a guide to the k-8 and high school publishers’ criteria for the ccssm
DESCRIPTION
A Guide to the K-8 and High School Publishers’ Criteria for the CCSSM. Dana Cartier ISBE Content Area Specialist Slides adapted from the K-8 Publishers’ Criteria. 3.OA.9 Task #1. Fill in the blank below and explain. 2, 4, 6, ____. 3.OA.9 Task #2. - PowerPoint PPT PresentationTRANSCRIPT
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A Guide to the K-8 and High School Publishers’ Criteria
for the CCSSMDana Cartier
ISBE Content Area Specialist
Slides adapted from the K-8 Publishers’ Criteria
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3.OA.9 Task #1
Fill in the blank below and explain.
2, 4, 6, ____
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3.OA.9 Task #2a) In each column and each
row of the table even and odd numbers alternate. Explain why.
b) Explain why the diagonal, from top left to bottom right, contains the even numbers 2,4,6,8, and 10.
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Compare the Tasks
What were the similarities and differences of the previous
tasks? Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License
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Objectives
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Introduce the K-8 & High School Publishers’ Criteria
Learn the why and how of using the criteria
Explore the math criteria
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What is the Publishers’ Criteria?
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Supports faithful implementation of the CCSSMDeveloped by the three lead authors Phil Daro, Bill McCallum, Jason ZimbaTwo different documents- similiar
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Why Do We Need This?
Standards cannot raise achievement.
Material should connect to assessment.
Educators complain about what is missing, but not about what has crept in.
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Wiggins, 2012
Because conventional textbook coverage is so fractured, unfocused, superficial, and unprioritized, there is no guarantee that most students will come out knowing the
essential concepts of algebra.
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How Can We Use This ToolInform purchase and adoption
Work with previously purchased materials
Review and guide teacher-developed materials
Plan professional development
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Part I: Major Shifts
Focus Coherence
Rigor Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License
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Focus
Consider what is not said
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Math “needs to lose a few pounds” (p.3)
“Teach less, learn more”
“Cannot add “just one more thing”
Grade-level work begins during the first two to four weeks of instruction
Differentiation
Extensions
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CoherencePractice-content coherence
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Math should make sense
A progression of learning
Use supporting material to teach major work
Coherence supports focus
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RigorBalance with equal intensity
– Conceptual understanding– Procedural skill and fluency– Application
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Conceptual Understanding
“Understand”High-quality conceptual problemsElicit conversationIdentify relationshipsMultiple representations
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Fluency“Fluently”
Methods are based on mathematical principles, not mnemonics or tricks
Quickly and accurate, to work with flow. It isn’t halting, stumbling, or reversing oneself.
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Fluency
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1. Write a simplified expression for the following: 7r + 2(r + 3)
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2. Fill in the blanks below to make the equation true for every value of x. Explain the steps you took, as well as any math properties you used.
Fluency Example
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ApplicationSingle-step and multi-step contextual problemsRequire students to make assumptions in order to model a situationModeling – a practice standard and a HS Conceptual Category
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Application ProblemMy phone beeps with a text from my friend who is an event coordinator:
My producer sent me only 50 feet of red velvet rope and 4 poles! I don’t know what he was thinking, how can I fit all of the VIPs in this section?“
What is the mathematical question?
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Application
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How many dinosaurs are standing in the lake?Explain how you know. Use words and mathematical language to explain your solution.
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Part II: Criteria for Materials and Tools
10 criteria to analyze mathematics curricular materials
1 criterion to align mathematics to other disciplines
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K-8 Publishers’ Criteria
Part II: Criteria for Materials and Tools Aligned to the K-8 Standards
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1. Focus on Major WorkBetter to inadvertently leave something
out than to teach too much
65%-85%of time is spent on the major work
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5th Grade PARCC Model Content Framework
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2. Focus in Early Grades
Don’t cover material earlyDon’t assess material early
Patterns only within arithmetic
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3. Focus and Coherence through Supporting Work
Supporting work enhances major work
Supporting work does not detract from focus
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2nd Grade Examplefrom Measurement and Data Progression
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4. Rigor and BalanceConceptual UnderstandingFluencyApplication
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Three aspects are not always together.
Three aspects are not always separate.
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5. Consistent Progressions
Grade-by-gradeGrade-level problems
Relating to prior knowledge
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6. Coherent Connections
Curricular material makes connections between clusters and domains
CCSSM are more than a sum of their parts
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7. Practice-Content Connections
Not separate
Present throughout
Grounded in the content standards
Accompanying teacher-support
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8. Focus and Coherence via Practice Standards
Connect practice and content standards as specified
– Structure for structural themes (MP7)– Using repetition to find mathematical
regularity (MP8)
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9. Careful Attention to Each Practice Standard
Full meaning and spirit of the entire practice standard
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10. Emphasis on Mathematical Reasoning
Construct viable argumentsProblem-solving as argument
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Construct Viable Argument25-50% of students’ time
Independent thinking, classroom discussion and written work
Critique arguments, error analysisMulti-step problems
Student-devised strategyCohesive arguments that can be verified and
critiqued Not a jumble of steps
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Specialized Language
“The language of argument, problem-solving and mathematical explanations are taught rather than
assumed.”
Language of representations – Diagrams, tables, graphs, symbolic expressions, drawing,
images, text – Helpful for ELL students
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High School Publishers’ Criteria
Part II: Criteria for Materials and Tools Aligned to the High School
Standards
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1. Focus on Widely Applicable Prerequisites
Material should coherently include all of the standards in High School (without the + standards), with a majority of the time devoted to building the particular knowledge and skills that are most applicable and prerequisite to a wide range of college majors and postsecondary programs
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2. Rigor and BalanceConceptual UnderstandingFluencyApplication
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Three aspects are not always together.
Three aspects are not always separate.
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3. Consistent Content
•Base course on content•Give students extensive work
with course-level problems•Explicitly relates course content
to prior knowledge
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4. Coherent Connections
Curricular material makes connections between clusters and domains
CCSSM are more than a sum of their parts
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5. Practice-Content Connections
Not separate
Present throughout
Grounded in the content standards
Accompanying teacher-support
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6. Focus and Coherence via Practice Standards
Connect practice and content standards as specified
– Structure for structural themes (MP7)– Using repetition to find mathematical
regularity (MP8)
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7. Careful Attention to Each Practice Standard
Full meaning and spirit of the entire practice standard
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8. Emphasis on Mathematical Reasoning
Construct viable argumentsProblem-solving as argument
Specialized languageContent contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License
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Connecting Criterion:Consistency with CCSSM
Materials for science and technical subjects are consistent with CCSSM
Grade-level appropriate mathematics in other disciplines
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Indicators of Quality
Variety in the pacing of each standard
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Problems are worth doing
Variety of student products
Separate teacher material
Best practices with manipulatives
Visual design is clear
Support for diverse learners
SHORT
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Avoid crosswalks
Align to the letter and spirit of the standards
Don’t take the common out of COMMON core
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Dana CartierISBE Content Area Specialist Area 5&6
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