oregon instructional materials evaluation toolkit (or … · evaluating instructional materials...

This worksheet is based on the Oregon Adopted Criteria for Mathematics (2014). Additional sources include the Achieve EQuIP rubric and Student Achievement Partners IMET rubric. OR-IMET (HS) Version 3.0, rev. 4/2015

Oregon Instructional Materials Evaluation Toolkit (OR-IMET) for Alignment in Mathematics, High School (HS)

In alignment with Oregon educational goals, including the 40-40-20 initiative, evidence of best practices in equity and inclusion are embedded in the OR-IMET. The Oregon Math IMET is designed to help educators determine whether instructional materials are aligned to the Shifts and major features of the Common Core State Standards (CCSS). The substantial instructional Shifts (http://www.corestandards.org/other-resources/key-shifts-in-mathematics/) at the heart of the Common Core State Standards are:

1. Focus strongly where the Standards focus 2. Coherence: Think across grades and link to major topics within the grade 3. Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application with equal intensity.

The OR-IMET draws directly from the following documents:

• Common Core State Standards for Mathematics (www.corestandards.org/Math) • K–8 Publishers' Criteria for the Common Core State Standards for Mathematics (Spring 2013) (achievethecore.org/publisherscriteria-math-k-8).

When to Use the OR-IMET This tool is designed to evaluate how closely aligned instructional materials are to the Shifts and the major features of the CCSS. It also provides suggestions of additional indicators to consider in the materials evaluation and purchasing process. The OR-IMET can be used to highlight specific, concrete flaws in alignment. Even where materials and tools currently in use fail to meet one or more of these criteria, the pattern of failure is likely to be informative. States and districts can use the evaluation to create a thoughtful plan to modify or combine existing resources in such a way that students’ actual learning experiences approach the focus, coherence, and rigor of the Standards. Additionally, those developing new programs can use this tool as guidance for creating aligned curricula. The OR-IMET is intended to be used when:

1. Purchasing materials 2. Evaluating materials currently in use 3. Developing programs

Please note this tool was designed for evaluating comprehensive curricula (including any supplemental or ancillary materials), but it was not designed for the evaluation of standalone supplemental materials. Who Uses the OR-IMET Evaluating instructional materials requires both subject-matter and pedagogical expertise. Evaluators should be well versed in the Standards (www.corestandards.org/Math) for all grades in which materials are being evaluated. This includes understanding the Major Work of the grade (www.achievethecore/focus), the Supporting and Additional work, how the content fits into the progressions in the Standards (www.achievethecore.org/progressions), and the expectations of the Standards with respect to conceptual understanding, procedural skill and fluency, and application. Evaluators also should be familiar with the substantial instructional Shifts (http://www.corestandards.org/other-resources/key-shifts-in-mathematics/) at the heart of the Common Core State Standards.

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http://www.ode.state.or.us/teachlearn/instructionalmaterials/1_14-math-adopted-criteria-pm.pdf

http://www.achieve.org/files/EQuIPmathrubric-06-17-13.pdf

http://achievethecore.org/page/783/instructional-materials-evaluation-tool-imet

http://www.corestandards.org/other-resources/key-shifts-in-mathematics/


http://www.corestandards.org/Math

http://www.achievethecore.org/publisherscriteria



http://www.achievethecore.org/focus

http://www.achievethecore/focus

http://www.achievethecore.org/progressions






Team/Cat____________ Evaluator ID__________ Submission #__________

Publisher______________________ Score_____________

. Criteria for the Review and Adoption of Instructional Materials for:

Category 1, 2, 3 and 4: (CCSS) Mathematics – Grades K-2, 3-5, 6-8 and 9-12 LEGAL REQUIREMENTS SECTION

A. BASAL INSTRUCTIONAL MATERIALS CRITERIA The submitted materials must make up an organized system of instruction that align with adopted state standards. Does the program meet the above requirements for basal instructional materials?

