Republic of Mathematics blog

Is there an algebra overkill?

Posted by: Gary Ernest Davis on: October 14, 2010

James J. Kaput
Algebra has been a big concern of mathematics educators for many decades. My late colleague and friend Jim Kaput, famous for his work on algebra learning, essentially moved away from traditional algebra to simulation and modeling as routes for students to learn about change in mathematics. Jim was a visionary, and the cognitive difficulty of algebra sent him exploring many routes to help all students obtain mathematical competency.
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Discussions about the utility, or otherwise, of algebra surface regularly. Recently an Education Week article “Is There an Algebra Overkill” tackled this question again.
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The author, John W. Myres, comments:
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“Most people add, subtract, multiply, and divide, using whole numbers, fractions, decimals, and percentages. They purchase food and clothing, balance checkbooks, create budgets, verify credit card charges, measure the size of rooms, fulfill recipe requirements, and even understand baseball batting averages or horse-racing odds. These activities don’t require a real knowledge of algebra.”
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I feel the implication here is that it is not the “average” person that John Myres wishes to refer to, but the “typical” person. The implication, to me, is that it is a relatively rare bird who would find a need for algebra in their lives, or am I misreading Mr. Myres? To be fair, he does write: “These activities don’t require a real knowledge of algebra.” Yet the tone of the article is that “most” people do not need to use algebra on a daily basis.
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Is Mr. Myres right? I know my wife does not use algebra in her job as a university administrator, though she does use arithmetic in her job and at home to balance budgets. I am am a mathematician and I rarely use algebra except when I am teaching it! or when I am teaching other parts of mathematics. Then I use it a lot. So, who else apart from mathematics professors like me, and other mathematics teachers, uses algebra on a regular basis as part of their job? If we can scarcely find anyone then Mr. Myres is right and we have to ask why we are inflicting on school and college students what is known to be a fairly painful experience, one at which many students are likely to fail miserably.
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Here’s a comment on the blog Intrinsically Knotted:

Efrique I use algebra every day, typically seven days a week. I use it a lot in my job (I work for a software company). A day I don’t use algebra to solve a problem in my work is likely a day where I haven’t achieved a whole lot. I use it to do research. I use it in my hobbies. I use it when I go shopping.  Mostly, I just use it to think.”

So here’s someone in a software company – we don’t know what sort of job – who claims to use algebra daily. Maybe lots of software jobs call for people to use algebra regularly. But are such people “typical”.

At Yahoo! answers wooliebear07 writes:

“I use it all the time in cooking. I often have to make recipes smaller because I only cook for two. Also, I am a campaign manager and use algebra all the time for determining my targeting. In high school or college I never thought I would need algebra for my job. It’s surprisingly useful in many different careers.”

We don’t know what wollibear07 does for a living, but if Mr. Myres is right, wolliebear07 is not typical.

Pisces ♥ Math writes that engineers, astronomers, statisticians and accountants use algebra in their everyday jobs. Supposing she is right, and also Mr. Myres is right, then people working in these professions are not “typical”.

Now to me it is beginning to sound suspiciously like Mr. Myres means that in certain aspects of our daily life – such as those he describes – we do not need or use algebra: this is, in fact, whet he writes. With that I agree. However, even a cursory examination suggests that in many numerate professions people do use algebra regularly. And in an highly educated society more and more people work in these sots of professions: they cannot be simply dismissed as atypical.

A huge educational problem is that school and college students do not see what happens in the daily work like of professionals. Shouldn’t that be part of a student’s education? Shouldn’t real life professionals be invited to school to say to students and teachers what skills they use daily? Shouldn’t that be part of a student’s education?

Postscript

Chancellor740 posted a interesting question about algebra on reddit.com: “Why does algebra make me want to kill myself?
The question and comments are worth reading.

5 Responses to "Is there an algebra overkill?"

What would be most useful is a survey of exactly how and when people are using algebra, as we humans are notoriously poor at self-reporting.

My background as a software engineer and generally functioning citizen leads me to think that some algebraic concepts may be useful for most people but certainly not the entire gamut of what we call Algebra I.

Agree completely Pete. We need a reliable audit of how people use math in their jobs. I know Celia Hoyles and others did something about this at Institute of Education in London some years ago. I will try to find details.

Just a brief comment to Pete Welter’s comment, before I hopefully arrange a response to this article –
We must avoid trying to break Algebra 1 as a course into separate fragments to try to figure out which fragments to teach to which students. Teach the WHOLE course of Algebra 1. We do not know how or which of Algebra a student will use later. Breaking Algebra into fragments and only teaching what we or the student thinks he’ll use is just too limiting.

Overkill — A year of Algebra in high school (Algebra 1) is not overkill. It is just right for most typical people. One important goal is to allow students to be able to clearly interpret some numeric situations and find solutions. For the atypical students, Algebra 1 will certainly be only a beginning before other more advanced courses.

How Early — Many students could benefit from some Algebra concepts before high school, but how soon and to what extent is difficult to say. Maybe this varies for each student. One problem in children learning basic math and Arithmetic is that the rules (or properties) are not always well expressed, so some students do not learn exactly how to know what to do for computations and for handling “word” problems. These students might not need nor be ready for a full one-year regular Algebra 1 course, but the rules should be systematically conveyed somehow for students who need this help. In my case, computations with fractions were mostly beyond me, UNTIL I STUDIED ALGEBRA 1 in high school. With Algebra, the rules and what to do with them finally became clear.

Who Uses —- even a lowly worker in a manufacturing situation could use some basic Algebra for volume calculations, volume & geometric length decision calculations, ingredient mixing & blending calculations and decisions. A rare situation in retail involving price and cost can use very simple Algebra in order to think clearly when no modern point-of-sale equipment is present (Yes, I visited such a shop). Prices of items were listed based on one amount of units on one list, and listed based on a different size of unit on another list, and items in untreated condition were sold at a specific discounted rate. Just a little bit of Algebra made the calculations very easy to arrange (and then a simple electronic calculator was easily used for actual computation of the refined expression for cost). So, sure, the actual Algebra was extremely simple, but it helped in the sale cost analysis process.

Point is, we never exactly know who will use any part of Algebra 1, where, or when. Just learn the whole year-long course.

I am not in disagreement. Yet many students suffer badly in algebra and never recover from the experience. Additionally, even several years of algebra does not seem to help many engineering students studying calculus – they do not have strong enough algebra skills.

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