A. One train leaves Station A at 6 p.m. traveling at 40 miles per hour toward Station B. A second train leaves Station B at 7 p.m. traveling on parallel tracks at 50 m.p.h. toward Station A. The stations are 400 miles apart. When do the trains pass each other?
B. 40 (t + 1) = 400 - 50t
If you're like me, you'd pick question B in a heartbeat. It's a trick question, however, since the two questions are actually the same.
Researchers at Ohio State University have found that college students learn math better from abstract equations like question B than ones incorporating "real-world" examples like question A.
Dr. Jennifer Kaminski told the New York Times:
"The motivation behind this research was to examine a very widespread belief about the teaching of mathematics, namely that teaching students multiple concrete examples will benefit learning. It was really just that, a belief.
The problem with the real-world examples 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. It’s really a problem of our attention getting pulled to superficial information."
The researchers found similar results when they tested 11 year olds, and they are now testing even younger children. Dr. Kaminski wants to know whether the manipulatives used in so many elementary school math programs are counterproductive.
It's an interesting question, but from what I remember of Piaget, young children's minds are much more concrete than older children's and adults. It's the whole "concrete operational" (5 or 6 up to 11 or 12) vs. "formal operational" (11 or 12+) thing.