Lesson Study Final Report
Mathematics Lesson Plan
Sixth Grade
Comparing Polyhedrons
Prepared by:
Lisa Armstrong
Jose E. Carrillo
Margaret Kesler
Connie Perez
Amanda Sanchez
April 25, 2007
Central Elementary School
Santa Clara, New Mexico
1
Lesson Study Final Report
Central Elementary School
Santa Clara, NM
Fourth and fifth grade teachers at Central Elementary School in Santa Clara, NM
were introduced to Lesson Study through the TIA-RETA Program in the fall of 2003. In
conjunction with NMSU and WNMU professional development was provided to this
group of teachers integrating technology and the lesson study concepts. At that time the
focus of the research lessons was science due to low achievement test scores. Central
Elementary School was afforded the opportunity to take Lesson Study as a class,
receiving three university credit hours, as well as technology equipment to use in the
classroom.
In the fall of 2004, lesson study became the school-wide professional
development plan. Science continued to be the area of focus for the research lessons.
Participation in lesson study increased because of the incentives that teachers received
through the TIA-RETA Program and through the encouragement of the building
administrator. The lesson study process was beginning to be realized by participants as a
valuable teacher-led professional development process.
For the following two school years, the subject area of the research lessons
changed from science to math. The staff decided to continue with lesson study although
the program was not fully funded. The technology incentives that the participants
received in the past were no longer available. The intrinsic value of the lesson study
process was appreciated by participants. It was realized that lesson study impacts
teaching and learning.
In October of 2006 Central Elementary School received information about a
lesson study project through New Mexico State University. The building administrator
and four teachers felt it was a great opportunity to receive professional development from
an expert on lesson study, Dr. Akihiko Takahashi. The lesson study group goal was
developed and emphasized during the development of the lesson. The goal was,
“Students will actively construct, utilize, and communicate mathematical concepts.”
During the lesson the students connected their prior knowledge to the new knowledge
presented. They utilized this new information to solve problems and use mathematical
concepts. The students also communicated orally and in written form their knowledge of
polyhedrons and their attributes. The following is a synopsis of the process of the
research lesson project.
2
Central Elementary Lesson Study Group Activities 2006-2007
October 2006-April 2007; regular meetings and public research lessons
 1st Lesson Study Conference, October 27-28, 2006, 8:30-3:30 at NMSU, Las
Cruces, NM
 1st Meeting, October 30, 2006, 2:00-3:00
 2nd Meeting, November 13, 2006, 2:00-3:00
 3rd Meeting, November 14, 2006, 2:00-3:00
 2nd Lesson Study Conference, November 17-18, 2006, 8:30-3:30 at NMSU, Las
Cruces, NM
 4th Meeting, November 20, 2006, 2:00-3:00
 5th Meeting, November 29, 2006, 2:00-3:00
 6th Meeting, December 11, 2006, 2:00-3:00
 7th Meeting, December 21, 2006, 2:00-3:00
 8th Meeting, January 8, 2007, 2:00-3:00
 9th Meeting, January 9, 2007, 2:00-3:00
 10th Meeting, January 11, 2007, 8:00-3:30
 11th Meeting, January 12, 2007, 8:00-11:30
 12th Meeting, January 16, 2007, 2:00-3:00
 13th Meeting, January 17, 2007, 2:00-3:00
 1st and 2nd Public Lessons and Debriefings, January 18, 2007, Las Cruces High
School, Vista Middle School, Las Cruces, NM 8:30-3:30
 14th Meeting, January 23, 2007, 2:00-3:00
 15th Meeting, January 30, 2007, 2:00-3:00
 Research Lesson and Debriefing, February 1, 2007, Central Elementary School
 16th Meeting, April 13, 2007, 2:00-3:00
 17th Meeting, April 16, 2007, 2:00-3:00
 18th Meeting, April 18, 2007, 8:00-11:30
 19th Meeting, April 19, 2007, 3:00-5:00
 20th Meeting, April 20, 2007, 12:00-3:30
 21th Meeting, April 23, 2007, 2:00-4:00
3
6th Grade Public Research Lesson on February 1, 2007,
At Central Elementary School
Mathematics Lesson Plan for Sixth Grade
For the Lesson on Friday, January 19, 2007
At Central Elementary School, Santa Clara, New Mexico
Lesson Study Group: Lisa Armstrong, Jose Carrillo,
Margaret Kesler, Connie Perez, Amanda Sanchez
1. Title of the Lesson: Comparing Polyhedrons
2. Goals:
a. To identify solid figures
b. To name and count the faces, edges, and vertices of prisms and pyramids
c. To learn how different views of a solid figure compare
d. To compare and contrast polyhedrons and explain the relationships
3. Relationship of the Lesson to the New Mexico Grade-level Standards,
Mathematics
Standards
Geometry (6th Grade)
 Students will understand
geometric concepts and
applications.


