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OCR for page 3
The two-and a half-day workshop The Study of Teaching Practice as a Medium for
Professional Development focused on the use of teaching practice as a way to study
what elementary mathematics teachers need to know to teach well. The opening
sessions were designed to share background information about the education of
mathematics teachers in the two countries. The first whole day of the workshop
addressed practice by studying the preparation for and enactment of an actual lesson,
through an investigation and analysis of Japanese Lesson Study. On the second day,
participants considered records of teaching that included a video of a classroom lesson
and an analysis of a case describing teachers and their work.
After the workshop, two of the participants wrote papers describing the events from
their perspective as mathematics educators. The following two papers reflect their
overviews of the workshop, their sense of what they learned, and how the workshop
experience related to their own background and work as mathematics teacher educators.
Observations from the Study of Teaching Practice as a Medium for Professional
Development
Henry S. Keener, Jr., University of Wisconsin-Milwaukee
Building an International Community: Sharing Knowledge and Experiences in
Professional Development for Mathematics Education
Carol E. Malloy, University of North Carolina-Chape! Hill
OCR for page 4
OCR for page 5
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Henry S. Kepner, Jr., University of Wisconsin-Milwaukee
The workshop considered the study of
teaching practices as a medium for
professional development. Three main
approaches were identified and discussed
at length during the conference: the
lesson study a frequent practice in
Japan, and two evolving practices using
records of study in the United States-
classroom video and written case study.
The overall workshop activities repre-
sented a clear difference in approach to
professional development priorities and
background. First, the Japanese partici-
pants reflected an almost unanimous
awareness and acceptance of content and
its placement in the national curriculum.
When a mathematical topic was identified,
they responded by knowing the grade
level of its presentation and what students
should already know at that time. This
clear and consistent assumption of stu-
dent mathematical content background
was not evident among the U.S. partici-
pants. As Deborah Schifter and others
noted, in the United States the local
control of schools combined with diverse
teaching strategies and curricula often
supports professional (levelopment that
focuses on isolated topics that may not be
closely related to the mathematics in the
curriculum such as group work, use of
~_.
manipulatives, or problem solving.
Second, throughout the workshop,
Japanese participants focused more
consistently on the mathematical structure
and clear student performance expecta-
tions in a lesson. Each move made by the
teacher was first addressed with regard to
the mathematical goal of a lesson. Again,
this single purpose was not as evident
among the U.S. participants. Often, other
issues related to the observations, such as
a teacher's skill in eliciting student ideas,
arose first before the attention to the
mathematics and its structure.
This stu(ly of teacher (levelopment as
advocated in two countries brought
together (lifferent perspectives on what
teachers coul(1 learn from two (lifferent,
yet similar, sets of evidence with a focus on
teacher planning, instructional materials,
classroom activity, and student work
both through videos or observations and
written work. The positions, presente(1 by
several members of Japanese anti U.S.
mathematics educators, teachers, anti
mathematicians, showe(1 both perspectives.
The lesson stu(ly format, with slight
variations, is con(lucte(1 by a group of
teachers, often with a university educator,
who develop a lesson in great detail for
self-stu(ly anti sharing among colleagues
OCR for page 6
who come to observe the lesson taught by
a member of the group. The lesson study
has an accepted place as professional
development in the elementary schools
and to a lesser extent in the middle
schools. It is not accepted as needed by
most secondary teachers of mathematics.
In both plenary and small group discus-
sions, the Japanese university participants
repeatedly saw the lesson study as a way
to help elementary teachers improve their
reportedly minimal mathematical back-
ground.
The lesson study team makeup and
purpose vary (lepen(ling on the primary
reason for a lesson study. The activity
may be for the professional growth of the
teachers at a school or district or for a
focus group of teachers where the activity
is primarily a demonstration lesson for the
engagement and growth of those partici-
pating the team and observers on that
day. It was reported that a university
person was often invited to be a team
member or a reactor for a local lesson
study. University participants at the
workshop noted that a university person
who does not contribute significantly to
the team or review process would not be
invited back to future lesson study efforts.
Lesson study is constructed to do
research on the feasibility or effectiveness
of a lesson. The lesson might be necessary
for a new mathematical topic inserted in
the curriculum, a different lesson approach
or structure for a standard topic, or a new
approach for a topic that is perceived as
(difficult to teach. Such lessons are often
done at demonstration schools associated
with universities anti less often at other
schools.
In the lesson study process, teachers
from the host school and frequently from
surrounding schools and universities
observe the class and participate in
professional discussion following the
lesson. Although there was substantive
professional discussion along with chal-
lenge or disagreement among the teacher,
lesson study team, and observers, for the
most part there was a politeness and
cautious consideration for the teacher and
team-(levelope(1 lesson. When pressed,
several of the Japanese participants
indicated that the actual conclusion of a
lesson study process was "a party" at
which there might arise substantive
criticism of, or disagreement about, the
lesson and/or its delivery.
