Teacher Work Sample

Student C Elementary Spring 2012

Scottsbluff Public Schools

Longfellow Elementary

First Grade

2/12/2012

Chadron State College

Table of Contents

Instructional Setting / Contextual Factors…………………………………………………………………………….3

Assessment Plan………………………………………………………………………………………………………7

Description of data analysis of pre-assessment data…………………………………………………………10

Description of data analysis of post-assessment data………………………………………………………..11

Instructional Plan……………………………………………………………………………………………………..13

Instructional Decision-Making, Reflection, and Self-Evaluation…………………………………………………….15

Appendices…………………………………………………………………………………………………………….19

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Instructional Setting/Contextual Factors

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Community

Longfellow Elementary is located in central Scottsbluff, a small town in Western Nebraska. Scottsbluff’s population is approximately 15,000 people. Scottsbluff is a relatively stable community, considering the current economy. The unemployment rate is 5.2% compared to the United States 9.1%.1 It is predominantly politically conservative, and the community is generally supportive of educational endeavors. Community support was evident as recently as 2009, when Scottsbluff voters passed a $14 million bond referendum that allowed the district to completely renovate the middle school, which was in need of repairs due to its age.

District

Scottsbluff Public School District is comprised of eight educational facilities including one preschool, five elementary schools, one middle school and one high school. The district emphasizes small class size, up-to-date technology that all students can access, a school breakfast program, researched based reading and writing curriculua, Response to Intervention for all students, positive behavior supports and after school programs.

The district has recently purchased new Science and Writing curricula, and does not expect to purchase a new math curriculum for at least two years. After attending the all first grade district meeting, it is clear that teachers are not satisfied with the current math curriculum, and use it only as a resource. The district curriculum directors have established academic standard-driven pacing guides for multiple subjects, including math, so that all first grade students are learning relatively the same things at the same times, and spending the same amount of time on each unit of study.

School

Longfellow Elementary serves students from Kindergarten through fifth grade. The current school population is 356 students. There are currently twenty-five teachers, one counselor, ten paraeducators, one speech provider, and one principal.

Longfellow is located in a middle-class neighborhood, and is Title I eligible. 51% of students qualify for free or reduced lunch. 135 students qualify for free lunch, and 47 students qualify for reduced lunch. Longfellow is comprised of 51.7% (184) White/Caucasian students, 42.7% (152) Hispanic students, 2.8% (10) American Indian students, 1.4% (5) Black non-Hispanic students, and 1.4% (5) Pacific Islander students.2

Classroom Factors

The classroom where assessment and instruction took place for this teacher work sample was a first grade classroom under the direction of Tristica Stemple. After a discussion with the Mrs. Stemple, I decided the best curricular area in which to complete pre-assessment, instruction, and post-assessment was mathematics, focusing on several introductory subtraction concepts.

The classroom is a relatively large rectangle, subdivided into several areas that are conducive to whole group and small group instruction. Students sit at desk clusters facing each other, but so that both white boards, and the Bright Link Board are visible from every desk.

1 http://www.bestplaces.net/economy/county/nebraska/scotts_bluff

2 http://findgoodschool.com/school/317647001579-LONGFELLOW-ELEMENTARY-SCHOOL-SCOTTSBLUFF-NE

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Available technology includes a Bright Link projector, so that anything on the computer can be displayed using the dry erase white board as a projection screen. This also gives the teacher the ability to use dry erase markers as part of presentations. The classroom also has two laptop computers, and one desk top computer, and two compact disc / tape players.

This particular classroom follows procedures that give a variety of learning opportunities and formats for students. Engaged learning time, based on the classroom schedule, is approximately 40% teacher led (whole group instruction), 30% guided practice (small group instruction with guided practice), and 30% independent student directed (workstation/learning center time). For whole group instruction, students sit at desk clusters. The seating arrangement places one high achieving student, one middle achieving student, and one low achieving student together, so that students can support one another.

For reading and math small group instruction and workstations, the classroom teacher has divided the class into groups of two or three students. These groups are based on achievement within the reading and math curriculum, but are flexible groups throughout the year so that students who need extra support and students who exhibit rapid growth can move within the groups to receive instruction and practice that best meets their needs. There are two separate groupings, one set of groups for reading, and one set for math, because there are a few students who struggle in reading but are excelling in math, and vice versa.

