equip mathematics student work protocol washington, dc may 19, 2014

EQuIP Mathematics Student Work Protocol

Washington, DCMay 19, 2014

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Specific Objectives of the Student Work Protocol

1. To confirm the alignment of the assignment with the letter and the spirit of the targeted CCSS.

2. To determine how students performed on an assignment as evidence of how well designed the lesson/unit is.

3. To provide criterion-based suggestions for improving the assignment and related instruction.

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The Student Work Protocol invites teachers to…

1. Develop a common understanding of the challenging work required by the CCSS.

2. Close the gap between the expectations embodied in assignments and what students are supposed to be learning.

3. Create more equitable educational opportunities for students.

4. Improve assignments and instructional practices/strategies.

5. Engage in structured, thoughtful conversations about standards-based instruction with colleagues that can deepen the existing collaboration among states and districts.

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What You Need To Conduct Review

1. A team of reviewers*

2. The directions or prompts for the task/assignment

3. Any accompanying answer keys, rubrics, and/or scoring guides

4. A copy of the CCSS, and particularly those standards targeted by the task/assignment

5. Forms to record Notes & Observations and Task-to-CCSS Alignment Recording Chart

6. Copy of Alignment of Task rating descriptors

7. Several pieces of student work

* This process may be completed by a single reviewer

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The Five-Step Process

• STEP 1: Review the Instructional Materials.• STEP 2: Without consulting the standards or the

lesson/unit, analyze the purpose and demands of the assignment as evidenced by the directions and the rubrics/scoring guides.

• STEP 3: Compare the alignment of the content and and performance(s) to the targeted standards.

• STEP 4: Diagnose student work.• STEP 5: Provide criterion-based suggestions for

improving the assignment.

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The Five-Step Process

• STEP 1: Review the Instructional Materials.• STEP 2: Without consulting the standards or the

lesson/unit, analyze the purpose and demands of the assignment as evidenced by the directions and the rubrics/scoring guides.

• STEP 3: Compare the alignment of the content and and performance(s) to the targeted standards.

• STEP 4: Diagnose student work.• STEP 5: Provide criterion-based suggestions for

improving the assignment.

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When working with a review team…

• If reviewers are part of a team, each step should be completed individually before sharing observations with others.

• If working with reviewers new to the process, the team should pause to discuss Notes and Observations after each step.

• More experienced review teams may choose to complete all steps individually before discussion.

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EQuIP Student Work Protocol Applying the Steps to an Example

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• Record the grade and title of the lesson/unit on Student Work Protocol recording form.

• Locate the assignment/task to be evaluated and record the assignment title or description on the recording form.

• Locate the student work that corresponds to the assignment.

• Scan the lesson/unit to see what it contains and how it is organized.

* Note: This step should be done quickly. This is not a deep study of the lesson or the assignment.

Step 1: Review the Instructional Materials *

Try it now – on your own at first.

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Step 1: Review the Instructional Materials

This performance task is the Common Core-aligned culminating task for a grade 3 unit of instruction presented by NYC DOE with the same name.

Unit Table of ContentsOverview and Standards…………………………………..page 1Performance Task: Cookie Dough……………………..pages 4-5Rubric, Scoring Guide, Descriptors…………………….page 6-8Instructional Supports……………………………………….pages 19-88(Student Work Samples are in a separate document)

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Step 2: Identify content and performances. *

• Without consulting the standards or the lesson/unit, analyze the purpose and demands of the assignment as evidenced by the directions/prompts and the rubrics/scoring guides.

Guiding Questions:

— Based on the directions and/or the scoring guides for the assignment, what is its likely purpose?

— Based on the directions and/or the scoring guides for the assignment, what demands does it make of students?

* Note: This step requires a more in-depth look at the task/assignment, working the problem(s) and making notes about all grade-level strategies students are likely to use.

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Tips and Reminders:— Take the assignment at face value. — Stick to purposes and demands that are evident from the

written words on the page; do not assume skills and knowledge that are not readily apparent, even if all agree that is probably what was meant.

Step 2: Identify content and performances.

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Step 2: Identify content and performances.

