EQuIP Rubric & Quality Review Mathematics Training Module: Grades 9-12 1.

1

EQuIP Rubric & Quality Review Mathematics Training Module:

Grades 9-12

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:1. Develop a common understanding of the EQuIP quality review

process 2. Develop a common understanding of the EQuIP Rubric including

its criteria and rating scale 3. Practice using the EQuIP quality review process and rubric to

evaluate and provide feedback on CCSS-aligned instructional materials

Session Goals

1. Common Core: Before beginning a review, all members of the panel are familiar with the Common Core Standards (CCSS) for their grade band and discipline(s).

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 the panel 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.” Panel members are respectful of contributors’ work and make constructive observations and suggestions based on evidence from the work.

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

7. Understanding & Agreement: The goal of the process is to compare and calibrate our judgments so that we reach agreement about alignment and quality with respect to the CCSS.

EQuIP Quality Review ProcessPrinciples & 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:

EQuIP Quality Review ProcessRubric Dimensions

Alignment to the depth of the CCSS

Key shifts in the CCSS

Instructional supports

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.

5

Two Version of the Quality Review RubricThe Electronic VersionFor 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.

6

Two Versions of the Quality Review Rubric The One-Page Version

7

EQuIP Quality Review ProcessThe Five Steps

Step 1. Review Materials

Step 2. Apply Criteria in Dimension I

Step 3. Apply Criteria in Dimensions II – IV

Step 4. Apply Overall Rating and Provide Summary Comments

Step 5. Compare Overall Ratings and Determine Next Steps

8

EQuIP Quality Review ProcessThe Five StepsStep 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• Enter a rating of 0–3 for Dimension I

Note: Dimension I is non-negotiable. For the review to continue, a rating of 2 or 3 is required. If the review is discontinued, consider giving general feedback that might help developers/teachers make decisions regarding next steps.

9

EQuIP Quality Review ProcessThe Five StepsStep 3. Apply Criteria in Dimensions II–IV • Examine the lesson/unit through the “lens” of each criterion • Indicate each criterion met, record observations and feedback, and then rate 0–3

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

needed• Total dimension ratings and record an overall rating (E, E/I, R, N) based on total

score• Individually write summary comments for the overall rating on the Quality Review

Rubric PDF

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

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

10

EQuIP Quality Review ProcessThe Flowchart

Discussion and collaboration must occur after Dimension I and then again either for all dimensions after Dimension IV or …

… separately after each dimension and …

… always during the overall rating process and summary comments.

11

Secondary Two Mathematics: An Integrated ApproachModule 5 – Geometric Figures

Eight lessons each with the following components:• Experimental tasks to introduce concept(s) and technical

vocabulary; develop, practice or solidify understanding; and launch lesson

• Teacher notes to support teaching the lesson including:o Purposeo Core Standards Focuso Mathematics notes for the standardso Related standardso Launch instructions for experiments, exploration, discussion

• Student materials – “Ready, Set, Go”

EQuIP Quality Review ProcessStep 1: Review Example Materials

Review materials on your own to make sure you know what they contain and how they are organized. Work key tasks and study activities with the grade-level student strategies in mind.

12

EQuIP Quality Review ProcessStep 2: Apply the Criteria of Dimension I

The lesson/unit aligns with the letter and spirit of the CCSS:

Targets a set of grade-level CCSS mathematics standard(s) to the full depth of the standards for teaching and learning.

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.

Presents a balance of mathematical procedures and deeper conceptual understanding inherent in the CCSS.

Determine rationales for checks or no-checks individually for this dimension and then discuss and collaborate with your review team.

13

The lesson/unit aligns with the letter and spirit of the CCSS:

Targets a set of grade-level CCSS mathematics standard(s) to the full depth of the standards for teaching and learning.

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.

Presents a balance of mathematical procedures and deeper conceptual understanding inherent in the CCSS.

