2015 dodea college and career ready initiative pk–5 mathematics, day 1 summer 2015
TRANSCRIPT
2015
DoDEA College and Career Ready Initiative
PK–5 Mathematics, Day 1Summer 2015
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The goal of the initiative
DoDEA College and Career Ready Initiative: Mathematics
Build the capacity of educators to ensure that all students meet or exceed the expectations of the College and Career Ready Standards for Mathematics (CCRSM).
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DoDEA College and Career Ready Initiative: Mathematics
Participants will develop a common understanding of the College and Career Ready Standards for Mathematics and a strong working knowledge of the standards’ effects on teaching and learning.
Session goal
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DoDEA College and Career Ready Initiative: Mathematics
Using a set of structured tools to promote conversation and collaboration around the CCRSM, participants will…
• Identify and describe the components of the standards and the relationships among the components;
• Investigate vertical alignment to determine how learning around a big idea progresses across the grade-level standards; and
• Identify evidence of focus, coherence, and rigor and explain how these key shifts guide decisions about teaching and learning.
Learning expectations
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DoDEA College and Career Ready Initiative: Mathematics
• Understand that those who work, learn.
• Look for solutions, not blame.
• Focus on systems, not people.
• Recognize that everyone has expertise.
• Be honest.
• Challenge ideas.
• Share talk time.
Group norms
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DoDEA College and Career Ready Initiative: Mathematics
A quote
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DoDEA College and Career Ready Initiative: Mathematics
• Do you agree or disagree with the central idea of this quotation?
• What is the relationship between this quotation and the standards?
Reflect
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DoDEA College and Career Ready Initiative: Mathematics
They are...• Learning goals that work grade-by-grade so that when
students graduate, they are ready for what modern careers and colleges expect.
• These are high standards that help us help our students develop problem-solving and critical thinking skills with real-world applications.
What are the CCRSM?
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DoDEA College and Career Ready Initiative: Mathematics
In our fast-changing world, our students and workforce must be flexible and able to adapt to new situations by applying what they know to new and unforeseen problems.
Why do we need these standards?
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DoDEA College and Career Ready Initiative: Mathematics
Development of the standards
The College and Career Ready Standards for Mathematics do not provide…• A complete scope and sequence,• a course outline, or• all the essential skills and knowledge students could
have.
The College and Career Ready Standards for Mathematics do…• Outline the most important essential skills and
knowledge every student needs to master to succeed in college and career.
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DoDEA College and Career Ready Initiative: Mathematics
Key shifts in the CCRSM
• Focus: Narrowing in on fewer topics.
• Coherence: Linking topics and thinking across grades.
• Rigor: Pursuing—with equal intensity—conceptual understanding, procedural skills and fluency, and applications.
College and Career Ready Standards for Mathematics
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DoDEA College and Career Ready Initiative: Mathematics
5 x 14 = ____
• Describe this problem using words, interpreting it in at least three different ways.
• Solve the problem. Show how you solved it and connect it to one of your interpretations.
Preview of Engaging in Mathematics
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DoDEA College and Career Ready Initiative: Mathematics
The Structure of the CCRSM
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DoDEA College and Career Ready Initiative: Mathematics
The College and Career Ready Standards for Mathematics consist of two corresponding and connected sets of standards:
1. Standards for Mathematical PracticeA set of 8 standards that describe the ways in which the mathematical content standards should be approached.
2. Standards for MathematicsThese standards define what students should understand and be able to do in their study of mathematics.
The Structure of the CCRSM
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DoDEA College and Career Ready Initiative: Mathematics
Standard title
Narrative description
Standards for Mathematical Practice (K–High School)
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DoDEA College and Career Ready Initiative: Mathematics
Introduction• Provides important contextual information and calls out and describes
critical areas of focus.
Domain• Large groups of related standards; connects topics and content
between and among grade levels.
Cluster/Cluster Heading• Smaller set of related standards within the domain; identifies the primary
idea.
Content Standards• Describe what students should know and be able to do for that cluster
heading, domain, and grade level.
Standards for Mathematics: K–8
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DoDEA College and Career Ready Initiative: Mathematics
Standards for Mathematics: K–8
Introduction
Domain
Cluster heading
✓ Content standard
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DoDEA College and Career Ready Initiative: Mathematics
✓✓
✓✓
✓
✓
✓
✓✓
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DoDEA College and Career Ready Initiative: Mathematics
Numbering• The standards are numbered sequentially within each domain,
regardless of the cluster heading under which they fall.
Footnotes• Footnotes serve three purposes; enhance descriptions, provide
parameters, or reference the glossary. Footnotes can appear at the standard, cluster heading, or domain.
Examples• Examples are intended to clarify the standard. They are neither
obligatory nor limiting, but they should not be ignored.