Currently, there are seven math groups and nine workstations. Each group visits one workstation per day, rotating to all of the various workstations. The workstations are redesigned after all groups have visited each one, to provide needed practice based on what the students learn in whole group instruction. This format was excellent for my instruction, because I could assess what individual students needed, and group them according to their needs. Then I was able to deliver instruction and provide support to students with content, skills and strategies they needed to achieve the objectives.

Student Characteristics

Mrs. Stemple’s class is comprised of eighteen students. The students include nine boys and nine girls that are between six and eight years old. The class is comprised of ten Caucasian students, seven Hispanic students, and one Black non-Hispanic student. Five students in the class receive special education services. One is a high functioning student who receives only speech services. One is a high functioning student with Autism Spectrum Disorder who has a one-on-one Paraeducator for 90% of the school day. Three are academically low achieving students who are pulled out of the classroom and receive academic services in the resource room for thirty minutes, three times a day. Five other students receive reading instruction in the Title room as part of the RTI process. All students in the room are fluent English speakers, but three are being monitored by the district because another language is primarily spoken in their homes.

Another factor the classroom teacher must consider when planning instruction and activities for the class is that one student belongs to the Jehovah’s Witness church. This religion does not celebrate any holidays or birthdays, so the teacher must either notify her parents in the event of these special celebrations, or provide an alternative activity for her, such as skills practice on one of the classroom laptops.

Most of the students are curious and eager to learn. First graders, in general, are very concerned that all students are treated equally and fairly, and nearly all of the students in this classroom are concerned with following the rules, which is extremely helpful for an intern who is new to their learning environment.

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This year, the first grade teachers at Longfellow made a collaborative decision to concentrate their math instruction in the first part of the school year (October – December) on number sense and addition. They felt that building a foundation of number sense and a thorough understanding of addition was essential to the first graders’ success. Throughout my placement, the first grade teachers have reported that this decision was a success. They have repeatedly stated that their students seem to be ‘catching on’ to subtraction much more quickly than students in past years. This solid foundation of addition is also apparent in classroom discussions, when students consistently relate new information about subtraction back to their knowledge of addition. For example, when given the problem 4-2=, one student called out, “I know that is 2! Because of doubles! 2+2=4!” Not only does the foundation help them understand new material, but they are confident and enthusiastic about learning new math concepts.

Instructional Implications

All of these school and classroom factors guided my decision to teach and assess in the area of subtraction for this work sample. After familiarizing myself with the school and classroom procedures, the students’ enthusiasm for math was obvious. I also knew that math, as compared to other subjects, is sometimes easier to assess because it has clear performance indicators that show whether or not the student is achieving the objective. Furthermore, I was able to avoid any content that might exclude the student who belongs to the Jehovah’s Witness Church.

When designing my assessments in instruction, I utilized the district curriculum for first grade, which is Scott Foresman, Addison, and Wesley Mathematics Grade 1 Curriculum, published by Pearson Scott Foresman. Using this resource, I chose several introductory subtraction concepts for the teacher work sample. The objectives are guided by Nebraska academic standards, and I was able to utilize available materials.

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Assessment Plan

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Pre and Post Assessments

The same assessment was given for both a pretest and for the posttest. The pretest was used solely to determine student foreknowledge, and the posttest was used as a summative assessment for the unit of study. The assessment contains six learning objectives and ten questions. After giving the pretest, I had a wide variety of responses on nearly every question. I realized that I would have to be very clear about how I would assess the student’s performance, so I could consistently determine whether or not they met the objective.

For example, the two problems at the bottom of the first page (as shown) are pictures that show separation. Though blurry due to the quality of the copy, the first picture shows three children. Two are on the swing set, and one is walking away waving. Because there are no words to go with this problem, I got a variety of answers when the students attempted to write subtraction sentences. The objective was for the student to write a subtraction sentence that shows separation. Therefore, I accepted 3-1=2, and I also accepted 3-2=1. If there was a word portion of this problem that explained what was happening (i.e., Three kids were playing at the park. One went home. How many were still playing?), then the student would have had to respond 3-1=2. In the absence of a word problem, both of the above number sentences show separation, and would be considered correct.

In the problems with the dominoes on page 2, the objective was for students to compute subtraction problems horizontally and vertically. They had to have the right answer both in the top portion of the problem, written horizontally, and in the bottom portion, written vertically.

For the comparison problems, there were two objectives: 1) write a subtraction sentence to find ‘how many more,’ and 2) tell ‘how many more.’ Not only did students have to select numbers for the subtraction sentence, but they also had to derive meaning from the difference of their subtraction sentence, and put the answer in the right place.