When participants viewed or rea
descriptions of lessons and student
responses, there was a marke(1 (1ifference
in U.S. and Japanese reactions about the
students' content background. While U.S.
participants often had varying perspec-
tives on student mathematical background,
the Japanese participants reflected
apparent uniformity about where that
content would be presented in the school
curriculum anti the backgroun(1 students
woul(1 have experienced. This (lifference,
attribute(1 to a national curriculum by
Japanese participants, ma(le an e(luca-
tional (liscussion much more focused by
the Japanese. Although the lesson stu(ly
activities experienced and discussed at
the workshop encouraged each observer
to bring their own professional perspec-
tive, the presentations anti (discussions
in(licate(1 that the Japanese teachers hall a
common set of expectations anti points of
reference.
For the Japanese, there was an over-
ri(ling concern for the mathematics, its
structure, anti attempts to motivate stu-
dents to learn it. This was critiqued within
the lesson plan and the way the lesson
was implemente(l. Most questions starte(1
with issues of mathematical purpose along
with effectiveness of student motivation.
In small group anti follow-up (liscus-
sions, the function of a lesson stu(ly as a
REFLECTIONS ON THE WORKSHOP
OCR for page 7
device for professional development was
probed in depth. Conference participants
reported the development of both a set of
observation criteria and a language of
discussion useful in the professional
conversation. This was a means of
communicating the criteria or expectations
of the observers and the lesson study
team, including the classroom instructor.
Examples of pedagogical jargon, in the
English translation provided by Toshiakira
Fujii and other Japanese participants, led
to implied observation criteria. The
criteria, also associated with the develop-
ment of the lesson plan, included
· the opening problem setting with its
motivational focus;
· the teacher's questioning, both the
.
.
.
sequence of questions and attention to
hatsumon, "thought-provoking ques-
tions" important to mathematical
development and connections;
kikan-shido, "between desk walking" or
"purposeful scanning" referred to the
teacher's purposeful observations and
interactions while "walking among the
desks" observing student work;
the teacher's skill in anticipating
student thinking;
· hansho, or "blackboard writing,"
stressed the organization of student
work and key mathematical statements
or results recorded by the teacher on
the blackboard;
neriage, "raising the level of the whole
class discussion," through the orches-
tration and probing of student solutions,
usually in the whole class format; and
· matome, the teacher's mathematical
summary of the lesson for the whole
class, with attention to students' ideas
and contributions.
The extensive discussion of such criteria
was seen by all participants as important
to help both preservice and experienced
teachers to be productive observers of
classroom practice. Participants from
both countries indicated that training
in(livi(luals to be effective observers of the
content development was a difficult task
that occurs over time. In particular,
Deborah Ball noted the difficulty experi-
enced in helping teachers observe what
the demonstration teacher is really doing
to develop the mathematics.
From the Japanese participants, there
was a non-deviating focus on the correct-
ness of the mathematics during the lesson
and teacher summaries. It was frequently
noted that an underlying purpose of
lesson studies was to assist preservice
anti professional teachers to increase their
mathematical knowledge which univer-
sity participants reporte(1 as weak. This
purpose for lesson study presented a
challenge with respect to lesson study
team composition. While the team
typically included a group of teachers in
the host school, in some cases there was a
reference to the involvement of a univer-
sity mathematics educator or mathemati-
cian on the team. It would that if seem
this member is not an integral member of
the team, the lesson might lack the
mathematical precision and development
expected. Such team makeup is often an
area of concern in U.S. professional
evelopment when it is school based.
The Japanese e(lucational process
demonstrated in the lesson study examples
stressed the challenge to the teacher of
motivating the students about the math-
ematical topic without forcing the
teacher's view on the students in the
developmental portion of the lesson.
Although this position ha(1 similarities to
the lessons illustrate(1 at the workshop, it
was noted that this was in contrast to the
most common mo(le of U.S. instruction,
variations on a (lirect instruction format.
OBSERVATIONS FROM THE STUDY OF TEACHING PRACTICE
OCR for page 8
The teacher's intent to bring multiple
student presentations together controlled
the conclusion of a Japanese lesson.
However, in contrast to constructivist
lessons where student summaries often
are encouraged, the Japanese participants
adamantly stated that the final summary
of the mathematical conclusion must be
made by the teacher to ensure that
students heard correct mathematics
correctly stated.
A perspective of both approaches
centered on observing and reflecting
upon student work in the learning of
mathematics. In the lesson study process,
the teacher observers were intent on
observing what students did during the
observed class. Frequently each observer
would take responsibility for looking at
the seat work of a particular student and
even asking questions quietly during the
period, gathering information about
students' reactions to the lesson.