Notes & Observations

Performances Required (skills): Students must multiply (or skip count by 3’s, 4’s, and 5’s) and add whole numbers, solve word problems,

Content Required (knowledge): Whole number operations


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Step 2: Example

Requirements of the Cookie Dough Task:• Multiply and add whole numbers• Multi-step problem solving• The inverse relationship between multiplication and division • Quantitative reasoning

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Step 2: Example


Performances Required (skills): Students must multiply (or skip count by 3’s, 4’s, and 5’s) and add whole numbers, solve word problems, reason mathematically. They MAY use the inverse relationship between multiplication and division and/or repeated addition and subtraction.

Content Required (knowledge): Whole number operations

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Step 3: Compare Alignment to Targeted Standards

• Compare the alignment of the content and performance(s) of the assignment to the targeted standards for the lesson/unit.

Guiding Questions:— Do the directions, prompt(s), and/or scoring guide for the assignment

give students the opportunity to demonstrate all or part of the targeted standards for the assignment and lesson?

— How well aligned are the content and performance(s) of the assignment with the targeted standards in the assignment and the lesson?

— If the assignment is given a score of 1 or 0 for any one of the targeted standards, is there another assignment in the lesson that addresses that standard?

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Step 3: Compare Alignment to Targeted Standards

Tips and Reminders:— The student-work task need not address every targeted standard in

the lesson/unit as long as the requirements of the task are central to the lesson’s learning goals.

— In making suggestions for improvement, consider whether the assignment was intended to incorporate all of the targeted standards or if the assignment is one of a series in the lesson/unit used to assess student competency.

EQuIP Student Work Protocol Grade 3 Math: Cookie Dough

These standards are targeted for the unit:

3.OA.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each.

3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects and partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each.

3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

3.OA.5 Apply properties or operations as strategies to multiply and divide.

3.OA.6 Understand division as an unknown-factor problem. Cont.

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These standards are targeted for the unit (cont.):

3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP.3 Construct viable arguments and critique the reasoning of others.

MP.4 Model using mathematics.

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EQuIP Student Work Protocol The StepsStep 3 (cont.): Rate the alignment to each targeted standards using the 0 – 3 scale provided.

Try it now – on your own at first.3.OA’s and MP’s

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Step 3 (cont.): Alignment Ratings of 3 or 2Targeted CCSS

Standards/ Standards for Mathematical

Practice

Alignment Rating (0-3) Alignment Rationale

3.OA.1 2Students may use groups of cookie dough tubs at given prices per tub to determine total amounts of money raised or the number of tubs. However there is no clear requirement for students to interpret that product.

3.OA.3 2

Students will use multiplication in this performance task and the relationship between multiplication and division in #3. However it is not required that division be used, only that there be an understanding of the missing factor in the multiplication problem (4 x ? = $32) or skip counting by 4's to $32. [NOTE: This happens elsewhere in the unit.]

3.OA.4 2Students may not be technically using a written equation but will be finding the unknown factor for #3 and repeat that thinking for #4.

3.OA.5 2While students are not asked to express an understanding of the properties of multiplication, they will be using those properties in their process for all of the problems in the performance task.

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EQuIP Student Work Protocol Grade 3 Math: Cookie DoughStep 3 (cont.): Alignment Ratings of 3 or 2

Targeted CCSS Standards/ Standards

for Mathematical Practice


MP.1 3

This performance task requires that students make sense of one-and two-step word problems. In solving #4 they will have to make sense of a problem that may require inverse multiplication (or division/repeated subtraction) with a remainder and must reason out a good solution and then "explain how they figured it out."

MP.2 2

In this performance task students must use abstract reasoning to solve the problems. They will decontextualize the verbal description in order to manipulate the numbers and then re-contextualize when presenting their solution and reasoning. If the units were not provided with each answer line, but were instead expected as part of the answer, this rating would be a 3.

MP.3 2

Students are asked to "show how you figured it out" for three of the four problems in this performance task. This meets the most critical part of the standard: construct viable arguments. However they are not asked to critique the reasoning of others. [NOTE: This is addressed elsewhere in the unit.]

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Practice



3.OA.3 2




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Practice



3.OA.3 2




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Practice



3.OA.3 2




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Practice



3.OA.3 2




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MP.1 3

This performance task requires that students make sense of one-and two-step word problems. In solving #4 they will have to make sense of a problem that may require repeated addition or inverse multiplication (or division/repeated subtraction) with a remainder and must reason out a good solution and then "explain how they figured it out."