Formative Assessments

Formative assessment took place throughout my instruction time in small groups. Due to the math groups, I was able to focus instruction based on student need. When I felt that a group had reached mastery of one of the objectives, I would do an independent performance assessment. Indication that they had reached mastery included the following behaviors: little hesitation, confidence using the

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strategy, and consistent accurate responses in a group setting. When these behaviors were observed, I gave independent performance assessments. If they solved the problem with 80% accuracy (responded accurately to 4 out of 5 prompts), I considered them proficient. If they solved the problems with 100% accuracy (responded accurately to 5 out of 5 prompts), I considered them to have mastered that objective. When this an individual reached mastery, they were given enrichment problems. When the entire group reached mastery, we moved on to the next objective. The following is a list of example questions and performance assessments I gave for each objective.

Objective 1 – Use counters and pictures to solve problems that show separation.

This was a review from their addition unit, and all but one student answered correctly on the pretest, and so no instruction was given for this objective.

Objective 2 – Solve subtraction problems using pictures and manipulatives.

Each student was given a different flash card with a subtraction problem on it and asked to solve it using pictures or manipulatives.

Performance indicator: Student chooses and utilizes a strategy (white board and dry erase marker to draw pictures, or circle counters) and solves the problem.

Objective 3 – Write a subtraction sentence that shows separation.

Oral Word Problem: There are four students on the monkey bars, one falls down and runs away. How many are still on the monkey bars?

Performance indicator: Students write the subtraction sentence: 4-1=3.

Objective 4 – Write and compute subtraction problems horizontally and vertically.

Horizontal and vertical subtraction flash cards are displayed at random.

Performance indicator: student writes the subtraction problem both horizontally and vertically, and solves each problem choosing and using a strategy they are familiar with.

Objective 5 – Write a subtraction sentence that uses subtraction for comparison.

Oral problem: “I have three red counters and six yellow counters. How many more yellow counters do I have?”

Performance indicator: write the subtraction sentence on their dry erase board 6-3=3.

If students were deemed proficient with the counters, I would give less concrete oral problems, such as “Mrs. Stemple’s class has 18 students, but Mrs. Engleman’s class has 20. How many more students does Mrs. Engleman’s class have than Mrs. Stemple’s class?”

Performance indicator: write the subtraction sentence 20-18=2.

Objective 6 – State ‘how many more’ answers to subtraction with numbers or words.

Doing the subtraction is only one part of subtraction comparison problems. Students then have to derive meaning from the difference they compute, and verbalize answers. This was challenging for many.

Performance indicator: Students respond with an answer such as, “Mrs. Engleman’s class has two more students than Mrs. Stemple’s class.” Or simply, “2 more.”

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Description of Data Analysis of Pre-Assessment Data

Table 1

Objective.Question

Average of Pretest Response

s1.1 92.86%2.1 85.71%3.1 14.29%3.2 7.14%4.1 57.14%4.2 64.29%4.3 35.71%5.1 42.86%5.2 35.71%6.1 14.29%6.2 7.14%Average Total 45.24%

The pretest was administered as an introduction to the unit of study. Students had never been exposed to subtraction concepts before, and the pretest was administered with a purpose of gathering prior student knowledge. After administering the pretest, I used Microsoft Excel to analyze the data. I entered data organized by objective, question and student and used a pivot table in Microsoft Excel to manipulate the data.

Table 1 displays student achievement by objective and question on the pretest by the percentage of students who accurately answered each question. Based on the data, I introduced subtraction with familiar concepts, such as those in objectives 1 and 2, and then focused the majority of my instructional time on objectives 3-6.

I also organized data by student, so that I could track the progress of individual students. Table 2 displays each student’s individual achievement on the pretest.3

Table 2

Student

Average of Pretest Answers

1 67%2 42%3 50%5 25%7 50%9 50%

3 Students 4, 6, and 8 were not included in the data analysis because they were absent for either the pretest or posttest, and I did not have sufficient data to compare their scores and use them in the analysis of the class’s total scores.

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10 92%11 42%12 50%13 25%14 17%15 67%16 33%17 25%

Table 3 displays one student’s achievement on each individual objective. The individual student tables, when compared student to student, were helpful for showing me which students understood specific concepts, and which students needed similar instruction. Their present level of performance guided the formation of groups for instruction, so that students could learn at a level that supported and challenged them.

