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
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
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.
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.
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
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.