Observers are careful not to become
teacher's aids. In the case study approach,
reflections of videotapes and samples of
student work were used for a similar goal.
The professional development culture
of lesson study provides a real-time obser-
vation and discussion for the observers, a
portfolio notebook kept at the host school,
and perhaps a short article on the lesson
in a local Japanese education periodical.
The best of these lessons becomes part of
the teaching resources for others to use in
teacher preparation or professional
development.
Although there was an educational
history of lesson study as an ongoing
activity, participants noted that the use
and involvement were uneven. Discussion
indicated that schools attached to univer-
sities do many lesson studies while public
schools (lo far less. Several participants
from public schools indicate that lesson
studies were often omitted due to other
priorities of the school staff or administra-
tion. Workshop participants indicated that
many teachers serve as the lesson study
teacher only once or a few times in a
career. The impact of lesson study is
primarily on the teacher team that created
the lesson. They spend considerable time
outside of their daily practice preparing
the lesson and postlesson reflection and
documentation. For observers, this is an
opportunity to establish and continue
professional communication and take
away ideas for implementation or refine-
ment. For preservice teachers, this can
have a powerful impact on learning from
the demonstration of more experienced
teacher teams. For experience(1 teachers,
a lesson may present a new curriculum
piece or a new pedagogical strategy.
During the workshop, (liscussions in
small groups anti in(livi(lual conversations
considered the merits of using the differ-
ent forms of studying practice. The live
observation of a teacher anti class in
action around a focused lesson plan
brings a strong cultural component to
lesson stu(ly for the Japanese participants.
Their continual reference to "seeing with
the eyes" is the essence of professional
growth. The use of videos of lessons along
with samples of student work anti an
opportunity to have reflections from the
classroom teacher seemed to make a
classroom video a possibility for reflection
on a lesson. However, the written case
approach was not seen as valuable by the
Japanese because of the lack of an
authentic teacher anti students. Also, the
participants were concerned that the
perspective of the writer limite(1 the
opportunity of each participant to bring
their own perspective to the (liscussion.
Lesson stu(ly requires the actual
enactment of the lesson stu(ly process for
preservice or professional (levelopment
for a set of in(livi(luals. In contrast, the
REFLECTIONS ON THE WORKSHOP
OCR for page 9
video and written case study records of
practice, organized and packaged for on-
demand use, could be used at the
inshructor's choice in settings across time
and geography. That is, a collection of
records of practice could be used semes-
ter after semester in a teacher preparation
program for preservice teachers. Or a
record of practice could be used for
professional development in school
dishricts across the counbry.
One comparative shrength of the
records of practice approach is the
opportunity to develop these records over
time with the same children or different
children. How does their mathematical
· ~
commun~cahon grow over a year, or even
over years? Records of practice (videos,
written student work, hranscripts) could
be collected and organized for such study.
When used for research or professional
development, the records could be
revisited repeatedly for purposes of
argument or clarification of a classroom
act by student or teacher. The real-time
observation in a lesson study would not
have this opportunity to "see it again."
Lesson study has its roots in the lesson
on the day of observation, although lesson
study is about much more than a single
lesson. Japanese educators are concerned
about students' growth in mathematics
and communication, how lessons are
sequenced and how ideas are built across
lessons and grades despite the existence
of a national curriculum.
The workshop clearly presente(1 two
approaches to professional (levelopment
through the study of teaching practice.
Two models of records of practice, video
and written case studies, were identified
as providing tools that multiple audiences
could use at convenient times and loca-
tions. The need to develop a package that
coul(1 be use(1 by those (1istant from the
teaching being recorded and with varying
leaders was an important consideration in
effective use of these tools for profes-
sional development. Lesson study was
con(lucte(1 with primary attention to
professional development by those
present at the lesson. The resulting
lesson plan and indications of student
responses might be written for a local or
national professional journal to give
teachers a plan (letermine(1 effective by
the observers and those who conducted
the lesson study.
OBSERVATIONS FROM THE STUDY OF TEACHING PRACTICE
OCR for page 10
Carol E. Malloy, University of North Carolina-Chapel Hill
Mathematics educators in the United
States and in Japan are working to provide
preservice and practicing teachers with
exemplary professional development in
mathematics teaching. However, situations
confronting the United States and Japan in
mathematics education are quite different.
The United States is faced with a teacher
shortage in mathematics education (Riley,
2000), and numerous mathematics classes
at the elementary and middle grade levels
are taught by teachers without substantial
mathematics training (Dossey and
Usiskin, 2000~. A(l(litionally, over 30
percent of U.S. students at grade 4, 6, and
12 perform below the basic level of
achievement on the National Assessment
of E(lucational Progress (Dossey, 2000~.
