Student Work Sample

Annie Olson
Hamline University
Fall Semester
December 6, 2007

LEARNER OUTCOMES

Student will be able to orally count in order from 0-10 (preferably in Spanish).
[MN State Mathematics Standards, Kindergarten, II. Number Sense, Computation, and Operations. A. Number Sense. Standard: Represent quantitites using whole numbers and understand relationships among whole numbers. 1. Count forward to 31, backward from 10].

Student will be able to apply one-to-one correspondence when counting objects.

Student will be able to produce the appropriate number of objects (0-10) when requested.
[MN State Mathematics Standards, Kindergarten, II. Number Sense, Computation, and Operations. A. Number Sense. Standard: Represent quantitites using whole numbers and understand relationships among whole numbers. 2. Count the number of objuects in a set and identify the quantity.]

Student will distinguish the difference between the numbers 0-10 as written numerals.

TEACHING CONTEXT
Wellstone elementary is situated on the riverfront in downtown St. Paul in an eight floored building. School demographics are approximately 41 percent African American students and 40 percent Hispanic students with the remaining 19 percent fairly evenly distributed between Asian, American Indian, and caucasian students. As of 2006, our school had 95 percent of its student population receiving free or reduce priced lunch.
Our classroom, room 203, hosts two dual-immersion classrooms. When both classes (kindergarten and first grade) are in our space, we have fifty two students, two teachers and an eductional assistant.
I believe that if society is taught in schools, teachers should take the opportunity to help teach our students how to take part in forming a better society- a society where roles of all kinds are split more equally between people. I can model that in my classroom by attempting to keep equality and fairness at the front of my mind. Student roles and ability to help our classroom family should be modeled, taught and scaffolded. During my student teaching, my belief about roles and responsibilities has been strengthened. Students love to help out and they like to be responsible for something and do a good job at it.
I believe that every child can learn, and it will be my responsibility as a teacher to decode how each of my students learn best. I believe in the importance of recognizing and teaching to the multiple intelligences. I want to reach all my students by frequently using different types of activities, centered around multiple intelligences and different learning styles. During my student teaching I found that if I don't use different activities tailored to the multiple intelligences, my students (especially my bodily-kinesthetic leaners) would drive me crazy.
I know that the education that students leave my classroom with – not only academic facts, but their abilities to understand themselves, relate to others, problem solve, and live in the broader world – will affect them for their whole lives.
My students, as I have observed, represent several of the multiple intelligences. Many of my students seem to be bodily-kinesthetic learners. Most of my students are wiggly. They NEED to move at least every fifteen minutes and usually more often than that. These students benefit from partner clapping exercises where we count and dance the numbers in order. Several of my students are very musically inteligent. They hum and sing our counting chants and songs while they are working at their tables, they remember and can recount numbers without recognizing them because of the sing song patterns that we use to count with. Most of the rest of my students seem to be verbal-linguistic learners. This could be, however, that their rote understanding of the world is still emerging and their learning styles will likely change as they mature. In my kindergarten class I have students who are five and six years old. Some of my students are more advanced in their development, physically, emotionally, and as learners. Some of them come from homes where education is very important, and their parents have spent time with them, teaching them numbers, colors, letters, e.t.c. My students love stories. They love fantastical characters like Spiderman and beautiful female characters like Cinderella.
PRE-ASSESSMENT
When students came to Wellstone Elementary's Welcome Night, Miss Nelson and I individually tested each student on basic numerical knowledge. These tests required students to verbally count as high as they could, recognize and name written numerals out of order and represent numbers with manipulatives such as blocks. This test allowed us to gain an accurate understanding of where our students were starting from. This test showed us a realistic picture of what our students already knew and what they did not yet know. This test helped us find a starting point from which to begin teaching. (Please see attached testing templates.) This test was not one of my own design, and had I the chance to organize the class into groups for the next semester, or the next year, I would do things differently, (please refer to the reflection section of this paper).
FORMATIVE ASSESSMENT
I reviewed students' in-class verbal mathematical reasoning in small group work, their participation in whole group activities, as well as written work that was turned into me. These, in combination with the formative formal/post-testing, helped me identify students who needed extra instruction. Day to day classwork built on itself as much as the Everyday Math curriculum would allow me to, and at times, I was probably more flexible in my teaching than the curriculum would have liked me to be because I wanted to see the majority of my class progressing at about the same rate, with the same successes. If I observed, for example, that the majority of my students were not using one to one correspondence when counting objects with a partner, I re-grouped the class to re-teach, and then extended the lesson into the “theme time” or “snack time” of the day. We often reviewed lessons from the previous day before working on that day's lesson, which was not built into the spiral curriculum of Everyday Math as much as I wish it had been.
FINAL ASSESSMENT
I used the exact same test that we had used for our pre-testing to accurately measure exactly how far my students had come in their mathematical understanding. Students were not explicitly informed of their scores or the results of their tests, but from this test, and from informal assessments of their classroom work, I identified a small set of students who needed additional individual practice and instruction. At this point, I decided that this small group had still not achieved the outcomes that I wanted them to. Specifically, they were still not recognizing the numerals 0-10 out of order. So, my final assessment also served as another formative assessment. I took this small group of students and re-taught the numerals using Touch Math. After re-teaching in small group, I pulled them out one-by-one during class work time to tutor them on the numerals. I also placed a Touch Math number strip at each of their desk spaces. After a week of this, I re-tested the students on their numeral recognition and at that point, the majority of the students recognized every numeral from 0-10 out of order.

