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Adopt or Adapt in Math: Support for

Districts and Schools on Curriculum Decision

Making

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Necessary Tools for Assessing Qualityof Common Core Math Curriculum

•Common Core Mathematics Standards•Standards for Mathematical Practices•The Shifts for Mathematics•Math Content Emphases•Key Fluencies by Grade Level•Learning Progressions•Publishers’ Criteria for Mathematics•EQUIP Rubric for Mathematics

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These Standards are not intended to be new

names for old ways of doing business. They

are a call to take the next step. … It is time to

recognize that standards are not just promises

to our children, but promises we intend to

keep.

CCSSM, p. 5

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Instructional Shifts in Mathematics Demanded by the Core

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Shifts in Assessments

Six Shifts in Mathematics Assessments

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Six Shifts Three Shifts

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Mathematics topics

intended at each grade by

at least two-thirds of A+

countries

Mathematics topics intended at each grade by at least two-thirds of 21 U.S. states

The shape of math in A+ countries

1 Schmidt, Houang, & Cogan, “A Coherent Curriculum: The Case of Mathematics.” (2002).

8

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K 12

Number and Operations

Measurement and Geometry

Algebra and Functions

Statistics and Probability

Traditional U.S. Approach

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Focusing Attention Within Number and Operations

Operations and Algebraic Thinking

Expressions and

Equations

Algebra

→ →

Number and Operations—Base Ten

→

The Number System

→Number

and Operations—Fractions

→

KK 11 22 33 44 55 66 77 88 High SchoolHigh School

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Math Content Emphases

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Math Content Emphases

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Math Content EmphasesFor Grade 3

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Required Fluencies in K-6Grade Standard Required Fluency

K K.OA.5 Add/subtract within 51 1.OA.6 Add/subtract within 10

2 2.OA.22.NBT.5

Add/subtract within 20 (know single-digit sums from memory)Add/subtract within 100

3 3.OA.73.NBT.2

Multiply/divide within 100 (know single-digit products from memory)Add/subtract within 1000

4 4.NBT.4 Add/subtract within 1,000,0005 5.NBT.5 Multi-digit multiplication

6 6.NS.2,3 Multi-digit divisionMulti-digit decimal operations

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http://ime.math.arizona.edu/progressions/

Learning Progressions

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Publishers’ Criteria

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The K–8 Publishers’ Criteria

I. Focus, Coherence, and Rigor in the Common Core State Standards for Mathematics

II. Criteria for Materials and Tools Aligned to the K–8 Standards

III. Appendix: “The Structure is the Standards”

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II. Criteria for Materials and Tools Aligned to the K–8 Standards

1. Focus on Major Work: In any single grade, students and teachers using the materials as designed spend the large majority of their time on the major work of each grade.

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II. Criteria for Materials and Tools Aligned to the K–8 Standards

2. Focus in Early Grades: Materials do not assess any of the following topics before the grade level indicated.

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II. Criteria for Materials and Tools Aligned to the K–8 Standards

3. Focus and Coherence through Supporting Work: Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

4. Rigor and Balance: Materials and tools reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by (all of the following, in the case of comprehensive materials; at least one of the following for supplemental or targeted resources):

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II. Criteria for Materials and Tools Aligned to the K–8 Standards

4. Rigor and Balance: Materials and tools reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by (all of the following, in the case of comprehensive materials; at least one of the following for supplemental or targeted resources):

a. Developing students’ conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. b. Giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. c. Using the materials as designed to spend sufficient time working with engaging applications, without losing focus on the major work of each grade.

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II. Criteria for Materials and Tools Aligned to the K–8 Standards

5. Consistent Progressions: Materials are consistent with the progressions in the Standards, by (all of the following):

a. Basing content progressions on the grade-by-grade progressions in the Standards.

b. Giving all students extensive work with grade-level problems.

c. Relating grade level concepts explicitly to prior knowledge from earlier grades.

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II. Criteria for Materials and Tools Aligned to the K–8 Standards

6. Coherent Connections: Materials foster coherence through connections at a single grade, where appropriate and where required by the Standards, by (all of the following):

a. Including learning objectives that are visibly shaped by CCSSM cluster headings.

b. Including problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. c. Preserving the focus, coherence, and rigor of the Standards even when targeting specific objectives.

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II. Criteria for Materials and Tools Aligned to the K–8 Standards

7. Practice-Content Connections: Materials meaningfully connect content standards and practice standards.

8. Focus and Coherence via Practice Standards: Materials promote focus and coherence by connecting practice standards with content that is emphasized in the Standards.

9. Careful Attention to Each Practice Standard: Materials attend to the full meaning of each practice standard.

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II. Criteria for Materials and Tools Aligned to the K–8 Standards

10. Emphasis on Mathematical Reasoning: Materials support the Standards’ emphasis on mathematical reasoning, by (all of the following):

a. Prompting students to construct viable arguments and critique the arguments of others concerning key grade-level mathematics that is detailed in the content standards

b. Engaging students in problem solving as a form of argument.

c. Explicitly attending to the specialized language of mathematics.

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Collaboratively built tools

informed and approved by the authors of the CCSS,

which evaluate the Common Core alignment of curricular materials

Actualize the Publishers Criteria Collaboratively built tools

informed and approved by the authors of the CCSS,

which evaluate the Common Core alignment of curricular materials

Actualize the Publishers Criteria

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Dimension I

Alignment to The Depth of the CCSS

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Dimension II

Key ShiftsIn the CCSS

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Dimension III

Instructional Supports

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Dimension IV

Assessment

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Overall Rating

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Rating Procedures for Rubric

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Rating Procedures for Rubric

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Dimension I

Alignment to The Depth of the CCSS

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Dimension I

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Dimension II

Key ShiftsIn the CCSS

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Dimension II

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Dimension II

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Dimension III

Instructional Supports

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Dimension III

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Dimension III

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Dimension IV

Assessment

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Dimension IV

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Overall Rating

Context for Curriculum Work

• Vendor Partners: $26 MM (RttT) P-2 ELA: Core Knowledge 3-8 ELA: Expeditionary Learning 9-12 ELA: PCG & Odell Education P-12 Math: Common Core, Inc.

• Regents Research Fund/ SED = 3 FTE + 2 Mgrs

• Teacher Reviewers = 50 teachers @ 10 hrs/wk

• Intensive Review Cycles with SAP

• SAP calibration and gradual release to RRF/ SED

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What we’ve learned…• Highly Qualified Writers and Reviewers take up to 6

months to calibrate Devotion to/ experience in a content area does

not a CCSS writer/ reviewer make A good teacher does not a curriculum writer/

reviewer make Much of what must shift is sacred

• Rhetorical alignment and actual alignment are two different things

• CCSS stickers are easy to produce; true quality, rigor, and alignment are not

• It often takes 6-8 revision cycles to get to necessary levels of quality/ rigor/ alignment

• Deep understanding of the documents presented is critical