In Japan, students have historically
achieved at high levels in mathematics;
however, the results of the Third Inter-
national Mathematics and Science Study
show that 47 percent of Japanese students
do not like mathematics (Hashimoto,
1999~. In response to the national con-
cern that schooling should respond to the
needs of children, "in 199S, the Ministry
of Education, Culture, Sports, Science and
Technology reformed the Course of Study
for K-12 to emphasize the well-being of
human development of the child in a
changing international society" (National
Science Foundation, 2000~. This plan
reduces the number of (lays students are
in school and the mathematics content
hours that they experience. The plan also
mandated changes in university teacher
preparation programs that reduce the
preservice content course credits while
increasing the pedagogy course credits.
These changes in philosophy anti pro-
grams come to Japan at a time when there
is a surplus of mathematics teachers and a
decline in the population of school-age
children.
GOALS OF THE WORKSHOP
Both the Unite(1 States an(l Japan are
face(1 with challenges in the mathematics
education of their students. One strategy
is to address the challenges through a
dialogue of mathematics educators about
the delivery of professional development
to teachers. To promote this dialogue, the
National Research Council (NRC) held a
U.S. - Japan Workshop on Professional
Development in Makuhari, Japan, cen-
tered on the questions: What knowledge
of both content and pedagogy do teachers
need to teach well and how can teachers
OCR for page 11
come to acquire this knowledge in ways
that are usable in practice? The major goal
of the workshop was to use the expertise
of the participants to investigate these
questions to develop ideas and insights
that could address the issues surrounding
the preparation of mathematics teachers.
This workshop used an accessible
medium, teaching practice, as a too} to
address professional development of
mathematics teachers in both countries.
Before the conference, participants
received papers that explained and
demonstrated three forms of professional
development using teaching practice:
(a) lesson stu(ly, or jugyokenkyu as it is
practiced in Japan, and (b) two types of
records of practice cases and fairly
complete records of instruction including
classroom video called record study, from
the United States.
In this paper, ~ chronicle the events of
the conference through my experiences
as a mathematics teacher and teacher
educator from the United States. ~ begin
by explaining my position anti the approach
to professional development and teacher
preparation coming into the workshop.
Next ~ share my journey through the
workshop, the insight ~ gained, the
confusion ~ felt, and how this experience
reshaped my view of teacher preparation.
MY POSITION AS A TEACHER
EDUCATOR
In teacher education, as in many
disciplines, teaching and learning are 2.
intertwined. We learn our disciplines-
pe(lagogy and content and we learn
more about teaching as we practice our
discipline. To foster this type of teaching
and learning within the methods and
mathematics classes ~ teach and the
professional development ~ offer to
B U I LD I N G AN I ATE R NATI O CAL COMMU N ITY
practicing teachers, ~ use a "community of
learners" approach where the participants
and ~ interchange the roles of the teacher
and the learner. The tools that ~ use are
case discussion with narratives of teach-
ing and learning, lesson records through
the medium of video and student work,
reflection, and study groups. My goals
are to help preservice and practicing
teachers learn strategies to understand
how their students' learn, to develop
strategies to enhance student learning,
and to have a strong foundation in and
conceptual un(lerstan(ling of the math-
ematics they are teaching. As a commu-
nity, students in classes and teachers in
professional (levelopment sessions
explore educational topics and issues
through inquiry and critique, striving to
find answers to questions and formulate
positions. We use inquiry to explore the
mathematics content and related issues.
We develop and model what we think are
appropriate pedagogy strategies for
teaching mathematics and content for
middle and high school students. The
most important phase is our reflection.
Each of us personally reflects on our
teaching to assess how we are (loin" our
work to improve our practice and achieve
the goals we have individually set for
ourselves. Over the past 30 years ~ have
isolate(1 three essential components that
support this metho(1 of professional
evelopment:
love of anti passion for teaching anti
learning;
knowle(lge of content with the neces-
sary pe(lagogical skills anti ability to
assemble, synthesize, anti convey
course content to students; anti
continuous reflection that gui(les
learning anti teaching.
These three components were central
OCR for page 12
in the three forms of professional develop-
ment discussed at the workshop.
JOURNEY THROUGH THE
WORKSHOP
The workshop was planned to promote
a collaborative atmosphere between the
participants from the United States and
Japan who were teachers, teacher educa-
tors, and researchers from both countries.
We were assigned to seats so that we
could form small discussion groups that
would include people from both countries
and with varied backgrounds and careers.
The format for most workshop sessions
started with presenters sharing informa-
tion about key topics followed with
participants reacting to and discussing
what was shared in a group as a whole, in
small prearranged groups, or in clusters
based on seating assignment.