______Yes _____No

B. EQUITY CRITERIA Submitted materials must provide models, selections, activities and opportunities for responses which promote respect for all people described in ORS 659.850,

OAR 581-021-0045 and support program compliance standards described in OAR 581-021-0046. Does the program meet the above requirements for equity?

______Yes _____No C. National Instructional Materials Accessibility Standard (NIMAS)

Submitted materials must include assurance from the publishers agreeing to comply with the most current NIMAS specifications regarding accessible instructional materials.

Does the program meet the above requirements for NIMAS?

______Yes _____No

D. Digital Manufacturing Standards and Specifications (MSST Form B and M): Submitted materials must include assurance from the publishers agreeing to comply with the most current digital manufacturing standards and specifications.

Does the program meet the above MSST requirements?

______Yes _____No

4 Exceeds the criteria 3 Adheres to the criteria 2 Sometimes adheres to the criteria

1 Occasionally adheres to the criteria 0 Rarely adheres to the criteria

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Category 4: CCSS Mathematics – Grades 9-12

I. Alignment to the CCSS Mathematical Content** II. Alignment to the CCSS Mathematical Practices** III. Instructional Supports IV. Assessment

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

FOCUS ___1. Lessons and units targeting the widely applicable

prerequisites (at the standard and cluster level) provide an especially in-depth treatment, with especially high expectations. Lessons and units targeting supporting work of the grade (at the standard and cluster level) have visible connection to the widely applicable prerequisites and are sufficiently brief. Lessons and units do not hold students responsible for material from later grades.

COHERENCE ___2. The content develops through reasoning about the new

concepts on the basis of previous understandings. RIGOR

Requires students to engage with and demonstrate challenging mathematics with appropriate balance among the following: ___3. 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.

___4. Conceptual Understanding: Develops students’ understanding through brief conceptual problems and questions, multiple representations and opportunities for students to write and speak about their understanding.

___5. 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.

The instructional materials identify and utilize the Standards for Mathematical Practice (MP): ___6. The mathematical practices are explicit and central

to the lessons, handled in a grade-appropriate way and well connected to the content being addressed.

___7. Overarching habits of mind of a productive mathematical thinker • Engages students in productive struggle through

relevant, thought-provoking questions, problems and tasks that stimulate interest and elicit mathematical thinking. (MP.1)

• Uses and encourages precise and accurate mathematics, academic language, and terminology. (MP.6)

___8. Reasoning and explaining • Materials provide sufficient opportunities for

students to reason mathematically and express reasoning through classroom discussion, written work and independent thinking. (MP.2 & MP.3)

___9. Modeling and using tools • Encourages the strategic use of concrete or abstract

representations (e.g., pictures, symbols, expressions, equations, graphics, models). (MP.4 & MP.5)

___10. Seeing structure and generalizing • Requires students to look for and make use of

structure; and look for and express regularity in repeated reasoning. (MP.7 & MP.8)

Each lesson is responsive to varied teacher needs: ___11. Includes clear and sufficient guidance to support teaching and

learning of the targeted standards, including, when appropriate, the use of technology and media.

___12. Provides a discussion of the mathematics of the units and the mathematical point of each lesson as it relates to the organizing concepts of the unit.

___13. Recommend and facilitate a mix of instructional approaches for students with diverse learning needs, such as using multiple representations (e.g., including models, using a range of questions, checking for understanding, flexible grouping, pair-share).

___14. Gradually remove supports, requiring students to demonstrate their mathematical understanding independently.

___15. Teacher materials are organized and easy to use. The materials are responsive to varied student learning needs:** ____16. Differentiation for ELD, SPED, students above or below grade

level and other special populations is evident. The language in which problems are posed is carefully considered.

____17. Allow teacher/student access through digital media to deepen understanding.

____18. Cultivates student interest and engagement in math through culturally relevant practices free of bias regarding student race, ethnicity, disability status, gender, religion, sexual orientation, national origin, marital status, or color.

____19. Provides appropriate extensions scaffolding, differentiation and extra support for a broad range of learners, including supporting students above and below a given course level.

