## Monday, August 4, 2014

### Pedagogical MacGuffins

What's a MacGuffin? A MacGuffin is the key or stolen diamonds or secret code or NOC list that the characters  desperately pursue. Audiences, pretty much by definition don't care about MacGuffins, but they do enjoy watching characters pursue them. Sometimes the audience isn't even clear on what the MacGuffin is.

Do you know what a NOC list is?

A pedagogical MacGuffin is a type of problem we pretend to care about even though we really don't. Like its fictional counterpart, what's important with a mathematical MacGuffin is not the thing but the pursuit.

The classic example is factoring polynomials. A standard part of most algebra classes is to learn how to take a trinomial like

2x^2 - x - 15

and find two binomials you can multiply together to get it

(2x+5)(x-3)

Every once in a great while, you'll get a trinomial that won't factor but the rest of the time you'll get a nice clean answer where each binomial consists of an integer times x plus another integer. At least, that's how it works with the assignments. You may even be told that polynomial factoring is useful because it can help you solve equations. That part is a lie.

With a couple of notable exceptions (differences between two squares and perfect square trinomials), you will probably never even try to solve a problem by factoring a quadratic for the simple reason that most don't factor.

Not only does solving by factoring usually not work; we already have a simpler method that always works, the quadratic formula.

The truth is, we don't care whether or not you know how to factor a trinomial; we care about what you learned in the pursuit, things like problem solving skills and insights into how numbers work.

(2x+5)(x-3) is just something to keep the plot moving.

If you're interested, try a few randomly generated trinomials and see how many you can get to factor.