Gail Lindsay

ECE 7525

Mathematical Identity & Counting Profile Project

The first student I chose to work with for the Mathematical Identity and Counting Profile

Project was Felix. The assignment said to pick students that varied differently with their

identities. Felix is mixed race. His father is Puerto Rican and his mother is Irish. Felix’s

strongest identity is his Puerto Rican heritage. From the first day I met him, he told me all about

how he is part Puerto Rican and travels there to see his Papa frequently. He also speaks Spanish

at home with his father and takes Spanish lessons in the after school program. I also, chose to

work with Felix because he loves math. At the beginning of the year, I have parents fill out a

form titled “Getting to Know Your Child.” They had written that math was Felix’s favorite

subject, and I can see that he feels math is a strong subject for him. When I asked him how he

felt about math, he said “I feel good about it. I like to play math games at home and at school.”

I think that a lot of kindergarten math is an authentic experience. In kindergarten, they are

learning the very basics of what numbers represent, addition and subtraction, and shapes. They

most likely have already been questioning, exploring, and learning about these math concepts

because they are so real to them. Felix enjoys being challenged in math. When we work on

solving addition and subtraction word problems; as well as, comparing numbers I try to make

sure that they are real world problems. Lots of times, using food in word problems or with

comparing numbers makes it authentic for them. Also, Felix loves playing with Lego. This is an

authentic math experience for Felix. He is using his knowledge of shapes and lines when

creating with Lego. During the interview, I could see that Felix’s math identity was strong. He

was really excited to help me with the project when I had told him it was a math project. His

parents had also wrote on his form that he enjoys helping and being a leader. Felix had told me

on his heart map that he enjoys being a good helper. To affirm Felix’s identity, I praised him for

being a good helper, working so hard, and doing such a great job counting the items. I could see

that he really enjoyed the mathematical challenge and working one-on-one with me.

I put 43 counters in a box and asked Felix to count them. He took them out one at a time

and made one long row. He counted and kept track of the number he was on even though it took

him about 5 minutes to complete. Another student even came over and asked him a question and

he remembered what number he was on. His one-to-one correspondence was solid. When he

got to the end, he told me there were 43 counting bears. He was extremely deliberate and

careful. One bear fell off the table, and he picked it up and kept counting from where he was.

When he was done, he recounted them to make sure he was correct. Then I asked Felix to

recreate the number using Unifix cubes. I handed him 5 rows of 10 Unifix cubes. Felix took

each cube off and counted them one by one instead of keeping them in rows of 10. He did

accurately line up 43 Unifix cubes. Finally, I asked Felix to make me a representation that

shows me how many bears were in the box. Felix wrote the number 43 in numbers as one way,

and wrote in letters the number 43 as the other way.

Felix’s profile level is proficient. He showed a solid understanding of one-to-one

correspondence. His cardinality was accurate, and he was deliberate and careful. He counted by

ones and was able to count up to 43. He didn’t make it to the exemplary level because he didn’t

group the bears and count in groups. This was valuable information for me, so that I can work

on this with Felix to move him to the next level.

The second student I chose is named Suri. She is also one of my kindergarten students. I

chose Suri because she was identified EIP at the beginning of the school year. She has made

tremendous progress this year. I wanted to challenge Suri and document the growth she has

made. At the beginning of the year, the EIP assessment had her rote count 10 objects. Suri

wasn’t able to complete this task. She couldn’t do one-to-one correspondence. She counted 10

objects as 8. Suri also struggled with number sense and cardinality. Her math identity is strong.

Suri tells me that she likes math and feels that she is good at it. Her mother also wrote in the

form “Getting to Know Your Child,” that Suri loves to do math and play games. Her race is

white, and she identifies as Italian. Her family only speaks English. Suri comes from a single

parent home where her mother is raising six children ages 16-5 years old. I would say that Suri’s

strongest identity is her family. She is very close to her mother and older siblings. She is always

talking about them, and they play a very important part in raising Suri. Suri is very shy, but is a

hard worker. When I asked her three words that describe her, she said “silly, good girl, and

kind.” Her mother also wrote that Suri was very caring and loving. Some authentic

mathematical experiences that Suri engages in is trading her Shopkins. I hear her and other

classmates using math to count their collections and trade with one another. Also very similar to

Felix, Suri is using basic math and her knowledge of geometric shapes when she is building with

the class Lego or blocks. I hear Suri using the names of the 3D shapes correctly when playing

with other students. Suri’s math identity was strong during the assignment. She was excited to

help me with my project and wanted to work hard. Her mother had wrote that Suri was a people

pleaser and that she responded well to encouragement and praise. I affirmed this identity by

reassuring Suri that she was doing a great job, and I was proud of how far she has come.

