Improving math teaching through lesson study

iStock_000016934184XSmallResults of the Video Study of Teaching, conducted as part of the Third International Mathematics and Science Study (TIMSS), confirm that teachers in the United States continue to follow traditional teaching practices that differ from current instructional practices in countries whose children score significantly higher on math achievement tests. Recent research findings about how children learn have not created any fundamental changes in how math is taught in the United States; conclude James Hiebert, University of Delaware, and James W. Stigler, University of California/Los Angeles. The TIMSS video Study consists of videotaped lessons from randomly selected eighth-grade math classrooms in Japan, Germany and the United States. The goal was to examine differences in instructional practices that might shed light on their significantly different achievement levels on the TIMSS.

In addition to having their lesson videotaped, each teacher filled out a questionnaire describing the goal of the lesson, how typical the lesson was, and its place in the sequence of lessons. All lessons were transcribed and analyzed by teams of coders who were native speakers of the language in which the classes were conducted. The goal of Hiebert and Stigler’s analysis was to determine how math is taught in the United States, to compare U.S. instruction to instruction in Germany and Japan and to examine the influence of recommended reforms in math instruction on classroom practice in the U.S.

No significant reforms seen in U.S. math instruction

Ninety-five percent of the U.S. teachers said they were aware of recent research on learning and recommendations for effective math teaching. However, evidence from the videotapes suggests that U.S. teachers continue the traditional practice of simply stating a mathematical concept rather than developing it.

The reverse is true in Japan and Germany, whose children outscore U.S. children on international tests. In this random sample, no U.S. teachers worked through proofs or reasoned inductively with students. In contrast, 10 percent of German lessons and 55 percent of Japanese lessons included proofs. In addition, 96 percent of U.S. students’ seatwork was devoted to practicing procedures. Japanese students, in contrast, split their time evenly between practicing procedures and doing original work – inventing procedures or analyzing mathematical solutions in new ways. When asked how they believed their lessons were consistent with research on effective teaching, many U.S. math teachers said they incorporated real-world problems, hands-on activities, cooperative learning, and discussions of mathematical thinking and problem solving into their lessons. Videotapes revealed that these teachers used textbooks less often, had students work in small groups and assigned more seatwork than teachers who believed they had not incorporated current research findings into their lessons.

Hiebert and Stigler conclude, however, that while reform-minded teachers in the U.S. changed some activities and organizational features of their lessons in recommended ways, they had not changed the way students do mathematics. In fact, there were few significant differences between U.S. teachers who believed they had instituted reforms and those who believed they had not. Hiebert and Stigler gave the following example of one teacher’s attempt to engage students in mathematical thinking rather than simply practicing procedures: he asked students to “try and figure out the name of a three-dimensional object with 12 faces.”

Students working in groups asked each other if anyone knew the name. One student did and told the members of his group. Students in the other groups did not know and began talking about other things. When the teacher asked them for their “findings,” the one group suggested dodecahedron; the other groups said they didn’t know. In this example, the teacher changed the type of question he posed, but the students were unaware of the changed strategy and did not change their behavior. Changing just one or two elements is usually not successful in changing how students think and do mathematics. Any attempted changes simply get swallowed up in the old system.

Teaching as a cultural activity

After analyzing the TIMSS Video Study, Hiebert and Stigler conclude that teaching is a complex system involving the interaction of many elements embedded in a cultural context. Teaching evolves in ways consistent with a society’s beliefs about what and how students should learn. The depth of cultural differences surprised them. The most striking feature of teaching in the U.S. was that teachers almost always showed students what to do, and with relatively little mathematical development assigned problems similar to the worked examples. Japanese and German teachers, on the other hand, posed problems that students had to find ways to solve. Teachers in the three countries had very different goals. When asked what was the main thing they wanted students to learn from their lesson, 73 percent of Japanese teachers said thinking, while 25 percent said skills. Teachers in Germany and the U.S. heavily favored skills over thinking.