The first session was designed to give
us an understanding of the educational
systems, teacher preparation, and profes-
sional development in the United States
and Japan. There are clear similarities in
the structures that support mathematics
education in both countries. Neither
country has a nationally organized
system of professional development,
although professional development does
exist at the school, (listrict, university,
regional, and national levels. At the
elementary level teachers are generalists
teaching all academic subjects, and at the
high school level teachers are specialists
teaching in only one curricular area. The
textbook selection process is similar in
both countries. In the United States
individual states or school districts
authorize textbooks that match the
curriculum guidelines of states and
districts. In Japan the Minister of Educa-
tion, Science and Culture authorizes
textbooks that he deems suitable to be
used in schools, which match the Japanese
national curriculum Japan Society of
Mathematical Education, 2000~. With
guidance from principals anti (1istrict
(prefecture) administration, schools are
then allowe(1 to select from the list of
approve(1 texts for students.
Differences in structured programs far
exceed the similarities. The most obvious
difference is that Japan has a national
curriculum in mathematics, and the
United States does not. In the United
States individual states or districts control
educational programs for students,
resulting in varied educational curricula;
whereas in Japan the Minister of E(luca-
tion, Science and Culture controls educa-
tional programs, ensuring uniformity
throughout the country. Certification
requirements are different. Mathematics
teachers for the middle grades in the
Unite(1 States are not always certifie(1 in a
content area, while those teachers in Japan
are certifie(1 in mathematics only. This
enables Japanese preservice teachers for
the middle grades to take more math-
ematics content courses. Most certifica-
tion programs in the Unite(1 States require
that teachers participate in professional
(levelopment programs to retain their
certification. Atypicairequirementis six
credit hours every five years in education
courses not necessarily mathematics
courses (Dossey and Usiskin, 20001.
However, Japanese teachers obtain a
lifetime certification and are not required
to take a(l(litional courses (luring their
teaching careers. Requirements for initial
teacher preparation are (lifferent.
Teacher preparation programs in the
Unite(1 States require 12 to 15 weeks of
student teaching under the supervision of
a classroom teacher where teacher
preparation students observe anti in(le-
pen(lently teach the full sche(lule of their
REFLECTIONS ON THE WORKSHOP
OCR for page 13
· —
supervising teacher for at least 6 to ~
weeks. It is expected that new teachers
have gained the necessary skills to be
independent in their first years of teach-
ing, but many school districts have
induction programs where new teachers
have mentors who are available for
support. In Japan the system is slightly
reversed. Japan requires approximately
three weeks of student teaching where
they observe other prospective teachers,
and then they teach alone and in teams
with a master teacher. When most new
teachers are hired, they are paired with
experienced teachers for a year so that
they can team teach with the master
teacher as they develop their skills as
teachers. They also are required to attend
professional development sessions
throughout the year.
The forms and goals of professional
development in the United States and
Japan reflect the needs of teachers to
improve their practice, the needs of their
students, and the structure of each
country's teacher preparation programs
and certification requirements. Profes-
sional development in the United States is
structured to help teachers grow in a
variety of ways. Some may address
change in classroom practice to be more
inclusive of all students, or focus on
helping teachers understand the math-
ematics they teach, while others may help
teachers with pedagogical decisions and
strategies for effective instruction. Gener-
ally professional development is struc-
tured to support the accumulation of
continuing practice credits for certifica-
tion. Fried et al. (1998) provide a list of
professional development strategies used
in the United States, from teacher-led
learning within schools or classrooms
such as action research, study groups,
coaching, and mentoring to formal
opportunities outside the classroom such
B U I LD I N G AN I ATE R NATI O CAL COMMU N ITY
as workshops, institutes, courses, and
seminars. The most commonly used
strategies include short sessions at
meetings of professional organizations,
school-based workshops on specific
topics, or two- to three-week grant-
supported workshops in the summers
with follow-up sessions during the aca-
demic year. In many cases teachers who
participate in these forms of professional
development are not offered indepth
follow-up sessions to reflect on their
practice. None of these strategies inclu(le
avenues for teachers to use observation of
colleagues' teaching as a tool for learning.
Teachers in the United States are solitary
practitioners, coming together to learn
about teaching but working in isolation in
their classrooms (Lewis, 20001.
Similar to teachers in the United States,
Japanese teachers use professional
development to improve their practice, to
learn more mathematics and pedagogical
strategies, and to make better pedagogical
(recisions in their instruction. However,
teachers in Japan use observation anti
collaboration as the core of their profes-
sional development called konaikenshu
through lesson stu(ly. Lesson stu(ly is an
in-school teacher education strategy where
teachers are engaged in action research
about teaching (Yoshi(la, 19991. Lesson
studies are held to educate preservice
teachers, mentor anti instruct novice
teachers, improve the skids of all teachers,
maintain collaboration among teachers,
anti share ideas anti new approaches.
Shimizu (2000) explained that lesson
study consists of precollaborative work
among teachers, lesson observation, anti
postcollaborative work. This cycle is
repeated over time in an iterative process.
