Tuesday, July 7, 2020
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What we decide to teach about algebra

Football and mathematics are two fields that often result in massive irony.

Last week, I was in DeKalb, Illinois, covering the Illinois High School Association state championship football games, and next week, I’ll be in San Antonio reviewing scorer training materials for the PARCC test in high school geometry.

This week, I have a moment to reflect.

At halftime in one of the eight football games played last weekend at Northern Illinois University, I went down to the concession stand and bought a pretzel for $4.75. You might think that’s a lot to pay for a salted pretzel, but no matter.

I handed the cashier a $10 bill, and I was planning to donate the quarter to a bin on the counter intended to support the particular college sports team she represented by working at one of the concession stands for the IHSA.

She pulled out her smartphone, loaded the calculator app, entered 10 – 4.75 =, and gave me the correct change. Then I threw the quarter into the bin and went back into the cold to enjoy my pretzel, while she served the dozens of people in the line behind me.

Some of the geometry problems on the PARCC test involve a two-column proof, others involve trigonometry, and still others involve computing volumes of complex solids. The algebra test isn’t any closer to the real world in terms of the manipulation of numbers required of us in our daily lives. Which do we as a society value more: solving the quadratic equation or making change for a $10 bill?

Of course, we don’t test kids on their ability to make change for a $10 bill, so it’s likely the skill has been slimmed down in our ever-narrowing curricula. And that would be a mistake, because to be blunt, we should teach what we value, not what’s on some contrived test.

I’m not the first one to notice either. Three and a half years ago, Andrew Hacker wrote an op-ed in the New York Times entitled “Is Algebra Necessary?” in which he listed my continuing experience with kids’ lack of training in basic number sense as one of his chief issues:

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.

This op-ed is reportedly one of the most widely-circulated on the Times website. People seem to agree that as we direct our educational resources toward the skill of “mastering polynomial functions and parametric equations,” we direct those important resources away from “quantitative skills, critical for informed citizenship and personal finance.”

In the same way, politicians and even school superintendents bloat our schools with electronic devices in the interest of standardized testing but fail to acknowledge, as comedian Paula Poundstone did last week for CBS News, “The tech industry has profited from the ‘Every child must have a laptop in the classroom’ push, but education hasn’t. Research shows that the brain retains information better read from paper than from a screen, and students who take notes by hand are more successful on tests than those who type their notes on a computer.

“Yet, art, music, sports, play, healthy meals and green space—things we know help the developing brain—are on the chopping block of school districts’ budgets annually.”

To relate this back to algebra, we need only replace a few words in Ms Poundstone’s essay: The test-writing industry has profited from the ‘Every child must learn algebra’ movement, but math education hasn’t. Researchers agree that many kids need basic numeracy skills rather than advanced algebra skills, yet we continue to trim out those parts of our kids’ math education that will actually help them succeed in life in the interest of standardized testing in algebra.

You see, I’m very grateful that the girl got it right, even if it meant making people wait longer than they should have, instead of (a) trusting the customer about what the change should be or (b) getting it wrong and cheating either me or her worthy organization out of a dollar.

In April, Jonathan Cornick at the City University of New York wondered why advanced algebra skills are necessary to graduate when most people will never use them:

What about the … type of student who is generally capable of the academic work required to obtain a degree in a non-STEM field and be a productive member of society, but is prevented or delayed from doing so because they failed elementary algebra?

In many states, including Maryland, proficiency in algebra, as demonstrated on a standardized test, is one of the requirements for high school graduation. Mathematicians are asking, Why?

And so am I. When a girl can demonstrate proficiency in algebra enough to graduate from high school, she ought to be able to make simple calculations involving money in her head, without having to rely on a device that could fail.

Mr Cornick also points out that most people in the math world, including those who used to subscribe to the “everybody needs algebra” argument, say many ordinary people, routinely, rely on a basic set of number skills, similar to the “quantitative skills” Mr Hacker mentioned:

  • Percentages
  • Geometry and Trigonometry
  • Inferential statistics
  • Proportions: unit conversion skills related to supplies, materials, costs, nutrition, health, etc.
  • Descriptive Statistics: averages, describing distributions as well as being able to understand and interpret data and charts from business, politics, media, etc.

Is this what we really mean by numerical literacy, or numeracy?

If so, this is probably where we should focus our graduation requirements, not on algebra, which I must say is required for STEM majors in college and for business. As far as political science and other non-STEM majors go, however, I’m pretty sure you can go far in those fields without knowing how to solve a quadratic equation. But you won’t go far in any field if you can’t grasp simple numerical computations without relying on a smartphone.

Finally, I wanted to use this opportunity to tell you about a new book from Mr Hacker entitled The Math Myth: And Other STEM Delusions, due out in March. I’m looking forward to reading it. It’s now available for pre-order from Amazon.

Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.

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