P.A.C.T.

PACT Instructional Visuals


Form: "PACT - Elementary Mathematics - 1. Context Form"

Created with: TaskStream - Advancing Educational Excellence
Author: Sara Morris
Context for Learning Form

Please provide the requested context information for the class selected for this Teaching Event.
About the course you are teaching

Response Is Required1. How much time is devoted each day to mathematics instruction in your classroom?

My master teacher devotes ninety minutes to mathematics instruction daily.
About the students in your class

Response Is Required2. How many students are in the class you are documenting?

There are twenty-nine students in the class.

Response Is Required3a. How many students in the class are English learners?

There are five English Language learners.

Response Is Required3b. How many students are Redesignated English Learners?

Five students are redesignated English Learners.

Response Is Required3c. How many students in the class are Proficient English speakers?

There are 19 Proficient English speakers.

Response Is Required4.1.a. How many students are at the Beginning Listening CELDT level?

None of the students are at the Beginning listening CELDT level.

Response Is Required4.1.b. How many students are at the Early Intermediate Listening CELDT level?

None of the students are at the Early Intermediate Listening CELDT level.

Response Is Required4.1.c. How many students are at the Intermediate Listening CELDT level?

Three students are at the Intermediate Listening CELDT level.

Response Is Required4.1.d. How many students are at the Early Advanced Listening CELDT level?

Two students are at the Early Advanced Listening CELDT level.

Response Is Required4.1.e. How many students are at the Advanced Listening CELDT level?

None of the students are at the Advanced Listening CELDT level.

Response Is Required4.2.a. How many students are at the Beginning Speaking CELDT level?

None of the students are at the Beginning Speaking CELDT level.

Response Is Required4.2.b. How many students are at the Early Intermediate Speaking CELDT level?

None of the students are at the Early Intermediate Speaking CELDT level.

Response Is Required4.2.c. How many students are at the Intermediate Speaking CELDT level?

None of the students are at the Intermediate Speaking CELDT level.

Response Is Required4.2.d. How many students are at the Early Advanced Speaking CELDT level?

Four of the students are at the Early Advanced Speaking CELDT level.

Response Is Required4.2.e. How many students are at the Advanced Speaking CELDT level?

One student is at the Advanced Speaking CELDT level.

Response Is Required4.3.a. How many students are at the Beginning Reading CELDT level?

None of the students are at the Beginning Reading CELDT level.

Response Is Required4.3.b. How many students are at the Early Intermediate Reading CELDT level?

One students is at the Early Intermediate Reading CELDT level.

Response Is Required4.3.c. How many students are at the Intermediate Reading CELDT level?

Four of the students are at the Intermediate Reading CELDT level.

Response Is Required4.3.d. How many students are at the Early Advanced Reading CELDT level?

None of the students are at the Early Advanced Reading CELDT level.

Response Is Required4.3.e. How many students are at the Advanced Reading CELDT level?

None of the students are at the Advanced Reading CELDT level.

Response Is Required4.4.a. How many students are at the Beginning Writing CELDT level?

None of the students are at the Beginning Writing CELDT level.

Response Is Required4.4.b. How many students are at the Early Intermediate Writing CELDT level?

Two of the students are at the Beginning Writing CELDT level.

Response Is Required4.4.c. How many students are at the Intermediate Writing CELDT level?

Three of the students are at the Beginning Writing CELDT level.

Response Is Required4.4.d. How many students are at the Early Advanced Writing CELDT level?

None of the students are at the Early Advanced Writing CELDT level.

Response Is Required4.4.e. How many students are at the Advanced Writing CELDT level?

None of the students are at the Advanced Writing CELDT level.

Response Is Required4.5.a. How many students overall are at the Beginning CELDT level?

None of the students are at the overall Beginning CELDT level.

Response Is Required4.5.b. How many students overall are at the Early Intermediate CELDT level?

None of the students are at the overall Early Intermediate CELDT level.

Response Is Required4.5.c. How many students overall are at the Intermediate CELDT level?

Five of the students are at the overall Intermediate CELDT level.

Response Is Required4.5.d. How many students overall are at the Early Advanced CELDT level?

None of the students are at the overall Early Advanced CELDT level.

Response Is Required4.5.e. How many students overall are at the Advanced CELDT level?

None of the students are at the overall Advanced CELDT level.

Response Is Required5. How many students have Individualized Education Plans (IEPs) or 504 plans?

None of the students have an IEP or 504 plan.

Response Is Required6. How many students participate in a Gifted and Talented Education (GATE) program?

None of the students participate in a Gifted and Talented Education program.
About the school curriculum and resources

Response Is Required7. Describe any specialized features of your classroom setting, e.g., bilingual, Structured English Immersion, team taught with a special education teacher.

Each day, there is twenty minutes dedicated to English Language Development (ELD) for the English Language Learners (ELLs). The classroom teacher works with the ELLs while the rest of the class is working independently. The school uses the Into English! (National Geographic School Publishing) Instructional program. The program focuses on listening, writing, reading and speaking and is a content based and aligned with the CA English Language Development Standards.

Response Is Required8. If there is a particular textbook or instructional program you primarily use for mathematics instruction, what is it?

(If a textbook, please provide the name, publisher, and date of publication.)

