Final Paper of Lesson Study Grade 5 Group 5_4

7/30/2019 Final Paper of Lesson Study Grade 5 Group 5_4

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RUNNING HEAD: REFLECTION OF A LESSON STUDY

Reflection of a Lesson Study:

Seven Teachers and the Distributive Property

A. Conway

E. De La Cueva

L. Gomez

B. Holguin

M. Price

C. Rodriguez

J. Trantham

LIFT Institute, 2013


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REFLECTION OF A LESSON STUDY 2

Abstract

This paper outlines the collaboration of seven teachers from different grade levels who

participated in a process oflesson studyover the course of several weeks. Lesson study, for the

purpose of this paper, is defined as the in-depth focus of a team of teachers to create and present

a lesson around a particular concept. The team then presents the lesson in two separate settings,

making adjustments for the second lesson based on feedback from the observing members of the

team and from the participation of the students themselves. The concept which was tackled for

this particular study had to do with distributive property and the setting was two different fifth

grade classrooms. Two of the seven teachers had previously participated in lesson study and the

other five were new to the process. The paper is organized with an introduction to lesson study

and its organization, the focus of the mathematics learning, instructional strategies, and

individual teacher reflections after the process was complete.


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Section 1: Introduction

Lesson Study Outline

As we have progressed in our LIFT journey this semester, we have focused a majority of

our time on the idea of equity in the classroom. One way we were asked to address this was

through the strategy of lesson study. Lesson Study allows a group of teacher/colleagues to design

a lesson based on specific guidelines and components, teach it, make adjustments, and re-teach

it. The lesson is taught by one randomly selected participant while being videotaped and

observed by the rest of the group. Each observer looks for specific pieces of the lesson and

records his/her observations. At the end of the lesson, the group meets for a videotaped debrief.

There, the components of the lesson are discussed as a team, and adjustments are made to ensure

that the next lesson meets all of the necessary requirements. After the adjustments are made, the

lesson is re-taught by another randomly selected participant to another class of similar

demographics. Again, the rest of the group acts as observers recording new data and the lesson is

videotaped. Then another debrief occurs. Each participant again shares out observations and

learning from the activity.

Since we have been working on math progressions and the distributive property in the

Math portion of LIFT this semester, we decided to focus on the distributive property for our

lesson study topic. The distributive property can be used to demonstrate to students the

relationship between multiplication and addition. It states that multiplying a sum to get a product

is equivalent to multiplying the each addend and then adding the products together. As a

formula, it is most commonly noted as this:

a (b+c) = (ab) + (ac)


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It can also be understood through the concept of decomposing by breaking a number into two

addends and multiplying those addends by a multiplicand and adding the products. The second

understanding of distribution was the understanding of the teachers in the lesson study and

therefore, the focus of the lesson around the distributive property.

The group of participant teachers consisted of seven members, each of whom taught a

range of levels from 4th through 6th grade and one interventionist who works specifically with

grade 3-5 students for math. Although the distributive property isnt explicitly outlined as a

standard for fifth grade, after some debate, it was decided that we would focus our lesson

planning for a fifth grade classroom. For the lesson, the team chose the 5 th grade Common Core

State Standards [CCSS] 5.OA.1, which reads:

Write and interpret numerical expressions. 1. Use parentheses, brackets or braces

in numerical expressions, and evaluate expressions with these symbols.Again, the mathematical focus was on the concept of evaluating an expression that was written

using parenthesis or brackets in which a number was distributed to two additional factors.

We began by determining our research theme, then set upon searching for resources and

ideas for the best way to address our goals, and completed the MC2

LIFT Research Lesson

Template. Our research theme, or overarching goal, (see Appendix A) was as follows:

We would like our students to demonstrate critical thinking by asking questions

(of the teacher and peers), constructing viable arguments, and critiquing thereasoning of others while persevering in solving math problems.

The purpose of this overarching goal was to encourage our students to be critical thinkers who

actively evaluate problems and express their thinking using mathematical language. The team

felt that it was important for the students to deepen their understanding of operations and


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algebraic thinking in fifth grade by writing and evaluating simple expressions and interpreting

numerical expressions in order to prepare them for applying more purposefully the distributive

property in sixth and seventh grades. We used this information to create a learning target and the

criteria for success (See Appendix B). Then we dug through the lesson and developed a list of

target vocabulary (See Appendix C).

After several weeks of collaboration, the team was ready to present their lesson. Several

artifacts were created for the first lesson presentation and were outlined for the team and teacher

participant who would teach the lesson (See Appendix D and E). The basic lesson followed a

launch, explore, and summary and included an activity in which students would roll three dice to

create a two digit and one digit number. The students would then use these numbers to create an

expression which they could evaluate using the distributive property, an array model, and also

the traditional or standard algorithm for multiplication on a recording sheet created by the team

(See Appendix F). Two fifth grade inclusion classrooms were chosen at two different schools of

similar low socioeconomic status and demographics with a high ELL population. The lessons

were presented with a day apart between each lesson study.

These themes of the CCSS and distributive property, our overarching goal, and the

impact of the lesson study on the individual teachers who participated in the study will be further

developed in the following sections. The paper is organized under the headings of Mathematics

Learning, Instructional Strategies, and Lesson Study Process, which present the individual

reflections of the some of the teacher participants, and finally, the teams Conclusion of the

lesson study.


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Section 2: Mathematics Learning

This section will focus on the mathematic concepts of the lesson presented, some of the

strategies used by the team, and the learning involved of the teacher and student participants.