th
Algebra (6 Grade)
 Students will understand
algebraic concepts and
applications.



Benchmarks
(Geometry) Analyze characteristics
and properties of two- and threedimensional geometric shapes and
develop mathematical arguments
about geometric relationships.
(Geometry) Use visualization, spatial
reasoning, and geometric modeling to
solve problems.
(Algebra) Understand patterns,
relations, and functions.
(Algebra) Represent and analyze
mathematical situations and structures
using algebraic symbols.
(Algebra) Use mathematical models to
represent and understand quantitative
relationships.
This Lesson
Performance Standards
 (Geometry) Describe the properties of regular polygons, cylinders, cones, spheres, and cubes.
 (Geometry) Use appropriate technology, manipulatives, constructions, or drawings to recognize
or compare geometric figures.
 (Algebra) Solve problems involving proportional relationships.
 (Algebra) Make generalizations based on observed patterns and relationships.
 (Algebra) Use letters to represent an unknown in an equation.
 (Algebra) Develop and use mathematical models to represent and justify mathematical
relationships found in a variety of situations.
 (Algebra) Create, explain, and use mathematical models such as:
o three-dimensional geometric models
o graphs, tables, and charts to interpret and analyze data
4
4. Instruction of the Lesson
New Mexico sixth grade students are expected to make generalizations based on
observed patterns and relationships. They should be able to communicate these
mathematical generalizations verbally and in writing. After investigation of geometric
figures, students will conceptually understand proportional relationships and develop a
formula such as E=F + V – 2, where E=the number of edges of a polyhedron, F=the
number of faces of a polyhedron, and V=the number of vertices of a polyhedron.
Prior to the research lesson, students have been introduced to and explored basic
geometric concepts such as the study of lines, angles, and polygons; they have measured
angles, and constructed congruent line segments and angles. In further exploration the
students identified line and rotational symmetry. They also identified solid figures;
named and counted faces, edges, and vertices of prisms and pyramids; and modeled
prisms and cylinders from nets.
If students comprehend the numerical relationship between the faces, edges, and
vertices of polyhedrons and their algebraic connections, they can incorporate them to find
a formula such as E=F + V – 2. A lesson from Harcourt Brace Math Advantage, Faces,
Edges, and Vertices Algebra Connection, was chosen and revised. The lesson was
extended to help students realize the relationships between the faces, edges, and vertices
of polyhedrons. Students will use models of polyhedrons previously built to explore the
physical attributes of the solid figures. They will develop a method of communication to
present their observations.
5. Lesson Procedure
Learning Activities
Teacher’s Questions and
Expected Students’ Responses
Teacher’s Support
Points of Evaluation
1. Introduction
We explored polygons and
polyhedrons, we’ve built models
of polyhedrons, and we’ve
compared and classified pictures
of polyhedrons. Now we will
compare our models of
polyhedrons and your group will
present information about them.
Use the available materials to
visually present your findings to
the class.
Ask the question: “What do
we need to know to
compare the polyhedrons?”
Review prior knowledge;
pose the problem to the
class in written format on
the overhead projector.
Do the students know the
vocabulary?
Can the students apply their
knowledge to describe
polyhedrons?