MP.2 2

In this performance task students must use abstract reasoning to solve the problems. They decontextualize the verbal description in order to manipulate the numbers and then re-contextualize when presenting their solution and reasoning. If the units were not provided with each answer line, but were instead expected as part of the answer, this rating would be a 3.

MP.3 2


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MP.1 3


MP.2 2

In this performance task students must use abstract reasoning to solve the problems. They decontextualize the verbal description in order to manipulate the numbers and then re-contextualize when presenting their solution and reasoning. If the units were not provided with each answer line, but were instead expected as part of the answer, this rating might be a 3.

MP.3 2


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MP.1 3


MP.2 2

In this performance task students must use abstract reasoning to solve the problems. They decontextualize the verbal description in order to manipulate the numbers and then re-contextualize when presenting their solution and reasoning. If the units were not provided with each answer line, but were instead expected as part of the answer, this rating might be a 3.

MP.3 2


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CCSS Rating Alignment Rationale

3.OA.2 1

Interpretation of quotients is the most critical aspect of the standard, which is not specifically required in the performance task. However, there is a possibility that students would use this type of thinking for #3 and/or #4 and that they might include an interpretation of quotients in their work/explanation. [NOTE: This is addressed further elsewhere in the unit.]

3.OA.6 1While there is emphasis in other parts of the unit on understanding division, this task does not specifically require expression of that understanding. [NOTE: This is addressed further elsewhere in the unit.]

3.OA.7 0Fluency is not addressed in this performance task or unit. While fluency with whole number operations is a goal of this grade, it is not expected for this task. There are no substantial or specific fluency exercises included in this unit.

3.OA.8 1

The performance task requires solving 2-step word problems but does not specifically require that students use all four operations (only multiplication and addition) and does not ask students to use equations with variable symbols. Students are asked to "show" or "explain how you figured it out" but not to assess the reasonableness of their results or to use estimation strategies. [NOTE: Understanding and using all four operations are addressed further elsewhere in the unit.]

3.OA.9 1

While it is possible that students who use a skip counting strategy may be using arithmetic patterns, the most critical aspects of this standards are not met in the performance task. Students are not asked to use patterns or to explain them using the properties of operations. [NOTE: This is addressed further elsewhere in the unit.]

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MP.4 0

While it is possible that students might chose to create a model to solve the problems in this performance task, it is not specifically required. There is no specific request in the task to create/write an equation or to model the operations geometrically (with pictures or diagrams). [NOTE: This is addressed elsewhere in the unit.]

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Step 3 (cont.): Notes & ObservationsNotes & ObservationsGaps in Alignment:There are gaps in alignment with several of the standards targeted for the overall unit. Those that align (rating of 3 or 2) with the performance task are 3.OA.1, 3, 4, and 5; and MP.1, MP.2, and MP.3

Gaps in alignment (rating of 1 or 0) that are addressed elsewhere in the unit include 3.OA.2, 6, 8, and 9, and MP.4.

Only 3.OA.7 is not fully addressed in the task or in the unit.

RE: 3.OA.7 - Fluency is a goal of this grade but is not addressed specifically in the activities of the unit or this performance task. This may be addressed in other units.


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Step 3 (cont.): Notes & ObservationsNotes & ObservationsGaps in Alignment:There are gaps in alignment with several of the standards targeted for the overall unit. Those that align (rating of 3 or 2) with the performance task are 3.OA.1, 3, 4, and 5; and MP.1, MP.2, and MP.3

Gaps in alignment (rating of 1 or 0) that are addressed elsewhere in the unit include 3.OA.2, 6, 8, and 9, and MP.4.

Only 3.OA.7 is not fully addressed in the task or in the unit.

RE: 3.OA.7 - Fluency is a goal of this grade but is not addressed specifically in the activities of the unit or this performance task. This may be addressed in other units.

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Step 4: Diagnose Student Work

Guiding Questions:— What does the collection of student work communicate about

the kind and level of skills and knowledge students have learned and still need to learn?

— What are the most frequent and fundamental successes students appear to be having with the assignment?