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Table 3

StudentAverage of

Pretest Answers

Student 1 66.67%Objective 1-Question 1 100.00%Objective 2- Question 1 100.00%Objective 3-Question 1 0.00%Objective 3- Question 2 0.00%Objective 4- Question 1 100.00%Objective 4- Question 2 100.00%Objective 4- Question 3 100.00%Objective 5- Question 1 0.00%Objective 5- Question 2 0.00%Objective 6- Question 1 100.00%Objective 6- Question 2 100.00%

Description of data analysis of post-assessment data

The posttest was administered after approximately four weeks of large group, and focused small group instruction. All students been exposed to various types of instruction, and had opportunity to practice skills for each of the objectives.

After administering the posttest, I again used Microsoft Excel to analyze my data. I entered data organized by objective, question and student and used a pivot table in Microsoft Excel to manipulate the data.

Table 4 displays student achievement by objective and question on the posttest by the percentage of students who accurately answered each question.

Based on the data, I could look at what objectives I taught well, and which objectives needed to be re-taught, required differentiated instruction, or possibly needed a different method of assessment. There were some objectives that I was confident my groups had mastered in some contexts, but they seemed to struggle to relate those skills back to the original assessment.

I also organized data by student, just as I did on the pretest, so that I could track the progress of individual students. Table 5 displays each student’s individual achievement on the posttest.

Table 6 displays the posttest data from the same student (Student 1) displayed in Table 3. The individual student data, when compared student to student, was helpful for showing me which students understood specific concepts. It also gave specific information about which students would need differentiated instruction on certain objectives.

Table 5Student Average of

Posttest Answers1 100.00%2 75.00%3 91.67%5 83.33%7 75.00%9 83.33%

10 100.00%11 33.33%12 83.33%13 83.33%14 75.00%15 83.33%16 58.33%17 58.33%

Grand Total 77.38%

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Table 4

Objective.Question

Average ofPosttest

Responses1.1 100.00%2.1 96.43%3.1 71.43%3.2 50.00%4.1 85.71%4.2 100.00%4.3 85.71%5.1 64.29%5.2 64.29%6.1 57.14%6.2 57.14%Grand Total 77.38%

Table 6

StudentAverage of

Posttest Answers

Student 1 100.00%Objective 1-Question 1 100.00%Objective 2- Question 1 100.00%Objective 3-Question 1 100.00%Objective 3- Question 2 100.00%Objective 4- Question 1 100.00%Objective 4- Question 2 100.00%Objective 4- Question 3 100.00%Objective 5- Question 1 100.00%Objective 5- Question 2 100.00%Objective 6- Question 1 100.00%Objective 6- Question 2 100.00%

Measuring Student Progress

My goal was for all students in the classroom to score at least an 80% on the posttest after instruction. Unfortunately, I did not meet this goal. Only about half of them reached a proficient level at the conclusion of the unit.

I was encouraged, however, that all but one student (Student 11) improved, with most of them showing dramatic improvement. I would also consider Student 11’s data to be an outlier, simply because of what I know about this student. She consistently is one of the lowest achievers, but her achievement is directly correlated to how she receives instruction and assessment. She has difficulty listening and staying on task, and is easily distracted. When assessments are given in a group setting, she consistently does poorly. She usually does not listen to the questions being read, and guesses or colors on her paper. When she receives

instruction one-on-one with the teacher with appropriate materials, such as counters or a number line, she can solve problems more proficiently. For this student, I should have provided an alternative assessment. With students like this in the future, I will certainly remember this experience and remember to provide alternative performance assessments that will provide more accurate data about what they have learned.

The pie graphs below show the number of students who would be considered beginning, progressing or proficient. Students were considered at a beginning level if they scored between 0-60% on the assessment. Students were considered progressing if they scored between 61-80%, and considered proficient if they scored between 81-100%. The pie graphs show that in the pretest, only 7% of students scored proficiently on the assessment and only 14% scored to be considered progressing. After instruction, 43% of students were considered proficient, and 36% were considered progressing. The students certainly made progress toward the learning objectives, and the posttest data clarifies which students need more guided practice and/or re-teaching.

