Political Science Prof Asks: Is Algebra Necessary?

Capt.Albatross writes "Andrew Hacker, a professor of Political Science at the City University of New York and author of Higher Education? How Colleges Are Wasting Our Money and Failing Our Kids — and What We Can Do About It, attempts to answer this question in the negative in today's New York Times Sunday Review. His primary claim is that mathematics requirements are prematurely and unreasonably limiting the level of education available to otherwise capable students ."

Comments

Of course it is necessary...

[mikael]

Algebra is a subset of mathematics, and forms the basis for statistics. Statistical analysis is required in just about every science field as well as arts. Social studies and biology require analysis of population dynamics; geology and geography require understanding of hydrodynamic equations. Psychology requires statistical analysis in many different ways. There's even a mathematical package called SPSS - Statistical Package for the Social Sciences. Even history will require the use of probabilty analysis to determine the most likely chain of events.

Re:Mathematics is a tool

[Guy Harris]

NO.

It's the unintuitive ways in which it's taught (which in turn causes the societal alienation of the subject) that is the problem, not the fact that it's a requirement.

Mathematics is nothing less than the upmost tool of rationality. Lose it, and all progress decays.

Yeah. Somebody should point Prof. Hacker to this essay, in which the writer states that

Peter Braunfeld of the University of Illinois tells his students, “Our civilization would collapse without mathematics.” He’s absolutely right.

Algebraic algorithms underpin animated movies, investment strategies and airline ticket prices. And we need people to understand how those things work and to advance our frontiers.

Quantitative literacy clearly is useful in weighing all manner of public policies, from the Affordable Care Act, to the costs and benefits of environmental regulation, to the impact of climate change. Being able to detect and identify ideology at work behind the numbers is of obvious use. Ours is fast becoming a statistical age, which raises the bar for informed citizenship.

Perhaps if he were to read that, he'd change his mind. :-)

(Shorter me: "You did RTFA, right? If not, please do so before ascribing to Prof. Hacker opinions he does not hold.")

Re:yes

[fean]

If I have $50, and I have to buy lunch every work day for two weeks, how much can I spend on average?
X = $50 / (2 weeks * 5 days)
X = $50 / 10
X = $5

This is a hard question for people who don't know algebra. Those who DO know algebra do most of the math in their head because it's so ingrained.

The fact that you don't realize you're using algebra every day should be taken as how vital it is to teach it.

Re:yes

[FrangoAssado]

Not really. Arithmetic is about the operations you do with numbers (addition, multiplication, etc.). Algebra (or rather, elementary algebra) is basically solving equations. The examples the GP gave are usually solved by using very simple elementary algebra and arithmetic: build an equation representing the problem, solve it by isolating the variable (algebra), and then calculate the numeric answer (arithmetic).

Re:yes

[Qzukk]

I think you are confusing algebra with arithmetic.

"You bought ten Silly Bands for [whatever] dollars... how much did you pay for each one?"

10bands * x = $5, solve for x .

Re:yes

[Smallpond]

I haven't seen a cashier with any math skills in quite a while. In fact, if you really want to screw them up give them the extra penny. I had a chat with a cashier when the customer in front of me did that after she had rung up a payment of $10.00 and was unable to deal with being handed $10.01 (for a purchase of $9.51). She felt very abused about not being able to calculate the right change in her head. As far as I can tell, the cash register is in charge. She felt her job was to do whatever the cash register told her to do.

Re:yes

[narcc]

Math is a means of describing the world. It is not entirely abstract. It can be balls or calories or dollars.

If I may quote Whitehead:

Suppose we project our imagination backwards through many. thousands of years, and endeavor to realize the simple-mindedness of even the greatest intellects in those early societies. Abstract ideas which to us are immediately obvious must have been, for them, matters only of the. most dim apprehension. For example take the question of number. We think of the number 'five' as applying to appropriate groups of any entities whatsoever - to five fishes, five children, five apples, five days. Thus in considering the relations of the number 'five' to the number 'three: we are thinking of two groups of things, one with five members and the other with three members. But we are entirely abstracting from any consideration of any particular entities, or even of any particular sorts of entities, which go to make up the membership of either of the two groups. We are merely thinking of those relationships between those two groups which are entirely independent of the individual essences of any of the m.embers of either group. This is a very remarkable feat of abstraction; and it must have taken ages for the human race to rise to it. During a long period, groups of fishes will have been compared to each other in respect to their multiplicity, and groups of days to each other. But the first man who noticed the analogy between a group of seven fishes and a group of seven days made a notable advance in the history of thought.

More directly:

The point of mathematics is that in it we have always got rid of the particular instance, and even of any particular sorts of entities. So that for example, no mathematical truths apply merely to fish, or merely to stones, or merely to colours. So long as you are dealing with pure mathematics, you are in the realm of complete and absolute abstraction. All you assert is, that reason insists on the admission that, if any entities whatever have any relations which satisfy such-and-such purely abstract conditions, then they must have other relations which satisfy other purely abstract conditions.

From Science And The Modern World Lowell Lectures, 1925

Re:yes

[ObsessiveMathsFreak]

There's no algebra in that, it's a simple arithmetic word problem.

The word Algebra comes from "The Compendious Book on Calculation by Completion and Balancing" written in ~820AD by a mathematician called Muhammad ibn MÅsÄ al-KhwÄrizmÄ (algorithm). The word "al-jabr" was an arabic word standing I beleive for the idea of adding/subtratcing the same amount from both sides of the "equation" (I stand to be corrected)

The entire book is a giant collection of arithmetical word problems.

The term "algebra" came to be understood not as a single technique, but as a general term for the entire framework of techniques used to solve these arithmetical word problems. The problems could be understood and the solutions confirmed using arithmetic, but to actually find a solution, in a systematic way, required the application of the techniques that al-KhwÄrizmÄ espoused in his solutions.

Algebra is how we solve problems systematically, not the problem itself. If you solved the problem, even a basic one, you used some kind of algebra. Even if it was now now an unconscious operation, at some stage you were taught the technique explicitly, or learned it in class through solving problems.