Professional (levelopment also has other
forms in Japan. Teachers participate in
workshops at the university and in school-
base(1 stu(ly groups where they stu(ly a
OCR for page 14
variety of topics (Yoshida, 1999). Japan's
large-scare meetings of mathematics
educators may be focused around demon-
stration lessons.
ELEMENTS OF PROFESSIONAL
DEVELOPMENT IN THE
THREE RECORDS OF PRACTICE
Lesson Stucly
The first full day of the workshop was
dedicated to lesson study and reflection.
The (lay began with an optional viewing of
a videotape of a s~xth-grade lesson for
those who had not been able to attend the
actual lesson. The day's schedule included
presentations, small group discussions,
and group viewing of a second videotaped
lesson. The workshop then became a
postconference for the lesson study where
we reflected on the lesson with the
teacher and lesson team. As the presenta-
tions and conversations in small groups
progressed, the U.S. participants learned
that there are several forms of lesson
study. Because of language differences
and translations from Japanese to English,
there was some confusion about the
definition for lesson study. What follows
is my understanding of the two forms of
study. Lesson study is a school-based
strategy primarily used at the elementary
level directed by teachers within a school.
Teachers (leci(le on the content of the
lesson study and proceed through a
process that generally has five components:
(~) teachers plan the lesson collaboratively;
(2) the lesson is taught by one teacher
and observed by other teachers; (3) the
team of teachers meet to reflect on the
lesson and improve it; (4) the lesson is
taught again, usually by another teacher,
with refinement; and (5) the lesson is
discussed again and made into a booklet
that is available to other teachers. Lesson
study is an accepted part of teaching in
Japan at the elementary levels, although
the workshop participants indicated that
in some schools teachers had fewer than
two lesson studies a year. Teachers
interviewe(1 by Lewis (2000) sai(1 that if
they did not do research lessons, that they
woul(1 not be teachers.
Teachers also participate in a public
lesson study, called jugyokenky~, which is
open to teachers anti educators from
outside of the school and the prefecture
(district). Most elementary and lower
secondary schools conduct lesson study,
but the universities anti national schools
generally conduct public lesson stu(ly.
Also, when schools receive grants to
develop their educational programs, it is
expecte(1 that they will conduct a lesson
study to present their products and
findings. Stu(lylessons thelesson
itself at conferences become a metho
of transferring or transmitting good
teaching ideas from one teacher to
another throughout the country. With a
national curriculum anti textbooks autho-
rize(1 by the Minister of Education,
Science anti Culture, lesson stu(ly seems
to offer an efficient form of professional
(levelopment for teachers. Lewis (2000)
indicated that Japanese teachers credit
lesson study as the primary method they
use(1 to learn to teach.
Toshiakira Fujii, in his comments at the
beginning of the (lay, sai(l, 'The lesson is
the battlefiel(1 of teaching. An(1 the
teacher is evaluate(1 by the quality of the
lesson." Lesson studies are works in
progress where teachers strive for perfec-
tion through the iterative process of
(lemonstration anti reflection. Thus the
function of lesson stu(ly is twofol(l: a
method of research and a place to present
new approaches. The teacher's aim is to
ask colleagues to identify flaws in teach-
ing through their eyes anti to identify the
REFLECTIONS ON THE WORKSHOP
OCR for page 15
causes of the failure of the lesson
(Hirabayashi, 2000~. For this process to
be productive, the teacher has to prepare
a carefully planned and detailed lesson
that includes the purpose, topic, teaching
process, student activities, and intended
results. Hirabayashi (2000) describes
lesson study as the "method of research in
mathematics education that is the way to
grasp the true state of affairs of the
problem in its whole and bring the syn-
thetic, totally recognized interpretation
about it, being aware of many factors
which are subtly interacting to each other
as if it were in one organism" (p. I). He
believes that because lessons are compli-
cated processes and their results on
student learning are too subtle to express
in writing, lessons can only be evaluated
through close observation. You have to
see what actually occurred in the lessons-
both teaching and learning.
In this, my first observation of lesson
study through a videotape of the lesson
and a discussion of the participants in the
process, ~ was amazed and pleased with
the detail of the lesson and the reflection
of the participants. The teacher's ability
to pose the problem precisely, the func-
tional thinking of the students, the ques-
tioning that required each student to think
of multiple ways to solve the problem, the
varied representations of solutions and
the students' interpretations of the differ-
ent forms were impressive. The teaching
of mathematics content dominated the
lesson and the post-lesson reflection
session continued the focus, with the
teachers having a lengthy conversation of
the different meanings of 4 x 48 and
48 x 4. Although ~ was surprised with the
length of this conversation, it demon-
strate(1 the importance given by the
Japanese teachers to teacher and student
content knowledge.
