kindergarden lesson study

7/30/2019 Kindergarden Lesson Study

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_______________________________________________________________________________________Modified from MathStar Research Lesson TemplateWork in Progress (5/4/2013) 1

MC2LIFT Research Lesson Template

Grade Level: K Date: Feb. 26, 2013

Instructor: Nicole Coca/Glenda McShannon # of Students: 23/21

Class Time: 8:30 am and 1:30 pm Class Type (check one):

Location: Monte Vista/Loma Heights Elementary Regular SPED Bilingual/ESL Other

Context: (Describe social/ cultural context of school)

Both elementary campuses are funded by Title I, meaning high numbers of

children are from low-income families. The afternoon classroom is an

inclusion classroom, while the morning classroom is a regular education

classroom with some identified Sped students.

I. Goals:

A. Overarching Goal: (What kind of people do you want your students

tobe?)"All students, meaning students with diverse learning needs, engage confidently in solving problems by

self-selecting strategies and tools to find solutions, and communicate their mathematics thinking and

reasoning with each other."

B. Mathematics Process Goal: (What ki nd of mathematical th inkers do you want your students tobe?)Students will become critical thinkers and communicate their thinking and reasoning with others

verbally and with pictures, numbers, and words.

C. Math Content Goals: (Whatare your math goals for your students as a resul t of doing th is uni t?)Students will be able to decompose numbers from 1 to 10 in more than one way.

D. Research Lesson Goal: (How does this research lesson f i t with the other goals? What do you wantto learn about your students from thi s research lesson?)


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How do students decompose numbers less than or equal to 10 into pairs in more than one way?

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

CCSS.Math.Content.K.OA.A.3 Decompose numbers less than or equal to 10 into pairs in more than one

way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2

+ 3 and 5 = 4 + 1).

A. Sample mathematical mapping templateof your lesson (Idea influenced by the work of Liping Ma):

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

Exit Tickets in which students will be given a number to decompose.

Lesson Focus

Subitizing

see and say the numbers without

counting

Counting accurately

Number recognition Recognize a number and

hold it in their headsee

and say 5

Comparingone, two more,one two less Part part whole

Cardinalitylast

number names the set

Lesson Strand

Operations and Algebraic

Thinking
http://www.corestandards.org/Math/Content/K/OA/A/3http://www.corestandards.org/Math/Content/K/OA/A/3


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III. Description of the Research Lesson

Launch:

1. Building a context for the lesson (Connecting to meaningful things orprevious lesson):

The teacher will begin by building some background and introducing the domino:

Hand one student a domino, and ask the class, What is ------holding?

What is a domino? What do you notice about the dots? What do the dots tell you?

Why do we look at the dots?Have the students Think/Pair/Share about a domino.

Put the domino under the doc camera. There are two sides on a domino. Place a

few under the document camera, making sure one of them is 0)

What is the same about the dominos? What is different? Again have students

Think/Pair/Share the similarities and differences.

State/Share learning target to students by reading aloud and discussing

vocabulary:

Learning Target: How do you decompose a number into 2 smaller numbers?

(Use a cube tower to model decompose as a form of TPR)

Share/state the critieria for success:

How do we know we met our learning target? (objective/goal) This is how we willknow. We will show two ways to decompose a number.

Essential

Vocabulary

domino

dots

sort

decompose

2. Laying the framework for the learning experience (I ntr oduce researchlesson to students):

Model playing the game using the document camera.

We are going to do a domino activity with a partner.

Call up a student to model sorting the dominos on the mat first (Sorting only 07).

We will begin by sorting our dominos by matching the dots on the dominos to a

number on our mat.

Take turns with the student picking a domino, and sorting it on the mat. Tell thestudents that as they sort, their partner will double-check their choice and agree or

disagree. (Sentence Frame: Do you agree? Why or why not?

Once you sort all your dominos, you are going to turn them all over. (Model

doing this)

*Move to first explore of sorting (See Explore A below)

Launch 2:

Now, we will begin to decompose (TPR) numbers using dominos. I have a domino

in my pocket. (put domino in pocket) I want you to help me figure out what the

domino could look like if there is 6 dots on my domino.