Suri took each counting bear out of the box and clustered them into one big group.

She then touched each one to count it, but didn’t have an organized way to know which ones she

had already counted. She didn’t touch or move the ones she had counted. Suri must have

counted some of the bears twice because she said that there were 46 bears. I asked her to recount

them and she said there were 45 bears. I then gave Suri 5 rows of Unifix cubes. Each row has

10 cubes attached. I then asked Suri to show me 45 cubes. She took apart each row, lined them

up, and counted them to 45. She was accurate with this count. Her one-to-one correspondence

was accurate with the Unifix cubes. Suri’s cardinality was solid; however, she wasn’t deliberate

and careful with her count, or she would have touched or moved the bears she had counted. Suri

counted by ones and did attach a unit to her count. She said 45 bears. I asked Suri to show me

two ways to represent the number 45. She wrote in letters the number 45 (frode fiv). The other

way was that she used pictures to represent the number. The pictures weren’t accurate though.

She used the pictures to create the number 45. She made x’s in a pattern that looks like the

number 45.

I would say that Suri is in the Emerging Profile Level. Suri made a minor error when

counting 45. She only missed 2 out of such a huge box of bears to count. The standard for

counting to tell the number of objects in kindergarten is much smaller than this assignment. The

Common Core Standards state “Count to answer ‘how many?’ questions about as many as 20

things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered

configuration; given a number from 1–20, count out that many objects” (Common Core

Standards for Mathematics, p. 11). Suri is able to count up to 20 items. The main reason I feel

she is emerging is that she wasn’t organized in her counting. She didn’t implement a system for

keeping track of the bears she had counted. Also, she only attempted to count by ones. This

assignment has helped me see the great progress Suri has made this year, but also where her

weaknesses are with numbers and counting to help move her to the next level.

The last child I chose was Leo. Leo is an amazing kindergarten student. The first week

of class, I asked him who he liked to read with at home. He asked me “Do you mean in English,

Chinese, or French?” I selected Leo because he is such a strong student. Also, I chose him

because he is mixed race. He is half Chinese and half French. Leo has a lot of strong identities.

He attends Chinese school on the weekends and studies Chinese history; as well as, American

history. He is always telling me about a new biography he read over the weekend. Leo reads,

writes, and speaks three languages pretty fluently. He takes violin and chess lessons. His

parents had written on the parent form “Getting to Know Your Child” that he enjoys basketball,

reading, playing Lego, and the violin.” Leo told me that he enjoys “chess, violin, and getting

presents.” When I asked him how he felt about math he said, “I love math. I am great at it.

When I take a math test, I am curious. I like numbers, addition and subtraction, and math games.

I am adding up to 8 numbers together.” Some of the authentic mathematical experiences that

Leo has at school is that his group creates their own word problems based around their interests.

They have their groupmates solve them. They love to do this and incorporate their interests.

According to the CCSS, students should “Make sense of problems and persevere in solving

them” and “Construct viable arguments and critique the reasoning of others” (Common Core

Standards for Mathematics, p. 10). When solving their classmate’s word problems, they have to

defend their thinking and collaborate with each other. During the interview, Leo’s strong

mathematical identity manifested during this assignment. He wanted to do the best job he could

for me. His parents had written that what motivates Leo the most is his need to be the best. I

praised Leo for a job well done and told him that his mathematical thinking was very mature.

Leo pulled out each bear and put them into rows of 10. He then told me he is doing it this

way, so he can count the rows “10, 20, 30, 40 and a few more.” He counted the number of bears

accurately. His one-to-one correspondence was solid; as well as, his cardinality. He was

deliberate and careful when lining up the rows of 10. Then I gave Leo the 5 rows of 10 Unifix

cubes. Leo laid down 4 of them and then broke off 7 from the last row. He moved those away

and put down the 3. Lastly, I asked him to represent the number 43 in two other ways. Leo drew

43 X’s. These were also placed in rows of 10. He also wrote the number 43 in numbers.

I would say that Leo’s Profile Level is Exemplary. Leo counted the Unifix cubes and the

bears by groups of 10. He was accurate with his count and solid in his understanding of

numbers.

References:

Common Core State Standards for Mathematics. Common Core State Initiative: Preparing

America’s Students for college and career. p. 1-93.