Step 2: Apply Criteria of Dimension IExample Materials – Checked Criteria

14

Criterion: 1. Targets a set of grade-level CCSS mathematics standard(s) to the full

depth of the standards for teaching and learning.Observations and suggestions:

Step 2: Apply Criteria of Dimension I, Criterion 1Example Materials – Rationale for Checks

The standards are appropriately selected and compiled for the module. TheCCSS mathematics standards are clearly identified in each task. Core standards are identified, and when appropriate, related standards are also listed. The lessons are designed to insure that students reach a deep level of understanding of the three selected standards (G.CO.9, G.CO.10, G.CO.11). This deep level of understanding will ensure that students will solidify concepts that are fundamental to understanding geometry.

15

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.

Observations and suggestions:


The Standards for Mathematical Practice are not mentioned anywhere in this document. Although the Standards for Mathematical Practice are not identified, they are clearly evident in the provided materials. For example the primary concern of G.CO.9, 10 and 11 is to “construct viable arguments” as students wrestle with proving theorems about lines and angles, triangles, and parallelograms. Revisions to improve the module should include information for the teacher about how the Standards for Mathematical Practice will be observed and assessed throughout the lessons, including connections made to the tasks and activities.

16

3. Presents a balance of mathematical procedures and deeper conceptual understanding inherent in the CCSS.

Observations and suggestions:


Materials include balanced activities that encourage conceptual understanding as well as ample opportunities for practice to build procedural skill. This module is very well structured to push students to a depth of understanding that will develop concepts for students and create procedural fluency. While it is true that some students may need additional support to make the connection between the concepts and the procedures, the lessons provide opportunities for students to develop (see lessons 5.1, 5.2, 5.4), to practice (see lessons 5.4, 5.7, 5.8), and to solidify (see lessons 5.3 and 5.6) understanding.

17

EQuIP Quality Review ProcessUsing Dimension Ratings and Rating Scales

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

18





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


19





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


20

Compare Criterion-Based Checks, 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 in the rubric?

Step 2: Apply the Criteria of Dimension IExample Materials – Discuss and Collaborate

Determine and discuss your individual dimension ratings with your review team.

21

Rating: 2 Approaching CCSS Quality: Meets many criteria but will benefit from revision in others, as suggested in criterion-based observations.

Rationale: The Standards for Mathematical Practice that are central to the goals of the module need to be included and specifically connected with the activities and tasks of the lessons.

Step 2: Apply the Criteria of Dimension I Example Materials – Rating

EQuIP Quality Review ProcessConstructive Feedback

Effective feedback is vital to the EQuIP Quality Review Process. • Criterion-Based: Written comments are based on the criteria

used for review in each dimension. No extraneous comments are included.

• Evidence Cited: Written comments indicate that the reviewer looked for evidence of each criterion of a given dimension. Examples cite where and how the criteria are met or not met.

• Improvement Suggested: Improvements are specifically identified to meet criteria or strengthen the lesson or unit.

• Clear Communication: Written comments are constructed in a manner keeping with basic grammar, spelling, sentence structure and conventions.

Use these points to determine and discuss the observations and suggestions appropriate for this dimension with your review team.

23

Step 2: Apply the Criteria of Dimension IExample Materials – Providing Feedback

Observations/Feedback and RatingThe standards are appropriately selected and compiled for the module. The CCSS mathematics standards are clearly identified in each task. Core standards are identified, and when appropriate, related standards are also listed. The lessons are designed to insure that students reach a deep level of understanding of the three selected standards (G.CO.9, G.CO.10, G.CO.11). This deep level of understanding will ensure that students will solidify concepts that are fundamental to understanding geometry.The Standards for Mathematical Practice are not mentioned anywhere in this document. Although the Standards for Mathematical Practice are not identified, they are clearly evident in the provided materials. For example the primary concern of G.CO.9, 10 and 11 is to “construct viable arguments” as students wrestle with proving theorems about lines and angles, triangles, and parallelograms Revisions to improve the module should include information for the teacher about how the Standards for Mathematical Practice will be observed and assessed throughout the lessons, including connections made to the tasks and activities. Materials include balanced activities that encourage conceptual understanding as well as ample opportunities for practice to build procedural skill. This module is very well structured to push students to a depth of understanding that will develop concepts for students and create procedural fluency. While it is true that some students may need additional support to make the connection between the concepts and the procedures, the lessons provide opportunities for students to develop (see lessons 5.1, 5.2, 5.4), to practice (see lessons 5.4, 5.7, 5.8), and to solidify (see lessons 5.3 and 5.6) understanding..

