2015 DoDEA College and Career Ready Initiative PK–5 Mathematics, Day 1 Summer 2015.

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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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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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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• 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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A quote

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• 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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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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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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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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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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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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The Structure of the CCRSM

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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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Standard title

Narrative description

Standards for Mathematical Practice (K–High School)

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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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Standards for Mathematics: K–8

Introduction

Domain

Cluster heading

✓ Content standard

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✓✓

✓✓

✓

✓

✓

✓✓

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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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Coding convention for the CCRSM

3.OA.7

Grade Level

Domain

Standard Number

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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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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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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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• 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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College and Career Ready Standards for

Mathematics

Alignment

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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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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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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


Progressions Documents




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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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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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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…

2015 DoDEA College and Career Ready Initiative PK–5 Mathematics, Day 1 Summer 2015.

Documents

Transcript of 2015 DoDEA College and Career Ready Initiative PK–5 Mathematics, Day 1 Summer 2015.