Provide examples of
Can students describe
polyhedrons (see appendix). attributes of polyhedrons?
5
Now you will compare the
polyhedrons and use the
available materials to record Write students’ responses
on the board.
your groups’ findings.
Students will present their
findings.
Are students discussing and
recording their
observations? Are they
working collaboratively?
Provide the materials for the Are students appropriately
students to use during this
using vocabulary in
portion of the lesson.
context?
Call students to the front of
the class one group at a
time.
2. Posing Problem
Is there a way to combine our
information about the presented
polyhedrons?
Students’ anticipated responses:
 Organize information according
to polyhedron attributes such as
number of edges, faces, and
vertices
 Derive the formula for the
relationship between the number
of edges, faces, and vertices of
any polyhedron, E=F + V – 2.
If students cannot
graphically organize
their results according
to attributes, recall
prior examples of
graphic organizers.
Do students recall
methods of
presenting
information?
6
4. Summing up
a. Using the students’ representations of
polyhedron comparisons review what
students learned through their
explorations.
Ask open ended
questions to keep the
discussion going.
Can students
explain and
represent their
comparison of
polyhedrons?
b. Ask students to write a summary
explaining the relationship between
polyhedrons.
Ask the question “Is
there a shorter way to
express this
relationship?”
Do the students
use variables to
represent an
algebraic
expression?
“When letters are used
to represent numbers,
what is it called?”
Do students
appropriately use
variables in their
summaries?
6. Evaluation
a. As a small group were the students able to organize and present their comparisons of
polyhedrons?
b. As a whole group were students able to compile information and explain the
relationship between polyhedrons?
c. Independently were students able to explain their reasoning in written form?
7
Post Discussion for Research Lesson-Comparing Polyhedrons
Central Elementary School
Group Participants: Lisa Armstrong, Jose Carrillo, Margaret Kesler, Connie Perez,
Amanda Sanchez
Guest Observers: Daena Davis, Sonia Marrujo, Betsy Montes
Lisa Armstrong: The students understood faces, edges, and vertices of polyhedrons.
They discussed this but didn’t make the connection between them. There was a lot of
thinking, they used good organizational skills, but once they had to present their findings
they weren’t able to communicate their thinking because they were shy and learning
stops. They’re thinking it, but we didn’t know what they were thinking.
Daena Davis: Do you think that if they had stayed in their work areas they may have
been more at ease, rather than being at the front of the room. I find that students are more
comfortable presenting from where they are in the room.
Amanda Sanchez: Also maybe giving each group only one shape to discuss and present
on would help them to compare with other groups and have more discussion.
Connie Perez: I think a lot of learning took place in working with all of the shapes. If
you only focus on one then you can’t look at relationships.
Amanda Sanchez: The goal was the numbers part – in finding the relationship between
them.
Betsy Montes: The students had a lot of prior knowledge. Were the students aware of
what the goal was. The goal wasn’t met. Questioning while in their groups would also
stimulate more thought. Did kids know questions that were going to be asked? If they had
known what was expected, then they would have been ready. They could’ve written some
responses.
Margaret Kesler: In one of our lesson study sessions in Las Cruces/NMSU we talked
about not asking leading questions. If you ask leading questions their creativity could be
stifled and limit their discoveries. We kept that in the back of our minds when planning
the lesson however if we had asked questions during the presentations to stimulate their
thinking without being leading, it could’ve helped. For example, questions like “What
was the discussion in your group?”, “What was brought up?”, “What did you not agree
on?”
Amanda Sanchez- Perhaps a focus question that they will answer during their
presentations, maybe open-ended questions?
Connie Perez-We had considered some questions during planning but decided they were
leading and would tell them how to think.
8
Betsy Montes- Did you ask questions while they were in groups?
Lisa Armstrong: I walked around more as a facilitator.
Margaret Kesler: Maybe specific questions could have been asked to stimulate their
thoughts during the presentation of their findings.
Sonia Marrujo: Was your grouping of the students random? Some wee doing some of
the work or most of the work and others were not as active in the activity.