You will now be given a recording sheet to decompose (TPR)6.

Show them the recording sheet and model using the number 4. Call up a differentstudent helper.

I have a domino that equals 4 under this cup. Lets see what it could look like.

We can figure this out by decomposing (TPR) the number 4. My partner and I will

decompose 4 and record the dots onto these blank dominos. Ask your

partner/studentHow can you decompose 4 into 2 numbers? (If they respond

yes let them share. If not, challenge them to think about how many dots they

would want on each side of their domino to make 4. If they do not know, have class


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think about it and share their ideas. Then model drawing the dots onto the

domino. Ad lib as you go.)

We just found one way decompose (TPR) the number 4. I am going to ask my

partner, How do you know that you decomposed 4? Have your partner model by

asking you. Then respondI know because ____ and ____ make 4, and I double

checked by counting all the dots. If you are not sure you are correct, or if you and

your partner do not agree or get stuck, you can check your work by turning over

the dominos on your mat on the 4 column to see if 1 of them matches yours. Nowwe will record the numbers that make 4 by writing the number underneath the

dots. (Repeat with another student, again finding a combination of 4, and if time

permits, another student as well.)\

Lets look under the cup, and see if one of our combinations match the domino.

(Turn over cup, examine and match domino to one of the combinations.)

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

*Model counting

strategies for sorting

dominos (see it/say it,

subitizing for numbers 5

or less, counting on, or

___ = ____ and ____.)

*Counting, number

recognition to 10

Explore: Engaging students with concepts (Explor ing, I nvestigating, Problem Solving): 1520

minutes

Explore A: * Place students into pairs using prepared partner lists, pass out mats and sets of

dominos. Students will begin the Explore by working with a partner to sort their dominos. They will

turn them all over when they are finished.

Explore B: **Students will work with their partner to decompose the number 6. After they have

recorded at least 2 combinations for their number, the teacher will pass out a large paper domino for

them to record one of the combinations they came up with for their number. This will be used in the

share time later.

While they work:

*Walk around and observe their conversations, see their work, and pre-select 4 pairs of students you

want to share in the summary. If a pair has an incorrect representation, select them as one of the

pairs to share.


Misconceptions


Responses



part of the lesson?


*Students may countwrong, and have the

wrong domino on the

wrong

number column on their

mat.

*Students may only count

one side of the domino.

*Quick check fortime/pacing (Thumbs up

if you and your partner

have sorted all your

dominos?)

*For struggling students,

only give them dominos 0-

5. (Educational Assistant

*Number recognition,strong 1 to 1

correspondence, & how

to work cooperatively.

**Partpart- whole

relationship


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**Students may record

incorrect ways to

decompose.

**Students may record

their representations on 1

side of the domino, or two

ways to decompose on 1

domino. Hard to ask each other a

question

will work with them)

*How can you

prove/know that your

domino is on the correct

number?

**Give pairs another

number if they finish

quickly (7).**Are there any other

ways to decompose ____?

Teacher check-in -

What do you have to ask

your partner?

Post sentence frames.

Sharing ideas/solutions (Whole group, small group, wri tten):

Get students attention and call them up a table at a time to add their domino to the chart. (Mark

dominos of students that will be sharing)

We are now going to have a few pairs of students share how they decomposed the number 6.Students will share their thinking and explain the different ways they decomposed. If they have an

incorrect representation, ask questions to prompt them to explain their answer.

After all pairs have shared, teachers will reveal the dominos in their pocket and compare them to

chart with student dominos.

Did any of your dominos match the one in my pocket?


Misconceptions


Responses



part of the lesson?


*Chart students

representations on a

poster for the entire class

to see. (flip tablet)

*Explain how you

decomposed 6?

*Record representations

for their given number

*Be able to explain their

representations.

Summarizing (Gathering EvidenceHow wil l you know students met the learn ing goal?):

*Revisit Learning target and evidence of success. Our learning target asked, How do you

decompose (TPR)a number into 2 smaller numbers? and we had to find at least two ways to

decompose a number. Did we meet this goal? How do we know?

*Refer to chart of different domino representations shared by students.