Differentiated Student Learning

When conducting the lesson study over the distributive property, our goal was to

incorporate different tools for students to use. Not every student learns the same and we needed

to make sure we differentiated our instruction to meet the needs of all students. The first part of

the lesson study activity began with a launch of key vocabulary. The participating teacher

launched the lesson by reviewing/introducing vocabulary words that the teacher and students

would be using that day for the lesson. In addition to building student understanding of math

vocabulary around the distributive property, the team was also hoping to analyze whether this

process of reviewing vocabulary would encourage students to use math language in the

classroom throughout the lesson and thus one of the teacher observers during the lesson recorded

student usage of key vocabulary throughout the presentation of the lesson. Ultimately, however,

introducing the vocabulary was purposeful to try and help students who may have forgotten what

some words meant or introduced new words to students so that they would be able to use the

same vocabulary as their partners and other students around them. This established a more solid

foundation and the confidence of the teacher that all students were starting the lesson with the

same information.

During the exploration, or student-focused hands-on section of the lesson, some students

needed extra clarification on the directions, for which they had to rely on the teacher. Some

students were able to discuss with their partner and decide together what they were going to do.

While the students were working together, some of them were able to verbalize their reasoning


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right away where as other students needed some time and were able to explain after discussion

and questioning within their group and with the teacher. The robust understanding of this

learning was when individual students were able to explain to their classmates one-on-one why

they broke the multiplication apart the way they did. It was also when students explained to the

whole group and were able to defend their reasoning when others questioned them.

Prior Student Knowledge and Misconceptions

Prior to the presentation of the lesson study activity, students in both classrooms had

worked on multiplication of two digit by two digit numbers and multiplication of two digit by

three digit numbers. At the beginning of the year, students were shown how to break apart these

numbers into tens and ones, or hundreds, tens, and ones to simplify the multiplication. Students

are given a choice of whether to use the standard algorithm or to use the array model to multiply.

In both of the participating classrooms, neither students nor teachers had explicitly used the

vocabulary term distribute to name when students were breaking these numbers apart and then

multiplying them. Also before to the lesson in the two classrooms, students had been introduced

to math concept of order of operations. Both participating teachers shared that they had

previously talked about the order of operations and what you do first in order to solve a problem

a multi-operational math problem and what to do when encountering parenthesis in a math

problem. This background helped when they were presented with the lesson because the

participating students were able to distinguish where to put parenthesis in an expression and how

to solve equations with parenthesis.

We tried to insure that we had a strong conceptual understanding of our topic by thinking

of misconceptions the students may have had prior to teaching the lesson and thinking of

different ways to be able to explain or demonstrate them to a struggling student. This involved


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working with the concepts and materials ourselves to strengthen our own conceptual

understanding. Misconceptions that appeared during the lesson study cycle were:

1. Students would get the addition and multiplication signs mixed up when writing theirequation. Students would break down a number into the distributive property but thensolve what is in the parenthesis first instead of multiplying. Example: 7 x 34.. 7

(30+4)..students would solve 30+4 which is 34 then multiply it by 7. Instead they

should have done (7 x 30) + (7 x 4).

2. Some students would also confuse where to put the addition or multiplication signs. Suchas (7+30)x(7+4) instead of (7x30)+(7x4). This was able to be cleared up in some cases

when the students compared their work at one of the reflection breaks.

3. While planning the lesson we thought giving students graph paper would help themcreate their array models. However, some students used the graph paper to draw, create

pictures with the squares, and did not use the math tools in an effective way when

showing their expressions.

Ensuring Mathematical Gains

Throughout the lesson many different strategies were used to try and insure students

understanding. The first strategy was to introduce and focus student attention to the learning

goals of the lesson and how they could meet these goals through student-friendly criteria for

success. In order to insure student success and understanding of the math goals and reasoning

behind the lesson, there was to be constant revisiting of these goals throughout the lesson. By

sharing these goals with students at the beginning of the lesson, they know exactly what they are

going to be learning about and what they should know by the end of the lesson.

An additional strategy was the review of the vocabulary through student share out. This

allows students to review any vocabulary they already know and also helps to clarify any words

students are struggling with. The next strategy was having students work cooperatively in team

groups. Again, this insured that students had multiple resources beyond the teacher and brought

the lesson back to the overarching goal which was for students to construct viable arguments and

ask questions of the teacher but also of their peers. The final strategy to culminate the learning


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was the individual sharing. This was where students were able to show and explain their own

process and understanding of the math concepts involved in the lesson.

Conclusion of Mathematics Learning

As a result of this research lesson there are some interesting understandings to be developed

regarding students mathematical learning. The first is that students have a good foundation for

the reasoning that they were doing, specifically with multiplication. When students were not sure

what to do they used background knowledge to check themselves such as using the traditional

method to work out the multiplication problem and make sure that their answers were correct.

Students also demonstrated the fact that once they believe they had correctly solved a problem

they would continue to defend their reasoning even when another student challenged them. They

were able to discuss and see other views, which then sometimes resulted in a change of their

initial response due to a clearer understanding. The team took this into account when revising

the recording sheet to change the organization of the where and when the students see the

expression, distributive property, the area model, and the standard algorithm. By changing the

order, students focused their work moving from left to right on the new math concepts and used

their background knowledge to check for understanding and build their arguments.

