equip rubric & quality review training session: mathematics

EQuIP Rubric & Quality Review Training Session: Mathematics

2

Use the EQuIP quality review process to determine the quality and alignment of lessons and units to the Common Core State Standards (CCSS) in mathematics

During this session, reviewers will:• Develop their abilities to use EQuIP criteria to provide observations about CCSS-

aligned instructional materials and make suggestions for improvement• Develop a common understanding of the EQuIP quality review process• Develop a common understanding of the rating scale and descriptors for the four

rubric dimensions and the rating categories and descriptors for overall ratings• Develop their abilities to use EQuIP criteria, rating scales and rating descriptors to

accurately rate instructional materials

Session Goals

3

1. CCSS: Before beginning a review, all members of a review team are familiar with the CCSS.

2. Inquiry: Review processes emphasize inquiry rather than advocacy and are organized in steps around a set of guiding questions.

3. Respect & Commitment: Each member of a review team is respected as a valued colleague and contributor who makes a commitment to the EQuIP process.

4. Criteria & Evidence: All observations, judgments, discussions and recommendations are criterion and evidence based.

5. Constructive: Lessons/units to be reviewed are seen as “works in progress.” Reviewers are respectful of contributors’ work and make constructive observations and suggestions based on evidence from the work.

6. Individual to Collective: Each member of a review team independently records his/her observations prior to discussion. Discussions focus on understanding all reviewers’ interpretations of the criteria and the evidence they have found.

7. Understanding & Agreement: The goal of the process is to compare and eventually calibrate judgments to move toward agreement about quality with respect to the CCSS.

EQuIP Quality Review: Principles & Agreements

4

EQuIP Quality Review ProcessThe EQuIP quality review process is a collegial process that centers on the use of criteria-based rubrics for English language arts (ELA)/literacy and mathematics. The criteria are organized into four dimensions:

The Four Dimensions1. Alignment to the depth of the CCSS; 2. Key shifts in the CCSS;3. Instructional supports; and4. Assessment.

As educators examine instructional materials against the criteria in each dimension, they are able to use common standards for quality and generate evidence-based commentary and ratings on the quality and alignment of materials.

EQuIP Quality Review: Process & Dimensions

5

Using the Electronic Quality Review Rubric PDF Form

6

Using the Quality Review Rubric PDF Form

For each dimension:

• Select the checkbox for each criterion for which clear and substantial evidence is found.

• Make observations and suggestions related to criteria and evidence.

• Determine a rating for each dimension based on checked criteria and observations.

For Dimension I:• Use alignment rating to

determine whether to proceed with review.

Giving Feedback

Writing effective feedback is vital to the EQuIP Quality Review Process. Below are the four qualities of effective feedback. • Criteria-based: Written comments are based on the criteria used for review in each

dimension. No extraneous or personal comments are included. • Evidence Cited: Written comments suggest that the reviewer looked for evidence in the

lesson or unit that address each criterion of a given dimension. Examples are provided that cite where and how the criteria are met or not met.

• Improvement Suggested: When improvements are identified to meet criteria or strengthen the lesson or unit, specific information is provided about how and where such improvement should be added to the material.

• Clarity Provided: Written comment are constructed in a manner keeping with basic grammar, spelling, sentence structure and conventions.

Example 1: Mathematics

This unit clearly targets three CCSS, which are noted in the overview. The overview also indicates which Standards for Mathematical Practice are central to the lesson. The activities throughout the unit present a balance of mathematical procedures and deeper conceptual understanding of the standards. The activities reinforce the standards and are well-connected to the content. I think the activities might be challenging with a large class with classroom management issues.

Is this feedback criteria-based?Was evidence cited?Was there an improvement suggested?Is clarity provided?