Now I am going to put a different domino in my pocket. What could it look like if it has 8 dots? I

want you to think about it, and record it on this piece of paper. I want you to work on this all by

yourself. Do not look at your partners work.

*Pass out Exit Tickets and collect when students are finished.


Misconceptions


Responses



part of the lesson?


*Students who did not

grasp the concept will not

know what strategies to

*Prepare exit ticket with

blanks for students to

write in representations.

*Students need to

understand what it means

to decompose.


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use in order to decompose

8.

*E.A. will do exit tickets

with small group using a

domino with only 3 dots.

*Sorting mats are still

available to students who

may need them.


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Large Blank Dominos for Partner recording during Summary

DecomposingRecording Sheet


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4 =

_____ + _____

4 =

_____ + _____

4 =

_____ + _____

6 =


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_____ + _____

6 =

_____ + _____

6 =

_____ + _____

7 =

_____ + _____


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7 =

_____ + _____

7 =

_____ + _____Exit Tickets

8 =

____ + ____

8 =

____ + ____


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8 =

____ + ____

8 =

____ + ____

8 =

____ + ____

8 =

____ + ____


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Kindergarten Lesson Study

Decomposing Numbers

Nicole Coca

Melissa GilbertGlenda McShannon

Section 1 - Introduction:

As a group of four Kindergarten teachers, we participated in a lesson study in order to deepen our

understanding of a mathematics lesson. This process proved to be an eye opener and allowed us to pinpoint

our own misconceptions. Our Kindergarten team chose to focus on the CCSS Math Content K.OA.3

Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or

drawings, and record each decomposition by a drawing or equation (e.g., 5=2+3 and 5=4+1). This


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standard was a new addition to the kindergarten curriculum since it hadnt been covered in the NM

Standards and benchmarks that had previously driven our curriculum. Our team decided to find a lesson

outside of the Investigations curriculum since our district will be adopting a new math program for the

following school year. Lessons fromEnvision, Go Math and Georgia math were all contenders. As we

examined lessons from these three math programs we kept in mind our overarching goal: All students,

meaning students with diverse learning needs, engage confidently in solving problems by self-selecting

strategies and tools to find solutions, and communicate their mathematics thinking and reasoning with each

other. Ultimately a lesson from Georgia math was selected. We felt that it was important for students to

become critical thinkers and communicate their thinking and reasoning with others verbally and with

pictures, numbers and words while their methods of decomposing numbers less than or equal to 10 were

also being looked at.

This lesson was implemented twice, in two different kindergarten classrooms, at two different

elementary schools. In the morning the lesson was taught in a class of 23 students, four students receive

services for speech and language impairments. Of these four, one student is a C level special education

student and receives services outside of the classroom. The school has 68% of the population receiving free

or reduced lunch. In the afternoon the lesson was taught in an inclusion classroom of 21 students, four

receive special education services. Two students have speech and language impairments, one is legally blind

and another is emotionally disturbed. The school has 85.2% of the population qualifying to receive free or

reduced lunch.

Section 2Mathematics Learning:

By examining how different students learn about decomposing numbers, our group of teachers had

some powerful learning. Students have a tendency to imitate what teachers model. For example, in the first

lesson the teacher modeled counting the dots on the dominos and the students did the same when they

determined the total dots on their dominos in the sorting portion of the lesson. In the second lesson the


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teacher modeled the strategy of see it, say it (the concept of subitizing) and students were more

comfortable determining the total number without counting each individual dot. It is important that students

are exposed to various strategies for determining amounts prior to this lesson on decomposing numbers.

Students should be familiar with counting on strategies, and subitizing (being able to determine the amount

of objects presented at a glance). When students were asked to decompose certain numbers some relied on

the sorting mat and some used what they already knew about a number (ex. 3 and 3 make 6). Other students

drew dots on one side of their paper domino and then figured out how many remaining dots they needed to

draw on the other side. In order for students to demonstrate a robust understanding of decomposing

numbers, they would need to know that numbers can be decomposed into two smaller numbers in more than

one way. (ex. 5 can be decomposed into 4 and 1 as well as 2 and 3). Students would have to possess strong

number concepts in order to use strategies to break apart these numbers.

