Friday, January 21, 2011

Model this: Plain vanilla tests beat out "concept maps"

Any scientist who uses or teaches dynamic systems modeling of any kind at the college and university level faces an interesting problem when they encounter students who've been earlier taught by other, possibly trendier teachers using a technique called "concept mapping."

Concept mapping is outwardly similar to the first stage of a modeling problem, where charts with "circles and arrows" (see Arlo Guthrie's famous "Alice's Restaurant" for the reference) are used to make conceptual connections between phenomena.

The problem is, conceptual connections are not at all the same thing as physical flows of matter and energy, nor are they the same thing as "feedback" loops between statistically correlated phenomena.

Modelers restrict their modeling calculations to these two kinds of relationships. Computer modeling language in fact distinguishes between the two. There are differently shaped or color-coded circles and arrows, or boxes and arrows, to symbolize the relationships that are intended to differentiate flows of matter and energy from those that are intended to simulate cause and effect.

And of course, the aim of modeling is to actually quantify, mathematically the flows of matter and energy in the system, in light of the dynamics of the particular flows, and the cause and effect relationships that impinge on those flows.

Altogether, it's very much more mathematically-disciplined a thought process than this so-called "concept mapping."

In concept mapping as used in middle and high schools (and, woefully, some college classes), students are encouraged to draw circles and arrows more or less willy-nilly between whatever, often vaguely defined concepts they think are involved in a phenomenon.

This is encouraged by their teachers who are then easily pleased with the images that result, and reward the students with praise and so on. Little critical thought is applied to whether or not the relationships drawn actually exist, whether they can be detected or measured, or, perhaps most importantly, whether or not they satisfy basic physical laws such as the First and Second Law of Thermodynamics.

The problem develops when the student subsequently enters a college or university program where physical, chemical, or biological processes are modeled in one way or another using far more stringent rules that must satisfy statistical conventions and the Laws of Thermodynamics.

College teachers then have to undo and unpack the undisciplined and messy conceptual thinking that the students have become accustomed to being rewarded for.

This is often unpleasant for both teachers and students.

Another facet of trendy teaching silliness is this notion that we have to accept and praise whatever "creative" output a student provides.

Well, no, actually, we don't. Not when basic laws of science are contradicted.

Heaven forbid a teacher should actually correct a student for getting something wrong, and try to teach them the correct science fact instead!

So, after years of this particular struggle, I was pleased to see this NYT article that debunks concept maps as pedagogical technique.

It doesn't work.

I could have told you that.

Just drawing circles and arrows in an undisciplined fashion doesn't get you very far at all, not in my world. Pretty pictures are not the real world. The real world can sometimes be described symbolically and mathematically, in all its complication, using flow charts that are then specified quantitatively and used for prediction. Our society actually depends on this technique, especially when it's used in medicine, agriculture, industry, or resource conservation. But it generally takes a good deal of effort to make useful models that actually work for prediction.

No wonder we have such a hard time getting ordinary people to understand climate change. A lot of my students must think that climate scientists just draw charts with circles and arrows to make climate models from our creative imaginations. No wonder they're taken with a pinch of salt.

To be fair, and to give the article the proper interpretation, the researchers found that concept maps do work a little bit. They're just are not as successful at entraining long-term memory of ideas and concepts as conventional systems of tests and practice tests.


Now maybe we can put this behind us and learn some real modeling. When students have an appreciation of how disciplined modeling is, perhaps more of them will realize how rigorous climate models can be, and how likely it is that the major General Circulation Models will prove to be accurate in their predictions.

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