Example 1: Feedback

Criteria-based: YesEvidence Cited: PartialImprovement suggested: NoClarity Provided: Yes• This feedback could be more effective. The reviewer mentions three standards and cites

evidence: “which are noted in the overview.”• The reviewer states, “ The overview also indicates which Standards for Mathematical

Practice are central to the lesson.” The reviewer does not provided any evidence to support the assertion.

• The reviewer comments, “the activities through the unit present a balance of mathematical procedures and deeper conceptual understanding of the standards,” but does not cite specific details about why or how they are grade appropriate and well connected to the content being addressed.

• No improvements are suggested. The reviewer does insert a personal opinion when saying, “ I think the activities might be challenging with a large class with classroom management issues. Personal opinions and comments unrelated to the criteria should be avoided when providing feedback; criteria-based feedback is more effective.

• The written comments are constructed in a manner in keeping with basic grammar, spelling, sentence structure and conventions.

Example 2: Mathematics

The lesson targets two CCSS, which are highlighted in the lesson cover page. Although the lesson does integrate Standards for Mathematical Practice, including appropriate tools strategically, given the CCSS that are targets, modeling may be a better fit. The lesson does present a balance of mathematical procedures and deep content knowledge.

Is this feedback criteria-based?Was evidence cited?Was there an improvement suggested?Is clarity provided?

Example 2: Feedback

Criteria-based: YesEvidence Cited: PartialImprovement suggested: PartialClarity Provided: No• This feedback could be more effective. • Some specific evidence is cited to support the claims that criteria are present in the

lesson.• There is an improvement suggested with, “modeling may be a better fit,” however, it

would be beneficial to explain why.• The written comments are not constructed in a manner in keeping with basic grammar,

sentence structure and conventions.

12

Quality Review Steps

Step 1. Review Materials • Record the grade and title of the lesson/unit on the Quality Review Rubric PDF• Scan to see what the lesson/unit contains and how it is organized • Read key materials related to instruction, assessment and teacher guidance• Study and work the tasks that serve as the centerpiece for the lesson/unit, analyzing the

content and mathematical practices the tasks require

Step 2. Apply Criteria in Dimension I: Alignment to the Depth of the CCSS• Identify the grade-level CCSS that the lesson/unit targets• Closely examine the materials through the “lens” of each criterion• Indicate each criterion for which clear and substantial evidence is found • Record input on specific improvements needed to meet criteria or strengthen alignment• Compare observations and suggestions for improvement

13

Quality Review Steps

Step 3. Apply Criteria in Dimensions II–IV • Examine the lesson/unit through the “lens” of each criterion • Indicate each criterion met and record observations and feedbackWhen working in a group, individuals may choose to compare observations and suggestions for improvement after each dimension or wait until each person has rated and recorded all input for Dimensions II–IV.

Step 4. Apply an Overall Rating and Provide Summary Comments • Individually review comments for Dimensions I–IV, adding/clarifying comments as

needed • Individually write summary comments on the Quality Review Rubric PDFWhen working in a group, individuals should record summary comments prior to conversation.

Step 5. Compare Overall Ratings and Determine Next Steps • Note the evidence cited to arrive at summary comments and similarities and differences

among reviewers. Recommend next steps for the lesson/unit and provide recommendations for improvement to developers/teachers.

14

EXAMPLE:Common Lesson for Review — Mathematics

Grade 7 — Draft Unit Plan 7.NS.1-3: Operations with Rational Numbers

This lesson is part of a unit plan titled “Operations with Rational Numbers.” The state that developed this unit plan uses the CCSS and the EQuIP rubrics to guide development of instructional materials and has charged its developers with creating overall conceptual unit plans, based on the CCSS domains, with one standard-based lesson and lesson seeds, based on the cluster. Teachers are able to use these as a model in their planning or to further develop the unit plan.