24

Step 2: Apply the Criteria of Dimension IExample Materials – Providing Feedback

Observations/Feedback and RatingThe standards are appropriately selected and compiled for the module. The CCSS mathematics standards are clearly identified in each task. Core standards are identified, and when appropriate, related standards are also listed. The lessons are designed to insure that students reach a deep level of understanding of the three selected standards (G.CO.9, G.CO.10, G.CO.11). This deep level of understanding will ensure that students will solidify concepts that are fundamental to understanding geometry.The Standards for Mathematical Practice are not mentioned anywhere in this document. Although the Standards for Mathematical Practice are not identified, they are clearly evident in the provided materials. For example the primary concern of G.CO.9, 10 and 11 is to “construct viable arguments” as students wrestle with proving theorems about lines and angles, triangles, and parallelograms Revisions to improve the module should include information for the teacher about how the Standards for Mathematical Practice will be observed and assessed throughout the lessons, including connections made to the tasks and activities. Materials include balanced activities that encourage conceptual understanding as well as ample opportunities for practice to build procedural skill. This module is very well structured to push students to a depth of understanding that will develop concepts for students and create procedural fluency. While it is true that some students may need additional support to make the connection between the concepts and the procedures, the lessons provide opportunities for students to develop (see lessons 5.1, 5.2, 5.4), to practice (see lessons 5.4, 5.7, 5.8), and to solidify (see lessons 5.3 and 5.6) understanding..

25

Consider the rating for Dimension I:

• Is the overall rating for alignment a 3 or 2?

• Does the quality of the alignment to the CCSS warrant continuing with the review?

If yes, continue with Step 3 for Dimensions II – IV.

EQuIP Quality Review ProcessStep 2: Dimension I Reflection

If we agree that the materials warrant a 2- or 3-rating for Dimension I, we continue the review, applying the criteria of Dimensions II – IV.

26

EQuIP Quality Review ProcessStep 3: Apply the Criteria of Dimension II

The lesson/unit addresses key shifts in the CCSS:

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.

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.

27

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.

EQuIP Quality Review ProcessStep 3: Apply the Criteria of Dimension II


28

Step 3: Apply Criteria of Dimension II Example Materials – Checked CriteriaThe lesson/unit addresses reflects evidence of key shifts that are reflected in the CCSS: 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.

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.

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

29

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

Since CCSS high school standards do not have critical area descriptors, as is the case for K-8, we have to rely on other sources to determine the major work for high school levels. The standards targeted for this module are appropriate for an Integrated Mathematics I course, as indicated by the PARCC Model Content Frameworks. Although it is not completely clear from the module title, Secondary II Mathematics: An Integrated Approach, module appears to identify the module as Integrated Mathematics II. These standards do not appear in the Integrated Mathematics II course as outlined by PARCC, but are outlined as Integrated Mathematics I in Appendix A of the CCSS. Some information might be included in the front matter for the module to assist those wishing to use it as to the appropriate level to use the lessons of this module.

Step 3: Apply Criteria of Dimension II Example Materials – Rationale for Checks

1. Criterion-based? 2. Evidence Cited? 3. Improvement Suggested? 4. Clear Communication?

30

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

The module as a whole connects the major work and supporting work in a balanced, appropriate manner. Connections to prior learning are also clear. For example, the task two (5.2) Teacher Notes, beginning on page 15, establish connections between the student's current work with proofs and their prior work with proving triangle congruence and rigid transformations and congruence. Students are able to practice skills throughout the lessons; for example students practice the skill of finding the measures of angles in different contexts in several of the lessons of the modules.



