Algebra, Eroding Goals and Systems Thinking

A NY Times editorial wonders, Is Algebra Necessary?*

I think the short answer is, “yes.”

The basic point of having a brain is to predict the consequences of actions before taking them, particularly where those actions might be expensive or fatal. There are two ways to approach this:

  • pattern matching or reinforcement learning – hopefully with storytelling as a conduit for cumulative experience with bad judgment on the part of some to inform the future good judgment of others.
  • inference from operational specifications of the structure of systems, i.e. simulation, mental or formal, on the basis of theory.

If you lack a bit of algebra and calculus, you’re essentially limited to the first option. That’s bad, because a lot of situations require the second for decent performance.

The evidence the article amasses to support abandonment of algebra does not address the fundamental utility of algebra. It comes in two flavors:

  • no one needs to solve certain arcane formulae
  • setting the bar too high for algebra discourages large numbers of students

I think too much reliance on the second point risks creating an eroding goals trap. If you can’t raise the performance, lower the standard:

eroding goals
B. Jana, Wikimedia Commons, Creative Commons Attribution-Share Alike 3.0 Unported

This is potentially dangerous, particularly when you also consider that math performance is coupled with a lot of reinforcing feedback.

As an alternative to formal algebra, the editorial suggests more practical math,

It could, for example, teach students how the Consumer Price Index is computed, what is included and how each item in the index is weighted — and include discussion about which items should be included and what weights they should be given.

I can’t really fathom how one could discuss weighting the CPI in a meaningful way without some elementary algebra, so it seems to me that this doesn’t really solve the problem.

However, I think there is a bit of wisdom here. What earthly purpose does solving the quadratic formula serve, until one is able to map that to some practical problem space? There is growing evidence that even high-performing college students can manipulate symbols without gaining the underlying intuition needed to solve real-world problems.

I think the obvious conclusion is not that we should give up on teaching algebra, but that we should teach it quite differently. It should emerge as a practical requirement, motivated by a student-driven search for the secrets of life and systems thinking in particular.

* Thanks to Richard Dudley for pointing this out.

Is Algebra Necessary?

2 thoughts on “Algebra, Eroding Goals and Systems Thinking”

    1. Nice post.

      I think the point about long division is well taken – I remember once doing square roots by hand, but I can’t remember the algorithm, and I do math for a living. With my kids, I find that they can handle algebra and calculus more easily, and more willingly, than complex calculation tasks.

      I’d be particularly worried about being treated by a doctor who didn’t grasp the aspects of calculus that relate to bathtub dynamics. I know a nice example of this, which I couldn’t share at the time, but could probably tackle as a post.

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