15

EXAMPLE:Step 1. Review Materials• Record the grade and title of the lesson/unit on the Quality Review Rubric PDF

− Grade 7, “Draft Unit Plan – 7.NS.1-3: Operations with Rational Numbers”• Read key materials related to instruction, assessment and teacher guidance

− Unit overview narratives (pp. 1–3)− Unit alignment (pp. 4–10)− Common misconceptions (p. 11)− Vocabulary (pp. 13–15)− Lesson plan and materials – 7.NS.1 (pp. 16–34)– Lesson seeds – 7.NS.1b, 7.NS.1d (pp. 35– 40)

• Activities: − Four Corners− Traveling Around Maryland Gallery Walk− Rational Flow Chart− The Zero Circle and Block Party (Lesson Seeds)

16

Criteria for Dimension I: Alignment to the Depth of the CCSS

The lesson/unit aligns with the letter and spirit of the CCSS: 1. Targets a set of grade-level CCSS mathematics standard(s) to the full depth of the

standards for teaching and learning. 2. Standards for Mathematical Practice that are central to the lesson are identified, handled

in a grade-appropriate way and well connected to the content being addressed.3. Presents a balance of mathematical procedures and deeper conceptual understanding

inherent in the CCSS.

17

Dimension Rating and Descriptive Scales To Synthesize Judgment

Rating Scale for Dimensions I–IV: 3: Meets most to all of the criteria in the dimension 2: Meets many of the criteria in the dimension 1: Meets some of the criteria in the dimension 0: Does not meet the criteria in the dimension

Descriptors for Dimensions I–IV: 3: Exemplifies CCSS Quality — meets the standard described by criteria in the dimension, as explained in criterion-based observations 2: Approaching CCSS Quality — meets many criteria but will benefit from revision in others, as suggested in criterion-based observations 1: Developing toward CCSS Quality — needs significant revision, as suggested in criterion-based observations 0: Not representing CCSS Quality — does not address the criteria in the dimension

18

EXAMPLE:Step 2. Apply Criteria in Dimension I: Alignment


standards for teaching and learning. 2. Standards for Mathematical Practice that are central to the lesson are identified,

handled in a grade-appropriate way and well connected to the content being addressed. 3. Presents a balance of mathematical procedures and deeper conceptual understanding


19


Observations/Feedback and RatingThe lesson clearly targets 7.NS.1a, b and d as the content standard for the lesson. The lesson does not list 7.NS.1c, although the lesson includes discussion of additive inverse. Developers should re-evaluate the omission of 7.NS.1c. It is assumed that further development of lessons beyond the two lesson seeds provided will address the requirements of 7.NS.2 and 7.NS.3.

The lesson plan identifies all eight of the Standards for Mathematical Practice as being addressed in the lesson/unit. And although references to the Practices are listed throughout the lesson/unit, it is not clear how central practices connect to specific activities and tasks. Those that are most central should be identified and their connection clearly defined. Those central Practices should serve as a focal point for the lesson and those that are not central should either be eliminated or noted as serving in a supporting role.

The balance between mathematical procedures and conceptual understanding is strong in the unit. As refinements are made, and as the Lesson Seeds are more fully developed, care needs to be taken to ensure that this balance is maintained. Rating: 2 (missing clear connections between the Practices and the activities)Approaching CCSS Quality — meets many criteria but will benefit from revisionin others, as suggested in criterion-based observations

20


Compare Criterion-Based Checks, Observations and Feedback• What is the pattern within our team in terms of the criteria we have checked?• Do our observations and feedback reference the criteria and evidence (or lack of

evidence) in the instructional materials?• Does our feedback include suggestions for improvement(s)?

21

Criteria for Dimension II: Key Shifts in the CCSS

The lesson/unit addresses key shifts in the CCSS:

1. Focus: Lessons and units targeting the major work of the grade provide an especially in-depth treatment, with especially high expectations. Lessons and units targeting supporting clusters have visible connection to the major work of the grade and are sufficiently brief. Lessons and units do not hold students responsible for material from later grades.

2. Coherence: The content develops through reasoning about the new concepts on the basis of previous understandings and provides opportunities for students to transfer knowledge and skills within and across domains and learning progressions.

