Blake E. Peterson

Research Japan My Textbook Links


Building on MOSTs

Mathematically significant pedagogicial Openings to build on Student Thinking(MOST)

Keith Leatham (Brigham Young University), Shari Stockero (Michigan Tech University), Laura Van Zoest (Western Michigan University) and I are currently working on a project in which we are defining "teachable moments" in a mathematics classroom. In conjunction with this work we have given several talks together (PMENA-2010, AMTE-2011, PMENA-2011, AMTE-2013, PME-2013, AMTE-2014, PME-2014, AMTE-2015, NCTM-2015, PMENA-2015, AMTE-2016, NCTM-2016, PMENA-2016).

We have also received a 4-year NSF grant to further investigate how to help teachers learn to recognize and productively use students' mathematical thinking in the classroom. This grant started in October of 2012 and will conclude in October of 2016.

For more information on this work, go to our project website.

University Mathematics Education Programs in Japan

In May of 2012, I visited Saitama University for 2 weeks to study the mathematics and mathematics education classes taken by perspective mathematics teachers at Saitama University. Professor Hiroyuki Ninomiya arranged for me to visit and video record several mathematics education classes every day. I plan to analyze these mathematics education classes and characterize things like the nature of the tasks done, the discourse that occurs, the norms established, etc.

Students of Teaching Project

Dr. Keith Leatham and I are currently working on a project that restructures student teaching in a way to focus the experience more on teaching and student mathematical thinking and less on classroom management. Many of the ideas for the structure came from my experience observing Japanese student teaching. In anticipation of changing the structure of student teaching we conducted a survey of mathematics cooperating teachers to assess their perception of the purpose of student teaching. This data contributed to the structure that we ended up with. An outline of this new structure is listed below:

Guiding Principle: In order for student teachers to become students of teaching, they need to spend significant, structured time studying the craft of teaching.

• Two student teachers will be placed with each of 3 cooperating teachers in each of 3 neighboring schools
• Student teachers will only teach one lesson per week during the first few weeks of the student teaching experience as outlined below:

o Week 1: Each of the cooperating teachers will be observed once by all 6 student teachers and a reflection meeting will follow.
o Weeks 2-6: The pairs of student teachers at each school will plan and teach one lesson per week (each student teacher will teach a different period), will be observed by the other 5 student teachers and will participate in a reflection meeting about the lessons taught.
o Weeks 7-14: Each student teacher in a pair will be responsible for 2-3 specific periods of the day.

The student teacher pairs will be encouraged to continue to plan lessons together, observe each other and debrief on the jointly planned lessons.
• Other activities during weeks 1-6:

o Structured Observations
o Activities focused on student thinking

Japanese Student Teaching

While on sabbatical during 2003, I visited Ehime University in Matsuyama, Japan to observe the student teaching process at the junior high school affiliated with the university. With the help of Professor Hiro Ninomiya, I obtained support from the Japan Society for the Promotion of Science. The following paper, summarizing some of the preliminary results, was presented at ICME in Denmark July, 2004. This paper will be published in the proceedings of the Thematic Afternoon A session of the conference.

Mathematics Student Teaching in Japan: Where's the Management?

During the summer of 2002, I visited Professor Yoshinori Shimizu at Tokyo Gakugei University, Professor Yasuhiro Sekiguchi at Yamaguchi University, and Professor ShinyaYamamoto at Kumamoto University to study the student teaching process at the affiliated junior high schools of these universities. A paper summarizing my observations, entitled Student Teaching in Japan: The Lesson, was published in the Journal for Mathematics Teacher Education in the first issue of 2005.


Preservice Lesson Study (with graduate students Julie Stafford Plummer, Thomas Earl Ricks, and Matthew Webb)

As part of the mathematics methods class that I teach for our secondary methods class, I have implemented lesson study. The students are placed in groups of 3 or 4 and matched with a teacher in the public schools. After selecting a lesson study goal with the cooperating teacher, the preservice teachers prepare a lesson that will be taught in the public schools at the end of the semester. Midway through the semester, they teach this research lesson to their peers in the methods class. Based on the data that they gather, they revise the lesson for it's final teaching in the public schools.

Julie was the first graduate student to work with me on investigating the dialogue that occurs in a lesson study group of preservice teachers. She looked at how the mathematical dialogue in the lesson study groups affected the preservice teachers beliefs about themselves as mathematical experts. The current draft form of this paper is called A preservice Secondary Teacher's Moves to Protect Her View of Herself as a Mathematical Expert.

Tom was the second graduate student to look at lesson study in a preservice situation. He focused on how reflection manifested itself in the lesson study process. All three of us presented our work at the NCTM research presession in April, 2004. My portion of the presentation was about the cultural barriers that I have observed as we have implemented lesson in this methods class. The contents of my presentationare found in Overcoming Cultural Barriers in Lesson Study.

Currently, Matt Webb is studying how the preservice teacher characterize anticipating student responses.Matt gathered data on one group's lesson study experience during fall semester of 2004. He is scheduled to complete his analysis and writing by August of 2005.

Mentoring in Student Teaching (with Dr. Steven Williams)

Steve Williams and I studied the dialogue that occurs between mathematics student teachers and their cooperating teachers. We selected student teacher/cooperating teacher pairs and recorded the conversations that they had during the student teaching process. We also interviewed all of their participants twice over the course of the study. One of the papers, Mentoring Styles in Mathematics: Two Contrasting Cases, is currently being reviewed for publication.

One of the findings is the lack of conversation about mathematics and the teaching of mathematics. The cooperating teachers feel that the student teacher is very well qualified in mathematics because of their college experience. The student teacher, on the other hand recognizes some weaknesses but is often afraid to discuss because of the evaluative nature of the relationship. Thus, there is a need to be discussing mathematics but nobody dares to bring it up. The paper discussing this concept is titled Factors that Affect Mathematical Discussion among Secondary Student Teachers and their Cooperating Teachers and is currently being reviewed for publication.

One part of our analysis found that in separate interviews, both the coorperating teacher and the student teacher emphasized the same things as significant parts of their conversations. In some cases, these common themes were driven by the interests and beliefs of the cooperating teacher and in other cases they were driven by a weakness or a need of the student teacher. We are currently writing a paper summarizing these findings.