A course or longer units should: ____20. Demonstrate an effective sequence and a progression of

learning where the concepts or skills advance and deepen over time.

The lesson/unit regularly assesses whether students are mastering standards-based content and skills: ___21. Is designed to elicit direct,

observable evidence of the degree to which a student can independently demonstrate the targeted standard.

___22. Includes aligned rubrics, answer keys and scoring guidelines that provide sufficient guidance for interpreting student performance.

___23. Uses varied modes of curriculum embedded assessments (selected, constructed, extended response items, and performances tasks) that may include pre-, formative, summative and self-assessment measures.

___24. Assesses student proficiency using methods that are accessible and unbiased, including the use of grade-level language in student prompts.

___25. Provides extensions for students with high interest or working above grade level.

Digital Assessment materials: ___26. Are easy to manipulate and

customize ___27. Are clearly linked to the adopted

standards ___28. Have sufficiently large enough

problem banks

Oregon Definition of Instructional Material: Units/lessons and materials that make up the major instructional vehicle for a given course of study as described in OAR 581-011-0050.

Rating Scale for Criteria #1-10 Rating Scale for Criteria #11-23 4: Meets all criteria (exemplary) 2: Meets criteria 3: Adheres to the criteria 1: Partially meets/some evidence 2: Sometimes adheres to the criteria 0: Does not meet criteria 1: Occasionally adheres to the criteria 0: Does not meet the criteria

Overall Rating for the Instructional material:

**Key Criteria (#1-5) (Scores 0-4)



Supporting Criteria (#11-15, #20-28) (Scores 0-2)

Exemplifies Quality 100% 3 or 4 100% 3 or 4 100% 1 or 2 100% 1 or 2 Approaching Quality ≥80% 3 or 4 ≥80% 3 or 4 ≥75% 1 or 2 ≥50% 1 or 2 Does not meet standards <80% 3 or 4 <80% 3 or 4 <75% 1 or 2 <50% 1 or 2

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http://arcweb.sos.state.or.us/pages/rules/oars_500/oar_581/581_011.html


SECTION I: KEY ALIGNMENT CRITERIA TO MATHEMATICAL CONTENT

Criterion 1: FOCUS Lessons and units targeting the widely applicable prerequisites (at the standard and cluster level) provide an especially in-depth treatment, with especially high expectations. 4: Meets all Criteria

(8 points) 3: Adheres to the Criteria

(6-7 points, no zeros) 2: Sometimes adheres to the

criteria (4-5 points, or at least 1 zero)

1: Occasionally adheres to the criteria (1-3 points)

0: Does not meet the criteria (0 points)

Quality indicators How to Find the Evidence Rating Notes for evidence or possible improvement

1a. In any given HS course, both student and teacher materials, when used as designed, devote the majority of time to the Widely Applicable Prerequisites. For context, read criterion #1 in the High School Publishers' Criteria for the Common Core State Standards for Mathematics (Spring 2013).

Familiarize yourself with the Widely Applicable Prerequisites. Review the table of contents and any pacing guides. Do not stop there; also review units, chapters, lessons, homework assignments, and assessments. (Review both student and teacher materials.) Note: you could consider time spent outside Widely Applicable Prerequisites to help determine whether students and teachers using the materials as designed will devote the majority of time to the Widely Applicable Prerequisites

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1b. Student work in Geometry involves significant work with applications/modeling and problems that use algebra skills.

Review the table of contents and any pacing guides. Do not stop there; also review units, chapters, lessons, homework assignments, and assessments. (Review both student and teacher materials.) Note: Since Geometry contains relatively fewer Widely Applicable Prerequisites, this criterion is important to help foster students’ college and career readiness. Problems that use algebra skills might include, for example, algebraic geometry problems in a coordinate setting, or problems of measurement involving unknown quantities.

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Final Comments 1c. Materials are organized around major themes consistent with critical areas found in the standards.

For context, read criterion #3a in the High School Publishers’ Criteria for the Common Core State Standards for Mathematics (Spring 2013).

