Running head: COUNTING PROFILE

Counting Profile

Kayla Easley

Kennesaw State University

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The first student I interviewed for my counting profile was Graham. I chose this student

because I teach his older brother mathematics. Having never worked with siblings in different

grade levels, I was curious to see if similarities between personalities and learning styles existed.

Graham’s strongest identity lies in his familial roles. His identity manifested while completing

the heart map. Without labels or details I struggled to identify what Graham was drawing. When

asked to explain his drawings, he was quick to tell me that he cares deeply for his mother, father,

brother, and dog. He then began to ask me questions about his brother’s mathematics skills. It

was evident that he is proud of his brother and looks to him as a role model. I attended to his

identity as a brother by engaging in conversations about their relationship. He also expressed

concern as a pet owner. I attended to this identity by asking Graham how he cares for his dog. I

affirmed this identity by offering praise for his responsible pet owner behaviors. Graham

communicates disinterest in mathematics. While completing the heart map, Graham stated that

he gave himself a funny face because that is how math makes him feel. Graham emulates his

brother. An authentic experience that Graham engages in is basketball, as his brother enjoys

playing. Basketball could be mathematized. One example is for Graham to add the number of

attempts his brother’s team makes in scoring a point. He could tally each attempt and then add

the tallies. A second authentic experience that Graham is engaging in currently is divorce. While

this topic is sensitive for younger students, older students could mathematize this concept by

completing statistical work on other students with divorced parents.

For the counting profile I gave Graham a container with 44 circular counters in it. In the

beginning of the activity, he dumped the counters and arranged them in rows as he counted

aloud. When counting, he placed the counter on the desk and then told me the number’s name.

This strategy worked well until he became tired of making rows. Once he stopped forming rows,

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Graham began to quickly make mistakes. After the 29th counter Graham said 80. Upon

completion of this task I asked Graham to create a group of counters that contained the same

number of counters as the first group. This portion of the task was done carelessly; he grabbed

multiple counters at once and consequently was unable to accurately recreate the group.

Regardless of how many counters were grabbed, Graham’s numbers only increased by two when

orally counting. Finally, I asked Graham to represent how many objects were in the counting jar.

He drew the number nine. I restated that I wanted him to represent how many counters were in

the container. Graham was satisfied with his result and did not wish to make modifications.

Graham falls within the emerging level of counting. I decided to place him into this level

based upon the descriptors on the classroom counting profile. According to the profile students

in this level can work with numbers between 20 and 42. Graham was able to count 29 of the 44

objects without naming the units. One-to-one correspondence is likely to contain sloppiness at

this level. Graham began his count with precision and cardinality but lost interest and began to

carelessly grab counters, resulting in major errors. His inability to keep track impacted the

accuracy of his total count. Despite this careless counting, Graham has a firm grasp on the

cardinality of a set and counting patterns He immediately named the last number in the set orally

and was able to count on with correct patterns despite having skipped from 29 to 80. When asked

how many items were in the set, he repeated the same number confidently. When asked to re-

create the set, a similar pattern emerged. Graham began slowly and was meticulous. As the task

progressed, he became bored and his accuracy suffered as a result. When looking at Graham’s

skills within the context of Common Core, he needs support in saying number names in standard

order. He shows understanding of naming sets by the last number counted and pairing numbers

with single objects (“Common core,” n.d.).

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The second student I interviewed for my counting profile was Sadie. I chose her because

I was interested in seeing how an English learner would perform on this task. Sadie is in the very

early phases of language acquisition. She speaks in two and three word phrases. In order to dilute

the impact that language might have on the assignment I spoke interchangeably in Spanish and

English. I found that the quality of her answers was highly improved when she responded to

questions posed in Spanish. Sadie’s strongest identity is that of a Guatemalan child with a

traditional Spanish culture. She feels strong ties to her family and shows respect for adults.

Sadie’s identity manifested as I began to ask her questions. She was very quiet and offered little

information about herself when I spoke in English. When I spoke in Spanish, however, she began

to tell me about her family and special things that they do together. After realizing that Sadie

feels more comfortable communicating in her native language, I began to use English only if I

could not recall the word in Spanish. In this way, I attended to her identity as a Spanish speaker.

During the interview I spoke to Sadie about how she communicates with her teachers. I shared

my belief that teachers should try their best to communicate with students who are learning

English in different ways. My hope is that this conversation helped to affirm Sadie’s role as an

English learner and instilled some Spanish pride into her. When I asked Sadie how she felt about

math, she said that she does not enjoy it. Her teacher believes that she does enjoy math. My

assumption is that the language barrier makes Sadie struggle with effectively communicating her

feelings with her teacher. An authentic experience that Sadie engages in is helping her mother

cook. Food can easily be mathematized. By giving equal shares of food to each sibling, Sadie is

working on foundational fraction skills. Cooking also provides opportunities to practice

measurement and telling time.