Lisa Armstrong: For the most part they chose their own groups.
Betsy Montes- They were interacting, they were learning.
Mr. Carrillo: I observed that one group, Jose, Brittney, and Zita rotated the tasks. Each
one was looking at the shapes, one writing, one facilitating, one cutting-that assured that
they were understanding the process. They all had an equal opportunity to share their
work. There were other groups that each student only had one task.
Betsy Montes: I wondered if roles were assigned.
Connie Perez: One group continued to work during the others’ presentations, they all had
different ideas about how to present the information on their board.
Amanda Sanchez: They were trying to draw them when they saw everyone was using the
pictures, and they were almost done. Then they started to use the pictures and they
finished really fast.
Margaret: Drawing them out might have helped some students. They really got a feel for
the shapes and the attributes of them.
Amanda: That is why I think each group having one shape to focus on may have been
good.
Connie Perez: It was nice that you used 3-D objects. I noticed that when one student was
using the picture of the shape he needed to recount.
Amanda: I think having the different types of manipulatives, they all chose something
different, they all had enough materials to work with.
Jose Carrillo: As far as evidence of student learning: one of the students was asking
probing questions. She kept involving other members of the group but it was interesting
that she didn’t take what she was doing at face value but asked the others in her group.
She would engage them “Do you think?” “Do you think?” … As far as the different
groups, most of them would go back and ask questions and check their work.
9
Connie: I think in the area of algebra, and considering the development of the students
that perhaps the goal – finding the algebraic equation was not appropriate. Finding the
pattern between the numbers would have been more appropriate at this time.
Amanda: According to the standards and benchmarks students should have been able to
come up with an equation. Students should already be finding the algebra part of it.
They have to come up with their own formulas from a problem. They did get a lot of
those types of problems on the practice tests. They had to come up with an equation from
the information given.
Daena: Have the students been exposed to formulas?
Lisa: A little bit.
Betsy: I noticed some used variables. Have you used variables?
Lisa: Yes, in that F=faces E=edges V=vertices before the lesson.
Connie: Yes, using the variables in that way. In actually using the variables in
equations, I think the first step would be in finding the pattern in looking at all the
polyhedrons and move from there.
Daena: You could have given them only one of them but some of the kids can’t see the
pattern in one, but need to compare them to other shapes to see what is going on between
them.
Amanda: But, if one group focused on one and they see the numbers, then when they
presented it, presented their shape, then they would get the rest of them and as a class
they could have come up with relationship between all of them.
Lisa: I see what you are saying and what Connie is saying. The relationship between the
numbers is the pattern. If they had time and could look through the numbers, they could
see the pattern. Working with the variables then they could have probably come up with
the equation.
Daena: In one group you could see the formula the way their chart was set up. I think if
they would have had time to focus on the chart they might have been able to come up
with it.
Amanda: I was thinking if they focused on one shape and they focused on the numbers
part and they present the numbers part, the whole class is going to label it as a class.
Once all the numbers are there then we could say something and they could maybe see
the relationship. I think because they had so much information of geometry they focused
more on the geometry part and not the algebra part.
10
Connie: Initially because of the lesson study groups within our school geometry was a
strand, and so that it would meet with the algebra component with the NMSU group, we
tried to tie the two together, but initially the focus was geometry. That’s why thinking all
this algebra at this point was still asking too much. They were still working on many
geometry concepts, the students did not realize the algebra concepts we had intended.
The students really never got to look at the posters and compare them. They only saw
them briefly. That would be the next step and that in itself would be another lesson in
finding the Aha in patterns and relationships. It was a valuable lesson. They needed to
have this lesson and work in their groups with all of the information and then do as
Amanda said and take each piece and compare them. First finding the relationship and
THEN finding the equation. It was expecting too much to move from the geometry
concepts to the algebraic formula in one lesson.
Sonia: Yea it was too much.
Daena: You need to take baby steps.
Mr. Carrillo: Any other comments
Connie: It was fun, and you could feel the energy and the kids talking and excited about
their work.
