Mr. Jones’s eighth-grade math class is working on geometry. Last Friday the students measured all six interior angles of a hexagon and added up the results. Everyone got a total of approximately 720 degrees. Today they soon agree that that number would stay the same even if the hexagon’s shape changed.
Jacquille: “Seven hundred twenty.”
Jones’s lesson wouldn’t seem familiar in Japan or Germany. In those countries the class would typically have proceeded in a different direction, according to James Stigler and James Hiebert in The Teaching Gap, which is based in part on the TIMSS videos. The typical Japanese or German teacher wouldn’t have just told the students the formula. Instead, he or she would have invited the students to think about various polygons and either led or encouraged them to devise a way of figuring out what their angles add up to. The students might struggle and flounder for a while, but the teacher would have planned and orchestrated the lesson so that in the end they would not only learn the formula but get a feeling for where it comes from and why it works.
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School reforms based on these complaints have kept politicians and lobbyists busy for decades, but they rarely reach the heart of the matter: the American way of teaching isn’t doing the job most Americans want done.
The Third International Mathematics and Science Study is the biggest and most sophisticated research project yet in a series of international comparisons that have almost always made American students look bad. In mathematics, eighth-graders from Singapore, Korea, Japan, Canada, France, Australia, Hungary, and Ireland all scored significantly higher than ours (German kids scored about the same).
Even seemingly trivial events in the school day are part of this teaching pattern. Stigler and Hiebert and overseas colleagues gathered one day to watch the tape of a U.S. lesson. “The teacher in the video was standing at the chalkboard in the midst of demonstrating a procedure, when a voice came over the public-address system: ‘May I have your attention, please. All students riding in bus thirty-one, you will meet your bus in the rear of the school today, not in the front of the school. Teachers please take note of this and remind your students.’ A Japanese member of our team reached over and pushed STOP on the VCR. ‘What was that?’ he asked. ‘Oh, nothing,’ we replied as we pushed the PLAY button. ‘Wait,’ protested our Japanese colleague. ‘What do you mean, nothing?’ As we patiently tried to explain that it was just a P.A. announcement, he became more and more incredulous. Were we implying that it was normal to interrupt a lesson? How could that ever happen? Such interruptions would never happen in Japan, he said, because they would ruin the flow of the lesson.” The tapes bore him out. Thirty-one percent of American lessons were somehow interrupted from outside the classroom, but not one Japanese lesson was.
“If teachers learned to teach by studying books and memorizing techniques”–the conscious, explicit way most grown-ups learn to use, say, their computers–“written recommendations might have their intended effect,” write Stigler and Hiebert. But most people don’t learn to teach the way they learn to compute. They learn how to teach long before they ever set foot in a college of education, the way we all learn how to behave at Thanksgiving dinner–mostly implicitly and by example.