After a few hours of learning about
B U I LD I N G AN I ATE R NATI O CAL COMMU N ITY
lesson study, we understood that the work
required to prepare a lesson for observa-
tion and review was extensive. Most of
the U.S. participants wondered how
teachers could take so much time with
planning. When we inquired, we were
told that lesson studies are not the norm
for instruction. The Japanese teachers
explained that most of their lesson plans
were in the teacher's editions of the
textbooks. Lesson studies were tools to
improve instruction, not to develop daily
lesson plans. The concept of lesson study
is an effective tool to create a community
of learners throughout Japan because of
the capacity to share research and
approaches to teaching within schools,
prefectures, and the national education
community. Knowing this, we were
surprised to learn that even though many
elementary and some lower secondary
teachers participate in research lessons, it
rarely occurs in the upper secondary
schools.
RecorcIs arc! Practice
In Deborah Ball's opening comments
on the first (lay of the workshop, she
questioned how teachers in Japan and the
Unite(1 States use practice to work on
their teaching. She expanded the battle-
field concept expressed by Toshiakira
Fujii to the use of recor(1 stu(ly anti case
stu(ly as tools to analyze anti learn the
practice ofteaching. Deborah Ball
believes that practice is not learne(1 by
just (loin" it, nor is it learne(1 by just
acquiring knowle(lge or watching expert
performances. To learn a practice teachers
have to progress through the steps of
studying, trying, analyzing, improving,
anti (1eveloping new knowle(lge, as is the
case with lesson stu(ly anti recor(1 stu(ly.
In the secon(1 (lay of the workshop, we
learne(1 about professional (development
through records of instruction. Records of
OCR for page 16
instruction used in the United States
include videotapes of classroom instruc-
tion, written cases that describe actual
classroom situations and issues that arise,
student's written work, transcripts of
lessons, teachers notes, and lesson plans.
Record study is useful for many reasons.
Records are used to provide a context for
learning and place professional develop-
ment in the context of practice. The
ability to select records to be studied
ensures that the knowledge generated is
useful and usable in practice. Specifically,
the use of record study allows teachers to
select particular problems of mathematics
teaching and learning to be studied and
can provide exposure to practices that
teachers have not seen or do not know.
Most importantly for U.S. teachers, the
use of records for analysis allows teachers
to critique practice in a safe environment
where they are not asked to criticize each
other's teaching. Record study can be
problematic because not all records are
worthy of study. It is difficult to design a
good task for learning that will help
develop norms for the professional study
of teaching. Additionally there are chal-
lenges as teachers move from evaluation
and judging to the analysis of teaching
and in balancing the analytic work with
practical outcomes (Ball and Bass, 20001.
The challenges of the use of record
study can be addressed through the
appropriate (resign anti enactment of
recor(1 stu(ly. For instance, video records
and case records accompanied by focused
questions about the records provide
teachers with an opportunity to (levelop
the ability to analyze and reflect on their
practice. Record study can enable teachers
to understand and improve their peda-
gogical content knowle(lge. "Pe(lagogical
knowledge is a special form of knowledge
that bun(lles mathematical knowle(lge
with knowle(lge of learners, learning, anti
pedagogy" (Ball and Bass, 2000~. Records
can expand the pedagogical content
knowledge that teachers possess because
records afford teachers the opportunity to
view, un(lerstan(l, analyze, anti reflect on
situations that they have not experienced
in their classrooms. Margaret Smith
explaine(l, in the session on case studies,
that records "create generalities that
teachers can use to think about their own
teaching." They allow teachers to investi-
gate instruction through records to
develop generalities that might be applied
to their practice. Moreover, recor(1 stu(ly
can help teachers learn (a) how to pay
attention to anti teach every student in the
class, (b) how to know anti use math-
ematical knowledge to help students
learn, and (c) how to work with others on
(leveloping knowle(lge for teaching (Ball,
20001.
In my practice ~ use case anti video
records, thus ~ was not surprise(1 with the
information shared at the workshop.
was please(1 that the readings anti the
presentations on recor(1 stu(ly stressed
the nee(1 for pe(lagogical content knowI-
edge. ~ believe that questions asked of
the participants both at the beginning of
the workshop anti in our small groups
coul(1 not be answere(1 without a foun(la-
tion in pedagogy, content knowle(lge, anti
pe(lagogical content knowle(lge. It was
clear to me that the three forms of profes-
sional (levelopment on teaching practice
(lesson stu(ly, video records, anti cases)
coul(1 be part of the answer, but we were
just beginning a long journey.