What did we learn about the math content presented in this lesson? The content relies on

students having an understanding of the fact that they are able to manipulate the numbers to

simpler versions or decompose numbers. Additionally, the students were more successful if they

applied their knowledge of arrays and how they are arranged, a concept that taught in the fourth

grade curriculum used in the district in which the participating classrooms were located. The


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students also needed to be able to use their problem solving skills to evolve their thinking about

what happens when they used larger multiplicands.

One of the greatest lessons learned about the math content by the team of participating

teachers was that it wasnt as easy for students to grasp as we originally perceived. While

developing the lesson, the participating teacher whose classroom was used in the first lesson

study felt certain her students would understand the concept of the distributive property easily

and be able to complete the activity with very little misconceptions and mistakes. One of the

major teacher misconceptions of the team was the amount of time needed for deep student

understanding of the math content that went beyond a surface level breaking apart numbers to a

stronger foundational application of the distributive property.

Some of the ways that students learning and misconceptions informed instructional strategies

as well as changes from one lesson study to the next will be highlighted in the following section.

Section 3: Instructional Strategies

Instructional Strategies for Mathematical Concepts

One of the target goals was for students to use precise vocabulary when discussing their

thinking, and to engage in meaningful conversations among each other in order to build their

common understanding, or schema. To encourage students to use the math vocabulary, the

teacher reviewed the vocabulary terms using a quick self-pre assessment of wherein the students

showed thumbs up, thumbs in the middle, or thumbs down for their own individual

understanding of the math term; from this quick-check with the students the teacher reviewed the

terms according to student need, directed the students to the clear examples displayed on a chart,


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and marked the words that were new or challenging with post-its as a cue to help them remember

to refer back to the chart. The teacher continued promoting the use of the terms by referring back

to the chart throughout the lesson.

The lessons learning goals were written on a chart and the teacher and students read the

goals in the beginning of the lesson, a quick formative pre-assessment of the students

understanding of the distributive property was utilized once again using a thumbs up, middle,

and down which gave the teacher input about their schema. During the summary, the teacher and

students quickly reviewed the goals, and a quick post-assessment allowed the teacher and

students to see how their understanding of the distributive property had been affected by this

lesson.

An additional strategy to meet mathematical concepts included a visual cue through the

use of the distributive property video during the launch. This brief animation helped the students

conceptualize what it meant to distribute numbers according to place value in order to multiply.

The teacher used the images but muted the sound in order to lead the discussion and have more

interaction during the launch, using what the students knew or were not sure about as a guide to

what she reviewed with the students. This was effective in allowing the teacher to immediately

address misconceptions.

Another instructional strategy was modeling the exploration dice activity with a student

volunteer using an overhead projector in order to encourage a better understanding of the activity

and eliminate misunderstanding of the directions.

Table tents with sample questions were used to promote the use of questioning and

dialogue between the students, specific space was set aside throughout the lesson to stop,

discuss, and reflect about the concepts being covered where students were reminded that the


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tents were available to help guide their conversations. The students then had an opportunity to

record their thinking to the questions they chose to answer in an organizing sheet.

Furthermore, anticipating that many students would grasp the concept quickly, the

teacher used a challenge dice with numbers 7-12 in order to create more difficult expressions,

therefore eliminating the disengagement of those students.

Changes Made from First Presentation to Next and Why

In the original incantation of the lesson, the team planned for four reflection questions in

the first lesson (See Appendix G). In the debrief it was realized that one question was asking

them to simply rewrite one of the expressions they had already solved, so we eliminated that

question and settled for three cognitively challenging questions in the second lesson. This also

lightened some of the time constraints we experienced in the first lesson.

In the first lesson, the team observed a lot of misunderstanding from the students about

how to actually play the dice activity in the first lesson; the students were not clear about how to

come up with their expressions with the three dice. To address this, in the revised lesson, the

teacher participant called a volunteer to the front and played a round with him, using a real-life

example to review the rules and steps to complete the activity addressing student misconceptions

in real time in front of the class.

We changed the final reflection question, the students in the first class quickly noted that

it contained a 7 as one of the numbers rolled, for the second lesson, the 7 was changed to a 3

(Appendix H).

Student Engagement, Assessment, and Summary

The students were engaged by launching the lesson with a video, by participating during

the vocabulary review, they were eager to raise their thumbs to show their understanding of


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familiar terms. Throughout the exploration activity involved the random generation of numbers;

they had a choice about the expressions they developed based on those numbers. The reflection

questions allowed them to talk to their partners or small groups about the ideas they were

developing. Those students who were provided with challenge dice became excited to meet the

challenge. The students were partnered statistically according to personality and opportunities for

peer support. As a final assessment, the teacher participant shared a final exit question which

included an example of a fictional student who had used the distributive property incorrectly;

asking students to analyze why a problem is wrong is a high yield strategy that would give us

great insight on their understanding of the concepts we had targeted. The students were asked to

help this fictional student by explaining what she did wrong and helping her to use the

distributive property correctly. This final assessment came, however, after student collaborative

exploration of the distributive property. modeled talk and questioning through the use of table

tents, a small group discussion of strategies, and student work voluntarily shown to the class on

the through the projector.

Summary of Instructional Strategies

This lesson study project has reinforced and shined new light on the importance of using

proper mathematical communication in all forms in the classroom, during the semester, we read

about the difference in student achievement between a classroom where the teacher is an

exemplary model of communicating precisely, and a teacher who is not. This lesson really

helped support that notion; we were able to witness first-hand how powerful it is when students

have the tools to reflect, clarify, and expand their ideas and understanding of mathematical

relationships. The lesson reinforced the importance of vocabulary, by emphasizing it at the


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beginning of the lesson; the level of vocabulary the students used to describe and communicate

their understanding throughout the lesson was impressive.