31

Rigor: o Application: o Conceptual Understanding: o Procedural Skill and Fluency:


Task sets include problems designed to support student application, conceptual understanding, and procedural skill and fluency. Although many questions target more than one aspect of rigor, application is a strength of this module. Students are able to see angle measures in real world situations, as well as explore real world problems to develop their thinking further. The building of conceptual understanding in this module is very strong through the use of student experiments. Students are often asked to make important, high-level conjectures, which may lead to the need for more support in developing this conceptual understanding after the student experiments. Students are given some opportunities to develop their procedural skills (see Lessons 5.5 and 5.8), but the module could be even stronger if it provided students more opportunities to practice the skills they are learning.


32

Compare Criterion-Based Checks, Observations/Feedback and Rating

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



Step 3: Apply Criteria of Dimension II Example Materials – Discuss and Collaborate

Determine and discuss your individual dimension ratings with your review team…

33

Rating: 3 Exemplifies CCSS Quality – Meets the standard described by the criteria in the dimension, as explained in criterion-based observations.

Rationale: Attention to Focus, Coherence, and Rigor, the key shifts in the CCSS, is evident in the materials.

Step 3: Apply Criteria of Dimension II Example Materials – Rating

34

EQuIP Quality Review ProcessStep 3: Apply the Criteria of Dimension III

The lesson/unit is responsive to varied student learning needs:

Includes clear and sufficient guidance to support teaching and learning of the targeted standards, including, when appropriate, the use of technology and media.

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.

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

Addresses instructional expectations and is easy to understand and use.

35

EQuIP Quality Review ProcessStep 3: Apply the Criteria of Dimension III 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.

* Note: All three of these components are required in a high quality lesson or unit.

36


A unit or longer lesson should: longer lessons:

Recommends and facilitates a mix of instructional approaches for a variety of learners such as using multiple representations (including models), using a range of questions, checking for understanding, flexible grouping, pair-share, etc.

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

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

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.

37

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

when appropriate, the use of technology and media. 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. Engages students in productive struggle through relevant, thought-provoking questions, problems and tasks

that stimulate interest and elicit mathematical thinking. Addresses instructional expectations and is easy to understand and use. 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.

A longer unit or lesson should: Recommends and facilitates a mix of instructional approaches for a variety of learners such as using

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





38

Step 3: Apply Criteria of Dimension III Example Materials –Sharing FeedbackINDIVIDUALLY:• Closely examine the materials through the “lens” of each criterion• Check each criterion for which clear and substantial evidence is found • Record evidence for each check or where you looked and were unable to

find evidence • Write feedback using the four qualities for ONE of the criterion that you

checked/did not checkedCOLLECTIVELY:• Compare and discuss checks and evidence• 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?• Choose ONE piece of feedback for the group to share with entire roomDetermine rationales for checks or no-checks individually and then discuss and collaborate with your review team. For this dimension we will pause to share some of our findings with the larger group…

39

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

when appropriate, the use of technology and media. 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. Engages students in productive struggle through relevant, thought-provoking questions, problems and tasks

that stimulate interest and elicit mathematical thinking. Addresses instructional expectations and is easy to understand and use. 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.

A longer unit or lesson should: Recommends and facilitates a mix of instructional approaches for a variety of learners such as using

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




Step 3: Apply Criteria of Dimension III Example Materials – Checked Criteria

40

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

standards, including, when appropriate, the use of technology and media. The teacher notes provide adequate support in the use of these materials, including the use of multiple representations for many concepts and a mix of instructional approaches. Some additional support on the incorporation of technology would be helpful. For example, some tasks mention online apps or dynamic geometry software, but no specific directions for the use of these tools are provided. Students are expected to make high-level conjectures throughout the module on topics that will apply to many different types of geometry problems and geometric reasoning. Since the expectations for students’ proofs and conjectures are high, it would be helpful to teachers to provide example student responses and answer keys for all student materials to make sure that teachers clearly understand the expected level of rigor.