EnVision is the mandated instructional program for mathematics instruction at the school, and is used in this fifth grade classroom. The full name of the instructional program is Scott Foresman-Addison Wesley enVisionMATH, by Pearson Education, Inc. My master teacher typically uses the following instructional elements: interactive learning, visual learning, guided practice and independent practice. For homework she assigns the corresponding workbook page. For formal assessments, she has the students take the unit tests provided by the program.

Response Is Required9. What other major resources do you use for instruction in this class?

Other major resources used for mathematics include the SmartBoard, manipulatives, books and games.
Context Commentary

Please address the following prompts.

Response Is Required1. Briefly describe the following:


- Type of school/program in which you teach, (e.g., middle/high school, themed school or program)

- Kind of class you are teaching (e.g., third grade self-contained, sixth grade core math/science) and the organization of the subject in the school (e.g., departmentalized, interdisciplinary teams)

- Degree of ability grouping or tracking, if any

I teach at a public elementary school in Van Nuys, California, which is part of the Los Angles School District. I am teaching a fifth grade self-contained class with twenty-nine students. There is no ability grouping or tracking in this classroom environment.
2.

Describe your class with respect to the features listed below. Focus on key factors that influence your planning and teaching of this learning segment. Be sure to describe what your students can do as well as what they are still learning to do.

Response Is Required2a. Academic development

Consider studentsí prior knowledge, key skills, developmental levels, and other special educational needs. (TPE 8)

This specific unit is structured around estimating strategies, in line with the California Mathematics Content Standard Number Sense 1.1 (estimate, round, and manipulate very large numbers (e.g. millions) and very small numbers (e.g. thousandths) numbers). The students proficient in solving basic operation problems, identifying numbers from the hundred millions to the thousandths place value and adding and subtracting whole numbers to the hundreds place. They need additional instruction in problem solving strategies and increased exposure to solving basic operational problems with very large (i.e. millions) and very small (i.e. hundredths) numbers. In addition, they need support in representing numbers, especially in terms of estimating to the correct place value. Many of the ELLs, and about five of the other students, have may have difficulty understanding key mathematics vocabulary words. The lessons in this unit incorporate a vocabulary review to activate prior knowledge and provide additional scaffolding for ELLs. In addition this unit incorporates visual, oral and kinesthetic components to meet the learning preferences of all students.

Response Is Required2b. Language development

Consider aspects of language proficiency in relation to the oral and written English required to participate in classroom learning and assessment tasks. Describe the range in vocabulary and levels of complexity of language use within your entire class. When describing the proficiency of your English learners, describe what your English learners can and cannot yet do in relation to the language demands of tasks in the learning segment. (TPEs 7, 8)

Based on discussions, assessments and samples, I have determined that there is a wide range in terms in terms of language development in the class. Based on recent fluency assessments, sixteen students are in or above the seventy-fifth percentile in fluency, reading over 126 words correct per minute. Nine of the students are between the fiftieth and seventy-fifth percentile, and the remaining four students are between the twenty fifth and fiftieth percentile if fluency. One of the ELLs in the class is in the seventy fifth percentile, three fall in the second category, and one ELL is in the twenty fifth to fiftieth percentile. About thirty percent of the class score above an eighty percent on comprehension assessments, and about fifty percent of the class score above and eighty percent on spelling and vocabulary quizzes. In terms of oral language development, they answer questions in complete sentences and have an average vocabulary. They are able to read their English Language Arts textbook, but struggle with inferences, some vocabulary words and summarizing.

While they are performing at an average rate in English Language Arts, they are not able to transfer their language skills to other content areas. They struggle with story problems in math, specifically identifying key words. They are able to perform the math operations, but often confuse the terms, such as referring to addition problems as subtraction problems. This is especially true of the ELL students who need additional support in vocabulary development and comprehension skills.

Response Is Required2c. Social development

Consider factors such as the studentsí ability and experience in expressing themselves in constructive ways, negotiating and solving problems, and getting along with others. (TPE 8)

A majority of the students are developing social skills at an average rate and able to work well in groups, show respect in the classroom and follow classroom and school rules. There have been serious behavior problems amongst five of the students, including physically fighting, teasing, disrupting the class and not following directions. These students create constant distraction in the classroom and the master teacher has done little to support their development.

The master teacher has not created a community of learners in the classroom. She has not set clear classroom rules, and does not incorporate group projects in the curriculum. The students need instruction on working in groups and pairs.

Response Is Required2d. Family and community contexts

Consider key factors such as cultural context, knowledge acquired outside of school, socio-economic background, access to technology, and home/community resources.

The school serves a diverse student body. Just over half of the students are Hispanic, thirty-two percent are White (non Latino) and eleven percent of the students are African American. The remaining five percent are Asian and Fillipino. A quarter of the students are classified as English Learners, with five percent of the student body reclassified as Fluent English Proficient. In addition, eleven percent of the students are in Special Education, and six percent are in a Gifted and Talented Education program.

The majority of students on this campus participate in the free or reduced-price lunch program, with sixty percent of the students classified as economically disadvantaged. Due to the socioeconomic status of these students, few resources, such as computers, are available at home. In the community, resources such as the public library, are available.

Response Is Required3.

Describe any district, school, or cooperating teacher requirements or expectations that might impact your planning or delivery of instruction, such as required curricula, pacing, use of specific instructional strategies, or standardized tests.