The development of students mathematical communication shifts in precision and

sophistication throughout the primary, junior and intermediate grades, yet the underlying

characteristics remain applicable across all grades. During whole-class discussion, teachers can

use these characteristics as a guide both for interpreting and assessing students presentations of

their mathematical thinking and for determining discussion points.

Section 4: Individual Reflections

The following section is formed directly from the teacher participant of this lesson study.

Each member of the lesson study theme was asked to reflect on their own participation in the

lesson study process through the lens of impact to their work and colleagues, a reflection on how

lesson study supported their growth as a teacher, and the strengths and weaknesses of the lesson

study process. The names of the participants as well as the names of the school sites at which

these teachers work have been omitted and the section is organized by the grade level the

participant teacher is currently instructing.

Reflection of Math Interventionist, Grades 3-5

My involvement in the lesson study has tremendously impacted the way I work with my

colleagues at my school. With the expert help of my school support team leader, we have

implemented two Lesson Studies at my school site. The process was amazing. Teachers

efficacy was greatly increased, and we worked together as a team to create two strong lessons

that aided in students math problem solving capabilities. The first lesson created was for a third

grade classroom, focusing on the use of the distributive property. The second lesson created was

for a first grade classroom focusing on decomposing numbers into tens and ones. We followed

the lesson planning guide which allowed us to use the LES (launch, explore, summary) structure.

Teachers were very accepting of the model and agreed that it enhanced students problem

solving capabilities. One objective I had during the planning and implementation of lesson study

was to show teachers the importance of the usage of learning targets and criteria for success.

This strategy gives students access to the curriculum that otherwise would not. If students are

clear from the get go as to what is going to be expected of them, they are more successful. This

is not far from what we have been doing for our PDSA cycles when identifying the plan for the


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week; however the learning targets are more specific to daily use. Being that 75% of the

students in our school are ELL students this strategy of identifying learning targets and criteria

for success and reviewing them throughout the lesson, aids in focusing our lesson and students

attention to what the goals for the lesson are. Clearly defined goals and criteria for meeting the

goal prove to be a successful strategy that will be utilized at my site.

Lesson study also strengthened my growth as a teacher. Having the opportunity to sitback and watch a lesson that I helped developed, was an amazing opportunity. I was able to

have a birds eye view to see students misconceptions and success when dealing with the

distributive property. Delivering the lesson a second time gave us, as a team, an opportunity to

address these issues. I now have a solid lesson in my hip pocket that I can deliver at anytime to

address the distributive property at a fifth grade level. The CCSS introduce the distributive

property in third grade; the lesson can be easily modified for a fourth grade or even a third

grade classroom, just by changing the numbers students use when rolling the dice.

Having the opportunity to work with such a high caliber of teachers and pull together all

of our greatest assets was such an uplifting experience. Before participating in lesson study, I

was a little unclear of what the distributive property entailed, and now I feel that I have a clear

understanding of what the distributive property encompasses and how it can be effectively usedto aid in students understanding of multiplication.

One of our goals for lesson study was to have students participate in the questioning of others. I

feel that we came up with a strong strategy for helping students engage in effective questioning

strategies. By providing time during the explore, and question stems, students were engaged in

dialogue that promoted questioning and the use of precise language. We also identified a list of

vocabulary terms and made an anchor chart displaying the words along with a picture to

represent the words. This resulted in students using the words accurately and effectively when

engaging in dialogue.

I am not going to sugar coat it, it is not easy for seven teachers to come together and

agree on one lesson, and this process took a lot of time. There was a vast amount of time spent

negotiating the lesson. The conversations we had while planning the lesson were extremely

valuable. Misconceptions that I had were cleared up and a solid lesson was derived. The only

suggestion I would have would be to find a way to shorten the time, however I feel that it was

time well spent and necessary for the development of a strong lesson that met all of our criteria.

Reflection of a Fourth Grade TeacherCurrently the Lesson Study process has not impacted the way I collaborate with other teachers at

my school. We have so many new initiatives in our district at this point in time that I have not attempted it

yet. I would like to plan a lesson with them, however, that focuses on a skill that all of our students

struggle with. Perhaps by addressing the area with the Lesson Study process, we can discover the most

effective way to teach the content skill. I think that having a progression of a math skill from K-5, like we

have done in LIFT would give us an awesome visual of the importance of specific skills as a foundation

for the upper grades.I began this Lesson Study not completely understanding what we were supposed to be

doing. After the first lesson and debrief, I began to see the value of this process. Seeing the

results of our adjustments with the students from the second lesson really clinched it for me. I

was very intimidated by the process, thinking it was a teacher evaluation tool, but quickly

discovered that was not the purpose of this strategy. The point was to develop and improve a

lesson until it works perfectly to most effectively teach students. I have been tempted to try this

on my own, but it really needs some outside perspective to give the best evaluation of the lesson.


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I cannot both teach and observe. I will strive to get my fellow teachers willing to try this out, as I

believe it will be a very effective for improving our instructional practices.