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.

The vocabulary and problem types are appropriate for the indicated standards and precise and accurate mathematics are encouraged throughout the module.

Step 3: Apply Criteria of Dimension III Example Materials – Rationale for Checks

41

The lesson/unit is responsive to varied student learning needs: Engages students in productive struggle through relevant, thought-provoking questions,

problems and tasks that stimulate interest and elicit mathematical thinking.Not only are the questions thought provoking, they are revisited throughout the module to support the cohesiveness of the materials and the standards. While students are definitely engaged in challenging and thought provoking tasks through the lesson experiments, it would be helpful to have more student example responses to the questions in the instructional supports.

Addresses instructional expectations and is easy to understand and use.

The provided materials are teacher-friendly and very usable. Support for lesson presentation is provided in the Teacher Notes, including the purpose of the lesson explained in detail. Copy-ready masters for student materials are very helpful.


42

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.Scaffolding, differentiation, intervention and/or support for diverse learners needs to be more evident in the tasks. The module could be improved by providing supports for students that do not reach the conclusions of the lessons as quickly as others or for students who need more support with procedural skills. Some students might need more support throughout the lessons in order to get and retain the important information needed to understand the concepts. There is also no mention of ELL student support.


43

A unit or longer lesson should: Recommends and facilitates a mix of instructional approaches for a variety of

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

Each task begins with a group activity and then progresses to an individual problem solving activity. Teachers are instructed to “explore,” “discuss,” “launch,” and then to repeat.


Materials purposefully and gradually remove supports to require students to demonstrate their mathematical understanding independently. For example, the Task 2 Teacher Notes clearly state that the task is "particularly moving from reasoning with a diagram to reasoning based on a logical sequence of statements that start with given assumptions and lead to a valid conclusion."


44

A unit or longer lesson should: (cont.) Demonstrates an effective sequence and a progression of learning where the

concepts or skills advance and deepen over time.The flow from beginning to end of the module, with understanding continuing to deepen over the course of the lessons, provides an effective sequence. The sequencing of tasks highlights key concepts and helps students develop deep understanding.


Students are taken from experiments to developing understanding, to solidifying understanding, and then to practicing the skills learned. This cycle is repeated multiple times with clear expectations for both procedural skill and conceptual understanding.


45





Step 3: Apply Criteria of Dimension III Example Materials – Discuss and Collaborate

Determine and discuss your individual dimension ratings with your review team…

46


Rationale: Scaffolding, differentiation, intervention and/or support for diverse learners needs to be more evident in the tasks.

Step 3: Apply Criteria of Dimension III Example Materials – Rating

47

EQuIP Quality Review ProcessStep 3: Apply the Criteria of Dimension IV

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

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

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

sufficient guidance for interpreting student performance.

In addition, for units and longer lessons: and longer lessons: Uses varied modes of curriculum-embedded assessments that may include pre-,

formative, summative and self-assessment measures.


48

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

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

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

sufficient guidance for interpreting student performance.

In addition, for units and longer lessons: and longer lessons: Uses varied modes of curriculum-embedded assessments that may include pre-,

formative, summative and self-assessment measures.

Step 3: Apply Criteria of Dimension IV Example Materials – Checked Criteria

49

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

student can independently demonstrate the targeted CCSS.The design of the materials of the module encourage student discussion and teacher observation of discussion, which can be used to gather evidence of student learning. The "ready, set go" sections included with each lesson also provide opportunities for independent formative and/or summative assessments. However without clear rubrics and scoring guidelines it may be difficult for teachers to know exactly what evidence of student learning is to be observed.

Assesses student proficiency using methods that are accessible and unbiased, including the use of grade-level language in student prompts.

There is no evidence of bias in the lessons. Language and prompts are appropriate and accessible to all high school students.

Step 3: Apply Criteria of Dimension IV Example Materials – Rationale for Checks

50

Includes aligned rubrics, answer keys and scoring guidelines that provide sufficient guidance for interpreting student performance.