22

Criteria for Dimension II: Key Shifts in the CCSS

3. Rigor: Requires students to engage with and demonstrate challenging mathematics with appropriate balance among the following:

o Application: Provides opportunities for students to independently apply mathematical concepts in real-world situations and problem solve with persistence, choosing and applying an appropriate model or strategy to new situations.

o Conceptual Understanding: Provides opportunities for students to demonstrate conceptual understanding through challenging problems, questions, and writing and speaking about their understanding.

o Procedural Skill and Fluency: Expects, supports and provides guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.

23




24

EXAMPLE:Step 3. Apply Criteria in Dimension II: Key Shifts in the CCSS

The lesson/unit addresses reflects evidence of key shifts that are reflected in the CCSS:



EXAMPLE:Step 3. Apply Criteria in Dimension II: Key Shifts in the CCSS 3. Rigor: Requires students to engage with and demonstrate challenging mathematics

with appropriate balance among the following:– Application: Provides opportunities for students to independently apply

mathematical concepts in real-world situations and problem solve with persistence, choosing and applying an appropriate model or strategy to new situations.

– Conceptual Understanding: Develops students’ conceptual understanding through tasks, brief problems, questions, multiple representations and opportunities for students to write and speak about their understanding.

– Procedural Skill and Fluency: Expects, supports and provides guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.

26


Observations/Feedback and RatingThere is strong focus on 7.NS.1 in the unit plan, including the model lesson plan and lesson seeds—particularly on 7.NS.1a, 7.NS.1b, and 7.NS.1d. The concepts and level of rigor prioritized in the standards are evident in the lessons/lesson seeds. 7.NS.1c is not clearly evident, and may be addressed in future lesson seeds.

There are clear connections made to prior learning in the section on Vertical Alignment. There are other references among the UDL Components, the Overview and Teacher Notes. In the Enduring Understandings there is a hint at how the concepts of this unit will be carried forward. However, more information might be provided for the teacher in how the real number system will evolve from the learning in this unit.

There is evidence of opportunity for application of some skills with the activities involving real-world context (card sort, gallery walk). However, many activities provide the opportunity for students to work in small groups or with partners, so there are few clear opportunities for independent application of concepts and skills to real-world contexts.

27


Observations/Feedback and Rating cont.The guiding questions and other question prompts provide tools for teachers to probe for understanding. It is not clear, however, if all students will be expected to respond to questions verbally or in writing or if questions will be used solely to guide student discussion. Students are not presented with contextual problems that require deeper thinking and persistence and that can provide an indication of deeper conceptual understanding.

The unit emphasizes procedural skill and there are specific references in the unit to the development of fluency with operations with rational numbers as a goal of grade 7. However, it is not clear how much calculator usage is allowed, causing some concern as to how quickly and accurately students might perform calculations and procedures without this tool. Rating: 2 (missing rigorous application problems and opportunities for deep conceptual understanding)Approaching CCSS Quality — meets many criteria but will benefit from revision in others, as suggested in criterion-based observations

28


Compare Criterion-Based Checks, Observations/Feedback and Rating

• What is the pattern within our team in terms of the criteria we have checked?

• Do our observations and feedback reference the criteria and evidence (or lack of evidence) in the instructional materials?

• Do our ratings correspond to the rating and descriptors on the rubric?

29

Criteria for Dimension III: Instructional Supports

The lesson/unit is responsive to varied student learning needs:1. Includes clear and sufficient guidance to support teaching and learning of the targeted

standards, including, when appropriate, the use of technology and media.2. Uses and encourages precise and accurate mathematics, academic language,

terminology, and concrete or abstract representations (e.g., pictures, symbols, expressions, equations, graphics, models) in the discipline.

3. Engages students in productive struggle through relevant, thought-provoking questions, problems and tasks that stimulate interest and elicit mathematical thinking.

