For almost a decade, a debate has raged over the best way to teach mathematics and science.
Should teachers instruct students in the subjects’ facts and procedures and then give them the opportunity to apply their new skills and knowledge? Or should they guide their students toward discovering the principles behind math and science and then help them use what they learn in real-life situations?
While arguments have been heated in professional circles, a new study suggests teachers can use either approach successfully.
“We do our kids a disservice by choosing one pedagogy and using it all the time,” said Iris R. Weiss, the president of Horizon Research Inc. and the lead researcher on the project, which analyzed more than 300 lessons in a cross-section of math and science classrooms. “Teachers need to use their personal style and try a variety of approaches.”
“Looking Inside the Classroom: A Study of K-12 Mathematics and Science Education in the United States,” is available from Horizon Research, Inc. (Report sections require Adobe’s Acrobat Reader.)
The problem is that most teachers are not using either approach effectively, the study suggests. Overall, researchers scored 59 percent of the lessons as low-quality and just 15 percent as high-quality. The rest fell in the middle. The average math and science lesson is “far from the ideal,” the study concludes.
Taking a Look
For “Looking Inside the Classroom: A Study of K-12 Mathematics and Science Education in the United States,” Ms. Weiss and a team of four other researchers observed 364 math and science lessons in 31 districts that make up a representative sample of the nation’s schools. The observers graded the content of the lesson, the instructional strategies the teacher employed, and the classroom environment.
The study, which was underwritten by the National Science Foundation, is one of the few large-scale examinations of how American teachers do their jobs.
Earlier this year, another federally backed study, based on an analysis of videotaped math lessons in the United States and six other countries, found essentially the same thing: American teachers aren’t offering challenging lessons to their students.
In reviewing the videos, researchers found that American teachers failed to communicate the underlying mathematical ideas that help students understand how the skills they’re learning are part of a logical and coherent intellectual discipline. (“Taped Lessons Offer Insights Into Teaching,” April 2, 2003.)
As in Ms. Weiss’ study, the researchers found no link between the type of instruction and the success of the lesson. Countries where teachers spent a lot of time lecturing performed just as well on tests as those where teachers challenged students to discover the material on their own. The common link in high-achieving countries was that teachers ensured that students understood the basic principles of mathematics, as well as the skills needed to perform its procedures.
“This is using different methods, and the picture we come up with is pretty much the same,” said James W. Stigler, a professor of psychology at the University of California, Los Angeles, and the director of the videotape study for the Third International Mathematics and Science Study—Repeat, known as TIMSS-R. “We do have a problem, no matter how we look at it.”
Mr. Stigler and his research team are continuing to analyze videotapes of science lessons, and the results are due next year.
Probing Questions
The findings from Ms. Weiss’ study, although disappointing, match what advocates for math and science education say they see in classrooms.
“Even visiting exemplary classrooms, it’s usually disappointing,” said Senta A. Raizen, the director of the National Center for Improving Science Education, a Washington-based project of WestEd, a federally funded research laboratory. “If they’re not exemplary, it’s dismaying.”
But the study, published in May, did find several examples of what researchers considered to be excellent lessons taught from a variety of approaches.
One anatomy lecture on nerve receptors helped students understand how the body responds to touches, ranging from a gentle poke to excruciating pain. By the end, students were asking questions about whether nerves worked the same way for taste, hearing, and sight.
In an elementary school math lesson, pupils worked in pairs to plot graphs and then demonstrated their results on an overhead projector. The discussion that followed showed that the children understood the concepts the teacher was hoping to get across.
The common characteristic of the successful lessons, Ms. Weiss said in an interview, was that students could make sense of the mathematical or scientific content and then apply it in other situations.
But, she said, “the whole system is not set up with either the capacity or the incentives for teaching for understanding.”
The researchers saw that in a variety of cases, the report says, including a math lesson in which students solved problems on a worksheet and the teacher later gave out the correct answers. The approach was inadequate because the students were never challenged to explain the mathematical reasoning behind the problems.
And an elementary science lesson in which the teacher assigned students to draw their favorite animals fell short, because the teacher never talked about any scientific content related to the animals.
“We see the absence of sense- making,” Ms. Weiss said. “That seems to be the part that’s hardest.”
The study suggests that teachers need a variety of communications skills to ensure that students are learning.
“Content [knowledge] is not enough to make a person a good teacher,” said Johnny Lott, the president of the National Council of Mathematics Teachers and a professor of mathematics at the University of Montana-Missoula. “You have to have a teacher who knows how to ask the deep, probing kind of question. The big question is, how do you teach people to ask those questions?”
Changing teachers’ practice isn’t easy, the researchers acknowledge.
“Looking Inside the Classroom” suggests that professional development should model the types of lessons teachers should be doing in their classrooms. That means teachers need to be focused on helping their students achieve a set of specific learning goals, and they should use a variety of strategies, from lectures to inquiry-based projects.
Improving Practice
“The emphasis has been on pedagogy, rather than on getting students to learn,” Ms. Weiss said of the professional development related to the voluntary national standards in math and science. “What teachers get out of it isn’t what we had hoped.”
Mr. Stigler, the UCLA researcher, said teachers also need to see high-quality lessons so they can figure out ways to change their own practice. He has started LessonLab, a Santa Monica, Calif.-based company that collects videotaped lessons and creates professional development for teachers using them.
“Teachers need to learn how to analyze lessons and know what a quality lesson looks like,” he said. “We need that in the same way a student needs to know what an A essay looks like and why he got a C.”
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Coverage of research is underwritten in part by a grant from the Spencer Foundation.