Review both student and teacher materials to see how the materials organize topics around major themes for each course. These should be consistent with the types of critical areas of focus found in the standards. 0 1 2

1d. Materials give all students extensive work with course-level problem and include appropriate supports for both high and low performing students to engage in course level content.

For context, read criterion #3b in the High School Publishers’ Criteria for the Common Core State Standards for Mathematics (Spring 2013).

Review both student and teacher materials. Note: Look for resources that support differentiated learning; consider whether lower-performing students have needed supports to engage with course-level problems. Also consider whether higher-performing students are given opportunities to learn current course-level content in greater depth.

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http://achievethecore.org/content/upload/Widely%20Applicable%20Prerequisites.pdf

http://www.ode.state.or.us/teachlearn/instructionalmaterials/ccssm-critical-areas.pdf



Criterion 2: COHERENCE The content develops through reasoning about the new concepts on the basis of previous understandings. 4: Meets all Criteria







2a. Materials include learning objectives that are evidently shaped by CCSSM cluster headings. For context, read criterion #4a in the High School Publishers’ Criteria for the Common Core State Standards for Mathematics (Spring 2013).

Select at least three different clusters from the Widely Applicable Prerequisites from each course being evaluated. Clusters selected should reflect more than one domain in a given course. Review teacher and student materials in relation to these clusters. 0 1 2

2b. Materials include problems at a level of sophistication appropriate to high school (beyond mere review of middle school topics) that involve the application of knowledge and skills from grades 6-8. For context, read Table 1 on Page 8 of the High School Publishers’ Criteria for the Common Core State Standards for Mathematics (Spring 2013).

Review lessons, chapter/unit assessments, and homework assignments. Note: Courses should include application of the following topics from grades 6-8: ● Ratios and proportional relationships. ● Percentage and unit conversions, e.g., in the context of complex measurement

problems involving quantities with derived or compound units (such as mg/mL, kg/m3, acre-feet, etc.).

● Basic function concepts, e.g., by interpreting the features of a graph in the context of an applied problem.

● Concepts and skills of geometric measurement, e.g., when analyzing a diagram or schematic.

● Concepts and skills of basic statistics and probability (see grades 6–8.SP) ● Performing rational number arithmetic fluently.

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Final Comments 2c. Materials relate course-level concepts explicitly to prior knowledge from earlier grades or courses. The materials are designed so that prior knowledge becomes reorganized and extended to accommodate the new knowledge. For context, read criterion #3c in the High School Publishers’ Criteria for the Common Core State Standards for Mathematics (Spring 2013).

Review student and teacher materials, looking for problems that involve extending the knowledge learned in earlier grade levels and courses. The materials provide specific scaffolds to support English Learners and Students with Disabilities in accessing course-level concepts.

Note: An example of evaluating this criterion might be to look at whether materials connect the equation of a circle with the distance formula and the Pythagorean theorem.

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2d. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a course, in cases where these connections are natural and important.

For context, read criterion #4b in the High School Publishers’ Criteria for the Common Core State Standards for Mathematics (Spring 2013).

In the course being evaluated, choose two or more clusters, two or more domains, or two or more categories for which connections are natural and important. Review the units, chapters, and lessons that deal with the chosen topics, looking for problems and activities that serve to connect the chosen clusters or domains. Note: An example of evaluating this criterion might be to look at whether materials include problems in which students analyze a situation by building a function, graphing it, and using it to create and solve an equation.

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Criterion 3: 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. 4: Meets all Criteria







3a. Materials are designed so that teachers and students spend sufficient time working with engaging, culturally relevant applications, without losing focus on the Widely Applicable Prerequisites For context, read criterion #2c in the High School Publishers’ Criteria for the Common Core State Standards for Mathematics (Spring 2013).