The teachers have developed a quarterly mathematics curriculum pacing plan which is reviewed and adjusted in weekly grade level meetings. The teachers use the EnVision instructional program as a guide, but tailor the plan to align with the CA State Standards, and prepare the students for the California Standards Test.
In terms of the lessons required for this assessment and to meet the needs of my program, my master teacher has allowed me to create my own lesson plans for a select number of lessons in the classroom. I have been required to follow the pacing plan determined by the 5th grade teachers. In addition, the students were required to take the EnVision unit
Form: "PACT - Elementary Mathematics - 2. Planning Commentary Form"

Created with: TaskStream - Advancing Educational Excellence
Author: Sara Morris
Write a commentary that addresses the following prompts.

Response Is Required1.

What is the central focus of the learning segment? Apart from being present in the school curriculum, student academic content standards, or ELD standards, why is the content of the learning segment important for your particular students to learn? (TPE 1)

The focus of this learning segment was to teach students how to estimate by rounding and using compatible numbers. This skill is important for students to master for a number of reasons. First, it provides them with an effective tool to check their answers and determine if they computed a reasonable answer. By integrating estimating strategies with basic operational problems, students can solve the problem and immediately check to see if they close. This promotes self-regulated learning.

Second, it is an important skill for them to use in their daily lives. By structuring the lessons to include real-world examples, students are able to make connections to the skill and their everyday lives. Seeing the importance of and application for estimating strategies helps reinforce the value of this unit and increases student motivation.

It is important for students to develop number sense. In an effort to reinforce place value, the students will use a place value chart in all three lessons. In addition, the students will underline the place value that is being rounded. By doing so, students will identify the place value and ensure that all numbers are being rounded to the same place value.

Response Is Required2.

Briefly describe the theoretical framework and/or research that inform your instructional design for developing your studentsí knowledge and abilities in both mathematics and academic language during the learning segment.

Principles of the sociocultural and constructivist learning theories will be used to inform my instructional design for this unit. The overall objective of the unit is for students to develop skills and strategies for estimating numbers. In terms of the sociocultural learning theory, the unit will focus on students participating in real world experiences, with their peers to promote cognitive growth. The unit will incorporate opportunities for students to acquire tools to help them solve tasks that they are likely to face in life, called cognitive tools.

This unit will also focus on providing students with social activities, also considered a key tenet of this learning theory. Students will work together to solve complex problems, within their zone of proximal development. In addition, according to this theory, students develop complex problem solving strategies through social interactions. This occurs naturally within the context of everyday activities as these activities evolve into internal mental activities, called internalization. In addition, the social activities planned for this unit will provide the students with various peer perspectives on estimating and opportunities to use language to discuss topics, which is critical for cognitive and English language development.

This unit will also incorporated many tenets of the constructivist learning theory. This theory stresses the importance of students constructing their own knowledge by interacting and experimenting with their surroundings. To emphasize conceptual understanding, this unit focused on one core idea, estimating, which the students were able to explore in depth. Students will work in collaborative teams, use realia and solve problems based in their everyday lives to support construction of new knowledge.

Response Is Required3.

How do key learning tasks in your plans build on each other to support studentsí development of conceptual understanding, computational/procedural fluency, mathematical reasoning skills, and related academic language? Describe specific strategies that you will use to build student learning across the learning segment. Reference the instructional materials you have included, as needed. (TPEs 1, 4, 9)

This unit is designed to progress from estimating the sums and difference of whole numbers, a basic operation, to a more complex operation of estimating the sums and differences of decimals to an even more complex operation of estimating the product of whole numbers. This progression is designed to help students develop the skill and apply in to a variety of situations, progressing in difficulty.

Every lesson includes a vocabulary review at the beginning of the lesson to reinforce the academic language that would be used throughout the lesson. The students will use the Think-Pair-Share strategy to define the key academic vocabulary words, which will then posted in the room for the remainder of the unit. The academic language will be reinforced throughout the lesson.

In order to ensure that students will have the skills needed to build on the new knowledge, I will incorporate many instructional materials. Every lesson will require that students use a place value chart. By introducing the place value chart in the first lesson, students will be able to practice lining up the numbers by place value. The students will solve the problems in their math journal, which has grid paper to help them organize the numbers. By reinforcing the importance of aligning numbers by place value, students will be able to apply that knowledge to the unit on decimals, which they had previously struggled with in previous lessons on adding and subtracting decimals.

Response Is Required4.

4. Given the description of students that you provided in Task 1.Context for Learning, how do your choices of instructional strategies, materials, technology, and the sequence of learning tasks reflect your studentsí backgrounds, interests, and needs? Be specific about how your knowledge of your students informed the lesson plans, such as the choice of text or materials used in lessons, how groups were formed or structured, using student learning or experiences (in or out of school) as a resource, or structuring new or deeper learning to take advantage of specific student strengths. (TPEs 4,6,7,8,9)

The unit is designed to present the information strategically with the first two lessons focusing on direct instruction on the estimating process and problem solving, and the final lesson applying the skill to other operations. The materials are all created in advance of the lessons, with the charts posted on the board, to save time and ensure that students have the materials needed throughout the lesson. In addition, the Smart Board will be used to provide an interactive learning experience.

Each task is planned based on real life experiences the students face outside of the classroom. These examples provide relevant information for the students to work with and support the students in making connections to the material. The examples include calculating the estimated sum of the number of laps student run at school (I will use real data from the school), the estimated number of pages that a student read over the summer based on popular fifth grade books, etc. Some of the charts will be used throughout the unit so students can learn the value of estimating the same material for different purposes. This will also help the English learners focus on the task at hand instead of the content.