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Student Average of Pretest

Answers

Average of PosttestAnswers

% of Increase

1 66.67% 100.00% 33.33%2 41.67% 75.00% 33.33%3 50.00% 91.67% 41.67%5 25.00% 83.33% 58.33%7 50.00% 75.00% 25.00%9 50.00% 83.33% 33.33%

10 91.67% 100.00% 8.33%11 41.67% 33.33% -8.33%12 50.00% 83.33% 33.33%13 25.00% 83.33% 58.33%14 16.67% 75.00% 58.33%15 66.67% 83.33% 16.67%16 33.33% 58.33% 25.00%17 25.00% 58.33% 33.33%

Grand Total 45.24% 77.38% 32.14%

79%

14%

7%

Pre Test Score Distri-bution

0-60% 61-80%81-100%

21%

36%

43%

Post Test Score Dis-tribution

0-60%61-80%81-100%

Instructional Plan

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Learning Objectives

In determining my area of instruction, and which objectives I would use in my work sample, I first looked at the Nebraska Mathematics Standards for grade 1. I chose to teach subtraction based on Nebraska State Mathematics Standard MA 1.1.3d: Use a variety of methods and tools to compute sums and differences.

The following is a table that shows the alignment of the state standards with the objectives for this work sample.

Standard ObjectiveMA 1.1.2.c Use objects, drawings, words, and symbols to explain subtraction as a separate action.

MA 1.3.2.a Model situations that involve the addition and subtraction of whole numbers 0-20 using objects and pictures.

Objective 1 – Use counters and pictures to solve problems that show separation.Objective 2 – Solve subtraction problems using pictures and manipulatives.Objective 3 – Write a subtraction sentence that shows separation.

MA 1.1.3.b Fluently subtract whole number differences from 10 using appropriate strategies and tools.

Objective 4 – Write and compute subtraction problems horizontally and vertically.

MA 1.2.e Use objects, drawings, words, and symbols to explain subtraction as a comparison.

Objective 5 – Write a subtraction sentence that uses subtraction for comparison.Objective 6 – State ‘how many more’ answers to subtraction with numbers or words.

Procedure:

Students will be administered a pretest containing six learning objectives and ten questions. Based on their achievement on the test, students will be divided into seven small groups of two or three students. Students will receive whole group instruction for 20 minutes from the regular classroom teacher in accordance to state standards and district pacing guides. They will also receive small group instruction with me, the teacher intern, for 20 minutes of the math period. I will work with one group per day, for seven days, instructing and using formative performance assessments, and noting error analysis during this small group instructional time to measure student progress toward the learning objectives. At the end of the first rotation of the groups, I will analyze my data from formative assessment and error analysis, and will then design a second block of instruction and teach each group again during small group instruction. At the end of the second rotation, the same test used as a pretest will be administered as a posttest, and then I will analyze student performance.

See Appendices for samples of lesson plans.

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Instructional Decision-Making, Reflection, and Self-Evaluation

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Student Engagement

Students were very engaged in the small group instruction. Hands on activities, such as using counters and whiteboards motivated the students to pay attention and participate in the instructional and guided practice activities. The student are occasionally allowed to use their whiteboards during large group writing and math instruction, and they are very enthusiastic about this kind of practice, so I decided to use this for small group instruction.

I had to be conscious of student attention during small group instruction, especially with the higher ability groups. Many of the students grew bored with a certain type of question, and I would have to modify the guided practice during the session to keep them interested. For example, when we used counters to solve subtraction problems, many would already know how to do the subtraction in their head and would be irritated that they had to show me with counters. If this was the case, I would ask them to ‘think out loud’ and show me what strategy or brain process they were using if they did not need the counters. I would then give bored students enrichment problems to challenge them. For example, one student had most subtraction facts memorized from 0-10, so I gave him problems with differences from 10-20. He had to use counters to solve these problems at first, so he was still meeting the objective, just with more challenging content. Likewise, some lower achieving students would grow frustrated with larger numbers, so I kept their numbers lower, (with subtrahends and differences less than 10), and increased the value of the numbers in their problems as their confidence grew.

Standard Driven Instruction

The academic standards were essential for designing this instruction, however, the broadness of the standards made it difficult for me to decide what strategies the students should use when solving the problems. For example, math standard 1.1.3.b for first grade states that students should be able to “fluently subtract whole number differences from 10 using appropriate strategies and tools.” There are so many strategies and tools available, that I needed to find a balance of quality and quantity when deciding which strategies to teach. I needed to give students enough strategies so that different students, based on ability and learning style, could choose one that worked well for them, without teaching them so many that they were overwhelmed or confused about when and how to use the strategies. I found that counters were essential for some students, while others did not need them at all. I also found that certain students could use a number line proficiently every time, but struggled with touch math or using their fingers. I taught and re-taught strategies, and encouraged students to repeatedly practice a variety of strategies, and not limit themselves by utilizing just one strategy for every problem.