Select at least three different clusters from the Widely Applicable Prerequisites and/or Focus by Domain for each course being evaluated that relate specifically to application standards to use throughout the questions associated with this metric. Note: Some examples of clusters or standards that call for application include: N-Q.A, A-SSE.B.3, A-REI.D.11, F-IF.B, F-IF.C.7, F-BF.A.1, G-SRT.C.8, S-ID.A.2, S-IC.A.1

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3b. Materials include single- and multi-step contextual problems, including non-routine problems, that develop the mathematics of the course, afford opportunities for practice, and engage students in authentic problem solving. Note: Problems should attend thoroughly to content standards where expectations for multi-step and real-world problems are explicit.

Review lessons, chapter/unit assessments, and homework assignments. Note: Look for opportunities for independent application, as well as for group-based application. Materials should also present problems of the same concept at varying levels of complexity. Students in need of practice can cycle through rounds of activities with gradual released support.

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Final Comments 3c. Materials support Modeling expectations that build slowly across courses, with applications that are relatively simple in earlier courses and when students are encountering new content.

Review lessons, chapter/unit assessments, and homework assignments. Note: In high school, modeling should be prominent features of high school materials. The modeling cycle within curricular materials should grow in sophistication using more authentic applications as student move to higher level courses (CCSSM, p.72).

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3d. The materials include language supports to assist students in explaining the process behind solving multi-step, contextual problems.

The materials present academic language supports for mathematic specific language required for the task (i.e., language to describe cause and effect, language to compare and contrast, and language to describe sequence). 0 1 2

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SECTION I: KEY ALIGNMENT CRITERIA TO

MATHEMATICAL CONTENT

Criterion 4: CONCEPTUAL UNDERSTANDING Develops students’ understanding through brief conceptual problems and questions, multiple representations and opportunities for students to write and speak about their understanding. 4: Meets all Criteria







4a. Materials support the development of students’ conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. For context, read criterion #2a in the High School Publishers’ Criteria for the Common Core State Standards for Mathematics (Spring 2013).

Select at least three different clusters from the Widely Applicable Prerequisites and/or Focus by Domain for each course being evaluated that relate specifically to conceptual understanding to use throughout the questions associated with this metric. Note: Some examples of clusters or standards that call for conceptual understanding include: N-RN.A.1,A-APR.B, A-REI.A.1, A-REI.D.10, A.REI.D.11, F.IF.A.1, , F-LE.A.1, G.SRT.A.2, , G-SRT.C.6, S-ID.C.7

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4b. Materials feature high-quality brief conceptual problems (e.g. “find a number greater than 1/5 and less than ¼” or “What is the maximum value of the function f(t) = 5 – t2”).

Review lessons, chapter/unit assessments and homework assignments, paying attention to work aligned to standards that explicitly call for understanding or interpreting.

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Final Comments 4c. Materials feature high-quality conceptual problems and discussion questions written at a variety of cognitive rigor levels.

Review lessons, chapter/unit assessments, and homework assignments. Note: Examples of conceptual problems might include such questions as “What is the maximum value of the function f(t) = 5 – t2 ?” or “Justify whether or not √2 is a polynomial.” Or “Create a function that models breaking distances at various speeds for a given car, and determine at what point will a driver outrun their headlights.”

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4d. Materials feature opportunities to identify correspondences across mathematical representations.

Review lessons, chapter/unit assessments and homework assignments.

Note: An example of evaluating this metric might include looking at whether materials support students in identifying correspondences among the expression that defines a function, the graph that shows the relationship, and the behavior of the phenomenon being modeled (if any).

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http://static.pdesas.org/content/documents/M2-Activity_2_Handout.pdf



Criterion 5: PROCEDURAL 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.

4: Meets all Criteria (8 points)

3: Adheres to the Criteria (6-7 points, no zeros)

2: Sometimes adheres to the criteria (4-5 points, or at least 1 zero)




5a. Materials are designed so that students attain the fluencies and procedural skills required by the Standards. For context, read criterion #2b in the High School Publishers’ Criteria for the Common Core State Standards for Mathematics (Spring 2013).