In addition, each lesson provides students with the opportunity to work with peers allowing them to work within their zone of proximal development to solve more complex problems. In the first lesson students will be placed in heterogeneous pairs, with an advanced student to support the needs of a student who struggles. The second lesson will feature homogenous groups, allowing differentiation in problems to challenge more advanced students and to reinforce the skill for those still working on mastery. The third lesson will be a mix of the two, with heterogeneous pairs for students at the far end of the scale, and homogenous pairs for the remaining students. I will also ensure that during all three lessons ELLs will be paired with non-ELLs. This will ensure that every student is challenged, yet able to accomplish the task successfully.

One of the lessons focused on estimating sums and differences of decimals. In order to support student learning, the students were provided with U.S. coins. The students counted with the coins and created equations based on their interactions. In addition, there were large magnetic coins posted to the board which we used for the whole class discussion.

Each day will begin with the students answering "problems of the day" in their math journals. These problems will focus on what the students learned in the previous lesson. It will serve as a reinforcement of the concept and assist students by activating prior knowledge before beginning the new lesson. The problems will be reviewed as a whole class. Students will solve problems on the board, talking through their thinking process to serve as peer models.

Every lesson in the unit will have an extension activity for students who finish early and show an understanding of the concept. Students will apply knowledge from the lesson in new situations. This will keep them challenged and engaged.

Response Is Required5.

Consider the language demands of the oral and written tasks in which you plan to have students engage as well as the various levels of English language proficiency related to classroom tasks as described in the Context Commentary. (TPE 7)

a. Identify words and phrases (if appropriate) that you will emphasize in this learning segment. Why are these important for students to understand and use in completing classroom tasks in the learning segment? Which students?

b. What oral and/or written academic language (organizational, stylistic, and/or grammatical features) will you teach and/or reinforce?

c. Explain how specific features of the learning and assessment tasks in your plan, including your own use of language, support students in learning to understand and use these words, phrases (if appropriate), and academic language. How does this build on what your students are currently able to do and increase their abilities to follow and/or use different types of text and oral formats?

a. This unit incorporates academic language. The words that the students will need to know to successfully complete this unit are as follows: sum, difference, product, quotient, estimate, rounding and compatible numbers. The students have been exposed to these words in previous lessons To ensure that students understand the vocabulary, each lesson will begin with a vocabulary review. Students will think, pair, share to define the key terms. Then we will review as a whole class. Finally, the definitions, with examples and symbols, will be posted on the board throughout the unit.

b. I will use the academic language throughout the lesson, stopping to check for understanding at key intervals. I will model the correct use of academic in my correspondence with the students. I will point to and underline the words in the problem to reinforce to definition. In addition, when solving a problem, I will use complete sentences including the academic language.

c. In terms of learning and assessment, the students will be required to underline key words in problems. The students will underline the digit in the place value being rounded. When reviewing material, I will check to see that students are underlining the correct digit and connecting the words to the correct operation. Students are able to answer story problems, but often confuse the terms. By reinforcing the operation associated with the term students will be able to apply this knowledge to other content areas.

Response Is Required6.

Explain how the collection of assessments from your plan allows you to evaluate your studentsí learning of specific student standards/objectives and provide feedback to students on their learning. (TPEs 2, 3)

Each lesson includes a variety of informal assessments to assist me in determining the students understanding. I will walk around the room and ask students to describe how and why they are estimating a certain problem. I will listen to the group discussion and create a list of students who need additional support. I will work with this group of students during independent practice.

The students will solve problems in their math journals. At the end of each lesson, I will collect their math journals and review, noting students individual progress in mastering the skill. I will adapt the lesson for the following day, focusing on a review of concepts and problems that the students, as a collective group, need additional support. The students will complete the corresponding workbook pages for homework, which will be reviewed daily, and used to adapt the following lessons. The homework will not be graded.

Each lesson will close with a problem that the students will work on individually that will be assessed by the attached rubric. The scores from the closing problem will be averaged to create a unit assessment.

Response Is Required7.

7. Describe any teaching strategies you have planned for your students who have identified educational needs (e.g., English learners, GATE students, students with IEPs). Explain how these features of your learning and assessment tasks will provide students access to the curriculum and allow them to demonstrate their learning. (TPEs 9. 12)

There are no GATE students or students with IEPs in this class, however, I have incorporated several method to provide support to English learners in this unit. There will be a comprehensive vocabulary review at the beginning of each lesson. In addition, the English learners will be paired in heterogeneous groups with non-English learners. Students will have time to think-pair-share prior to reviewing the problem with the entire class. English learners can practice their responses with a partner prior to meeting as a larger group. The material will be provided in chart form, and sentence form. In addition, we will work on problems as a whole class, then in pairs, and then based on understanding students will work independently or with me in a small group.

In order to assess their understanding of the material and to demonstrate their learning, students will explain the process of estimating by rounding or using compatible numbers and its purpose to their partner. Then students will have an opportunity to share with the whole class. In addition, one lesson in this unit focuses on estimating the sums and differences of decimals. In order to support the English learners, I will provide students with United States coins.