I discovered that the Lesson Study process was a challenging idea for increasing the

effectiveness of our lessons. It can be a powerful tool that revolutionizes how we look at our

instruction. However, a high level of trust among the teachers must be present in order for the

Lesson Study strategy to work, because there is always the possibility, or the fear, that someonecould use this process against you. I would love to see how to adjust it for my personal use, so I

could self-evaluate my instructional practices and effectiveness. I think I will consider video-

taping my instruction to allow me to look for specific things that I may or may not be doing well,

so I can make adjustments. However, that will not give me the whole perspective of the lesson.

As to improving the process, clarity on all the paperwork that must be filled out would

make the Lesson Study more accessible. I was unsure about what we were doing and why, and

sometimes the answers were rather ambiguous, which was not helpful. There were sample

questions available, but not with explanations. Im glad that we were working as a team to

complete the assignment, or it would have been quite a struggle to accomplish.

I am not sure how to adapt the process to fit within my school context. There would be

problems with class coverage for the three of us in my grade level while a lesson was taught, andthen time for adjustments and re-teaching. This would be somewhat facilitated by the fact that we

are at the same building, so we wouldnt have to be driving back and forth to other schools.

However, the primary obstacle would be buy-in on the part of my grade level colleagues to even

engage in this process. The second obstacle would be getting agreement on the topic. Perhaps if

there were videos from previous participants that they could watch to see how the process works,

they would be more likely to be willing to try it. Also, if the process just involved us in the grade

level with no administration or principal types observing, they would probably be more willing

to participate. It is something I will have to pursue further.

Reflection of a Fifth Grade Teacher

The lesson study process has allowed me to work with a group of teachers to ensure the

success of students. While the group of teachers did not originate from my school, the process

has allowed me insights of how other teachers feel and think about working with students and

math. This will help create a foundation of understanding to work successfully with the teachers

at my school and grade level.

Lesson study has supported my growth as a teacher by giving me exposure to new ways

to think and present math. Ways such as: working with math vocabulary, use of different media

during a launch and how the curriculum is delivered to the students. Even though it was the

same lesson, there was a difference in how each teacher handled the delivery due to our

debriefing. That debriefing helped us to really focus on the learning of the students based on

how we presented the material.

What are the strengths and weaknesses of the Lesson Study process?

Strengths Weaknesses (Room for Improvement)

a) Working collaboratively to plan alesson. Being able to brainstorm

with others about teaching math

effectively.

a) Having to get comfortable withteaching in front of a group, and a

camera.

b) As a non-cohort member, not


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b) Seeing the different ways to presentthe same material.

c) Being thoroughly prepared to teachthe lesson and concretely thinking

about road blocks that might

hamper learning.d) Creates a lesson that could beusable for our non-cohort members.

e) Able to break up pieces that weobserve into manageable pieces so

that it will help with the fly-on-

the-wall gathering of information.

f) We concentrate primarily of thesubject area and not the teacher

because of the team effort.

having access to drop box.

c) There really needs to be a CD foreach member of the lesson study

team so that all are able to really

dissect the lesson.

How can the Lesson Study process be adapted to better fit within your school context? I dontreally think that it needs to be adapted. I think that with repeated times doing it we will feel

more comfortable doing it and implementing at our schools. There will always be a time issue,

but as long as there is administrator or district buy in, they can help provide time at our sites.

Reflection of a Fifth Grade Teacher

When we first started the process of conducting a lesson study with two fifth grade

classes, I had no idea what to expect or what I would learn from this process. But after planning

our lessons, implementing them, and analyzing the changes from one lesson to another I feel it

has opened my eyes to what lesson studies can do when you work with a group of teachers. This

is especially helpful when working with colleagues from your own school with whom you canplan multiple lesson studies and be able to focus on skills students are struggling with. My

involvement with the lesson study through the cohort has allowed me to become a resource to

other teachers at my school that want to conduct a lesson study. Being involved in a lesson study

allowed me to grow as a teacher and analyze my lessons to make them have a bigger impact on

my students. For example, I know how important vocabulary is when introducing a lesson and

having the vocabulary words up for students to see. This allows them to remember the words and

use them in throughout the lesson. Another thing I took away from this is time management.

Sometimes when I plan a lesson I want to incorporate so much, it takes too much time when I am

teaching it and I am rushed to get through it. The students are then rushed and are not given the

time they should have when exploring the lesson. I decided that it is ok to have a simpler lesson

as long as it is rich with vocabulary, student interactions, and allowing them time to talk with

other students about how/why they solved the problems the way they did. Also having the

objectives and criteria for success up for students to refer back to during the lesson will remind

them of what their learning responsibilities are for that day. All in all, I think the lesson study

process was beneficial to me, however it did take a lot of time to plan for just two, one hour long

lesson. I think time would be the biggest factor when planning a lesson study with my grade level

team because they do take a lot of time to plan. It would be easier if we planned to do a lesson

study three or four times a year and spread them out so that it wouldnt be so stressful. For


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example if I did one with my partner teacher we could plan on doing a lesson study once every

nine weeks, and take a couple of days out of the week to plan and carry out the lesson, then a

couple more days to analyze the results. The whole thing I would estimate to take a week. After

completing our lesson study I was surprised by what I learned and hope that other teachers have

a chance to participate in one. I hope to use what Ive learned, and take it back to my school, to

help other teachers get started with a lesson study.

Reflection of a Sixth Grade Teacher

I was excited from the beginning to start the lesson study process, although I did not

realize the impact that it would have. One particular impact that the lesson study process has

had in how I work with my colleagues at my own site is that it has set a precedent of the

importance of working with colleagues across grade levels. The lesson study team was

comprised of teachers that taught all the way from third grade through sixth grade. This model

proved critical to my own site because we are a small school without grade level partners.