Betsy: In groups there was a lot of interaction. You see more evidence of learning when
students work in groups There was a lot of learning going on
Connie: When they applied their knowledge in their groups today it was fun to watch
Margaret: Each group developed their own system. I know we had said that some took
over in their groups, but all students were involved somehow. Many of them checked
each other. It seemed that Oliver had done all of the work, but in watching the video
today I noticed that Nicholas really checked his answers.
Lisa: I thought it was interesting the way they isolated the apex from the vertices. We
had never said the apex is not a vertex.
Mr. Carrillo: Our goal wasn’t met. What do we need to do to get there?
Betsy: It was a great assessment of their prior knowledge – now they’re ready to go to the
next step to reach the goal. The lesson should continue into further lessons.
Ideas
 Each group focus on at least two shapes, manipulating the numbers in different
ways. They are asked to compare the numbers. Groups will then discuss and
compare their findings with the entire class.
11

The class will then compare the findings from each small group to find
patterns/relationships.

Questions are asked to keep students thinking. (What will the questions be?)
Outcomes
In reviewing the goals and expectations of the lesson, three out of the four goals were
met.
Goals that were met:
a. To Identify solid figures
b. To name and count the faces, edges, and vertices of prisms and pyramids
c. To learn how different views of a solid figure compare
Goals that were not met:
d. To compare and contrast polyhedrons and explain the relationships
The above goal was not met in this particular session, however with the right
questioning in other lessons we may be successful in guiding students to this
discovery.
12
Connie Perez
Reflection
Lesson Study NMSU
I learned of lesson study three years ago when my principal invited each teacher
at our school to become participants in a class at WNMU. The class was designed to help
teachers enhance instruction through the use of the Lesson Study concept integrated with
technology. Tuition was funded with grant money provided by TIA-RITA. The grant
also provided incentives for teachers to assist them in increasing their use of technology
in the classroom. I had no knowledge of lesson study but I accepted the invitation
because of the technology component. Technology is not one of my strengths and I
considered this an excellent opportunity to improve in this area. However as I became
familiar with the lesson study concept, my focus changed and each component of the
class became of equal value to me.
During this first year, I discovered that lesson study is a paradigm of instruction in
which the students are active, responsible learners and the teacher is a facilitator of their
learning. This method makes teaching a collaborative process and makes learning fun,
exciting, and involved. Concepts are explored, taught, and learned comprehensively.
Instruction is qualitative rather than quantitative. If this method of instruction was the
norm, I believe that our students would be more prepared for the standardized test which
requires them to explain their learning. After this first year, I was eager to continue
learning about the lesson study model to help me improve my classroom instruction.
Over the next two years, the administrator and teaching staff at my school have
continued the lesson study process in spite of the decrease in funding. Because of this
decrease, my building administrator sought out other means of financing. As a result of
this search, he learned of the program at NMSU and invited the lesson study facilitators
at Central Elementary School to take part in this program. My colleagues and I thought
we were attending a two day workshop presented by Dr. Takahashi. We were excited to
have an expert be the facilitator. However, as we listened to opening statements, we soon
realized that we would be involved in another lesson study process which was to include
middle and high school teachers and students and would run over the course of several
months. Initially, I was apprehensive and felt somewhat intimidated because I teach
primary math concepts to young children and have not had the opportunity to instruct
students at a higher mathematical level. However, after participating in learning
activities with Dr. Takahashi as our facilitator, I now recognize the connection of what I
teach to what is taught at higher levels.
As I observed the students during the lessons at Las Cruces High School and
Vista Middle School, I realized these students are no different than the young children I
teach. I noticed that the students were at different levels of understanding and assumed
different roles as they participated in the small group activity. The high school students
were in groups but several of the groups did not work as a group and seemed to struggle
with the task. I observed that the majority of middle school students in the small groups
benefited from the hands-on activity based instruction as the teacher guided and
facilitated their learning. It was exciting to watch as the students made mathematical
discoveries. The students appeared to enjoy and benefit from the lesson. I gained insight
13
into the lessons during each de-briefing session. Having Dr. Takahashi and Dr. Tad share
their expertise and views about the strengths and weaknesses of the lessons was helpful.