4. Addresses instructional expectations and is easy to understand and use.5. Provides appropriate level and type of scaffolding, differentiation, intervention and

support for a broad range of learners.— Supports diverse cultural and linguistic backgrounds, interests and styles.— Provides extra supports for students working below grade level.— Provides extensions for students with high interest or working above grade level.

30

Criteria for Dimension III: Instructional SupportsA unit or longer lesson should: 6. Recommend and facilitate a mix of instructional approaches for a variety of learners

such as using multiple representations (e.g., including models, using a range of questions, checking for understanding, flexible grouping, pair-share).

7. Gradually remove supports, requiring students to demonstrate their mathematical understanding independently.

8. Demonstrate an effective sequence and a progression of learning where the concepts or skills advance and deepen over time.

9. Expect, support and provide guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.

31




32

EXAMPLE: Step 3. Apply Criteria in Dimension III: Instructional Supports

The lesson/unit is responsive to varied student learning needs: 1. Includes clear and sufficient guidance to support teaching and learning of the targeted

standards, including, when appropriate, the use of technology and media. 2. Uses and encourages precise and accurate mathematics, academic language,



4. Addresses instructional expectations and is easy to understand and use. 5. Provides appropriate level and type of scaffolding, differentiation, intervention and

support for a broad range of learners.— Supports diverse cultural and linguistic backgrounds, interests and styles.— Provides extra supports for students working below grade level.— Provides extensions for students with high interest or working above grade level.

33

EXAMPLE: Step 3. Apply Criteria in Dimension III: Instructional Supports

Observations/Feedback and RatingThe guiding questions posed in the unit are thought provoking and are likely to stimulate student interest and some mathematical thinking. However the level of rigor required does not indicate that they are likely to engage students in a productive struggle. The Possible Student Outcomes defined in the Draft Unit Plan help clearly define the instructional expectations. The varied questions and activities offered in the Model Lesson Plan provide teachers with a range of ways to address instructional expectations. The materials are user-friendly and generally easy to understand. There is not enough support for students working below grade level in the unit or those with language difficulties. The concepts presented in this unit might prove to be challenging for English-language learners, who would benefit from the use of manipulatives and visual supports to demonstrate their mathematical understanding independently. There are places in the unit where activities are listed for intervention (a video), extension (writing a rap song), and for ELL (using the Frayer method of writing definitions). It is not clear how these activities would support those students needing more support from this lesson. Rating: 1 (missing strategies for engaging students in productive struggle, support for diverse learners, and gradual removal of support with an emphasis on independent understanding)Developing toward CCSS Quality — needs significant revision, as suggested in criterion-based observations

34

EXAMPLE:Step 3. Apply Criteria in Dimension III: Instructional Supports

Compare Criterion-Based Checks, Observations/Feedback and Rating

• What is the pattern within our team in terms of the criteria we have checked?


• Do our ratings correspond to the rating and descriptors on the rubric?

35

Criteria for Dimension IV: Assessment

The lesson/unit regularly assesses whether students are mastering standards-based content and skills: 1. Is designed to elicit direct, observable evidence of the degree to which a student can

independently demonstrate the targeted CCSS. 2. Assesses student proficiency using methods that are accessible and unbiased, including

the use of grade-level language in student prompts.3. Includes aligned rubrics, answer keys and scoring guidelines that provide sufficient

guidance for interpreting student performance.

A unit or longer lesson should: 4. Uses varied modes of curriculum-embedded assessments that may include pre-,

formative, summative and self-assessment measures.

36

The Dimension Rating Scale and Descriptors



37

EXAMPLE: Step 3. Apply Criteria in Dimension IV: Assessment

The lesson/unit regularly assesses whether students are mastering standards-based content and skills: 1. Elicits direct, observable evidence of the degree to which a student can independently

demonstrate the major targeted grade level CCSS standards with appropriately complex text(s).

