11 July 2010

Creative Problem Solving

Fair warning that this post will be more rambly than usual. I am hoping that your insights will help me glue some ideas together.

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?


jentropy said...

It's interesting, because your post addresses a bit of my thought process before the tweet. I'm currently doing instructional design for an IT security course. I love this stuff. I started thinking about how, more than anyone I know, I am the one who always tears things apart and makes alternate connections. I'm always finding new uses for things, and I see things in different ways.
I'm reading all these ethical (and some not so much) hacking books, and the stuff thrills me. But I can't get past the math. I started looking at degree programs in IT security and in general IT. I'd never be able to do the math.
I somehow talked my way through 2 college degrees, and only took one consumer math course. In high school, I only made it through geometry. I don't see the world in a way that relates to numeric symbols and formulas as representative of how things work.
I see patterns other people don't see, and I think I'm a creative problem-solver. I just think my mind works better with abstract concepts, than it does with symbolic representation of concrete facts.

Katie said...

I have always liked math, but what was really good for problem solving was organic chemistry. I had to learn all of these reactions and then figure out how to put them together to synthesize the correct compound. I don't remember any of the reactions now (8 years later), but I do remember the process of looking for patterns and putting things in order.

In terms of subjects I can't retain, I just can't learn economics. I get as far as the supply-demand curve, and then I'm just lost. I've taken a couple of classes, and it just doesn't make sense to me, even though I can do the math.

Tim said...

As a former math teacher, I cringe when people bemoan their inability to "do" math, or even worse, when they boast about it. The problem lies not in some innate skill but in exactly what you discuss in this post. The fault is in how we define "mathematics" in American public education.

Starting in the lowest grades, we spend far too much time in the curriculum on teaching kids to memorize and apply algorithms to artificial problem situations instead of helping them develop a natural sense of problem solving as it relates to numerical situations.

Instead of pushing everyone through the Algebra-Geometry-Trig-Calculus gauntlet in high school (and increasingly starting in middle school), I'd be happy if every student graduated with a solid, practical understanding of probability and statistics as it is applied (or more often misused) in the real world. The country would have fewer lottery players and more people who question polls and surveys, but those are both good things in my mind. :-)

The Science Goddess said...

I can't help but wonder if we (as a society) are just missing the big picture: If we want creative problem solvers, then we need to quit being so math focused. If organic chemistry builds the skills for some, I think that's great. Others might need Jen's approach. Some will get it through math.

I keep thinking that all of this relates to the difference in the way Dan Meyer describes the difference between textbook problems and the type he devises for students.

Dorothy said...

This makes me kinda squeamish, and that might be because I have a couple of degrees in math and used to teach math. But more than that, it reminds me of all the talk about teaching critical thinking skills. Especially when my son was in elementary school I thought a lot about this. He went to a gifted program that claimed to be big into critical thinking. And that's just what he needed and wanted, to wrestle with ideas and have others wrestle with him. Unfortunately, that didn't happen. Really, it was mostly "project based" learning where the projects were dioramas and posters and all sorts of things to produce something to show, but with very little depth. Progress report after progress report would say "X is thoughtful and contributes well to discussions" but my son only recalls two isolated incidents in five years where the rest of the class actually maintained any level of depth in a discussion.

Then, in high school, the Social Studies department decided to stop offering the challenging European History AP course that half the students elected to take and require all students to take an AP social science class -- Human Geography. One of their many arguments why this was a good idea was that it would do a better job at teaching critical thinking skills, and that content didn't matter. There is so much wrong with that I just don't know where to start.

OK, enough rambling.

What I mean to say is that I found the implementation of what other people thought was good critical thinking skills to be dreadfully lacking. Then I read a paper that resonated with me, that said studies show that teaching critical thinking skills in one discipline does NOT translate into other disciplines. So content does matter, and so does lots and lots of depth and practice. (I am on a different computer and cannot find my link. Will continue to look.)

I am afraid that creative problem solving is even more vague a term than critical thinking skills. Many of my son's teachers were not good in critical thinking skills themselves (imnsho) so no wonder they couldn't incorporate it into their teaching. I have no better feeling about creative problem solving in education. Sounds like too many teachers would miss the point and there would be even more creative! dioramas of civil war battles and even less discussion of understanding the reasons for war and the reasons for the outcome.

The Science Goddess said...


I get a little squeamish, too, when I think about the suggestion that advanced math skills might not be necessary. I think you're definitely right---there are some kinds of thinking skills which must be done within the discipline itself because transfer doesn't happen.

I also agree that both critical and creative thinking skills are sorely lacking in general.

I wonder what we should do?

hillby said...

I like your thinking, and I'm very pleased that you actually backed this up with some neurological research. I'm okay with all of that.

How would you structure a course in creative problem solving? Because what you've cited so far sounds an awful lot like good project-based learning or inquiry science.

The Science Goddess said...

I don't know that I've really done more than ramble. :) And I haven't thought much further ahead.

Twenty years ago, I did my Master's work in G/T...and amassed a lot of resources that could have been pulled together into such a course. I'm hopeful that there are better items by now.

We'll see how the new science standards (a la Common Core for math) look. My hunch/fear is that they are going to suffer from the same fate as math: lots of bits of knowledge, very little on what to do with it.