Prior to teaching this lesson the kindergarten classrooms had been working on many concepts.

Among them were counting, keeping track, recording numbers, and adding numbers with sums up to 10.

The lesson on decomposing numbers was building on the students knowledge of numbers and the quantity

they represent, as well as addition being parts that make a whole. It also built upon writing equations,

cooperative learning and communicating their mathematical thinking to peers. With decomposing, students

were now presented with a whole number and then being asked to find its parts. Extensions to the lesson

were carried out in three of the classrooms and they involved using a tower/wand of cubes for students to

physically practice decomposing a number into two parts. Once students were comfortable using these

towers/wands they were then asked to record the ways they decomposed numbers.

When looking at the misconceptions connected to the lesson, the misconceptions were actually

demonstrated by the teachers. In the first lesson the word combination was used frequently and took the

place of decomposing. During the debriefing the teachers realized that by using the word combination,

students were actually encouraged to compose, make numbers, rather than decompose, break them apart.


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Another teacher misconception was in the way the equations and the sorting mat were presented. In order

for students to better understand that they are starting with a whole and breaking the number into parts, the

sorting mat should look like this:

0 1 2 3 4 5

6 7 8 9 10

By having the numbers on top it allows the students to visualize that they are in fact breaking a

whole number apart. In the mats used in the lessons the students werent able to make that connection since

the numbers were located on the bottom of the box and implied that students were combining parts to make

a whole. Example of the mats used in the lesson:

0 1 2 3 4 5

6 7 8 9 10

Another change that was made involved the way the students were presented with equations. In the

morning lesson the recording form asked students to record using this format ___ + ___= 6. The revised

forms asked students to record using 6 = ___ + ___.


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At the conclusion of the lesson the students were provided with Exit Tickets as a way for us to

check for understanding and to see if the goals of the lesson were met. These Exit tickets contained a

blank domino template for the students to fill in with dots on each side of the domino, representing what a

domino with 8 dots might look like. It also provided blanks for the students to write in the numbers to

match their representation (See figure 1). We collected these Exit tickets and examined them to see if the

lesson was successful as well as what misconceptions the students had, and we were able to reflect on how

we could use this information to help improve and modify the lesson before implementing it in the second

classroom in the afternoon. After learning from our misconception about how the word decompose was

presented and represented, we did modify the Exit Ticket for the lesson in the afternoon (See Figure 2).

Another insight gained from the first lesson taught in the morning was that, since students had their

sorting mats available as a resource with different ways to represent numbers decomposed into pairs, many

students utilized them to record answers for their Exit Ticket, rather then having to figure out how to

decompose the number on their own. Because of this, the Exit Tickets were not an accurate depiction of

the overall class understanding of the lessons learning target. The afternoon lesson Exit Tickets were a

better depiction, given that the students were not instructed to use the soring mats as a resource to help the

students decompose different numbers; therefore, when filling out the Exit Tickets, the afternoon class did

not use the sorting mats as a resource. This gave us a more accurate representation of the class

Figure 1Sample Exit Tickets from the first lesson

Figure 2Modified Exit Ticket for the second

lesson

8 =

___ + ___


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understanding of the concept. We did feel that the lesson was a great introduction to the concept of

decomposing numbers into pairs; however, we believe it is necessary to have follow-up lessons in order to

provide multiple opportunities for students to practice decomposing numbers and really become proficient

in this standard.

Having participated in this lesson study and really unpacking this standard on decomposing

numbers, we have developed a better understanding of what students need in order to be successful with this

concept and in their mathematical thinking. In order for students to fully comprehend that numbers can be

decomposed, students need to understand numbers and what they represent. They should have a strong

foundation in number sense, which includes students being exposed to different ways of seeing and

representing numbers. If students are given opportunities to see numbers in different patterns, and build

number relationships, they will have a basis for this standard. Also, strategies such as counting on and an

understanding of part-part-whole relationships are great tools to support the concept of decomposing.

These early number sense concepts are the basis for all the standards in the domain of Operations and

Algebraic Thinking in kindergarten, and support mathematical learning for students as they progress in this

domain vertically throughout the grade levels.