Form: "PACT - Elementary Mathematics - 3. Instruction Form"

Created with: TaskStream - Advancing Educational Excellence
Author: Sara Morris
Video Label Form

Candidate ID #

7620022177
Elementary Mathematics Clip(s)

Response Is RequiredLesson from which clip(s) came: Lesson #

The clip came from Lesson #1.

Response Is RequiredIf Electronic, Video Format of Clip(s): (check one)

* Quicktime

Instruction Commentary
Write a commentary that addresses the following prompts.

Response Is Required1.

Other than what is stated in the lesson plan(s), what occurred immediately prior to and after the video clip(s) that is important to know in order to understand and interpret the interactions between and among you and your students? Please provide any other information needed to interpret the events and interactions in the video clip(s).

The clip was taken at the beginning of the lesson. Prior to the taping the students solved math problems based on the prior units, addition and subtraction number sense and reviewing multiplication of whole numbers. The lesson started after reviewing the math problems and completing the morning tasks, including attendance and lunch count.

After the video ended, we finished solving the following problem as a whole class, "Use rounding to the hundreds place to estimate about how many laps the entire school ran last week." I had a student come to the board to solve the problem, and instructed the students to solve the problem in their math journal. I told a student who was already solving the problem that they were doing a good job and setting an excellent example. The student at the board did not add the numbers correctly, he forgot to carry a number. I asked him to double check his answer and walk me through the process. When he got to the place where he forgot to carry the number, he realized his mistake and corrected the problem.

I reviewed the problem. I told the students the exact number of laps ran and asked them if that was a reasonable estimate. Most of the students agreed it was reasonable. I then asked how we could have gotten a more accurate estimate. The students were quiet, so I asked them to think-pair-share to figure out how to get a more accurate estimate. When I called them back, a student raised his hand and said, "you could round to the tens place." This showed me that he understood that there were many ways to estimate and by rounding to a different place value the answer would become either more or less accurate. I asked the class if someone else could explain why that would have given us a more accurate estimate. One of the ELLs said that the numbers would be closer.

After we completed the exercise, I had the students work in pairs to answer two more questions based on the same data, but rounding to the thousands place, instead of the hundreds. The students were asked to compare the number of laps the fifth grade class ran compared to the grade that ran the most laps. Then they needed to figure out about how many more laps they would need to run to beat the grade that ran the most laps. I gave them five minutes to work in pairs to solve. I walked around the room asking questions to gauge understanding and made a list of students who needed additional support.

Response Is Required2.

Describe any routines or working structures of the class (e.g., group work roles, class discussion norms) that were operating in the learning task(s) seen on the video clip(s). If specific routines or working structures are new to the students, how did you prepare students for them? (TPE 10)

Many of the students daily routines were integrated into this lesson. The students always work on mathematics at the beginning of the school day, so this lesson took place at the usual time. Students have a math journal that they use during math. The students used this journal to record their results during the unit. In addition, the journal has grid paper which the students use to organize the numbers by place value. The students were instructed to continue doing so for this unit. The students have been exposed to many strategies, which were included in the unit. These include using a place value chart, number line, underlining the place value being rounded to, and identifying key words in a story problem.

There were new elements to this unit as well. The students had worked in pairs previously, but in the second lesson they were exposed to role-playing. The students took turns being the waiter and customer at a restaurant. I modeled the roles, reviewed responsibilities, and posted a chart guiding the students on the specific tasks that needed to be completed (see ppt presentation).

Response Is Required3.

In the instruction seen in the clip(s), how did you further the studentsí knowledge and skills and engage them intellectually in understanding mathematical concepts and participating in mathematical discourse? Provide examples of both general strategies to address the needs of all of your students and strategies to address specific individual needs. (TPEs 1, 2, 4, 5, 7, 11)

I engaged students by providing an example that relates to their everyday life. As soon as I posted the chart with the number of students on it, one student raised his hand and asked if that was real. I explained that I used the real number of students at Chandler Elementary school. I also involved students in my demonstration, by having them round the numbers. I asked them to provide examples of times in which it might be relevant for them to use rounding outside of the classroom to help them connect the skill to their daily lives.

Throughout the lesson I used strategies to address the needs of all my students. I had the information neatly organized and posted on the board. I provided the questions both orally and visually. I incorporated visual cues when needed, such as writing a number line on the board when a student got confused. The place value chart was posted on the board.

I modeled my cognitive process so that student understood why I rounded to certain place values, how I rounded and why I thought that the answer was reasonable.

To meet the needs of my ELLs, I spoke slowly and provided wait time allowing them to process their thoughts before responding. I clarified key academic terms and provided visual examples of each terms. The definitions and examples remained on the board throughout the unit.

Response Is Required4.

Given the language abilities of your students as described in Task 1. Context for Learning, provide examples of language supports seen in the clips that help your students understand the content and/or academic language central to the lesson. (TPEs 4, 7)

The segment of the lesson highlighted in the clip featured strategies incorporated to support the language needs of the students. There was a review of the academic terms that featured the definitions as well as examples. After the review, the terms were posted to the board and remained there during the lesson. I modeled corrections by using academic terms in my response to students. I also checked for understanding of key academic terms by asking students to define them throughout the lesson. As the unit progressed, I introduced new academic vocabulary words, and posted them beneath the existing terms.

