poster place a dot on each continuum. – rate your familiarity with the content portion of the new...

Poster

• Place a dot on each continuum.– Rate your familiarity with the content portion of

the New Illinois Learning Standards for Mathematics

– Rate your familiarity with the practice standards portion of the New Illinois Learning Standards for Mathematics

– Rate your familiarity with the PARCC assessment and supporting materials.

Math Foundational Services

Heather Brown & Dana CartierISBE Math Content Area Specialist

Who is in the Room?

• Teachers• Curriculum or Content Specialists• School or District Administrators• County or State representatives

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Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

EQuIP Rubric(Educators Evaluating Quality

Instructional Products)

The History Behind the Tool

The Tri-State Collaborative

EQuIP

(Educators Evaluating Quality

Instructional Products)


Purpose Instructional Materials Guidance

Lesson/Unit Alignment

Develop a deeper understanding of the CCSS


The EQuIP Rubric Design

Multi-Day Lessons

Units


Single task or activity.


How States May Use The Rubric

• Guide development • Evaluate• Gain deeper understanding of the CCSS• Inform vendors


EQuIP Rubric

1.Guide for lesson plan/unit alignment

2.Rating scale - NOT recommended for classroom use or teacher evaluation


EQuIP Rubric

Educational organizations may use the backside of the rubric to determine the quality and alignment of lessons and units to:

1. Identify exemplars/models for teachers’ use within and across states;

2. Provide constructive criteria-based feedback to developers,

3. Review existing instructional materials to determine what revisions are needed.


The Rubric Organizes Criteria That Describe Quality Lessons/Units

Criteria that define the rubric are organized to describe quality in four dimensions.

Slide taken from Tri-State Quality Review Rubric & Process (Achieve)

Dimension #1 Alignment to the

Depth of CCSS

Dimension #2 Key Shifts of Focus in the CCSS

Dimension #3 Instructional

Supports

Dimension #4 Assessment


Assessment

Alignment

Focus

Supports

CCSS Alignment is Four Dimensional


1st Step: Make a foldableShow only Dimensions I And IV

Backward PlanningGoals Assessment Methods


Backwards Design/EQuIP Rubric

1. Identify the results desired

2. Determine acceptable levels of evidence that support the desired results

3. Design activities that will make the desired results happen


Dimension I: Alignment to the CCSS

Targets Standard(s)• Content standards• Practice Standards

Balance• Procedural Skill• Conceptual Understanding

Dimension II: Key Shifts in CCSS

Focus

Coherence

Rigor

Guidance

Accuracy

Engagement

Instructional Expectations

Differentiation

Dimension III: Instructional Supports

Dimension IV: Assessment

Observable Evidence of Learning

Assesses Proficiency

Aligned Rubrics/Scoring Guides

Rubric Activity


Multi Day Lesson/

Unit Plan

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: Yes

Evidence Cited: Partial

Improvement suggested: Partial

Clarity 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.

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Quality Review Steps

Step 1. Review Materials • 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

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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 recorded all input for Dimensions II–IV.

Step 4. Provide Summary Comments (if group determines summary valuable)• Individually review comments for Dimensions I–IV, adding/clarifying comments as

needed • Individually write summary comments When working in a group, individuals should record summary comments prior to conversation.

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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.

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• 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)

EXAMPLE:Step 1. Review Materials

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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.

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

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.

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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.


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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)?

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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.

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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.

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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:

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.

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.

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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.


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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.


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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.

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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.

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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.

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

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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.

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

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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.

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EXAMPLE:Step 3. Apply Criteria in 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. Use varied modes of curriculum-embedded assessments that may include pre-,

formative, summative and self-assessment measures.

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Observations/Feedback and Rating

This 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.

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

Where to Access Sample Lesson Plans/Units

• http://www.achieve.org/equip • www.achievethecore.org

Click Mathematics

Click Lessons

• Participants bring their own multi-day lesson plan/unit.

• Other ideas?


http://www.achieve.org/equip

http://www.achievethecore.org/

EQuIP ResourcesOptional Lesson Plan Template

Grades K-12

Web-based version

PDF version

www.ilclassroomsinaction.org and

www.education.illinoisstate.edu/casei/math/


http://www.ilclassroomsinaction.org/

http://www.education.illinoisstate.edu/casei/ela/



Share Out!


What are the benefits of doing this activity with schools in your ROE?

What are the challenges of doing this activity with schools in your ROE?

What ideas do you have?

Next Steps Planning


Dana Cartier – [email protected] Brown – [email protected]

mailto:[email protected]

mailto:[email protected]

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