Unpacking this standard on decomposing numbers has really highlighted the importance of

understanding math vocabulary as a teacher, before sharing it with your students. The first lesson taught in

the morning was designed in a way that students would be finding combinations of a number or different

ways to represent a number. After implementing the first lesson we realized that we were having the

students compose rather than decompose or break apart a number. By having the recording sheets and Exit

Tickets set up with the numbers or combination preceding the total amount, the students were actually

composing. Because of this, we were not staying true to the standard or giving students an accurate

understanding of what it means to decompose. By modifying the recording sheets and Exit Tickets to

show the total amount first, followed by the numbers, we provided an accurate representation of


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decomposing. We also discontinued the use of vocabulary such as combinations, which lent itself to

composing. This realization also led to a wonderful reflection process in which we discussed other

activities that would support this concept of decomposing rather than composing and would enhance the

mathematical learning of the concept.

Section 3 - Instructional Strategies:

Our group used a variety of instructional strategies to enable our kindergarten students to be successful.

One of the strategies used was going over the learning target and criteria for success so our students would

understand the goal of our lesson. We also introduced and reviewed vocabulary to help our students

comprehend the activities. For example, we introduced the word decompose with a total physical response

(TPR) to enable our students to understand this words meaning. Since the majority of our students had not

used dominos we felt it was necessary to provide them with the opportunity to discuss and explore using

these manipulatives before engaging in decomposing numbers. With a student partner we modeled using the

strategies ofsee it, say it andcounting on to encourage our students to not just count but add numbers.

Another strategy was utilizing two launches (introductions) in order to avoid giving our kindergarten

students too much information at once, causing them to not be able to follow the directions that were

presented.

To ensure cooperative learning, we placed our students into strategic pairs that were purposefully grouped to

eliminate frustration and provide an optimum learning opportunity. Our students were allowed to respond

several different ways. For example, our students not only wrote the numbers and equations but represented

the numbers by drawing dots on domino shapes. An equity strategy we utilized was providing dominos and

mats for students who needed this tool as a resource.

After conducting our first lesson in the morning our group made a number of changes to improve our

lesson plan. As mentioned earlier, after our debriefing session we became aware that in our first lesson we

were not teaching decomposing but composing. This resulted in the changes in the lesson that were shared


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earlier. Lastly, our first lesson was very long and our students struggled maintaining focus for this length of

time thus had difficulty engaging during the summary. To address this issue, we reduced the amount of

time students spent sorting by removing some of the dominos.

To engage and peak ourstudents interest and to sustain it during our lesson we used an assortment of

instructional strategies. Our lesson was designed to be a problem solving activity which challenged our

students to determine which domino the teacher might have in their pocket. We engaged our students

throughout the lesson by constant use of TPR (Total Physical Response) and having them work with a

partner. Also, we used a hands-on material, dominos, which our students could manipulate. In addition, we

had our students responded by both drawing representations and writing numbers and equations. To

encourage student-to-student communication during our lesson we had them work with a partner while

using a sentence frame, Do you agree? To monitor the students understanding during the lesson the

teacher went around and asked students questions about their work and written responses. We closed the

lesson with a summary, which consisted of placing a large domino to demonstrate one way to decompose.

An exit card was also completed.

Conclusion:

The lesson study process provided us with a deeper insight on the concept of decomposing numbers.

Many times as educators, we present a lesson without taking the time to critically examine the

misconceptions that may arise within ourselves, or the students we teach. This process allowed us to not

only recognize these misconceptions, but tackle them head on. We were aware of our instructional strategies

and were able to use them to encourage students to have conversations about mathematics throughout the

lesson. The debriefing held between the morning and afternoon lessons allowed us to truly see what worked

and what needed modifications. It is rare that educators are able to fully digest what went well or what did


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not during lessons. It is also rare that they get to discuss this in depth with their colleagues. This process

would be beneficial for fellow educators in order to have meaningful conversations about mathematics

education. Just as we encourage our students to participate in these types of conversations we as educators

can use each other as a resource to deepen our own knowledge of math concepts.

kindergarden lesson study

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