Select at least three different clusters from the Widely Applicable Prerequisites and/or Focus by Domain for each course being evaluated that relate specifically to fluency and procedural skill to use throughout the questions associated with this metric. Note: Some examples of standards that call for procedural skill and fluency include: A-SSE.A.1b, A-SSE.2, A-APR.A.1, A-APR.C.6, , F-BF.B.3, , G-GPE.B.4, G-GPE.B.5, G-GPE.B.7, G-CO.A.1 , G-SRT.B.5

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5b. Materials support progress toward fluency and procedural skill by interweaving students’ developing conceptual understanding of the operations in question.

Review lessons, chapter/unit assessments, daily routines, and homework assignments for evidence that the development of fluency and procedural skill is supported by conceptual understanding. Academic Language Supports Look for specific language tasks to support students (including EL, SPED, etc.) as they describe and explain procedures. These supports should exercise the specific language required for the task.

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Final Comments 5c. Materials include more than purely procedural problems and exercises. This would include cases in which opportunistic strategies are valuable and generic cases that require efficient algorithms.

Review lessons, chapter/unit assessments, daily routines, and homework assignments. Note: Problems in which opportunistic strategies are valuable might include such examples as solving x2 + 5 = 49 + 5 or (3x − 2)2 = 6x − 4. Generic cases that require efficient and general procedures might include such problems as solving c + 8 – c2 = 3(c – 1)2 − 5).

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5d. Materials in high school courses provide practice toward attainment of fluency within Key takeaways from grades 6-8.

Review lessons, daily routines, and homework assignments for evidence of repeated practice toward attainment of fluency within key procedural skills from grades 6–8. Note: Examples could include (but are not limited to): Solving problems that require using ratios and proportional relationships; Solving real-world and mathematical problems involving angle measure, area, surface area, and volume; Computing fluently with positive and negative fractions and decimals; and Fluently performing rational number arithmetic.

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SECTION II: KEY ALIGNMENT CRITERIA TO MATHEMATICAL PRACTICES

Criterion 6: MATHEMATICAL PRACTICES The mathematical practices are explicit and central to the lessons, handled in a grade-appropriate way and well connected to the content being addressed. 4: Meets all Criteria







6a. Materials address the practice standards in such a way as to enrich the Widely Applicable Prerequisites; practices strengthen the focus on Major Work instead of detracting from it, in both teacher and student materials. For context, read criterion #6 in the High School Publishers' Criteria for the Common Core State Standards for Mathematics (Spring 2013).

Familiarize yourself with the Widely Applicable Prerequisites and Major Work of each course being evaluated (e.g. Focus by Course Level documents). Review teacher and student materials for evidence that the mathematical practices support and connect to the focus of the course.

Note: An example of evaluating this criterion might include looking at whether materials use regularity in repeated reasoning to illuminate formal algebra as well as functions, particularly recursive definitions of functions.

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6b. Over the course of any given year of instruction, materials provide multiple points of access to each mathematical practice standard for students with diverse learning needs.

Review lessons, chapter/unit assessments, and homework assignments for evidence of each mathematical practice being meaningfully present in instruction. Materials provide a variety of tools to facilitate differentiation. The materials might include an easy to use glossary, a collection of supporting scaffolds, functional language supports for language-heavy tasks (i.e., sequencing, comparing/contrasting, describing cause/effect)

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Final Comments 6c. Materials support the development of the practice standards across courses. Practice standards in early courses are appropriately challenging and display an arc of growing sophistication across the course sequence.

Review lessons, chapter/unit assessments, and homework assignments

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6d. Teacher-directed materials explain the role of the practice standards in the classroom and in students’ mathematical development. Materials include accurate alignments to practice standards.

Review teacher materials, paying attention to explanations of the role of the practice standards in the classroom and in students’ mathematical development.

Review documents aligning lessons to practice standards for accuracy.

Note: Examples to look for when evaluating this metric might include the following: a highly scaffolded problem should not be aligned to MP.1; or a problem that directs a student to use a calculator should not be aligned to MP.5; or a problem about merely extending a pattern should not be aligned to MP.8.

