One of my favorite lessons was developed not by me but by a group of student teachers. While conducting research on student teaching in mathematics classes at a Japanese junior high school, I observed a group of seven Japanese student teachers participate in a lesson study to develop a lesson on the Pythagorean theorem. The goal of the lesson was for the students to understand the meaning of the theorem. The student teachers looked in many textbooks, studied the different proofs of the theorem, and consulted their cooperating teachers.

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### Blake E. Peterson

n the fall of 2003, I had the opportunity to conduct some research on the student teaching process in Japan. During my seven weeks of research at the junior high school affiliated with Ehime University in Matsuyama, Japan, I observed mathematics lessons taught by student teachers as well as many more lessons taught by experienced teachers. The basis for most of these lessons was wonderfully rich mathematics problems. In these lessons a problem was posed to students, time was given for them to explore it, and then a discussion of the solutions to the problem took place. A detailed description of similar problem-based lessons can be found in *The Teaching Gap (Stigler and Hiebert 1999) and The Open-Ended Approach: A New Proposal for Teaching Mathematics* (Becker and Shimada 1997).

### Blake E. Peterson

In fall 2003, I had the opportunity to conduct some research on the student-teaching process in Japan. During my seven weeks of research at the junior high school affiliated with Ehime University in Matsuyama, Japan, I observed mathematics lessons taught by student teachers as well as many more lessons taught by experienced teachers. The basis for most of these lessons was wonderfully rich mathematics problems. In these lessons, a problem was posed to the students, time was given for them to explore the problem, and then solutions were discussed. Similar problem-based lessons can be found in The Teaching Gap (Stigler and Hiebert 1999) and The Open-Ended Approach: A New Proposal for Teaching Mathematics (Becker and Shimada 1997).

### Blake E. Peterson

At some point in any geometry class, students examine the sums of the measures of interior and exterior angles of simple polygons. These concepts can be further reinforced by examining the sums of the interior angles of other polygonal shapes. What began as an investigation of a question about a fivepointed star with one of my classes became an extended problem-solving and problem-posing experience that led us to computer explorations on The Geometer's Sketchpad (Jackiw 1991) and conjectures of broad generalizations through inductive reasoning.

### Blake E. Peterson

IN 1994, THE WORLD CUP SOCCER CHAMPIONships were held in various cities and in a variety of stadiums across the United States. Unlike American football, soccer is played almost exclusively on natural grass. The need for grass presented a problem for Detroit because its stadium, the Silverdome, is an indoor field with artificial turf. Growing grass in domed stadiums has not yet been successful, so the World Cup organizers turned to the soil scientists at Michigan State University. The scientists grew the grass outdoors on large pallets and then moved these pallets into the stadium in time for the games.

### Blake E. Peterson and Introduction by: Jennifer Outzs

From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.

### Blake E. Peterson, Patrick Averbeck, and Lynanna Baker

Each Summer for the past six years, middle school students from rural communities in Oregon have come to Oregon State University for the three-week-long SMILE summer physics camp. SMILE, Science and Math Investigative Learning Experience, an after-school enrichment program for rural minority students, is administered by Oregon State University.

### Eric J. Knuth and Blake E. Peterson

In “Fostering Mathematical Curiosity” (Knuth 2002), Eric Knuth discusses the idea of problem posing as a means of fostering students' mathematical curiosity. A mathematician colleague, after reading the article, commented that a significant amount of the mathematics in the discussion of the various problems and their solutions had been “left out” —and he was right. The author's primary intent in writing that article, however, was to illustrate “what it might mean to engage students in problem posing and how teachers might begin to create classroom environments that encourage, develop, and foster mathematical curiosity” (Knuth 2002, p. 126), not to discuss in detail the mathematics underlying the solutions to the problems posed.

### Blake E. Peterson, Steven R. Williams, and Penelope H. Dunham

The most crucial stage in the process of becoming a teacher occurs at the very outset, during the transition from student to student teacher to novice teacher. Many people can provide vital support to the new teacher: cooperating teachers, university supervisors, instructors of methods classes, and more experienced teachers in the school can all act as mentors. What is known about the mentoring process? What is unique to mentoring mathematics teachers? In this article we hope to outline what is known and offer some guidance for those wishing to be effective mentors.

### Blake E. Peterson, Douglas L. Corey, Benjamin M. Lewis, and Jared Bukarau

What can American teachers learn about high-quality mathematics instruction from the Japanese teacher education process?