— What are the most frequent and fundamental problems students appear to be having with the assignment?

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Step 4: Notes & Observations



Notes and Observations:There is a full range of response levels in the student work associated with this task.Level 4 students: Student responses meet the demands of the entire task with few errors and also include explanations that are clear and complete.Level 3 students: For most of the task the students’ response shows the main elements of the performance demands of the task and is an organized attack on the core of the problem. In some cases there were errors in calculations or in interpretation of the work. Work shown may be limited but appears to show mathematical understanding.Level 2 students: Students show partial understanding of the problem but either misread or misinterpreted some parts of the problem. In some cases the student was unable to work backward – or understand the inverse relationship between multiplication and division. In part 4 students at this level misinterpreted the question.Level 1 students: Students at this level have minimal success. In some cases even when questions are answered correctly, the work shows misunderstandings and flawed reasoning. Students appear to be stuck at the conceptual understanding of multiplication.

Step 4 – Example Responses

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Step 5: Improving the Assignment & Lesson

Guiding Questions:- How does the assignment fit into the overall lesson or unit plan?

- What does the review of student work suggest are the strengths and weaknesses of the assignment and related instructional materials? Use the criteria in the EQuIP quality review rubric to guide this feedback.

- What should be kept, deleted, and/or added to the assignment or lesson/unit for tighter alignment with the depth of the targeted standards?

- Do the rubrics/scoring guides accurately communicate CCSS expectations for proficiency? If not, how might they be improved?

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Step 5: Improving the Assignment & Lesson

Tips and Reminders:- Avoid trying to force-fit an assignment to a standard. If it clearly

doesn’t fit any standard, overhaul the assignment so that it is a good fit.

- Pay attention to strengthening and clarifying the directions to students, in addition to the dimensions of the assignment itself.

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EQuIP Student Work ProtocolGrade 3 Math: Cookie Dough

Step 5: Notes & ObservationsNotes & Observations

Suggestions to strengthen the lesson/unit:

Suggestions to strengthen the assignment:

Suggestions to strengthen the scoring rubric:


Notes and Observations:At all levels student performance would be improved by making complete explanations and justifications. Better and more detailed prompts could alleviate that problem somewhat.

Interpretation of quotients, the most critical aspect of 3.OA.2, is not specifically required in the performance task. However, there is a possibility that students would use this type of thinking for parts 3 and 4. Revising the prompt to specifically require using a quotient would provide alignment with this standard.

In this performance task students must use abstract reasoning to solve the problems (MP.2). They decontextualize the verbal description in order to manipulate the numbers and then re-contextualize when presenting their solution and reasoning. If the units were not provided with each answer line, but were instead expected as part of the answer, alignment to MP.2 would be improved.

As it stands, this task does not require modeling (MP.4). If the directions, “Write an equation to represent the problem” were added to “Show how you figured it out” on parts 2, 3, and 4, alignment to MP.4 would be improved.

Step 5 – Example Response

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EQuIP Student Work ProtocolGrade 3 Math: Cookie Dough

http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWork/default.htm

The full annotated version of these student work samples (and several other full units) are available at:






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Achievewww.achieve.org1400 16th Street, NW / Suite 510 Washington, DC 20036

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EQuIP Student Work Protocol Grade 3 Math: Cookie DoughStep 3: Compare the alignment of the content and performance(s) of the assignment to the targeted standards for the assignment or lesson/unit.The relevant CCSS:• 3.OA.1 Interpret products of whole numbers, e.g., interpret 5 x 7 as the

total number of objects in 5 groups of 7 objects each. • 3.OA.3 Use multiplication and division within 100 to solve word problems

in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

• 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

• 3.OA.5 Apply properties of operations as strategies to multiply and divide.

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EQuIP Student Work Protocol Grade 3 Math: Cookie DoughStep 3 (cont.): Compare the alignment of the content and performance(s) of the assignment to the targeted standards for the assignment or lesson/unit.

The relevant CCSS Math Practices:• MP.1 Make sense of problems and persevere in solving them.• MP.2 Reason abstractly and quantitatively.• MP.3 Construct viable arguments and critique the reasoning of

others.

equip mathematics student work protocol washington, dc may 19, 2014

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