2. Assesses student proficiency using methods that are unbiased and accessible to all students.

3. Includes aligned rubrics or assessment guidelines that provide sufficient guidance for interpreting student performance.

A unit or longer lesson should:4. Use varied modes of curriculum-embedded assessments that may include pre-,


38

EXAMPLE: Step 3. Apply Criteria in Dimension IV: Assessment

Observations/Feedback and RatingThis lesson includes a readiness assessment but no formative or end-of-lesson assessment to determine the degree to which students can independently demonstrate the targeted CCSS. An observation checklist for the teacher to use when observing students working collaboratively with others would be helpful, as would adding opportunities for independent demonstration of understanding and skill.

Since there are no actual assessment tasks, there is no evidence for this criterion.

Answer keys are provided for some, but not all, of the student activities. This feature will be very helpful for teachers but reviewers suggested that in some cases an answer key could be more fully developed.

Rating: 0 (missing a rigorous summative assessment that is supported by other assessment opportunities throughout the lesson/unit)

Developing toward CCSS Quality — needs significant revision, as suggested in criterion-based observations

39

EXAMPLE:Step 3. Apply Criteria in Dimension IV: Assessment

Compare Criterion-Based Checks, Observations and Feedback• What is the pattern within our team in terms of the criteria we have checked?


• Does our feedback include suggested improvement(s)?

40

Overall Rating and Summary Comments

Overall Rating for the Lesson/Unit:

E: Exemplar – Aligned and meets most to all of the criteria in dimensions II, III, IV (total 11 – 12)

E/I: Exemplar if Improved – Aligned and needs some improvement in one or more dimensions (total 8 – 10)

R: Revision Needed – Aligned partially and needs significant revision in one or more dimensions (total 3 – 7)

N: Not Ready to Review – Not aligned and does not meet criteria (total 0 – 2)

41

EXAMPLE:Step 4. Provide Summary Comments

4141

While this lesson plan needs improvement, it has great potential. The lesson plan offers numerous and varied opportunities for the skillful teacher to engage students in content, but the less-skilled teacher will need more guidance. All teachers would benefit from an instructional resource that demonstrates stronger alignment (including clear identification of the Standards for Mathematics Practice that are most central to the activities) and the addition of assessments that will provide clear evidence as to whether individual students grasp the knowledge, skills and conceptual understandings that are addressed in the unit. Supports for students with disabilities and English language learners will strengthen the lesson.

R (5 points)

42

EXAMPLE:Step 5. Compare Summary Comments and Determine Next Steps

Guiding questions to synthesize criterion-based observations and suggestions: • How do the observations and suggestions for improvement compare?• Are the observations and suggestions criterion-based?• Does this example serve as a model of CCSS instruction? What are its strengths? Areas for

improvement?

43

Reflection on Session Goals

• Did we use the EQuIP criteria to frame and explain evaluation of evidence found in instructional materials?

• Did we develop a common understanding of EQuIP criteria among reviewers?• Are there any criteria or evidence about which reviewers disagree?• Did we develop reviewers’ abilities to use EQuIP criteria, rating scales/categorizations and

rating descriptors to accurately rate instructional materials?• To what degree were there differences among reviewers when checking criteria,

assigning dimension ratings and assigning overall ratings? What do you think caused these differences?

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

Appendix:Slides for reviewing a unit

46

How To Use

The slides in this PowerPoint are currently set up to review the lesson plan titled 7.NS.1 . To prepare for a review of the unit “Operations with Rational Numbers,” use the following slides that reference the lesson in the place of previous slides that reference the unit.

47

EXAMPLE: Common Unit for Review — Mathematics

Grade 7 — “Operations with Rational Numbers”

This state uses the CCSS and the EQuIP rubrics to develop instructional materials and has charged its developers with creating overall conceptual unit plans, based on the CCSS domains, with one standard-based lesson and lesson seeds, based on the cluster. Teachers are expected to use these as a model in their planning and/or to continue to develop the unit plan. These instructional materials include a unit plan outline for 7.NS.1–3, a lesson plan for 7.NS.1, and lesson seeds for 7.NS.1b and 7.NS.1d. The lesson seeds are components of the unit plan and should not be reviewed as lessons.