Knowing that the students sometime struggle with story problems, I read the problem out loud and also posted it on the board. For the first two problems of each lesson, we reviewed the problem as a whole class identifying and underlining key words. We determined a strategy to solve the problem together. For the third problem, the students worked in pairs to review to the problem, identify and underline key words and determine a strategy to solve the problem. I walked around the room, meeting with each group, asking students to explain their problem solving strategies. Once students showed they understood the concept, they were able to work independently. The students who were close to understanding the concepts, continued to work in pairs, while the ones who struggled worked with me during independent practice.

In addition, I made sure to use language the students would understand in the examples provided. That way students could focus on the academic language relevant to the lesson, and not get confused by terms they did not understand in the questions. For example, I used a chart with the number of students by grade at Chandler Elementary school for many of the questions in lesson 1 and lesson 3. The students all knew what the chart was communicating and were able to focus on the story problem.

A few times in the lesson, I asked a question and the students did not respond. I realized that they may have been confused by the way I stated the question, so I asked the question a different way. For example at 9:05 in the video I asked a question that the students did not understand. I rephrased the question, and the students were able to answer it.

Response Is Required5.

Describe the strategies you used to monitor student learning during the learning task shown on the video clip(s). Cite one or two examples of what students said and/or did in the video clip(s) or in assessments related to the lesson that indicated their progress toward accomplishing the lessonís learning objectives. (TPEs 2, 3)

I monitored student learning during the task shown on the video by constantly checking for understanding and providing support where needed. At 2:15 in the video, a student says, "94 rounded to the tens place is 80." Instead of correcting her, I drew a number line on the board, placing 94 between 90 and 100. I underlined the digit begin rounded to and restated the problem. The student then responded with the correct answer. I was able to determine that she knew the process, but got confused, and was able to self-correct. It was not captured on the video, but I called on the same student later to in the lesson to make sure she understood the skill, and she was able to answer correctly.

At 7:34 in the video, I ask students if I had rounded to the hundreds place, would I still get a reasonable estimate. A ELL student said, "I don't think so because it wouldn't be the right numbers." This showed me that the student did not understand the concept. Instead of finding a reasonable estimate, he was focused on the exact numbers. To clarify, I redid the problem by rounding to the hundreds place, instead of the tens place, which was not part of the original plan. This exercise added time to the opening section of the lesson, but I felt it was important to help the students understand the concept. At the end of the problem, we compared answers as a class and found that it was reasonable to round to the hundreds as well. During group work, I asked the student a similar question and he worked out a problem by rounding to two different place values. He was able to determine that they were both reasonable.

Form: "PACT - Elementary Mathematics - 4. Assessment Commentary Form"

Created with: TaskStream - Advancing Educational Excellence
Author: Sara Morris
Write a commentary that addresses the following prompts.

Response Is Required1.

Identify the specific standards/objectives measured by the assessment chosen for analysis. You may just cite the appropriate lesson(s) if you are assessing all of the standards/objectives listed.

Each lesson in the unit focused on CA State Standard Number Sense 1.1, estimate, round, and manipulate very large numbers (e.g. millions) and very small numbers (e.g. thousandths),with the overall objective being that students will be able to estimate by rounding to solve problems involving large and small numbers. However the objective varied by lesson.

In lesson 1 the focus was on using rounding to estimate sums and differences. The objective was that students will be able to use rounding to estimate the sums and differences of whole numbers. They will verify their understanding by using rounding to estimate the sums and differences of story problems in their math journal and by writing about the purpose and value of using rounding as a math strategy.

In lesson 2 the focus was on using rounding to estimate sums and differences of decimals. The objective of this lesson is that students will be able to use rounding to calculate the sums and differences of decimals involving tenths, hundredths using U.S. coins. To verify understanding, students will role-play and record a restaurant scenario with a partner.

In lesson 3 the focus was on using rounding to estimate products of whole numbers. The objective of this lesson is that students will be able to apply the strategies of using compatible numbers and rounding to estimate products. To verify their understanding, they will solve a word problem that requires estimating the product of 3 numbers using either compatible numbers or rounding and explain their reasoning in their math journal.

Response Is Required2.

Create a summary of student learning across the whole class relative to your evaluative criteria (or rubric). Summarize the results in narrative and/or graphic form (e.g., table or chart). Attach your rubric or evaluative criteria, and note any changes from what was planned as described in Planning commentary, prompt 6. (You may use the optional chart provided following the Assessment Commentary prompts to provide the evaluative criteria, including descriptions of student performance at different levels.) (TPEs 3, 5)

As represented by the following chart, the majority of students obtained intermediate level at the conclusion of the unit.



Student Learning Level


Number of Students (29 total)

Beginner


4

Intermediate


18

Advanced


7

These levels were determined by the average of scores from the three lessons in the unit. Students who scored an average of 4 on the rubric are labeled as advanced. Students who scored an average between 2 and 3 are classified as intermediate. An finally, students who scored an average of 1 are classified as beginner.

Response Is Required3.

Discuss what most students appear to understand well, and, if relevant, any misunderstandings, confusions, or needs (including a need for greater challenge) that were apparent for some or most students. Cite evidence to support your analysis from the three student work samples you selected. (TPE 3)

After reviewing the work samples, I was able to determine that most students were able to estimate using rounding to solve sums, differences and products. In addition, most students were able to round to the place value identified in the story problem. However, some students struggled if a place value was not determined in the problem. An example of this was evident in the video, when a student did not think that they could round the number of laps ran by hundreds place after solving by estimating to the tens place. Additional support in identifying the place value to solve for would benefit the students.