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Sadie was given 44 circular counters and was asked to identify how many counters were

in the set. She demonstrated strong one-to-one correspondence when counting but could only

count up to nine. Once she reaches nine, Sadie starts back over at one regardless of how many

counters she has actually counted. Each time, Sadie demonstrated a strong understanding of

cardinality. She can consistently a name a set by the last number she said aloud. When counting,

Sadie was very careful. She touched each counter, named it, and lined it up in a neat row. Sadie

was unsuccessful in skip counting and could not name the set with a unit. However, I feel that

her language skills play a large part in this. Unfortunately, she did not have the skill set in her

native language. Sadie demonstrated complete accuracy for the first nine counters but as stated

prior cannot count beyond this number. When asked to re-create the set of counters, Sadie

carefully lined up each piece and counted aloud. Just as before, she stopped after nine and then

started again with a new set. I asked Sadie to represent the number nine on paper. She drew

various letters, indicating that she is unfamiliar with number symbols.

Sadie falls within the limited level of counting. I decided to place her in this level based

upon the descriptors of the classroom counting profile. According to the profile, students in this

level can work with numbers less than 20. Sadie’s ability to count to nine without naming units

fits within this constraint. Unlike students in this level, Sadie is able to deliberately keep track of

the objects she counts. Sadie’s accuracy is strong only up to number nine. Rather than guessing

additional numbers to count on, she begins again at one. This results in major errors in accuracy.

While students in this level typically display weak one-to-one correspondence, Sadie does not.

Again, this ability only extends to the number nine. When looking at Sadie’s skills within the

context of Common Core, she needs support in saying number names beyond nine and learning

the patterns found in numbers (“Common core,” n.d.).

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The third student that I interviewed for my counting profile was Kirsten. I chose her

because she is representative of a student from a lower socioeconomic bracket. While Sadie was

disadvantaged due to language, Kirsten is disadvantaged because of economic hardships.

Kirsten’s strongest identity is that of a member of society. Kirsten mentioned that she cares

deeply for her family, for the homeless, and for people in general. When asking Kirsten to

explain why she chose these three areas for her heart map, she explained me to that she likes to

help others and that it makes her sad when people do not have a warm bed at night or enough

food. She also explained that she cares deeply for her family, particularly her grandparents and

uncle as they are raising her. To attend to and affirm Kirsten’s identity, I asked her to discuss her

family as much as she desired to. She shared with me sweet details about family traditions like

praying each night at dinner and telling her uncle goodbye using their own secret phrases. I then

shared details about my family and we discussed the importance of being a loving family

member. Kirsten shared that she loves math. She represented her love with hearts and a smiling

face. Similarly to Sadie, an authentic experience that Kirsten engages in is cooking with her

grandmother. As stated prior, cooking is an excellent opportunity for students to practice

mathematic skills such as estimation, measurement, time, and fractions.

Kirsten was given 44 circular counters in a container. Her first task was to determine how

many counters were in the set. She was able to count all 44 counters correctly by creating rows

with the counters as she orally said each number, indicating strong one-to-one correspondence.

While she only counted by ones, I was impressed that Kirsten named the number and the unit

after she finished counting. The other students that I interviewed were unable to do this. This

particular skill made me curious as to which level of counting she would ultimately fall under, as

it seemed somewhat advanced for a kindergarten student. Kirsten consistently demonstrates

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strong cardinality and sense of quantity. This was evident during her counting task. It was also

evident when she was asked to recreate a group of counters to match the original group. Just as

before, Kirsten methodically created rows of counters. After creating a row, Kirsten re-counted

the entire collection and added additional counters. She repeated this process until she reached

44. While laborious, her results were accurate and impressive. When I asked Kirsten to represent

the number of objects in her set, she wrote the number 44 in numerical form.

Kirsten falls within the exemplary level of counting. I decided to place her in this level

based upon the descriptors of the classroom counting profile. According to the profile, students

in this level can work with numbers greater than or equal to 43. Kirsten was able to count 44

objects, signifying that she can go beyond an expected number size for kindergarten. When

naming numbers, Kirsten’s accuracy was perfect. According to the descriptor, this indicates that

she understands patterns beyond the 20s. Students in this descriptor also have a solid

understanding of cardinality. Not only does Kirsten have a strong understanding of this, she also

understands quantity. Her ability to name the unit after counting is evidence of her quantity

knowledge. When looking at Kirsten’s skills within the context of Common Core, she

demonstrates a strong understanding of counting and cardinality, as she knows number names

and the counting sequence. She also demonstrates mastery of this skill in her ability to count to

tell the number of objects (“Common core,” n.d.).

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Reference

Common core standard standards initiative (n.d.). Common core state standards for mathematics.

Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf.

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