What do chili peppers and mathematics have to do with each other? Last year, Kevin Kelly, Lexington (Mass.) High School pre-Calculus teacher would have said “nothing.” But today, his answer would be “everything.” Frustrated with the standard lecture approach to mathematics, he and his colleagues have developed a hands-on, interactive lesson that uses the relative heat of chili peppers to introduce and explore the mathematics concepts of properties and logarithms. Using an innovative Japanese teacher development program called “lesson study,” the teachers collaboratively developed mathematics lessons by observing each other in class and drawing on each other’s insights. Their lesson, “Hot Peppers: Making an Exponent Ruler,” and explore follow-up questions that led them to make observations that eventually revealed the properties of logarithms. “Now, students actually understand what’s going on rather than just learning properties by rote.”
Such cross-fertilization is the heart of “lesson study,” a method that has also captivated a group of EDC researchers, who have launched a three-year investigation into the adaptability of the model to the U.S. The project, funded by the National Science Foundation, follows the experiences of a few dozen Boston-area high school mathematics teachers to document the impact of this style of teacher development.
Lesson study is based on a simple proposition: teachers have much to learn from each other about how to engage students with stimulating and rigorous lessons. Through a range of collegial activities, lesson study provides a format for teachers to create effective classroom sessions, constructively critique each other’s classroom methods, and collaboratively work toward improvement. “On almost any topic, the interaction among teachers is what is key,” says Robin Fies of Watertown High. “You’re doing all that work together and saying, ‘gee, I never thought about it that way,’ and you modify your lesson.”
“This kind of professional development makes enormous sense to me,” says Jane Gorman, EDC project director. She sees lesson study as a self-sustaining model for gradual improvement of teaching that contrasts sharply with short term, fragmented approaches to professional development.
“Lesson study is a very teacher-centered approach,” says Gorman, a former high school mathematics teacher. “It’s a way teachers can claim ownership of their own learning on things that matter to them the most: what’s going on in their classrooms and how they can make that work better. One of the principal virtues of lesson study is that it tackles many of the most critical issues of instruction and teacher learning at the same time,” she adds.
Many teachers in the EDC project have used lesson study to improve their teaching of difficult mathematical topics that are most challenging to students, such as the geometric concept of slope. One team developed a lesson, “How Steep are Stairs?” that allowed students to investigate slope in a practical context before delving into the more abstract mathematics that defines the term . “They understood steepness and then they translated it into a more general concept of steepness of a line,” says Gorman.
Six Key Steps
In the EDC project, mathematics teachers will follow six key lesson study steps. First, a group of teachers (from a single department or grade level or schoolwide) agree upon a goal or “big idea” that will guide their classroom efforts. This theme will then be infused through the instruction. For example, a team of teachers might agree that they want students to become independent thinkers or better mathematical communicators.
Second, teachers work in small teams to develop a lesson plan that covers the subject material and also integrates the theme. They choose thought-provoking questions, discuss possible student responses, consider how to assess student understanding, and plan for optimal use of blackboard and manipulatives (such as geometric blocks or number cubes).
A few of the teachers present the lesson to their students, with their teacher team members observing student response and engagement. The group members take extensive notes, emphasizing observations of students’ thinking, reactions and work, and on how the lesson goals are being achieved.
Later the observers give feedback, advice and pointers and the team revises the lesson.
A second teaching of the lesson to another classroom often includes additional guest observers, and is followed by a meeting to discuss the details of the lesson as well as wider educational and mathematics issues that relate to it. For Paul Barnett and his group at Wareham High, deciding how to open the lesson prompted the most discussion. “We all have different styles,” he said. They experimented with three different approaches in their classes, discussed the results and created a hybrid that combined the best qualities of each.
The cycle concludes with the preparation of a detailed lesson plan and reflections from the study group on what they learned.
School support and interest in the project is strong, Gorman says. Some teachers might balk at the prospect of an added layer to their already busy day, but as they work with lesson study, they see it as an “improvement in their lives,” says Gorman. With lesson study, “they’re not talking about extra stuff. They’re talking about what they do as teachers.” One mathematics department chairman has devoted her staff meetings to lesson study because it allows them to work on all their long-standing priorities: curriculum, how students learn, and improving standardized test scores. Gorman says EDC strives to work within teachers’ time constraints. “We want teachers to be able to do this within the school day.”
Throughout, Gorman’s project will focus on three key research questions. 1) How does lesson study affect the prevailing, and often counterproductive, norms of privacy among teachers that are common in U.S. schools? 2) How does lesson study serve as a form of teachers’ professional development? 3) How does lesson study meet the particular needs of U.S. secondary school mathematics departments? The research protocol includes baseline and follow up surveys to all participants, interviews with ten teachers, observation of the full range of lesson study activities, case studies of three teachers.
Building on Prior Work
Gorman and her colleagues first encountered lesson study at a meeting of the International Congress of Math Educators in Japan. A newly published book, The Teaching Gap by James W. Stiglerand and James Hiebert, was calling for improved teaching in the U.S. and touting lesson study as a promising approach.
Intrigued, Gorman and her colleagues June Mark, Al Cuoco, and Michelle Manes, set up a small-scale project in the Watertown High School, where they had been working on other mathematics projects. “We decided that year, that lesson study was as exciting as we thought it would be,” says Gorman. They received National Science Foundation funding to conduct the expanded, three-year project that is now in its first phase. The project now operates at six high schools (Watertown, Wareham, Lexington, Brookline, Newton South, and Danvers) as well as one middle school (Watertown) and will ultimately involve 21 teams of secondary school mathematics teachers. EDC will supply onsite coaching and workshops to facilitate the work of the teams.
Originally published on December 1, 2002