Lesson study has been a worthwhile process. It has assisted me in improving how
I appraise student learning. It has also made me more cognizant of the type of questions I
ask my students. Lesson study has helped me to make better observations as my students
are engaged in learning activities. I am grateful that I was given the opportunity to
participate in the NMSU lesson study group.
14
Margaret Kesler
Reflections on Lesson Study
Learning about the lesson study process and being involved in lesson study
groups has helped me to seek associations between classroom lessons and student
learning. When planning a lesson I think about how the students in my class will be
impacted and what the results will be. I attribute this deeper thinking of student learning
to the involvement in lesson study: the valuable time spent with other teachers, the
opportunity to observe interactions in the classroom, and the in depth discussions that
bring about many ideas and questions.
I feel fortunate to work in a school that has supported the lesson study practice for
four years. This has given many of us the opportunity to grow in our experience with
lesson study and see the value of it. When lesson study was introduced to our small
group of teachers, I remember thinking that it was an ideal way to plan lessons consisting
of everyone’s best ideas; however I did not see it as a venture that would last due to the
time that is required for an effective process. Many times programs and new ideas are
short lived and fade quickly. The lesson study process at Central Elementary has been
supported and encouraged by our building administrator and therefore our lesson study
groups have continued, have grown, and it has become a school-wide practice.
I have had various opportunities to gain knowledge about lesson study. These
opportunities include: attending classes at WNMU where lesson study and technology
have been the focus, serving as one of the facilitators of lesson study groups at our school
– in both a primary group (pre-K – 2nd) and intermediate group (3rd – 5th grade), and
being part of the Lesson Study Project at NMSU.
The classes at WNMU provided the time to work in our groups and improve the
lesson study process. Serving as facilitator to groups within our school has given me the
opportunity to help plan, observe and discuss many lessons, ranging from grades prekindergarten through 6th grades. Being a part of so many different grade level lessons has
given me great insight to my own teaching – what my own students should know and
where I need to guide them in their learning.
During this school year our staff has not had any school wide professional
development to expand our lesson study program at Central Elementary, therefore a few
of us being a part of the NMSU Lesson Study Project has helped us to improve our
practices. In attending the meetings and discussing all of the components of lesson study
and the importance of each, realized that the observation piece in each of our groups
needed to be addressed. Observing other groups’ lessons and their debriefing process was
very enlightening. It has also been helpful to have knowledgeable experts in the area of
lesson study to share their thoughts and experience with us. We were able to share what
we learned with our own lesson study groups. Our public lesson was unfortunately
cancelled do to inclement weather. I think the insight from outside experts would have
benefited our teams.
I believe that we have made gains in our practices, but would benefit from more
ideas on the observation and debriefing portions of the process.
15
Lesson Study Reflection
Lisa Armstrong
I feel that I have grown as a professional through my experiences in lesson study.
I have gone from knowing nothing about the lesson study process four years ago to being
a facilitator for lesson study groups in my school. I have gained much professional
knowledge in the lesson study process through personnel from WNMU, and in 20062007 through NMSU and Akihiko Takahashi.
As a novice lesson study participant in 2003, I was given the opportunity to attend
a lesson study overview workshop given by experienced lesson study participants from
the Las Cruces School District. The workshop was moderated by Dr. Karin Wiburg of
NMSU. I thought that the presenters were very enthusiastic in sharing their experiences
about lesson study, and I left the workshop very confused about the process but with the
desire to learn more.
As part of the fourth and fifth grade lesson study team at my school, we began our
lesson study process by identifying the academic needs of the students in our classes. We
did this by interpreting standardized test scores to determine in which subject area there
was a need for further teaching and learning. We decided to study a lesson designed for
fifth grade students about chemical reactions called “Burnt Sugar.” This first research
lesson was difficult because our lesson study group was inexperienced, having never
participated in this kind of professional development before. With the help of our
facilitator and some WNMU faculty members, we completed our first lesson study and
gained much insight into the process.