Instructional Decision Making

I had to adjust instruction and content for each of my groups, based on student performance in the ongoing formative assessments. My three higher groups quickly mastered the objectives in the first rotation of groups. The groups that reached mastery went on to related facts and fact families.

The lower groups required re-teaching and more practice, and I had to change the ways I taught certain concepts. For example, I had to change my instruction by combining two objectives for my middle groups (See Appendix C for lesson plan). After the formative assessments, Groups 2 and 3 needed just a little bit of extra practice with objective 4, writing and computing subtraction sentences horizontally and vertically. They also consistently missed problems that had subtrahends from 6-15. To give them practice in both of these concepts without wasting time, I used the second rotation of groups and combined instruction. First, I sorted my flashcards by subtrahends into three groups. The first group had subtrahends from 0-5, the second from 6-10 and the third from 11-15. I then gave the students whiteboards, number lines and counters. As a group, the students were given a flash card. I gave them easier flashcards to begin with, so they could confidently go through the process a couple of times before working with

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cards that were challenging to them. They took turns making two choices: how to write the problem (horizontally or vertically), and what strategy they wanted to use to solve the problem (number line, counters, or fingers). If the student chose to write the problem vertically, all students in the group would write the problem vertically on their whiteboard. Then the students would each solve the problem using the chosen strategy with the teacher out loud. If the student chose counters, all students would use their counters individually and write the problem on their board. If the student chose the number line strategy, all fingers, including the teacher’s, would go on one number line and count back out loud moving their fingers the appropriate number of times. If they chose fingers, all students would hold up the appropriate number of fingers and count back out loud as they put their fingers down. Even after I had modified instruction in this format, some students would solve their problems much more quickly than others in within the small groups. I did not want these faster students waiting to learn, so I would give them a challenging problem for them to do independently and silently while other students were working on the group problem. This repetitive guided practice reinforced the concepts, and gave the students the opportunity to work at their individual level.

I also made a decision to completely change the materials I was going to use. For teaching comparison subtraction (how many more) problems, I originally had a math game called RINGO, in which students select number tiles and the appropriate number of rings and place them in the correct sequence to write a subtraction sentence. I originally thought this would be an excellent material because it eliminated the writing for the students who struggled with writing, and would help students focus on the math concepts such as counting, comparing and arranging numbers into subtraction sentences. The first time I used it, it was a complete disaster. Students were fiddling with materials, arguing about what colors they wanted, dropping the small pieces on the floor, and had very little focus for the math concepts because they were so excited about setting up their little stand, and arranging their tiles and rings. I quickly put the game away and went back to the white boards and counters, because they were still engaged and enthusiastic, but not distracted with the materials.

Evaluation

Having completed this work sample, the two instructional strategies that contributed most to student learning were the grouping arrangements, and the ongoing formative assessments. I was not surprised at the diversity of ability and effort in this classroom, and I know I need to be ready for this kind of diversity in any classroom. I really liked being able to differentiate instruction in small groups, but keep diverse students together for whole group instruction. This way, students who may start out as lower achievers still have access to all of the higher level instruction. Some of the students surprised and impressed me with their rapid growth. If placed in ability grouped classrooms, those students who began as lower achievers would never have the exposure or the opportunity to learn the higher level concepts, and would not be receiving an education that is appropriate for them. All students are exposed to the ideas that come out of the mouths of the higher achieving students, and the higher achievers utilize the higher level thinking skills when they get to explain their ideas and wonderings to other students.

The ongoing formative assessments were informal. They were easy to come up with without a great deal of planning, but gave me an excellent picture of what was happening in each individual brain. They shaped the entire process from the middle to the end, and gave me the most insight about the quality of my teaching as well.

The two greatest barriers to student learning were my inexperience, and the resulting low quality assessment that served to collect data for the work sample. Having never taught first grade subtraction before, I blindly chose objectives that were not the most important for the students to learn. I would have changed Objective 3 or just eliminated it altogether, because it the style of problem seemed to be confusing to the students, and did not clearly show if they understood the objective. Word problems would have still used pictures, but given a much clearer idea of

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what the student was supposed do. I also would have eliminated Objective 1, which students had previously been exposed to. Because they could count and understand separate groupings, it was not a challenging objective for them.