Often, teaming on site seems to focus on one grade level banded together, but experiencing the

impact of the vertical alignment with this group of amazing teachers solidified the potential forpositive, effective planning and design of curriculum based on core standards. The fact that we

chose to implement this particular activity that we created around distributive property in a fifth

grade classroom was almost insignificantas teachers what is significant is that we all walked

away with a deeper understanding of a critical math concept and how this concept builds in the

grade levels over time.

Personally, the process of lesson study has supported my growth as a teacher in several

ways, but I would like to focus on collaboration and reflection. The collaboration piece of this

process was challenging and rewarding. Just as all students have different learning styles, all

teachers have different teaching styles and marrying those styles and opinions to come to a

consensus on how a lesson should be taught or what the main objective of the lesson was to be

was at times trying to say the least. Regardless of my some of my frustration during the process,

as the participant randomly selected to teach the first presentation of the team lesson, I felt if I

strayed into my usual teaching style or adjusted the lesson to the needs of the students, I would

be betraying the process of lesson study and the team. In the debrief that followed the first

lesson, the anxiety was overwhelming for me because the lesson the first time around was,

despite all our work, a hot mess. Simply put, we had over planned. As an individual teacher

having presented that lesson for the first time, I might have given up on trying that lesson again

altogether. As a team member, part of an effort to create a cognitively demanding and

standards-based math lesson, however, we pushed through and worked at it so that it could be

taught again. That debrief was a much needed reflection in which teachers rarely get to engage.

Having teacher colleagues watch me present a lesson was challenging for me, but I was told

over and over that they were observing the lesson and not me as an individual. In the debrief that

followed, this was truly the case. The observation and opinions being shared were not of me a

teacher, as we are so used to in our field (classroom walk-throughs, evaluations, and merit pay

come to mind) but, rather, the focus was to the level of demand of the lesson and how we as a

team could make it better.

Therefore, the strengths of the lesson study process for me is the vertical alignment it can

demonstrate, the opportunity to collaborate with colleagues on- or off-site, and the rare

opportunity for teacher reflection to occur. There would need to be some adjustments for sites if


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they wanted to engage effectively in lesson study. Depending on the site, teacher buy-in could be

an issue or even getting classrooms covered so that teams can observe the lesson. These

adjustments, however, are not impossibilities. I think through the application of technology

(recording the lessons and getting together even for meetings over the Internet through Facetime

or GoToMeeting) that all sites have the potential to engage in the lesson study process if they

choose. This process has been, for me, very influential to my teaching and learning.

Reflection of a Sixth Grade Teacher

This is my first experience with Lesson Study, from the start I saw it was going to be

different than other development and professional opportunities in that seven teachers had to

come together with different ideas and perspectives, to develop one shared vision in a lesson.

The lesson became exactly that, one shared vision. By engaging in the development of our

overarching goal and learning targets, we were able to come together through the realization

that we were all committed to the same basic principles, effective teaching that promoted optimal

student learning. As a sixth grade teacher, I was especially interested in understanding what

students were learning in the grade before mine. I teach at a school where the teachers haveenvisioned the standards and have focused on vertical alignment as we prepare for full

implementation of the Common Core State Standards. However, rarely do we get to observe

another classroom. That missing component is crucial in that it offers insight about the students

conceptual development and progression. How many times do we plan what we believe is an

effective, solid lesson, only to realize halfway through the lesson that we didnt anticipate certain

issues that arise, such as student misconceptions, time restrains, or student engagement? The

lesson study process helps you anticipate and plan, implement, then rethink and revise the

lesson, a process that makes you very insightful about the way you plan future lessons. This

process has helped me rethink my instructional moves; it has made me cognizant about

vocabulary enhancement in the classroom. There are endless opportunities to develop

vocabulary and promote focused student communication; teachers can purposefully create

opportunities for students to engage in meaningful dialogue.

Lesson Study also helped me conceptualize the distributive property, not only as a

different way for students to multiply two digit by one or two digit numbers, we have also used it

to multiply mixed numbers and fractions, this has been especially beneficial to students who

struggle with simplifying fractions. Weve applied it to simplify algebraic expressions. By having

a clearer understanding of the distributive property, I can project that understanding to my

students and help them find multiple uses for the distributive property. Since everyone learns

differently, I need to expose them to a variety of strategies; the hope is that they can pull from

these resources to persevere through problems as they continue their math journeys. I hope to

participate in lesson study in my campus so that we make vertical alignment more purposeful

and applicable.

Section 5: Conclusion

Lesson study gives tremendous insight into how a team of teachers can collaborate to

design an effective lesson that allows students to actively engage in meaningful mathematics. It


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is vital that all students have an entry point into a lesson that is able to support beginning learners

while providing a challenge to more advanced students. Since teachers are working as a team,

there is the ability to see multiple points of the lesson from various perspectives, which allows

for a more well-rounded lesson design and implementation. Throughout this process, the team of

teacher participants demonstrated and applied new and challenging mathematical instruction and

instructional strategies. Lesson studies represent a true collaboration of colleagues that

challenges us as teachers to be more aware of not only our teaching practices, but of the learning

students are engaged in as well.


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Appendix A

MC2

LIFT Research Lesson Template

Grade Level: 5th

Grade Date: February 26, 2013Instructor: Allie # of Students: 23

Class Time: 9:50-11:00 Class Type (check one):Location: Regular SPEDBilingual/ESL Other

Booker T. Washington Elementary

School

I. Goals:A. Overarching Goal: (What kind of people do you want

your students tobe?)