During our participation in lesson study, my school has undergone many changes.
We have gone from having only a few participants to every teacher being involved in
lesson study. We have had to overcome obstacles such as scheduling planning sessions,
research lessons, and debriefings; and finding enough substitutes for every participant.
Our facilitation of groups has changed from university faculty to in-house facilitators.
I have been one of the lesson study facilitators at my school for two years. In that
time I have learned much about group dynamics. I have learned that the teachers at our
school work well together, share ideas, and collaborate to develop lessons. Because we
were given an opportunity to work together through lesson study, teachers feel more a
part of a family.
I have realized that even though I have participated in the lesson study process for
four years, I have much to learn. This year my participation in the NMSU Lesson Study
group has proven to be invaluable. It has given me additional background knowledge I
needed as a professional who is still learning through the lesson study process. Being an
observer in public lessons has given me a great opportunity to learn about observation
and debriefing in lesson study. The public lessons afforded the time to think about the
mathematical concepts that were involved in each of the lessons. Observing the students
and examining their responses is a benefit of being at a public lesson. Observing lessons
at different grade levels is allowed me to take a brief look at what skills my students at
the elementary level will need in the future.
Through my experiences in lesson study, I feel that I have become a teacher who
self-analyzes her teaching. My teaching has become more purposeful because I think
about my lessons in an in-depth manner. I purposefully pose questions to students so they
16
think more critically about their responses. I believe very much in the lesson study
method of teacher-led professional development and plan to continue to learn as much as
possible about the process. I plan to continue my participation in lesson study in future
years as a teaching professional.
17
Individual
Lesson Study Reflection
Amanda Sanchez
I have been participating in lesson study for three years and have used it to
enhance my teaching style. The first year of lesson study I was a student teacher
mentored by Mrs. Virginia Rodriguez. She suggested that I join the program because it
would be a vital tool in helping to assess lessons taught. I was excited, to be able to learn
from all of the experienced teachers in the group. During the planning process the group
improved the previous lesson taught and included more hands on activities for the
students. The lesson was in science and included all the human organ systems. The
lesson was led by Mrs. Rodriguez and included the other teachers involved. Each teacher
was in charge of mini-lessons taught in small groups of four students. Each lesson
focused on one of the organ system and was taught by with game situations. After all the
students were able to experience all the lessons, Mrs. Rodriguez had a power lesson at the
end to wrap up the mini lessons. The students were assessed with a written assignment in
their journals. I had decided then that lesson study was for me.
The next two years I was more involved as a teacher, and the focus subject
switched to math. The first year the lesson study group focused on an area that
kindergarten students will need in all grade levels, grouping. The lesson and preparation
was created by the kindergarten teachers with the help of the group. The lesson was great
the first time and the second time it was again a success. After the first lesson the group
decided to allow the students more time deciding which grouping situations worked best.
The teachers in the group that helped develop the lesson were also the ones that viewed
and debriefed on the lesson. This is the same type of observations that have been used.
The debriefing needed more focus on the lesson and not the students’ behavior, but that
was something the group changed the next year.
This year I was involved in two lessons one for my school and the Las Cruces
lesson study group. At the school the group decided to focus in an area where the
students did poorly on the test, geometry. I taught the second lesson, I was nervous and
overwhelmed. The group developed the lesson and the preparation. After the first lesson
taught the group noticed that there was only a little interaction between the students, as a
result we grouped the students the next time. The group also noticed that we needed to
change the questioning to higher end questions from the bloom’s taxonomy. The lessons
were successful both times they were taught.
During the Las Cruces lesson study I realized that as professional teachers we are
all trying to reach the same goal. We all want our students to become independent
thinkers, to be able to communicate using math vocabulary, and be successful. The Las
Cruces goal is one that could have been used in any of the lessons I have been involved
in. I enjoyed being a part of this lesson because I was able to see, outside of my district,
teachers plan, critique, and teach their lessons. It is also comparable to the lessons I have
been involved with in the sense of the planning and the teaching. However I think our
group at Central Elementary needs to focus more on the lesson taught and also having
outside observers that did not prepare the lesson. This type of observer is more
subjective to the lesson taught and can add significant information needed to create a
18
better lesson. All the teachers involved in the developing of the lesson then become
students learn how to improve their lesson for next time.