In the course of this process, I realized that my assessment needed to be much more sequential, and have a narrower focus. I would definitely use a different assessment for the pre and post assessments that are more focused on more appropriate components of subtraction. For example, I would have included objectives about specific strategies, because they are essential for mastering any of the mathematics standards.

If I were to do this again, I would follow the same format of pre-assessment, small group instruction with ongoing formative assessments and error analysis, a second rotation of re-teaching or enrichment, and a post-assessment. I would drastically change the focus of my objectives so that they were more pertinent to what students need to know to be successful in their education.

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Appendix A – Small Group Guided Practice, Rotation 1

Objective 2 – Solve subtraction problems using pictures and manipulatives.

Motivation: Students use whiteboards, dry erase markers and counters during small group instruction.

Vocabulary: minus, take away, difference

Body Of Lesson:

After watching the teacher model how to use counters and drawing pictures in subtraction during whole group instruction, students will break into small groups for guided practice and re-teaching. The teacher will give each child a white board, dry erase marker, and a handful of counters. The teacher will display flash cards or read word problems and students will use counters and white boards to solve the subtraction problems independently, with group member and teacher support.

Accomodations:

Students who struggle will have repeated practice with smaller values for subtrahends and differences. Students who excel will have enrichment activities with larger values, and with reading, writing and logic activities.

I.E. Word Problem: Eight students went to the library, but only 5 checked out books. How many students did not check out books? Write a sentence about the students who did not check out books.

Evaluation:

Teacher observation, ongoing formative assessment, and correct responses during small group instruction

Materials:

White boards, dry erase markers, erasers, counters

Standards:

MA 1.1.2.c Use objects, drawings, words, and symbols to explain subtraction as a separate action.

MA 1.3.2.a Model situations that involve the addition and subtraction of whole numbers 0-20 using objects and pictures.

MA 1.1.3.b Fluently subtract whole number differences from 10 using appropriate strategies and tools.

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Appendix B – Small Group Guided Practice, Rotation 2 Enrichment

Objective – Write number sentences to represent fact families.

Motivation: Students use whiteboards, dry erase markers, and will get to play a timed game and try to break their team record to fill in a partially completed fact family.

Vocabulary: number sentence, related fact, fact family

Body Of Lesson:

After watching the teacher model how to write number sentences that represent fact families, students will practice writing number sentences in small groups, and play a timed fact family game.

Accomodations:

During individual practice, students are given a set of three numbers each time they finish and have correct set of number sentences. Every student works at their own pace. During the game, group members work together and receive support from one another.

Evaluation:

Teacher observation, ongoing formative assessment, and correct responses during small group instruction

Materials:

White boards, dry erase markers, erasers

Standards:

MA 1.3.3.a Write number sentences to represent fact families

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Appendix C – Small Group Guided Practice, Rotation 2 Reteaching

Objectives: Write number subtraction sentences horizontally and vertically. Choose and utilize appropriate strategies to solve subtraction sentences.

Motivation: Students use whiteboards, dry erase markers, and counters in a small group setting with lots of teacher attention and interaction

Vocabulary: subtraction sentence, vertically, horizontally, counting back, number line, touch math

Body Of Lesson:

Teacher gives a group member a subtraction problem. Group members take turns making two choices: how to write the problem (horizontally or vertically), and what strategy they wanted to use to solve the problem (number line, counters, or fingers). If the student chose to write the problem vertically, all students in the group would write the problem vertically on their whiteboard. Then the students would each solve the problem using the chosen strategy with the teacher out loud. This repetitive guided practice reinforced the concepts, and gave the students the opportunity to work at their individual level.

Accomodations:

Some students solve their problems much more quickly than others in within the small groups. Faster students receive a challenging problem for them to do independently and silently while other students were working on the group problem.

Evaluation:

Teacher observation, ongoing formative assessment, and correct responses during small group instruction

Materials:

White boards, dry erase markers, erasers

Standards:

MA 1.1.3d: Use a variety of methods and tools to compute sums and differences.

MA 1.1.2.c Use objects, drawings, words, and symbols to explain subtraction as a separate action.

MA 1.3.2.a Model situations that involve the addition and subtraction of whole numbers 0-20 using objects and pictures.

MA 1.1.3.b Fluently subtract whole number differences from 10 using appropriate strategies and tools.

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