We would like our students to demonstrate criticalthinking by asking questions (of the teachers andpeers), constructing viable arguments, and critiquing the reasoning of others whilepersevering in solving math problems.

B. Mathematics Process Goal: (What kind of mathematical thinkers do you want yourstudents to be?)

Critical thinkers who evaluate and express using mathematic language.

C. Math Content Goals: (Whatare your math goals for your students as a result of doingthis unit?)

CCSSM 5.OA.1Operations and Algebraic Thinking: Write and interpret numerical expressions. 1. Use

parentheses, brackets or braces in numerical expressions, and evaluate expressions with

these symbols.Deepen their understanding of operations and algebraic thinking from fourthgrade by writing and evaluating simple expressions and interpreting numericalexpressions in order to prepare them for applying distributive property in sixth

and seventh grade.

Learning Target: How can I use the distributive property to solve equations?

Criteria for Success: I am able to break multiplication expressions into simpler numbers

so that I can multiply easily. I am able to make an expression into an array.

Vocabulary: equation, expression, sum, distributive property, precise, array, unmarked

array, parentheses, and value.


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D. Research Lesson Goal: (How does this research lesson fit with the other goals? Whatdo you want to learn about your students from this research lesson?)

II. Description of math content learning goal: (1 to 2 sentences)

Student will apply the distributive property and use parentheses accurately to solve

expressions.

B. What evidence will you collect to assess students learning of the target?

Reflection sheets that students are stopped periodically throughout the game to reflect on their

learning.

Exit slip where students are asked to evaluate a false statement and make it true.


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Appendix B


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Appendix C


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Appendix D

III. Description of the Research Lesson CCSSM 5.OA.1

Operations and Algebraic Thinking. Write and interpret numerical expressions. 1. Useparentheses, brackets, or braces in numerical expressions, and evaluate expressions with

these symbols.Launch: 15 minutes

1. Building a context for the lesson (Connecting to meaningfulthings or previous lesson):

Direct students to learning goals and criteria for success.Learning Target: How can I use the distributive property to solve

equations?

Criteria For Success: I was able to break expressions into simplernumbers so I can multiply easily.

I was able to make an expression into an array.

Take a minute to review the vocabulary using anchor chart. Have

students give thumbs up, down, middle to represent their ownunderstanding of the vocabulary words.

2. Laying the framework for the learning experience (Introduceresearch lesson to students):

Present distributive property slide show from enVisions 3.5.Pause to shoulder talk during presentation

EssentialVocabulary

equation

expressionsum

product

distributiveproperty

precise

array

rowscolumns

unmarked array

parenthesesvalue

algorithm

Possible Student Questions or

Misconceptions

Possible Teacher Questions/

Strategies/ Responses

What do students need to know/be

doing to successfully engage in this

part of the lesson?

Observed Lesson Data

Why is that true?

Can you make amodel to show that?Do you think this

would work with

other numbers?

Actively listening and

participating duringpresentation.

Able to communicate

any misunderstandingswith teacher for

clarification.

Have prior knowledge of

distributive property.Know how to break

numbers apart.

Know how to use

parentheses.

Teacherquestion

Studentquestions

How trueteacher

stays to

the lesson(timing)

Studentmisconcepti

ons

Student

vocabulary usage

Studentengageme

nt

OLE2indicators


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Explore: Engaging students with concepts (Exploring, Investigating, Problem Solving): 40

minutes

Mulitply and ConquerTeacher will introduce Multiply and Conquer Game and model how to play it, using the

Fish Bowl technique.

Students will roll three dice and choose one 2-digit number and one 1-digit number.Students will use these two numbers to form a multiplication expression. Using theirrecording sheet, students will record: expression, distributive property, use an unmarked

array, and use the algorithm.

Students will play the game in groups of two or trio if necessary.During the game, teacher will ask students to reflect on their thinking (play for 5 minutes;

record their thinking for 3 minutes). They will record their reflection on a sheet of paper

folded into quarters. Students will play for five minutes and record their thinking.Reflection Question 1: Pick one of the equations from the game, write it down, explain why

you broke it up, or distributed it, the way you did?

Reflection Question 2: Partner asks a question (based on table tent stems), and writes a

reflection/answer.Possible Student Questions or

MisconceptionsPossible Teacher Questions/


What do students need to know/bedoing to successfully engage in this

part of the lesson?


Students may not be

comfortable using

the algorithm.Students might not

use landmark

numbers (tens andones) to break up

their 2-digit number.

Students may notknow how toaccurately label an

unmarked array.

Can you make a

model to show that?

Can you explainwhat you have done

so far? What else is

there to do?Why did you decide

to use this method?

Do you think thiswould work withother numbers?

Could you try it

with simplernumbers?

How did you get

your answer?What if you would

have started with

rather than ?

Students should be able

to break numbers apart

into tens and ones (uselandmark numbers).

Students need to use the

distributive property tobreak up an equation

into easier numbers to

work with.Know how to useunmarked arrays.

Students need to work

cooperatively and bechecking each others

answers.

Know how to useparentheses accurately.

Know how to apply the

distributive property in

an equation and using anunmarked array.

Teacherquestion

Studentquestions

How trueteacher

stays to

the lesson

(timing) Student

misconcepti

ons

Studentvocabular

y usage

Studentengagement

OLE2

indicators

Sharing ideas/solutions (Whole group, small group, written): 20 minutesRemind students of learning target and criteria for success.