A new model of improvement: Lesson study

Hiebert and Stigler believe that attempts to reform instruction in the U.S. have largely failed because reformers have not understood that teaching is a cultural activity. To improve teaching in fundamental ways requires methods attuned to complex cultural activities. These authors believe that reformers must take a long-term view, recognizing that fundamental cultural changes are gradual and incremental. Dramatic improvements can occur, but these will result from accumulating small changes in basic classroom processes over time. Studying the TIMSS videotapes reveals that Japanese instruction varies significantly from that received by either German or U.S. students. Math lessons in Japan are designed, tested and reviewed by groups of teachers who use lesson planning as an ongoing form of professional development. Japanese teachers learn to improve their skills in the context of designing and implementing improved lessons in their individual classrooms.

While educational administrators set the goals of instruction, decisions for improving teaching and learning are made by teachers at the school and classroom level. This system provides Japanese teachers with access to ongoing learning opportunities in their own schools among their peers. When high-quality Japanese math lessons were analyzed, they were found to be more consistent, in some ways, with U.S. reform recommendations than were lessons in this country. The system of lesson study in Japanese schools enables teachers there to participate throughout their careers in a continuing in-service program built around the lesson-study group in their school. Typically, small groups of teachers meet once a week for several hours to collaboratively plan, implement, evaluate, and revise lessons. Many groups focus on only a few lessons during the year.

The process begins with reading about what other teachers have done, what ideas are recommended by various educational groups, what has been reported on student learning of this topic, etc. The group designs several lessons and one teacher tries them out in her classroom with the other teachers observing and evaluating what works. The group then revises the lesson. They often base changes in lessons on specific misunderstandings that students exhibit as the lesson progresses. They might change the wording of the opening problem or the kinds of follow-up questions they ask, or use information from the kinds of methods students invent to solve the problem. Then they try the lessons again, perhaps with other teachers watching.

Much attention is paid to anticipating students’ responses. This process can go on for several months until teachers believe they have perfected the lessons. When the new lessons are ready, complete with test and development information and expected student responses for each question and problem, they are shared with other teachers and other schools. A group’s report includes descriptions of the learning goals and activities, the rationale for the lesson design, and suggested reactions by the teacher to anticipated student responses. Ways to help students reach learning goals are linked to actual lessons and specific problems. The goal of the lesson study is not just to produce lessons that can be copied but also to produce knowledge about teaching upon which colleagues can build.

Lesson study in Japan reverses the pattern seen in the United States. In Japan, working on improving teaching yields teacher development, rather than vice versa. Designing and testing lessons provides a rich context in which teachers can improve their own knowledge and skills. While teachers are producing shareable work, they are learning what they need to learn to become more effective teachers. They learn more about their subject, about their students’ thinking, and about alternative forms of instruction.

Requirements of lesson study

Hiebert and Stigler see the process of lesson study as a particularly effective form of professional development. But the study process requires that teachers have time for study, observation and reflection with colleagues in their school. While it would require significant changes in the culture of U.S. schools, it fits well with the recent trend of teachers’ researching their own practice. Clearly defined learning goals for students are a necessary component of lesson study. Goals need to be expressed clearly enough that teachers can use them for planning instruction.

In addition, learning goals must be widely accepted. The success of the lesson-study process depends on teachers’ working together with the same goals in mind. Teachers need time for collaborative work built into their weekly schedules. Hiebert and Stigler report that there are some school districts in the U.S. that have successfully and economically created time for teacher collaboration. New York City’s Community District No. 2 is one example. Hiebert and Stigler assert that the Japanese experience shows that teachers can increase their general knowledge and skills by working deeply with a few lessons. Improving teaching does not depend on perfecting a huge number of lessons, but rather on engaging intensively with the issues involved in teaching any lesson. Japanese teachers say that the yearlong process of perfecting a few lessons helps them teach all lessons more effectively.

While it is foolish to think that a program can simply be imported and show the same results in a new country, these researchers believe it is foolish to dismiss promising ideas from other cultures. Reforms in the United States come with imperatives to show quick and dramatic change. This proposal will not bring quick results. These researchers suggest that states and school districts in the United States must decide whether they are willing to establish a long-term improvement strategy that guarantees teaching will be more effective in the years to come.

“A Proposal for Improving Classroom Teaching: Lessons from the TIMSS Video Study” The Elementary School Journal Volume 101, Number 1, September 2000 Pp. 3-20.

Published in ERN November 2000 Volume 13 Number 8

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