Teaching by example

A science teacher friend told me that “teaching by real life example” is all the rage these days. People have to run around the room pretending to be electrons, rather than learning about electrical current in the abstract. It’s supposed to make learning more “approachable” and easier. A creditable aim, but I am afraid that I have always despised that kind of teaching. It treats people like idiots, incapable of understanding abstract thought. And personally, I learn far more by learning the abstract concept. (Well, I’m an academic lawyer, of course I love abstract concepts.)

It seems that perhaps I am not alone in learning more readily by being taught an abstract concept.

A recent study suggests concrete examples may actually impede students from learning an abstract mathematical concept. The New York Times article explains:

In the experiment, the college students learned a simple but unfamiliar mathematical system, essentially a set of rules. Some learned the system through purely abstract symbols, and others learned it through concrete examples like combining liquids in measuring cups and tennis balls in a container.

Then the students were tested on a different situation — what they were told was a children’s game — that used the same math. “We told students you can use the knowledge you just acquired to figure out these rules of the game,” Dr. Kaminski said.

The students who learned the math abstractly did well with figuring out the rules of the game. Those who had learned through examples using measuring cups or tennis balls performed little better than might be expected if they were simply guessing. Students who were presented the abstract symbols after the concrete examples did better than those who learned only through cups or balls, but not as well as those who learned only the abstract symbols.

The problem with the real-world examples, Dr. Kaminski said, was that they obscured the underlying math, and students were not able to transfer their knowledge to new problems.

“They tend to remember the superficial, the two trains passing in the night,” Dr. Kaminski said. “It’s really a problem of our attention getting pulled to superficial information.”

The researchers said they had experimental evidence showing a similar effect with 11-year-old children. The findings run counter to what Dr. Kaminski said was a “pervasive assumption” among math educators that concrete examples help more children better understand math.

But if the Ohio State findings also apply to more basic math lessons, then teaching fractions with slices of pizza or statistics by pulling marbles out of a bag might prove counterproductive. “There are reasons to think it could affect everyone, including young learners,” Dr. Kaminski said.

As a teacher, I’ve always been a big fan of keeping it simple, and getting across the basic concepts. Seems like maybe I am on the right track. So I won’t be getting my class to pretend to be Torrens land titles or mere equities any time in the future.