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Criterion 7: OVERARCHING HABITS OF MIND OF A PRODUCTIVE MATHEMATICAL THINKER Materials are designed to build their perseverance in grade-level-appropriate ways by occasionally solving problems that require them to persevere to a solution beyond the point when students would likely give up. 4: Meets all criteria


(3 points) 2: Sometimes adheres to the

criteria (2 points)

1: Occasionally adheres to the criteria (1 point)



7a. Materials include opportunities for students to engage in productive struggle through relevant, thought-provoking questions, problems and tasks that stimulate interest and elicit mathematical thinking. (Make sense of problems and persevere in solving them - MP.1) Read Standard for Mathematical Practice 1.

Review teacher and student materials to ensure that students are given opportunities to reason with course-level mathematics. Academic Language Supports Look for specific language related to meta cognition to ensure that students (including EL, SPED, etc.) have the language to describe the habits of mind for mathematical thinking. Language should describe and explain procedures, as well as exercise the specific language required for the task.

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7b. There is evidence of activities that use and encourage precise and accurate mathematics, academic language, terminology and concrete or abstract representations. (Attend to precision - MP.6)

Do materials explicitly attend to the specialized language of mathematics? Is the language of argument, problem solving, and mathematical explanations taught rather than assumed? Review teacher and student materials, paying attention to how mathematical language is taught. Note: Examples of evaluating this criterion might include looking at whether students are supported in: basing arguments on definitions; using the method of providing a counterexample; or recognizing that examples alone do not establish a general statement.

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Final Comments

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Criterion 8: REASONING AND EXPLAINING Materials provide sufficient opportunities for students to reason mathematically and express reasoning through classroom discussion, written work and independent thinking. 4: Meets all criteria



criteria (2 points)




8a. Lesson structure frequently calls for students, in a course-appropriate way, to find solutions, explain their reasoning, and ask and answer questions about their reasoning as it concerns problems, diagrams, and mathematical models. (Reason abstractly and quantitatively - MP.2)

Do the materials support students in producing not only answers and solutions, but also, in a course-appropriate way, arguments, explanations, diagrams, mathematical models, etc., especially in the Major Work of the course? Familiarize yourself with the Major Work of the course being evaluated (see the Focus by Grade Level documents). Review teacher and student materials, to understand the types of work students are expected to produce.

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8b. Materials prompt students to construct viable arguments and critique the arguments of others concerning key course-level mathematics that are detailed in the content standards. (Construct viable arguments and critique the reasoning of others – MP.3)

Do the materials support students in constructing viable arguments and critiquing the arguments of others concerning course-level mathematics that are detailed in the content standards? Read Standard for Mathematical Practice 3. Review teacher and student materials to ensure that students are given opportunities to reason with course-level mathematics.

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Final Comments:

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Criterion 9: MODELING AND USING TOOLS Encourages the strategic use of concrete or abstract representations (e.g., pictures, symbols, expressions, equations, graphics, models). 4: Meets all criteria



criteria (2 points)




9a. Materials include ample opportunities for students to engage with modeling problems in all high school courses. Materials include opportunities for students to use both individual parts of the modeling cycle as well as the full modeling cycle. (Modeling with Mathematics –MP.4)

Read Standards for Mathematical Practice 4, Model with Mathematics. Review lessons, chapter/unit assessments, and homework assignments. Look in particular for opportunities for students to interpret their results in the context of the situation and reflect on whether the results make sense and possibly improve their solutions.

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9b. Materials include problems that allow students’ to make strategic decisions about how to use tools, or about whether to use them at all. (Use appropriate tools strategically - MP.5)

Read Standards for Mathematical Practice 5, Use appropriate tools strategically. Review lessons, chapter/unit assessments, and homework assignments. 0 1 2

Final Comments

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Criterion 10: SEEING STRUCTURE AND GENERALIZING Requires students to look for and make use of structure; and look for and express regularity in repeated reasoning. 4: Meets all criteria



criteria (2 points)




10a. Materials include organizational themes emphasized in the standards such as properties of operations, place value decompositions of numbers, numerators and denominators of fractions, numerical and algebraic expressions, etc. (Look for and make use of structure –MP.7)

Read Standard for Mathematical Practice 7. Review teacher and student materials to ensure that students are given opportunities to reason using course-level mathematics.