Reflection
At the en(1 of the workshop we realize
that we had only scratched the surface of
(leveloping answers to the questions that
focused the workshop: What knowle(lge
of both content anti pedagogy (lo teachers
nee(1 to teach well anti how can teachers
REFLECTIONS ON THE WORKSHOP
OCR for page 17
come to acquire this knowledge in ways
that are usable in practice? Questions and
comments were shared at the end of each
day as participants from each country
reflected on what they had observed,
heard, and learned. {chief Hirabayashi
explained that curriculum development is
composed of technology and humanity,
and we had only addressed the tech-
nology. He said that the humanity of the
teacher was evident in the way students
were attentive throughout the entire
period. But he said, "Lesson study is not
enough. We need good experienced
teachers to guide us. ~ videotape myself
every day as the mentor teachers
instructed me." He challenged us by
saying, "In the United States you have to
determine how to incorporate lesson
study into your school. What are you
going to do and what problems do you
anticipate when you return?"
Deborah Schifter suggested some
needs that teachers might have before
they participate in lesson study, including
understanding that mathematics is more
than being able to apply a single algorithm
and that understanding alternate forms of
mathematical procedures is the basis of
mathematical reasoning and valid think-
ing. Haruo Ishigaki explained that
teachers learn in the same ways that
students learn. He commented that
excellent teachers do not have perfect
knowledge, '~hey are 80 percent confi-
dence and 20 percent doubt. Their
knowledge has to be updated and restruc-
tured often." He stated that students see
extraordinary things but may make
mistakes. These mistakes, however, are
valuable and should be treated as a
resource by the teacher.
As ~ listened and reflected on my
experience, ~ was thinking, is it possible
for us, in the United States, to use what
we have learned to improve professional
B U I LD I N G AN I ATE R NATI O CAL COMMU N ITY
development for our preservice and
practicing teachers? First ~ had to think
about what ~ had learned. My overwhelm-
ing realization was that mathematics
educators from different parts of the
world, with (lifferent spoken languages
and cultures, spoke in unison as we
discussed our goals and needs to improve
mathematics education. Our strategies
and tools of delivery were different, but
we were seeking similar outcomes. The
most exciting new knowledge was my
personal un(lerstan(ling of the organiza-
tion and execution of lesson study and the
power of lesson study to improve content
knowledge and pedagogy of teachers and
the delivery of content to students. My
beliefs about the importance of teacher
collaboration and observation of each
other's teaching to improve practice and
the use of record study to help teachers
construct new pedagogical, content, and
pe(lagogical content knowledge were
reinforced.
Second, ~ had to personalize the ques-
tions for my own practice. How could ~
use all that ~ ha(1 learne(1 in my practice as
a teacher educator? How could my
students benefit from my experience?
PUTTING IT TOGETHER IN PRACTICE
Clearly, the most important experience
from the workshop to me was being part
of a community of learners from the
Unite(1 States an(l Japan coming together
to begin to answer questions regarding
professional (levelopment. Just as we ha
exten(le(1 our community to include each
other, ~ decided to try to broaden my
preservice students' community of
learners to inclu(le all of the mentor
teachers and students using a modified
lesson stu(ly approach. Normally each
student interacts with anti learns from one
OCR for page 18
mentor teacher in a full year practicum.
In the fall semester the students observe
their mentor teacher in all classes, tutor
students, help in the classroom, and
discuss lesson planning and teach a trial
lesson. During the second semester they
do their formal student teaching. ~ will
only have three preservice students in
mathematics this year, and ~ plan to place
them all in the same school for their
practicum.
All mentor teachers agreed to partici-
pate in a modified lesson study with the
mentor as the teacher. The mentor
teacher and student teacher will select a
class that the three students and ~ will
observe. Prior to the observation we will
meet with the teacher to learn about the
class and the lesson she plans to
present to learn her rationale for the
pedagogy and content and what she
expects from the class. Next we observe
the class, taking notes on what we see.
After the observation we will meet with
the teacher to discuss and critique the
lesson. These discussions are beneficial
for the teachers because they can see how
to improve the lesson and they are benefi-
cial for the students because they learn
how the teacher implements what she had
planned and begin to think as a teacher,
reflecting on what worked, what did not,
anti why.
Another change in my practice this year
will be the cooperative planning process
for student demonstration lessons.
Students will be require(1 to teach one
lesson in their mentor teacher's class. In
prior years each student would plan and
teach a lesson. The mentor teacher and
woul(1 observe anti critique the lesson.
Now, instead of having the students plan
their lesson independently, my three
students and ~ will act as a team to plan
three different lessons one for each
student. Our team and the mentor
teacher will observe and critique the
lesson. Our goal this year is to build a
community of learners that can depend
upon one another for knowledge and
support. We are trying to remove the
myth, through our mo(leling, that teachers
in the Unite(1 States have to be solitary
professionals. ~ hope that through these
two mollifications of lesson stu(ly, my
students anti their mentors will learn not
only more pedagogy, mathematics con-
tent, anti pe(lagogical content knowledge
but also the importance of peer observa-
tion, collaboration, and group planning.
REFLECTIONS ON THE WORKSHOP
Representative terms from entire chapter:
professional development
