PUTTING THE COMMON CORE MATH STANDARDS INTO ACTION

Sandy ChristieCraig Bowman

Spring 2012

Implementing the Common Core State Standards in Washington State

Our Vision: Every student will have access to the CCSS standards through high quality instruction aligned with the standards every day; and that all English language arts and mathematics teachers are prepared and receive the support they need to implement the standards in their classrooms every day.

Our Purpose: To develop a statewide system with aligned resources that supports all school districts in their preparation of educators and students to implement the CCSS. This includes building system-wide capacity for sustained professional learning that

can support CCSS implementation now and be applied to other initiatives in the future.

March 20, 2012 OSPI CCSS Mathematics Webinar - Part 3

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Our Core Values: This vision can only occur through core values of clarity, consistency, collaboration, coordination, and commitment from classrooms, schools, and communities to the state level.

Objectives• Awareness of history of CCSS and SBAC • Understand the language/content of a grade specific CCSS Domain/Cluster at a deeper level

• Analyze a CCSS Domain learning progression for a grade band

• Connect Cognitive Complexity to Mathematical Practices and depth of content standards

• Strategies to support implementation of Mathematical Practices to increase content depth

A BRIEF REVIEW OF THE COMMON CORE STATE STANDARDS

CCSS – Mathematics

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July 20, 2011

Washington confirmed its commitment to student success with the adoption of Common Core State Standards (CCSS)

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Where did they come From?• State-led effort coordinated by

• National Governors' Association (NGA)• Council of Chief State School Officers (CCSSO)

• A national set of standards but not a federal government product or directive

• Written by a consortium of content experts, teachers, and administrators

• Why now and not before?• Race To the Top educational reform being funded by the U.S.

Department of Education

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WHO ELSE HAS ADOPTED?

What Did We Get?• Two sets of standards K-12

• English – Language Arts & Literacyincludes integrated reading and writing standards for History/Social Studies, Science, and Technical Subjects

• Mathematics• Created by nationally recognized experts in each

field• An evolution of our current standards – not a

replacement

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Progression of Standards

Building a foundation

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SMARTER BALANCED ASSESSMENT SYSTEM

New Assessment System:What We Know So Far

A National Consortium of States

• 28 states representing 44% of K-12 students

• 21 governing, 7 advisory states

• Washington state is fiscal agent

March 20, 2012OSPI CCSS Mathematics Webinar - Part 312

•Key Assessment Activities

Grades Supported Through Smarter BalancedGrades Summative Interim

(Optional)Formative Tools and Professional

Learning(Optional)

✔ ✔ ✔

1-2 Performance Tasks as Required

to Cover CCSS

✔

EOC and Comprehensive

✔

✔ ✔

EOC and Comprehensive

✔

Optional ✔

EOC and Comprehensive

✔

3 8

9 10

11

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March 20, 2012OSPI CCSS Mathematics Webinar - Part 314

Time and format• Summative: For each content area - ELA & Math

• Computer Adaptive Testing• Selected response (MC), Constructed Response (open-ended), Technology enhanced (e.g., drag and drop, video clips, limited web-interface)

• Paper/pencil summative offered for three years (transition period)

• Performance Tasks (like our CBAs)• Up to 2 per content area in grades 3-8• Up to 6 per content area in High School

March 20, 2012OSPI CCSS Mathematics Webinar - Part 315

Time and format• Summative: - Administration window is last 12 weeks of school

- For each content area - ELA & Math•Shorter option for states (~3 hours ELA, ~2 hours Math)

• Scale score on comprehensive test (met/not met determination)

•Longer option for states (~5 hours ELA, ~3 hours Math)• Able to report data on claims for individual students

March 20, 2012OSPI CCSS Mathematics Webinar - Part 316

Time and format

• Interim assessments• Can be used as often as needed• Can be customized by districts/schools

• To focus on selected strands• To clone summative test

• Will use Computer Adaptive Technology• Released items from summative item bank

March 20, 2012OSPI CCSS Mathematics Webinar - Part 317

Washington’s Context…Proposed Summative Assessments in 2014–15

English/LA Mathematics Science

Grade 3 SBAC SBAC

Grade 4 SBAC SBAC

Grade 5 SBAC SBAC MSP

Grade 6 SBAC SBAC

Grade 7 SBAC SBAC

Grade 8 SBAC SBAC MSP

Grades 9-10 HSPE Rdg & Writing

???

EOCAlgebra/Geometry ???