19
José E. Carrillo
Reflection
The Cobre Consolidated School District has been very supportive of the efforts at Central
Elementary School and has invested substantially in the Lesson Study professional
development process for the past 4 years. In my observations and going through this
process of professional development, it appears to me that it has a very promising effect
on student learning and teacher practice. I have specifically learned that the teachers in
our group have become very knowledgeable about the Lesson Study process and want to
continue to improve their practice.
The first time I learned about lesson study was when I became the principal at Central
Elementary School. I inherited this professional development model, given that a group
of teachers had already started the process when I arrived at the school. I was invited to
join the group and became very interested in the whole process. Unfortunately, I was not
allowed to continue as an active participant because the collaborators from the university
felt that my participation could hinder the reflection and collaboration process.
Nonetheless my interest continued and I became passionate about the whole process and
began to do my own research. I felt that lesson study was a very promising professional
development approach for our staff and wanted to be a constructive supporter of their
efforts. At the beginning of the following year, I was able to join in and help lead our
Lesson Study efforts since some teachers wanted to continue even thought they were not
sure that our grant was going to be renewed.
Nonetheless, I continued to be an active participant and the research that I have done
brings up many questions such as: “How does the lesson study process fit into the
teachers’ existing work culture” (Friedman 2005). Patsy Wang-Iverson, Senior Scientist
with research for Better Schools addressed the question “Why lesson study?” in a paper
presented at the 2002 Lesson Study Conference. She also addressed the following
questions. “What makes lesson study so different from other forms of professional
development?” and “How does lesson study fit in with educational improvement?”
(Wang-Iverson 2002). Wang-Iverson’s response is that lesson study is meaningful
teacher collaboration “lesson study is not about studying a lesson in order to make a
perfect lesson. Rather, it is a professional development process in which teachers
systematically examine their practice in order to become more effective instructors and
teacher collaboration and collegiality are central to this model” (Wang-Iverson 2002).
She also states that the difference is “lesson study makes teacher collaboration concrete
and focuses on a specific goal: better understanding of student thinking in order to
develop lessons that advance student learning” (Wang-Iverson 2002). She says that
“lesson study, which builds upon teachers’ shared knowledge and insight, supported by
research, can help us overcome our own cognitive barrier concerning students’ ability to
learn” (Wang-Iverson 2002).
These and other questions have been for the most part positively answered or affirmed
through our Lesson Study process at Central Elementary. As an administrator, I am
always looking for better ways to assist teachers and staff in their own practice. I
20
certainly want all of our students and teachers to be successful. It is also my
responsibility that teachers continue with their professional development. I want teachers
to improve their practice and students to improve their learning. Furthermore, facilitating
student learning is the essence of the education profession and I believe that improved
student learning is possible through improved teacher practice. I believe that Lesson
Study, through the collaborative efforts of groups such as the NMSU Lesson Study
Project, has strong potential as being the professional development of choice in New
Mexico as well as all over the United States and I want to be a knowledgeable
constructive contributor in the reform effort.
21
Appendix 1
Instructional
Resources
22
23
24
Rectangular Prism
25
Rectangular Pyramid
26
Triangular Prism
27
Triangular Pyramid
28
Pentagonal Prism
29
Pentagonal Pyramid
30
Appendix 2
Bibliography
Mathematics 6B for Elementary School, Editors Heisuke Hironaka, Yoshishige
Sigiyama, Publisher Tokyo Shoseki Co., Ltd., date of issue 2/20/2006.
ISBN4-487-46621-0 C6341
Math Advantage Middle School I, Authors Grace M. Burton, Evan M. Maletsky,
Publisher Harcourt Brace, Copyright 1999.
ISBN 0-15-311439-8
31