Answer keys and rubrics are not provided for the "Ready, Set, Go" activities, including the Module 5 test. Although the teacher notes include discussion of the opening activities for each task, clear answer keys and suggested student responses to discussion questions would be useful for the teacher.

In addition, for units and longer lessons: Uses varied modes of curriculum-embedded assessments that may include

pre-, formative, summative and self-assessment measures.Although checks for student understanding are clearly made in these materials, other than the Module 5 Test, assessment is not directly mentioned in the materials. The module could be improved if a diagnostic assessment was provided, along with information about how to interpret student performance. The module could also be improved if there were indicators for teachers on how to use the formative assessments and the "ready, set, go" sections to inform student understanding and for re-teaching concepts.

Step 3: Apply Criteria of Dimension IV Example Materials – Rationale for Checks

51





Step 3: Apply Criteria of Dimension IV Example Materials– Discuss and Collaborate

Determine and discuss your individual dimension ratings with your review team.

52


Rationale: Scoring rubrics, answer keys, and suggestions for interpreting student work and responses to discussion questions are missing from the materials.

Step 3: Apply Criteria of Dimension IV Example Materials– Rating

53

EQuIP Quality Review ProcessStep 4: Overall Rating Descriptors

Overall Rating for the Lesson/Unit:

E: Exemplar — Aligned and meets most to all of the criteria in Dimensions II–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)

54







55







56

EQuIP Quality Review ProcessStep 4: Apply Overall Rating and Provide Summary• Go back through dimensions and add the individual

dimensional ratings to initially determine the overall rating category.

• Consider how your rating, based on the total points, matches your overall sense of the quality of the materials.

• Consider if your specific feedback statements are matched with the appropriate dimensions.

• Consider how your dimensional feedback supports your judgments.

• Consider if the lesson falls in the appropriate overall rating category.Determine and discuss your individual OVERALL ratings with your

review team.

57

EQuIP Quality Review ProcessStep 4: Developing Summary Comments

Summary Comments:

• Highlight the strongest aspects of the unit.

• Succinctly summarize key areas for improvement articulated in the dimensional comments.

Determine individually appropriate overall rating and summary comments and discuss with your review team.

585858

Step 4: Overall Rating and Summary CommentsExample Materials – Overall Rating and Summary

DIMENSIONAL RATINGS: 2322 E/I – [Overall rating]Overall, this module is very good. It encourages student exploration and discussion and provides an excellent model of CCSS-aligned instruction with attention to the key shifts apparent in the CCSS. Suggestions for improvement include the need to address the relevant Standards for Mathematical Practice, provide specific supports for students needing additional support, and give more specific attention to assessment and scoring rubrics/answer keys.

Geometric FiguresHigh School

Normed Response

59

EQuIP Quality Review ProcessStep 5: Discuss Summary and Next Steps

Compare overall ratings and synthesize feedback:

• How do our overall ratings compare?

• Does this example serve as a model of CCSS instruction? What are its strengths? Areas for improvement?

• What communication and support will the developer receive?

• What are the next steps for this material?

60

EQuIP Quality Review ProcessReflection

• What additional practice is needed on the EQuIP Review Process and Rubric?

• What other ways can the EQuIP processes and materials influence and be incorporated into our practice?

• How will we plan for applying the EQuIP Quality Review Process? Who will be involved?

61

EQuIP Quality Review ProcessThe Review Team

When forming and/or working with a review team:

• Make sure all team members have training in the process and know the CCSS (at least for their grade level).

• Have a review plan that considers the experience and expertise of all team members.

• Team members may choose to compare individual ratings after each dimension or wait until each person has individually rated and recorded all input for Dimensions II–IV before beginning discussion.

• Individuals should record their overall rating prior to discussion.

• Adjustments to ratings and/or commentary should take place as a part of the group discussion.

62

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

EQuIP Rubric & Quality Review Mathematics Training Module: Grades 9-12 1.

Documents

Transcript of EQuIP Rubric & Quality Review Mathematics Training Module: Grades 9-12 1.