It all started with this:
The quick and dirty answer to me is simply that we learn and retain what is most urgent to our needs. That could be for a test on Friday or for something you will continue to use throughout a lifetime. I could get slightly more esoteric and answer a question with a question: How long do you have to retain something in order to say that you've learned it? But out of everything in that original tweet, I somehow got fixated on the parenthetical comment about math.
I am not a math-hater or mathphobic. And yet, I can't claim that other than basic stats, I've ever put anything beyond my junior high math experience to use.
I know what you're going to say---it's all the same things I've heard myself saying to other people who go so far as to say high school math is a waste. (a) Some students do move into careers where they commonly use algebra, geometry, trig (and even pre-calculus). Just because some math might not be part of the daily lives of everyone doesn't mean it isn't useful to someone. (b) It's not the algorithms that are important, it's the mathematical reasoning that evolves. Math is a language of patterns. We learn to become better problem-solvers---a needed skill for everyone---through study of mathematics. (c) Math is all around you! Just because you don't use calculus does not mean calculus has not been used to shape the world you live in. (d) Science is an application of math. How can you do science and not use math?
Have I covered them all?
I'd really like to focus on B for the moment. A and C are cop-out sorts of arguments, even though I use them myself. And D? Not germane to my particular train of thought at this time. Maybe later, D.
I'm really struggling to buy B. Part of the reason I'm grasping at straws is that I have yet to see math standards for high school that did not focus on algorithms. Heck, take a look at the new Common Core Standards for math. It is a collection of math facts without the "why." Here's a taste from the functions portion:
My question is, why is this important for every child in America to know and be able to do? I'm not saying that this is math without purpose. There are professions which use this sort of thing on a regular basis. What I'm wondering is what the So what? is for everyone else? What is the nugget of reasoning everyone can take away? And if we can identify that...shouldn't that be the standard instead of the example algorithms?
Mixed in with my muddled thinking about this was a Newsweek article on The Creativity Crisis. It first made me shake my tiny fist at my former district, which defined "gifted" by IQ and used no other measures (such as the Torrance Tests for Creativity); but deeper inspection made me wonder if we are substituting math for creativity:
To understand exactly what should be done requires first understanding the new story emerging from neuroscience. The lore of pop psychology is that creativity occurs on the right side of the brain. But we now know that if you tried to be creative using only the right side of your brain, it’d be like living with ideas perpetually at the tip of your tongue, just beyond reach.
When you try to solve a problem, you begin by concentrating on obvious facts and familiar solutions, to see if the answer lies there. This is a mostly left-brain stage of attack. If the answer doesn’t come, the right and left hemispheres of the brain activate together. Neural networks on the right side scan remote memories that could be vaguely relevant. A wide range of distant information that is normally tuned out becomes available to the left hemisphere, which searches for unseen patterns, alternative meanings, and high-level abstractions.
Having glimpsed such a connection, the left brain must quickly lock in on it before it escapes. The attention system must radically reverse gears, going from defocused attention to extremely focused attention. In a flash, the brain pulls together these disparate shreds of thought and binds them into a new single idea that enters consciousness. This is the “aha!” moment of insight, often followed by a spark of pleasure as the brain recognizes the novelty of what it’s come up with.
Now the brain must evaluate the idea it just generated. Is it worth pursuing? Creativity requires constant shifting, blender pulses of both divergent thinking and convergent thinking, to combine new information with old and forgotten ideas. Highly creative people are very good at marshaling their brains into bilateral mode, and the more creative they are, the more they dual-activate.
I can see this sort of thing happening in math---but I can see it happening with all sorts of content. I can't help but wonder if we've gone math-crazy in this country because we think that teaching algorithms will model or mimic this creative process. (Or worse yet...in our Barbie-like attitude that "Math is hard." we begin to associate ability to do advanced math with "smart.")
What would happen if we replaced a requirement for upper level math in high school with courses in creative problem solving?