American teachers need to do more to help students understand the concepts behind math, not just teach them the mechanics of problem-solving, according to James Hiebert, Robert J. Barkley Professor of Education in CHEP's School of Education.
Hiebert bases his conclusion on a four-year study, for which he was a primary investigator, that analyzed videos of math teachers in the United States and six countries that traditionally score higher on math achievement tests--Japan, Hong Kong, the Czech Republic, Switzerland, the Netherlands and Australia.
The study addresses what Hiebert says is a key question that was not answered by a similar research project in which he previously participated--whether all high-achieving countries teach mathematics the way it is taught in Japan. Of the three countries in the previous study, Germany, Japan and the United States, only Japanese students perform at a consistently high level on international tests, he says.
"Because Japanese math teaching looked strikingly different from that found in Germany and the United States, it was natural to wonder whether their form of teaching is necessary for high student achievement. The results of this [most recent] study showed clearly that the answer is no," Hiebert says.
"The teaching methods found in other high-achieving, Asian and European countries differ substantially from Japan and from each other. In fact, the differences among the high-achieving countries, even on some features often considered important for students' learning, were quite surprising."
He stresses that this doesn't mean all teaching methods are equally effective or that teaching methods don't matter. He says American educators can learn from studying the different methods used by teachers in high-achieving countries.
"We found that the differences between mathematics teaching in the United States and in other countries were greater for countries that achieve much better than the U.S. than for countries that achieve only a little better. That is, the higher the achievement in a country, the more different from the U.S. are the teaching methods," he says.
"There are a few features of teaching that the higher-achieving countries share, which are absent from U.S. teaching. We should pay particular attention to these."
In brief, Hiebert said, in most higher-achieving countries a majority of class time is spent dealing with new content--concepts and procedures that students have not seen before. The majority of time in a typical U.S. lesson is spent reviewing old material. Additionally, most higher-achieving countries spend some time during a typical lesson discussing the conceptual underpinnings of a topic, such as why a formula or procedure works to get a correct answer. Almost no time is spent this way in typical U.S. lessons. U.S. students spend most of their time just practicing procedures they have been taught, Hiebert explains.
"There are no tricks from this study that U.S. teachers could quickly learn. Rather, the kinds of changes suggested will require time for teachers to study, understand and then practice in their own classrooms. We usually underestimate how difficult it is to change methods of teaching," he says.
A resource provided by the study is a set of videotapes of teaching in each of the seven countries involved. Four eighth-grade math lessons in each country are available, along with written commentaries by the teacher who taught the lesson and a researcher in the home country, the teacher's lesson plan and supplementary materials used during the lesson.
The videotapes are accessible online at [www.lessonlab.com], the web site for the research institute that coordinated the study.
"These videotapes will allow U.S. teachers to see their own practices with fresh eyes and to see some alternative practices that they might not have thought of before," Hiebert says.