Pairs will work with tablemates (4 students) to discuss reflection questions, can you think

of an example of how you were able to break an expression into simpler numbers tomultiply easily, or how you made an expression into an array.

Possible Student Questions or Possible Teacher Questions/ What do students need to know/be Observed Lesson Data


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Misconceptions Strategies/ Responses doing to successfully engage in this

part of the lesson?

What strategies did

you use?

How would you

tackle similar

problems?


to listen, communicate

their own thinking to

others.

Students should be ableto ask clarifying

questions, if they do notunderstand.

Teacherquestion

Studentquestions

How trueteacher

stays to

the lesson(timing)

Studentmisconcepti

ons

Studentvocabular

y usage

Studentengageme

nt

OLE2indicators

Summarizing (Gathering Evidence How will you know students met the learning goal?): 10

minutes

Exit SlipTeacher will share with students a false example of the game just played, and ask students

to explain why it is incorrect and how they could fix it. Students will record their

thinking on their reflection sheet.

Possible Student Questions or

Misconceptions

Possible Teacher Questions/


What do students need to know/be

doing to successfully engage in this

part of the lesson?


What do you think

about what ___

said?Can you convince

the rest of us that

your answer makes

sense?What are the key

points or big ideas

in this lesson?


to identify a

misconception using thedistributive property and

defend their argument.

Teacherquestion

Studentquestions

How trueteacher

stays to

the lesson

(timing) Student

misconcepti

ons

Studentvocabular

y usage

Student


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engageme

nt

OLE2indicators


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Appendix E

Time Frame with Teacher Moves

Time Task Teacher Moves Notes Materials

10:00

-

10:10

~10

min.

Launch Introduce and thankyou

Present LearningGoals/Criteria for

Success

o Anchorchart or sentence

strip

Review Vocabularyo Thumbs up,

down, middle for

unknown words

o Anchorchart/mark with

sticky notesproblem words?

o Whenreviewing precise,

refer to table tents.

o Remindstudents that this is

their word bank to

use today when

discussing math

Present DistributiveProperty slideshow

from envision

o Gage classduring review

o Mute or usenarrator as

necessary

o Ask studentsto turn to shoulder

partner to discuss.

o Stopslideshow at

distributive

property definition

Learning Target: How can

I use the distributive

property to solve

equations?

Criteria For Success: I was

able to break expressions

into simpler numbers so I

can multiply easily.

I was able to make an

expression into an array.

expressions

equations

sumdifference

distributive property

precise

array

parentheses

value

Envision:

www.pearsonsuccessnet.co

mGrade 5

Topic 3

Lesson 3.5 DistributiveProperty

Anchor Chart

Learning Goals/Criteria for

Success

Computer

Projector

10:10

-10:45

~35

min.

Explore Explain activity

whole groupo Model for

the class how to

participate

o Emphasizethat they are

sharing dice and the

responsibility of

checking their

partners work

Can you make a model to

show that?Can you explain what you

have done so far? What

else is there to do?

Why did you decide to use

this method?

Do you think this would

work with other numbers?

Could you try it with

simpler numbers?

Elmo/Projector

Activity Materials:3 dice per pair

Each: student recording

sheet,

Blank copy paper for

reflection

Table Tents with Question

Stems for students

Reflection questions


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before they take

their turn

o Share thatwe will be pausing

to reflect on

questions

throughout the

game

o Signal withhand clap that

means to pause and

reflect on the

question that will

be on the screen

Partner up withtablemate

Start activity andpause students after

every 5 minutes for a

three minute

reflection

How did you get your

answer?

What if you would have

started with rather than

?

Reflection Question 1: Pick

one of the equations from

the game, write it down,

explain why you broke it

up, or distributed it, the

way you did?

Reflection Question 2:

Partner asks a question

(based on table tent stems),

and writes a

reflection/answer.

Reflection Question 3: You

and your partner pick oneof the equations you did

and represent it with the

traditional algorithm, the

distributive property, and a

visual representation

10:45

-

11:00

Summar

ize Students will clean

up and reflect with all

tablemates and share

their thoughts on the

activity and discuss

their answers to the

questions they

recorded For groups that are

struggling to discuss

teacher can model

with the questions or

ask group to focus on

one question and dig

deeper

WITH TIME, shareout a few ideas whole

group

BUTMAKE SUREstudents have enough

time to independentlyrespond to the last

question as their

EXIT slip

Pick up exit slips

What strategies did you

use?

How would you tackle

similar problems?

What do you think about

what ___ said?

Can you convince the rest

of us that your answer

makes sense?

What are the key points or

big ideas in this lesson?

Display the last question

and have them explain the

students misconception.

Exit Slips/Reflection papers

(pick up)

Materials from activity


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Appendix F

Recording Sheet (Both versions)

Lesson 1:

Lesson 2:


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Appendix G

Reflection Questions

Annie rolled a 4, a 6, and a 7. She came up with the following expression

46 x 7She used the recording sheet and came up the following equations.

Help Annie by explaining the distributive property and telling her where she made a mistake,you may use words, pictures, or numbers to explain your thinking.


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Appendix H

Final Reflection Question

Annie rolled a 4, a 3, and a 6. She came up with the following expression

43 x 6She used the recording sheet and came up the following equations.

Help Annie by explaining the distributive property and telling her where she made a mistake,

you may use words, pictures, or numbers to explain your thinking.

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