DATA AND SELECTED WORK SAMPLES
I chose three students' work to represent the continum of mathematical understanding that was represented in my classroom.
The first student came into my classroom recognizing all the numerals 0-10 out of order, he could count to 100 in Spanish, and he/she could represent the numbers three, nine, five, and eight quickly and easily using manipulatives. This student was alone in the class in his advanced mathematical abilities and understanding. The student demonstrated complete understanding of one to one correspondence and he/she finished his/her work quickly and effectively. An example of this student's work is the number nine page. This student even demostrates his/her counting abilities on the page, by numbering the objects that he saw and drawing circles around the correct number of objects.
The next student came into my classroom recognizing three of eleven numerals 0-10. He/she could count to seven in Spanish, and he/she could represent three, nine, five, and eight effectively using manipulatives. This student was an average student in my class. The example of this student's work in the number seven page. He/she writes some of his/her numbers illegibly, does not completely understand how many seven is, as demonstrated from one correctly displayed group of seven and two mistaken “boxes.” However, he/she did not exhibit this lack of understanding until the number seven. He/she had understood the numbers up until that point.
The last student example is a student who came into my classroom recognizing three numerals 0-10 and naming some of the numbers letters. He/she could count to 12 in Spanish and could only represent the number three with manipulatives (out of three, nine, five and eight). This student was a lower achieving student in my classroom, and was one of the students who qualified for my lower set of students who received additional instruction in Touch Math. His/her work is represented by the number four page. He/she immediately started to struggle with representing groups of numbers. His penmanship and writing of the numbers was clear, but his one to one correspondence and understanding of quantitiy was lacking.
ANALYSIS OF DATA
As you can observe from the preceeding page, every student in my class improved their overall score on the final assessment. Eight of my students could identify every numeral from 0-10 correctly out of order compared with one student who could identify them in September before school started. Almost every students' ability to recognize numerals 0-10 drastically improved with many of the majority of them improving their scores by more than fifty percent. Unfortunately, one studbent could identify fewer numerals. Only three students still demonstrated that they were still struggling significantly, and these scores unfortunately do not represent their acheivments after instruction in Touch Math. Most of my students (17 of 28) could represent the numbers three, nine, five, and eight using manipulatives by the final assessment. Most of those who could not represent all of the numbers could represent at least two more numbers than they had been able to represent before school started. Three students were still unable to show two of the four numbers. All but one of my students could successfully count from 0-10 in Spanish. All of my students could count higher than they were able to at the beginning of the year. Only one student in my class was still unable to count to ten.
DATA PRIVACY
My students' privacy is important to me. I took every necessary step to protect and conceal the identity of my students. I have removed names from student work and identified my students in non-alphabetical order by number rather than name in any representation of my class as a whole.
REFLECTION


The test that I used for pre-assessment and final assessement was not one of my own design, it was a test that has been in place for many years, and the entire kindergarten team at my school uses it. Were I to re-design this tool (and thusly, what I did with it and how I used it) I would change the testing page only slightly. I don't think that it is necessary to place a nine and six next to each other on the test (please see included testing template). I think that this serves to confuse, and almost trick the students into self-doubt. When testing even the most bright of students, each of them in turn hesitated at that point. I would change my use of the information that I gained from the test quite drastically. My cooperating teacher did not use the information gained in the pre-assessment to inform her instruction. I would rank the information gained from the pre-assessment and use it in order to better form groups of mixed ability, as well as to form groups of similar ability, so that I could challenge the students at the level that they are on more appropriately. Doing this, higher achieving students would be less likely to be under-challenged and bored, while at the same time lower achieving students would not feel as overwhelmed or threatened. I would take the class ranking of mathematical score and “fold” the class in half, placing the one half of the medium students with higher achieving students and the lower students with the other half of the medium achieving students, and I would mix up these groups frequently.