Note: This unit was submitted to EQuIP for review in October 2012. The unit has been revised by the developers in response to feedback from the EQuIP quality review process. Do not distribute the version of this unit used in EQuIP Trainings. The revised lesson/unit can be found here.

http://www.achieve.org/files/Common%20Math%20Lesson%20MD_Unit%20Plan_ALL_7%20NS%201-3%20Operations%20with%20Rational%20Nu_1.docx

48

EXAMPLE:Step 1. Review Materials• Record the grade and title of the lesson/unit on the Quality Review Rubric PDF

– Grade 7, “Operations with Rational Numbers”• Scan to see what the lesson/unit contains and how it is organized

– Unit overview narratives (pp. 1–3)– Unit alignment (pp. 4–10)– Common misconceptions (p. 11)– Vocabulary (pp. 13–15)– Lesson Plan (pp. 16–34)– Lesson Seeds (pp. 35–40)

• Tasks: – Four Corners– Traveling Around Maryland Gallery Walk– Rational Flow Chart– The Zero Circle– The Block Party

49



standards for teaching and learning. 2. Standards for Mathematical Practice that are central to the lesson are identified,

handled in a grade-appropriate way and well connected to the content being addressed. 3. Presents a balance of mathematical procedures and deeper conceptual understanding


50


Observations/Feedback and Rating

The unit clearly targets a reasonable set of content standards and suggestions for supporting standards. However, there is some inconsistency between the understandings outlined in the CCSS and in the description in the “Enduring Understandings” section, making the unit goals seem less clearly aligned with the targeted standards. This could be cleared up by revising the “Enduring Understandings” to be more consistent with the goals of the standards.

The unit plan identifies all eight of the Standards for Mathematical Practice as being addressed. Those that are most central should be identified and serve as a focal point for the unit. Those that are not central should either be eliminated or noted as serving in a supporting role. In addition, references should be made throughout the unit as to how central practices relate to specific activities and tasksRating: 2Approaching CCSS Quality — meets many criteria but will benefit from revision in others, as suggested in criterion-based observations.

51


The lesson/unit addresses reflects evidence of key shifts that are reflected in the CCSS:



52


3. Rigor: Requires students to engage with and demonstrate challenging mathematics with appropriate balance among the following:

— Application: Provides opportunities for students to independently apply mathematical concepts in real-world situations and problem solve with persistence, choosing and applying an appropriate model or strategy to new situations.

— Conceptual Understanding: Develops students’ conceptual understanding through tasks, brief problems, questions, multiple representations and opportunities for students to write and speak about their understanding.

— Procedural Skill and Fluency: Expects, supports and provides guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.

53



The unit is exemplary in its focus on a reasonable portion of the major work of the grade. There is evidence of opportunity for application of some skills with the activities involving real-world context (card sort, gallery walk). However, many activities provide the opportunity for students to work in small groups or with partners, so there are few clear opportunities for independent application of concepts and skills to real-world contexts. The guiding questions and other question prompts provide tools for teachers to probe for understanding. It is not clear, however, if all students will be expected to respond to questions verbally or in writing or if questions will be used solely to guide student discussion.There are opportunities for students to display procedural skill and fluency, but with the calculator usage allowed, it is not clear how quickly and accurately students might otherwise perform such calculations and procedures.Rating: 2Approaching CCSS Quality — meets many criteria but will benefit from revision in others, as suggested in criterion-based observations

54


The lesson/unit is responsive to varied student learning needs: 1. Includes clear and sufficient guidance to support teaching and learning of the targeted

standards, including, when appropriate, the use of technology and media. 2. Uses and encourages precise and accurate mathematics, academic language,




support for a broad range of learners.— Supports diverse cultural and linguistic backgrounds, interests and styles. Provides extra supports for students working below grade level.— Provides extensions for students with high interest or working above grade level.

