what differentiation and integration are. This would require a semester-long calculus course (AP in high school counts, IMO). Science and Engineering students have to take college-level English and other humanities courses. The vast majority won't analyze what motivated King Lear or Odysseus when they're programming in Scala or assessing flow cytometry results. So why do they have to take the humanities classes? Because they're considered to be an essential part of what it means to be "educated."

Given this, why should humanities students get a pass on calculus? Calculus is beautiful way of mathematical thinking that can change your philosophical perceptions about of mathematics and physics, and, by extension, the universe we inhabit. The idea that you don't have to study calculus (or algebra) because "you won't use it at work" is incredibly short-sighted. Calculus, algebra, and geometry teach a way of thinking as much as a way of calculating, just like great works of literature expose us to news ways of thought. When our educators push students away from mathematics, they cheat them and do them (and our society) a disservice.

I didn't understand the difference between "college algebra" and "algebra I" or "algebra II" and why college algebra precedes calculus (a high school or first-year college course). Does this mean that students are repeating courses they took in high school when they get to college?

The answer seems to be yes. I did a web search for "college algebra syllabus." I found that "college algebra" is really "high school algebra taught at a college."

I agree with the writer that the path is wasteful, but I disagree that learning algebra is out of date. If anything, understand the basic abstractions that algebra teaches will become more important as our civilization becomes increasingly technological. I think a big problem is that elementary schools teach algorithms instead of true numeracy. When kids hit algebra and suddenly have to apply concepts, they can't ---- how can they if they never really learned them adequately?

So could this be an important reason for what seems to be a revolving door of algebra classes? Not to mention why high school algebra classes have been watered down so much?

And of course, there is also the argument that when our education leaders recommend a course of action that no longer requires algebra or waters down high school math courses, we actually raise barriers for low-SES students. These kids should be learning numeracy and algebra in free public schools, not learning it via student loans in college. They should be taking each of these math courses once, and our schools have a responsibility to provide them with a foundation that will let this happen. My neighbor's daughter (a bright young woman) passed the state high school exit exam on her first attempt in tenth grade, and ended up taking "college algebra" and having trouble with it. This is just wrong, and it happens all the time.

Yes, our civilization is going to magically become more and more technological through the magic of technology.

Nope, we won't ever go into reverse.

Can't happen.

Not to us.

Yes, of course...and if we end up hunting cows with spears and using smoke signals to communicate, we definitely won't need people who understand math. Not us. It's better resign ourselves to things like polio and starvation.

We are getting close to this point so I'll have more info soon, but my dds' school system has the following path for Algebra, which seems to indicate that they view "college algebra" as distinct from algebra I or II and, presumably, more advanced:
Algebra I, Geometry, Algebra II, College Algebra, Trig, Calculus AB (or taken as two classes: Calc A and then Calc B).

Do all colleges and universities require everyone to take English? (I don't think so, though I'm not sure. It was required at my small liberal arts college, I think. I was an English major, though, so I wasn't paying attention to this.)

Anyway, I disagree that English/writing classes (I suspect what's really required are classes with a substantial writing component, just as schools also have "quantitative" requirements) are required because of some concept of what it means to be educated. I think they're required because we want to people to be able to communicate in written English.

Now, I've never taken calculus, as previously established. Perhaps it would alter my life view in some way. But then, would it be more important than taking statistics? (I also haven't taken that--and I really wish I had!) Or economics? (I actually did take this, but it certainly isn't required anywhere that I know of.) Or world history 101? (Also not required most places.) Or, heck, basic biology? I could think of a decent list of courses that arguably should be required for a student to be "well educated," but that's not the way it works nowadays. I myself wish I'd taken more of these broad, basic survey courses when I was in school, but you can't talk sense to a 19yo.

Most colleges have made a determination of what it means to them to be educated and fr public unvierities the state weighs in there as well. All colleges, except for a few, follow some sort of core, major, elective system. All students take a few English classes, math, science, etc whatever and how many the university deems to be of value. Universities adjust baed on feedback from employers, students, grad schools etc. 30 years ago Cornell engineering separated itself from the pack by offering writing for engineering majors, after hearing complains from employers that engineers couldn't write reports, CU made it a priority and it became a selling point. Similarly, why so many group projects, because employers have people working in groups! Colleges also have had to figure out what to do with a population who doesn't know certain things - if it's not getting taught in elem, middle or HS and colleges deem it important than remedial effort has to occur. Many colleges offer science and math for non science majors because so many say they aren't good at it or wouldn't take it or couldnt take it.

And as with all things, these are being decided by committee, often made up of people with a stake in it. Just like you can't make the tax code simpler without damaging the tax preparer industry, you will also have lots of less popular majors fighting to say their courses are "essential" to beng an educated person - and sometimes they are right.

DeHe

Articles such as

http://www.nytimes.com/2012/08/19/business/new-wave-of-adept-robots-is-changing-global-industry.html
Skilled Work, Without the Worker
By JOHN MARKOFF
New York Times
August 18, 2012

suggest that the future belongs to people who have the ability to do things such as program a robot, but I am not optimistic that a much larger fraction of people in the U.S. can be educated to this level than are currently.

That's because we're trying to create Robot Utopia where everything is completely automated and we no longer have to work with yucky things like dirt, dust, and automotive grease.

See the self-driving car for details.