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10b. Materials include content to assist the development of student insight into repeated reasoning beyond simply extending patterns and/or perform repeated calculations. (Look for and express regularity in repeated reasoning - MP.8)

Read Standard for Mathematical Practice 8. Review teacher and student materials to ensure that students are given opportunities to reason with course-level mathematics.

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Final Comments

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SECTION III: ADDITIOAL INDICATORS OF QUALITY

Rate each indicator in Section III according to whether it is met, partially met, or not met. Award points for each indicator as shown.

The minimum passing score for Section III is blank. Before evaluation, districts should review Section III and decide the minimum passing score according to the needs of your district.

III - INDICATORS OF QUALITY: INSTRUCTIONAL SUPPORTS SCORE

Does not

meet

Partially meets/

Not sure Meets

EVIDENCE

The teacher materials are responsive to varied teacher needs:

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

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12. Provides a discussion of the mathematics of the units and the mathematical point of each lesson as it relates to the organizing concepts of the unit.

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13. Recommend and facilitate a mix of instructional approaches for students with diverse learning needs, such as using multiple representations (e.g., including models, using a range of questions, checking for understanding, flexible grouping, pair-share, etc.).

0 1 2

14. Gradually remove supports, requiring students to demonstrate their mathematical understanding independently. 0 1 2

15. Teacher materials are organized and easy to use. 0 1 2

The materials are responsive to varied student learning needs**:

16. Differentiation for ELD, SPED, students above or below grade level and other special populations is evident. The language in which problems are posed is carefully considered.

0 1 2

17. Allow teacher/student access through digital media to deepen understanding. 0 1 2

18. Cultivates student interest and engagement in math through culturally relevant practices free of bias regarding student race, ethnicity, disability status, gender, religion, sexual orientation, national origin, marital status, or color.

0 1 2

19. Provides appropriate extensions, scaffolding, differentiation and extra support for a broad range of learners, including supporting students above and below a given course level.

0 1 2

A course or longer units should:

20. Demonstrate an effective sequence and a progression of learning where the concepts or skills advance and deepen over time. 0 1 2

Total (20 points possible)

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SECTION IV: ADDITIOAL INDICATORS OF QUALITY (OPTIONAL)

Rate each indicator in Section III according to whether it is met, partially met, or not met. Award points for each indicator as shown.

The minimum passing score for Section III is blank. Before evaluation, districts should review Section III and decide the minimum passing score according to the needs of your district.

IV - INDICATORS OF QUALITY: ASSESSMENT SCORE

Does not

meet

Partially meets/

Not sure Meets

EVIDENCE

The instructional materials regularly assesses whether students are mastering standards-based content and skills:

21. Is designed to elicit direct, observable evidence of the degree to which a student can independently demonstrate the targeted standard. 0 1 2

22. Includes aligned rubrics, answer keys and scoring guidelines that provide sufficient guidance for interpreting student performance. 0 1 2

23. Uses varied modes of curriculum embedded assessments (selected, constructed, extended response items, and performances tasks) that may include pre-, formative, summative and self-assessment measures.

0 1 2

24. Assesses student proficiency using methods that are accessible and unbiased, including the use of grade-level language in student prompts. 0 1 2

25. Provides extensions for students with high interest or working above grade level. 0 1 2

Digital Assessment materials:

26. Are easy to manipulate and customize 0 1 2

27. Are clearly linked to the adopted standards 0 1 2

28. Have sufficiently large enough problem banks 0 1 2

Total (16 points possible)

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oregon instructional materials evaluation toolkit (or … · evaluating instructional materials...

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