EOC

Grade 11 SBAC SBACSBAC=SMARTER Balanced Assessment ConsortiumMSP= Measurements of Student ProgressHSPE = High School Proficiency ExamsEOC= End of Course exams

March 20, 201219 OSPI CCSS Mathematics Webinar - Part 3

Many details still to be worked out.

For more info:•Check out CCSS Math Webinar Part 3 on OSPI website.•www.SmarterBalanced.org

Smarter Balanced Assessment Consortium

DEEPEN UNDERSTANDING OF THE COMMON CORE MATH STANDARDS

Major Shifts within Mathematics CCSSFocus•Fewer big ideas --- learn more •Learning of concepts is emphasized

Coherence•Articulated progressions of topics and performances that are developmental and connected to other progressions

Application•Being able to apply concepts and skills to new situations

Mathematical Practices1. Make sense of problems and persevere in solving

them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the

reasoning of others.4. Model with mathematics5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated

reasoning.

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Structure of the CCSS

Transitioning… Year 1Grade level Focus Domains

K-2 3-5 6-8 High School

Year 12011-2012

School districts that can, should consider adopting the CCSS for K-2 in total.

K – Counting and Cardinality (CC); Operations and Algebraic Thinking (OA) 1 – Operations and Algebraic Thinking (OA); Number and Operations in Base Ten (NBT)

2 – Operations and Algebraic Thinking (OA);Number and Operations in Base Ten (NBT)

and remaining 2008 WA Standards

3 – Number and Operations – Fractions (NF)

4 – Number and Operations – Fractions (NF)

5 – Number and Operations – Fractions (NF)

and remaining 2008 WA Standards

6 – Ratio and Proportion Relationships (RP)

7 – Ratio and Proportion Relationships (RP)

8 – Expressions and Equations (EE)

and remaining 2008 WA Standards

Teach all of the 2008 WA Mathematics Standards for each course

and prepare for

Algebra 1- Unit 2: Linear and Exponential Relationships

Geometry- Unit 1: Congruence, Proof and Constructions andUnit 4: Connecting Algebra and Geometry through Coordinates

OSPI Grade Level Transition Documents

What does this document tell you?

What doesn’t this document tell you?

How might you use this document?

Let’s do some math…• Individually work your grade level problem…

• Discuss how you solved it with your table partners

• Identify what mathematical practices you used

• Determine the cluster/standard the problem addresses

• Whole group discussion

CCSS Grade Overview• Grade level overview… Read

• Where does the task that you just solved fit?• What else do you notice?

• Share with partners

Focusing on the Domain

Individual… Read and HighlightAs you read, what language might someone (parent or colleague) have trouble understanding?

Highlight those areas on the Domain Illustration Sheet

Whole group… Discuss areas of concern

Creating Personal Connections

• On the provided Domain Illustration…• Personal description or definition /Example• Non-example or misconception

• Whole group… share out

Finished Early?? – listen in and/or contribute to other teams conversations

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Grade Level Progression ProblemsIn grade bands (K-2, 3-5, 6-8, HS):

•Each partner group has a set of grade band problems•Order the problems in a learning progression for each grade •Combine into a grade band progression•Compare with other same grade band partner teams•Review “answers”

•Martha’s Carpeting Task

Martha was recarpeting her bedroom, which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?

•The Fencing Task

• Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen to keep the rabbits.

• If Ms. Brown’s students want their rabbits to have as much room as possible, how long would each of the sides of the pen be?

• How long would each of the sides of the pen be if they had only 16 feet of fencing?

• How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

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Comparing Two Mathematical Tasks

• Think privately about how you would go about solving each task (solve them if you have time)

• Talk with your neighbor about how you did or could solve the task

–Martha’s Carpeting–The Fencing Task

Solution Strategies: Martha’s Carpeting Task

Martha’s Carpeting TaskUsing the Area Formula

A = l x wA = 15 x 10A = 150 square feet

Martha’s Carpeting TaskDrawing a Picture

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Solution Strategies: The Fencing Task

The Fencing TaskDiagrams on Grid Paper

The Fencing TaskUsing a Table

Length Width Perimeter Area

1 11 24 11

2 10 24 20

3 9 24 27

4 8 24 32

5 7 24 35

6 6 24 36

7 5 24 35

The Fencing TaskGraph of Length and Area

Comparing Two Mathematical Tasks

How are Martha’s Carpeting Task and the Fencing Task the same and how are they different?

