A Guide to the K-8 and High School Publishers* Criteria for the

Report
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
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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 #2
a) 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?
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Objectives
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?
Supports faithful implementation of
the CCSSM
Developed by the three lead authors
Phil Daro, Bill McCallum, Jason
Zimba
Two 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 Tool
Inform purchase and adoption
Work with previously purchased materials
Review and guide teacher-developed
materials
Plan professional development
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Focus
Coherence
Rigor
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Focus
Consider what is not said
Math “needs to lose a
Differentiation
few pounds”
(p.3)
“Cannot
add “just one more thing”
Extensions
Grade-level work begins
during the first two to
“Teach less, learn more”
four weeks of instruction
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Math should
make sense
Coherence
Practice-content coherence
A progression of learning
Coherence supports focus
Use supporting
material to teach
major work
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Rigor
Balance with equal intensity
– Conceptual understanding
– Procedural skill and fluency
– Application
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Conceptual Understanding
“Understand”
High-quality conceptual problems
Elicit conversation
Identify relationships
Multiple representations
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.
Fluency
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Fluency Example
1. Write a simplified
expression for the
following:
7r + 2(r + 3)
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.
______ ( 2x + 2) - 4 =10x + ______
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Application
Single-step and multi-step
contextual problems
Require students to make
assumptions in order to model a
situation
Modeling – a practice standard
and a HS Conceptual Category
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My phone beeps with a text from
my friend who is an event
coordinator:
Application Problem
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
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 Work
Better 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 early
Don’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 Example
from Measurement and Data Progression
4. Rigor and Balance
Conceptual Understanding
Fluency
Application
Three aspects are not always together.
Three aspects are not always separate.
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5. Consistent Progressions
Grade-by-grade
Grade-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 arguments
Problem-solving as argument
Specialized language
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Construct Viable Argument
25-50% of students’ time
Independent thinking, classroom discussion and
written work
Critique arguments, error analysis
Multi-step problems
Student-devised strategy
Cohesive arguments that can be verified and
critiqued
Not a jumble of steps
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 Balance
Conceptual Understanding
Fluency
Application
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 arguments
Problem-solving as argument
Specialized language
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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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Problems are worth doing
Separate teacher material
Support for diverse learners
Indicators of Quality
SHORT
Variety in the pacing of each standard
Best practices with manipulatives
Variety of student products
Visual design is clear
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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 Cartier
ISBE Content Area Specialist Area 5&6
[email protected]
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