55



support for a broad range of learners 6. Supports diverse cultural and linguistic backgrounds, interests and styles 7. Provides extra supports for students working below grade level 8. Provides extensions for students with high interest or working above grade level

56


A unit or longer lesson should: 6. Recommend and facilitate a mix of instructional approaches for a variety of learners

such as using multiple representations (e.g., including models, using a range of questions, checking for understanding, flexible grouping, pair-share).

7. Gradually remove supports, requiring students to demonstrate their mathematical understanding independently.

8. Demonstrate an effective sequence and a progression of learning in which the concepts or skills advance and deepen over time.

9. Expect, support and provide guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.

57



The current level of detail in this unit plan does not provide enough support, particularly for new or struggling teachers. The inclusion of Universal Design for Learning will help teachers use strategies to support a range of learners, although the unit would benefit from specific strategies to support English language learners, students who have disabilities and students working above grade level. Online instructional resources and a variety of instructional approaches are identified within the lesson.While the unit includes a Vocabulary/Terminology/Concepts section, the unit itself does not clearly indicate what mathematical or academic language the lesson will help students acquire, develop and/or use. While there is some indication that precise language is preferred (questions in the gallery walk), attention to this is inconsistent. The word problems provide opportunities for students to engage in productive struggle with peers. The real-life motivation activity (4 Corners) is another example to engage with peers in productive struggle. Consider adding opportunities for students to create representations independently.Rating: 2Approaching CCSS Quality — meets many criteria but will benefit from revision in others, as suggested in criterion-based observations

58


The lesson/unit regularly assesses whether students are mastering standards-based content and skills: 1. Is designed to elicit direct, observable evidence of the degree to which a student can

independently demonstrate the targeted CCSS. 2. Assesses student proficiency using methods that are accessible and unbiased, including

the use of grade-level language in student prompts. 3. Includes aligned rubrics, answer keys and scoring guidelines that provide sufficient

guidance for interpreting student performance.

A unit or longer lesson should: 4. Use varied modes of curriculum-embedded assessments that may include pre-,


59



Other than a readiness assessment, this unit includes few other formal assessments. The exit ticket, which asks students to independently describe an authentic situation not addressed in class that exemplifies the concept of additive inverse, appears to be the only other assessment activity targeting individual students. Opportunities for informal assessment are abundant in the unit, including group discussion; a “Gallery Walk”; and think, pair, share activities. An observation checklist for the teacher to use when observing students working collaboratively with others would be helpful. The unit plan indicates assessments will be added at a later time. Since there aren’t actual assessment tasks or prompts, there is no evidence for this criterion. Rating: 0Not representing CCSS Quality — does not address the criteria in the dimension

60

EXAMPLE: Step 4 – Apply an Overall Rating and Provide Summary Comments

While this unit plan, and its accompanying components, needs improvement, it has great potential. The unit plan, lesson plan and lesson seeds offer numerous and varied opportunities for the skillful teacher to engage students in content, but the less-skilled teacher will need more guidance. All teachers would benefit from an instructional resource that demonstrates stronger alignment (including clear identification of the Standards for Mathematics Practice that are most central to the activities) and the addition of assessments that will provide clear evidence as to whether individual students grasp the knowledge, skills and conceptual understandings that are addressed in the unit. The introduction to the unit plan is complicated but contains a wealth of information. It could overwhelm even experienced teachers. Perhaps an outline of the progression of the unit would be helpful (as a table of contents). It is difficult to see the progression of understanding without a sequence of lessons outlined.

R (6 points)

equip rubric & quality review training session: mathematics

Documents

quality review processdevelop

review team

review processes

criteria evidence

use of criteria

checked criteria

evidencebased commentary

use alignment