Conventions and annotations
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DoDEA College and Career Ready Initiative: Mathematics
Coding convention for the CCRSM
3.OA.7
Grade Level
Domain
Standard Number
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DoDEA College and Career Ready Initiative: Mathematics
Kindergarten – Grade 2Counting and Cardinality (K only)
Operations and Algebraic Thinking
Number and Operations in Base 10
Measurement and Data
Geometry
Grades 6 – 7Ratios and Proportional Relationships
The Number System
Expressions and Equations
Geometry
Statistics and Probability
Grades 3 – 5
Operations and Algebraic Thinking
Number and Operations in Base 10
Number and Operations—Fractions
Measurement and Data
Geometry
Grade 8 The Number System
Expressions and Equations
Functions
Geometry
Statistics and Probability
Standards for Mathematics: K–8 Domains
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DoDEA College and Career Ready Initiative: Mathematics
Standards for Mathematics: K–8 and High School
K–8 High SchoolConceptual Category• Provides a coherent view of high school
mathematics.
Introduction• Provides important contextual information and
calls out and describes critical areas of focus.
Introduction• Provides important contextual information.
Domain• Large groups of related standards; connects
topics and content between and among grade levels.
Domain• Large groups of related standards; connects
topics and content between and among conceptual categories.
Cluster/Cluster Heading• Smaller set of related standards within the
domain; identifies the primary idea.
Cluster/Cluster Heading• Smaller set of related standards within the
domain; identifies the primary idea.
Standards• Describe what students should know and be
able to do for that cluster heading, domain, and grade level.
Standards• Describe what students should know and be
able to do for that cluster heading, domain, and conceptual category.
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DoDEA College and Career Ready Initiative: Mathematics
What? What did you learn as a result of the structure activity?
So What? What is important about what you have learned?
Now What? What actions will you take as a result of what you have learned?
Reflection
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DoDEA College and Career Ready Initiative: Mathematics
• A chart
• A textbook correlation
• A scope and sequence
• A curriculum guide
• A testing plan
These things imply alignment, but they do not give us alignment.
Alignment is more than…
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DoDEA College and Career Ready Initiative: Mathematics
College and Career Ready Standards for
Mathematics
Alignment
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DoDEA College and Career Ready Initiative: Mathematics
Alignment means EVERY educator…
• Understands what is expected of students.
• Understands these expectations within the context of the K–12 program.
• Accepts responsibility for meeting these expectations.
Alignment
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DoDEA College and Career Ready Initiative: Mathematics
As a group…
1. Select a big idea for your group to investigate.
2. Determine what your big idea means.
3. Study one grade level at a time. Consider all parts of the standards.
4. Write a summary in your template.
Investigating Vertical Alignment in the CCRSM
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DoDEA College and Career Ready Initiative: Mathematics
Vertical Alignment ChartBig Idea: Foundations and Conceptual Understanding of Multiplication
Grade/Course
CCRSM Code
Content Standards Summary
5 5.OA.2
4 4.OA.1
3 3.OA.13.OA.5
2 2.OA.42.NBT.2
1 1.OA.61.NBT.2a
KK.CC.1K.OA.3K.NBT.1
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5. As a group, discuss and come to a consensus on what students need to know and be able to do according to the standards at each grade level or course.
6. Record a group summary of each grade-level or course standard on the strips provided.
7. Use the strips to build a learning trajectory on chart paper.
8. As a group, analyze the trajectory, considering the following questions:
• What changes occur from grade to grade?
• Where are concepts introduced, developed, and finalized?
• Does an idea or skill get more complex, and if so, how?
Investigating vertical alignment in the CCRSM
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In order to provide support, progressions documents have been written to help educators understand the mathematics in the standards. There are total of 14 progressions, with 6 for grades K–5. They address all the domains, and can be found at:
http://ime.math.arizona.edu/progressions
DoDEA College and Career Ready Initiative: Mathematics
Progressions Documents
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DoDEA College and Career Ready Initiative: Mathematics
1. What does the classroom teacher gain from studying a vertical learning trajectory of the standards?
2. How does studying the standards in this way support students who have gaps in their learning?
3. How can this type of investigation influence conversations at different levels of the system (e.g., grade level, school, and district)?
Reflection
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DoDEA College and Career Ready Initiative: Mathematics
5 x 14 = ____
• Solve this equation two different ways, using pictures, words, and numbers.
• As you do so, think about how a third-grade student might approach this problem.
Engaging in the mathematics
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DoDEA College and Career Ready Initiative: Mathematics
Engaging in the mathematics
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DoDEA College and Career Ready Initiative: Mathematics
Engaging in the mathematics
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DoDEA College and Career Ready Initiative: Mathematics
One of your colleagues could not attend this session.
How would you describe the important learning points from today’s session to him/her?
What questions would you tell them you are left with after today’s experience?
Take a few minutes to think about this scenario, and jot down your thoughts.
Reflecting on the day…