In some cases, students would solve to determine the sum, difference and product and round the final answer. The students would benefit from receiving clear instructions regarding what phase in the problem they should apply the skill. Clear directions and additional practice would help students construct the value of estimating when used to solve problems, not estimate final answers.

At the end of the unit I had the students fill out an anonymous form to reflect on their learning. This served as additional support to determine how well students understood the skill. The form had the following questions: please rate the lessons on a scale of 1 -10 (10 being the highest), did you learn something new in the lessons, if so, what did you learn, what was your favorite part and what would you change. Based on the student feedback, for about 25% of the students the unit was a review, the rest of the students mentioned learning about lining up numbers by place value and/or how to round. The second lesson was the overwhelming favorite. Many students mentioned that they enjoyed using coins, playing waiter and customer and working together.

Response Is Required4.

From the three students whose work samples were selected, choose two students, at least one of which is an English Learner. For these two students, describe their prior knowledge of the content and their individual learning strengths and challenges (e.g., academic development, language proficiency, special needs). What did you conclude about their learning during the learning segment? Cite specific evidence from the work samples and from other classroom assessments relevant to the same evaluative criteria (or rubric). (TPE 3)

The following provides a brief overview of the students whose work samples were selected:

Student


ELL Status


Prior Knowledge

1


Yes - Level 4 (Intermediate CELDT level for listening, reading, and writing. Early Advanced CELDT level for speaking.)


Student is at an early advanced level in basic operations with whole numbers, place values and solving story problems. Student has shown strength in mathematics, but due to English Language Development struggles with identifying key words in story problems. Student scored at the basic level in Language Arts and at the proficient level in Math on the 2010 CST.

2


No


Student is at an advanced level in basic operations with whole numbers, place values and solving story problems. Student is a redesignated English Learner. Student scored at the advanced level in Language Arts and at the advanced level in Math on the 2010 CST.

3


No


Student is at an intermediate level in basic operations with whole numbers, place values and solving story problems. Student is a proficient English speaker and has a strong knowledge of academic terms, however, struggles with multi step problems. Student is a redesignated English Learner. Student scored at the proficient level in Language Arts and at the proficient level in Math on the 2010 CST.

Student 1 showed mastery of the skill. The student was able to round to the specified place value and solve complex story problems. However, the student did not apply strategies such as underlining the place value. In addition, the student did not include the context of the problem in the answer.

Student 2 showed emerging understanding of the skill. In lesson 1, the student used rounding prior to determining the sum of pages read, then solved the problem with the exact numbers to determine the amount of pages the student still needed to read. This shows that the student needs additional support in applying the strategy to solve multi-step problems. In addition, this student used mental math during lesson 2 instead of writing down the problem and answers in the math journal. The student needs support in terms of clear instructions.

Student 3 showed mastery of the skill. The student was able to solve complex multi-step problems and justify the answers. This student answered the extension problems and showed they can apply the skill to new situations.

Response Is Required5.

What oral and/or written feedback was provided to individual students and/or the group as a whole (refer the reviewer to any feedback written directly on submitted student work samples)? How and why do your approaches to feedback support studentsí further learning? In what ways does your feedback address individual studentsí needs and learning goals? Cite specific examples of oral or written feedback, and reference the three student work samples to support your explanation.

All feedback was provided orally to the students. Specifically, feedback was provided in terms of questioning. It was important for students to answer questions and come up with the answer independently. I spent time with each pair of students and asked questions such as "why did you decide to round to that place value?" The questions let the students work with their partner and the material to come up with strategies to solve the problem.

This approach created a student centered learning experience. The students were able to construct their own knowledge, based on questions. In addition, I could observe students explaining the process to their partners. This reinforced their understanding of the skill in terms of application and value. In order to master the skill, the students needed to be able to understand the purpose and apply the skill in situations they may face in their everyday lives. This approach created an environment in which students felt comfortable practicing the skill.

Response Is Required6.

Based on the student performance on this assessment, describe the next steps for instruction for your students. If different, describe any individualized next steps for the two students whose individual learning you analyzed. These next steps may include a specific instructional activity or other forms of re-teaching to support or extend continued learning of objectives, standards, central focus, and/or relevant academic language for the learning segment. In your description, be sure to explain how these next steps follow from your analysis of the student performances. (TPEs 2, 3, 4, 13)

Based on the student performance it would be appropriate to introduce larger and smaller numbers into future lessons about estimating. Prior to doing so, I would review the strategies such as underlining the place value being rounded and rounding numbers prior to solving problems with the whole class. I would have the students at the advanced level work in small groups to create and solve problems using very large and very small numbers. This would allow me to see how they would apply the skill in their everyday lives and allow them to work on challenging problems.

For students, such as student 2, who struggled with multi-step problems, I would provide direct instruction in problem solving strategies such as underlining key words in a story problem, breaking down the problem into smaller, more manageable parts and using prior knowledge to check the reasonableness of their answers. After reviewing the strategies I would have students at the intermediate level work to solve story problems with large and small numbers.

For students who are still at the beginning level, I would work with them as a small group and re-teach the skill, breaking down the problems to manageable steps. To begin with, we would round numbers to a predetermined place value. Then we would underline key words in the problem and create an equation based on the underlined words. Next, we would repeat to solve the next step of the problem. After reviewing as many problems as necessary as a group, I would have them work in pairs then individually to solve additional problems.