Similarities and Differences

Similarities• Both are “area” problems

• Both require prior knowledge of area

Differences• The amount of thinking and

reasoning required• The number of ways the

problem can be solved • Way in which the area

formula is used • The need to generalize• The range of ways to enter

the problem

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Mathematical Tasks:A Critical Starting Point for Instruction

Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.

Stein, Smith, Henningsen, & Silver, 2000

•Level 1 (Recall)

….includes the recall of information such as a fact, definition, term, or a simple procedure, as well as performing a simple algorithm or applying a formula. That is, in mathematics a one step, well defined, and straight algorithmic ‐ ‐procedure should be included at this lowest level.

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•Level 2 (Skill/Concept)

….includes the engagement of some mental processing beyond a habitual response. A Level 2 assessment item requires students to make some decisions as to how to approach the problem or activity, whereas Level 1 requires students to demonstrate a rote response, perform a well known algorithm, follow a set ‐procedure (like a recipe), or perform a clearly defined series of steps.

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•Level 3 (Strategic Thinking)

….requires reasoning, planning, using evidence, and a higher level of thinking than the previous two levels. This may require a student to explain their thinking or make conjectures. The complexity does not result from the fact that there are multiple answers, a possibility for both Levels 1 and 2, but because the task requires more demanding reasoning.

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•Level 4 (Extended Thinking)

….requires complex reasoning, planning, developing, and thinking most likely over an extended period of time.

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Refer to the Carpeting and Fencing Tasks-What are their levels of cognitive

complexity?

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Sorting Activity• Individually: Categorize tasks into Level 1, 2, 3, or 4 using Cognitive Complexity Levels for Grade 7. Record your responses on the provided worksheet.

• In table teams: Share your results and come to consensus at your table.

• Whole group: Share results and review criteria groups used for low and high levels.

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Sorting Questions to ponder……

• How did you determine between levels 2 & 3?• Does a task presented as a word problem always have a high level of cognitive complexity?

• Does using a manipulative indicate a higher level of cognitive complexity?

• If a task requires an explanation, does it have a high level of cognitive complexity?

Changing the Cognitive Complexity Level

• Each team member picks out a task that was placed in level 1 or 2. Individually determine how you would modify your task to be a level 3 task.

• Share out with your team & determine which task you will share with the entire group.

• Share out entire group.

Cognitive Complexity & Mathematical Practices

Which levels of cognitive complexity allow students to develop the mathematical practices?

Update your Domain Illustration column 5.

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Are there various levels of Cognitive Complexity in Your Instructional Materials?

• Review several types of problems/tasks found in your instructional materials.

• What level of cognitive complexity are these tasks?

• Level 1 (Recall)• Level 2 (Skill/Concept)• Level 3 (Strategic Thinking)• Level 4 (Extended Thinking)

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Share at your table the types of problems/ tasks you found :

• What are the prevalent levels of complexity in your instructional materials?

• How will this impact meeting the standards for mathematical practice?

Whole group share out

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Gas Mileage Activity

• Complete the Gas Mileage Activity• Discuss responses

• Review “original” Gas Mileage Activity

• Compare/contrast both versions

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Who’s Doing the Thinking?

Watch Dan Meyer video

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Video Debrief

• How much is too much support, how much is too little?

• How does scaffolding interfere/promote the standards for mathematical practice?

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Impact of Teachers

• Read case studies (scenarios) of how Fencing Task was implemented.

• Use worksheet to write your thoughts on cognitive complexity students experience.

• Share out in table teams• Whole group share out

Who’s Doing the Thinking?

Brainstorming Session:• What instructional strategies can be used to promote student thinking and develop mathematical practices?

• How does this relate to content depth?

Shifts in Classroom Practice Handout

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•If time…………………..• Watch Annenberg Video for Mathematical Practices:

• Partner 1: Look for Mathematical practices students are exhibiting. What are they doing/saying?

• Partner 2: Look for teacher “moves” that encourage student development of mathematical practices.

Partner Shareout…………………Whole Group Shareout

Objectives Revisited• Awareness of history of CCSS and SBAC • Understand the language/content of a grade specific CCSS Domain/Cluster at a deeper level

• Analyze a CCSS Domain learning progression for a grade band

• Connect Cognitive Complexity to Mathematical Practices and depth of content standards

• Strategies to support implementation of Mathematical Practices to increase content depth

Resources

http://psesd-math.wikispaces.com/

Common Core Tools

Thank you…………

Clock hours reminder– turn in forms