Form: "PACT - Elementary Mathematics - 5. Reflection Commentary Form"

Created with: TaskStream - Advancing Educational Excellence
Author: Sara Morris
Write a commentary that addresses the following prompts.

Response Is Required1.

When you consider the content learning of your students and the development of their academic language, what do you think explains the learning or differences in learning that you observed during the learning segment? Cite relevant research or theory that explains what you observed. (See Planning Commentary, prompt # 2.) (TPEs 7, 8, 13)

The tenets of the sociocultural and constructivist learning theories that were incorporated in the instructional design for this unit impacted student learning. The activities in the unit focused on students participating in real world experiences, with their peers to promote cognitive growth. This created engagement and motivation that was key to their learning experience. In addition, the content was based on estimating, a strategy that will help students solve tasks that they are likely to face in life, called cognitive tools. The students developed valuable thinking skills by applying the cognitive tool to real life experiences.

This unit also provided students with multiple opportunities to work with their peers. This supported students academic language development, as they had the opportunity to practice the academic language in a relevant situation. In addition, according to this theory, students develop complex problem solving strategies through social interactions.

This unit was structured to provide assistance, or scaffolding, to the students. Throughout the lesson I modeled how to round and use compatible numbers to estimate answers to mathematics problems. I paced the lesson to start with addition and subtraction of whole numbers, then introduced addition and subtraction of decimals, and finally multiplication of whole numbers. The progression of similar tasks to more complex made it easier for students to master the skill. I provided specific guidelines and asked questions to keep the students focused on the current task. In addition, I used relevant examples to get students engaged and motivated.

This unit also incorporated many tenets of the constructivist learning theory. To emphasize conceptual understanding, this unit focused on one core idea, estimating, which the students were able to explore in depth. In addition, the unit presented the concept in terms of authentic activities, similar to what they encounter outside of the classroom, which provided them the opportunity to construct the importance of mastering the skill on their own. This was accomplished by interacting with their peers. Through a variety of exercises including Think-Pair-Share, role playing, and group projects, every student in the classroom was able to actively participate and share their insights with each other. Each lesson in this unit provided students with the opportunity to reflect on their learning and suggest other opportunities in which they may use the acquired skill.

Response Is Required2.

Based on your experience teaching this learning segment, what did you learn about your students as mathematics learners (e.g., easy/difficult concepts and skills, easy/difficult learning tasks, easy/difficult features of academic language, common misunderstandings)? Please cite specific evidence from previous Teaching Event tasks as well as specific research and theories that inform your analysis. (TPE 13)

The experience of learning mathematics is based on accessing prior knowledge and building on that knowledge. The students have been working on basic operations and problem solving strategies since the primary grades. Piaget's theory of cognitive development, specifically the concept that children organize their knowledge into schemes which are used repeated to respond to familiar situations, may support the student ease of acquiring the skill. The students were able to build off their prior knowledge and develop new knowledge. This reinforces the need to provide students with the opportunity to access prior knowledge before introducing new, related concepts.

In addition, the students benefited from a mediated learning experience, a principal of Vygotsky's learning theory. Through asking questions that encouraged students to think about a learning experience, students begin to develop meaning. Instead of providing students with answers, I asked questions that got them thinking about how to solve problems. This experience helped students acquire a more complex understanding of the application and value of the new skill.

In order to facilitate learning, the information was presented using a constructivist approach. The material was relevant and meaningful to the students, which led to high levels of student engagement. In addition, students used realia in terms of US coins to apply new knowledge. In addition, the students worked with partners to share various interpretations and jointly construct knowledge.

Response Is Required3.

If you could go back and teach this learning segment again to the same group of students, what would you do differently in relation to planning, instruction, and assessment? How would the changes improve the learning of students with different needs and characteristics? (TPE 13)

If I could go back and teach the same unit to the same students, I would build on my experience and do some things differently.

In terms of planning, in lesson 1, I would not assign a specific place value for the problem in the demonstration phase. I would encourage students to solve the problem in pairs, then discuss the various answers. This would reinforce the fact that there are many ways to round to determine an estimate.

During the instruction phase I would keep the examples posted on the board longer. Instead of erasing them before starting a new problem, I would keep them up so that the students could reference them through out the lesson. I would also have added key problem solving terms to the vocabulary list to support students in solving story problems.

In this unit, I had to reteach the skill many times, especially when it came to fact that there were many ways to estimate a problem. This ended up adding time to the introduction. While it is extremely important, I could have incorporated opportunities to think, pair, share earlier in the lesson. This would keep the students engaged, and provide an opportunity for them to figure out and apply the strategy with a partner. It may help clear up any misunderstandings in terms of academic language for my English learners, as well.

While the assessment was helpful in determining student understanding of the skill, it would have benefited the student and provided a more accurate representation if I had reviewed the rubric prior to assigning the problems. Prior to teaching, I felt that the questions provided enough detail for the students to be able to understand and answer to meet the rubric, however, in retrospect it appears that was not the case. While I was able to gage the skill level of the students, many did not connect the answer to the information provided in the charts.

In addition, in terms of assessing a skill such as using estimating strategies to solve problems, it is important to monitor student understanding of the purpose of the skill. In order to do so, and to promote use of academic language in literacy development, I would have included a writing prompt in the assessment.