Problems and Concepts and Skills, Oh My…

Facilitator: Dr. Karen M. BeererDiscovery Education

What does this have to do with the Common Core Mathematics Standards?

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CCSS Mathematics StandardsThe Structure: 8 Standards for Mathematical Practice which span K-12 Grades K-8 have grade-level specific standards High School Standards are listed in conceptual categories (e.g., Functions, Number & Quantity)

K 12

Number and Operations

Measurement and Geometry

Algebra and Functions

Statistics and Probability

Traditional U.S. Approach

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What is a learning trajectory?“Learning progressions,” or, as the concept more often is termed in the mathematics education literature --- “learning trajectories” --- are labels given to attempts to gather and characterize evidence about the paths children seem to follow as they learn mathematics. Hypotheses about the paths described by learning trajectories have roots in developmental and cognitive psychology and, more recently, in developmental neuroscience. These roots… describe the ways children’s actions, thinking, and logic move through characteristic stages in their understanding of the world…

- Daro, 2012

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Grade Standard Required FluencyK K.OA.5 Add/subtract within 5

1 1.OA.6 Add/subtract within 10

2 2.OA.22.NBT.5

Add/subtract within 20 (know single-digit sums from memory)Add/subtract within 100

3 3.OA.73.NBT.2

Multiply/divide within 100 (know single-digit products from memory)Add/subtract within 1000

4 4.NBT.4 Add/subtract within 1,000,000

5 5.NBT.5 Multi-digit multiplication

6 6.NS.2,3 Multi-digit divisionMulti-digit decimal operations

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The best thing about the Math Common Core Standards is…

30 second pause…• The structure of the Math CCSS• The focus and coherence of the Math CCSS• The placement of topics in the K-8 CCSS Math

curriculum• Learning trajectories and the CCSS Math

curriculum• Computational fluency in the Math CCSS• The CCSS Mathematics instructional shifts

http://padlet.com/wall/mathccss

Kid Snippets Video

Focus Coherence RigorLearning

Trajectories

Standards for

Mathematical Practice

Rigor

Coherence

Learning Trajectories

Focus

Standards for Mathematical Practice

☐ Have you…”unwrapped” the Standards for Mathematical Practice?

What do these SMPs look like?

Third Grade SMP video

On Common Ground with the Common Core Webinar Series

Which Standards of Mathematical Practice were evident in the problem you just viewed?

______Make sense of problems and persevere in solving them.

______Reason abstractly and quantitatively.

______Construct viable arguments and critique the reasoning of others.

______Model with mathematics.

______Use appropriate tools strategically.

______Attend to precision.

______Look for and make use of structure.

______Look for and express regularity in repeated reasoning.

Common Core Math Implementation Considerations

1. An Instructional Model

2. An Instructional Planning Tool

3. Instructional Strategies and Tools

4. Assessments

Common Core Math Implementation Considerations

1. An Instructional technology integration Model

2. An Instructional technology Planning integration Tool

3. Instructional technology integration Strategies and Tools

4. Assesstechnology integrationments

Publish - requiring deep consideration of audience, purpose, structure, text features, and format. Collaborate - forcing students to plan, adopt, adapt, rethink, and revise, all higher-level practices. Evaluate - necessitating that students make critical judgment calls about how information is presented and shared.Integrate - emphasizing design, and producing considerable cognitive load on a learner.

CCSS requires students to:

A CCSS Math Instructional ModelStep One: Task First!

Consideration #1:

Dan Meyer’s Three Act Math Tasks

The Top Five Sites for CCSS Math Tasks

The Top Five Sites for CCSS Math Tasks

The Mathematics Common Core Toolbox: www.ccsstoolbox.com

The Top Five Sites for CCSS Math Tasks

Inside Mathematics: www.insidemathematics.org

The Top Five Sites for CCSS Math Tasks

Illustrative Math: www.illustrativemathematics.org

The Top Five Sites for CCSS Math Tasks

Mathematics Assessment Project:Map.mathshell.org

An Instructional Planning Tool

Consideration #2:

An Instructional Planning ToolPhase 1: Assess Students Describe your exploration assessment activity:       Key Reminders: Anticipate the likely student responses to

cognitively demanding mathematical tasks Monitor student responses to the task during

this exploration phase

An Instructional Planning ToolPhase 2: Learning Goals Based on Student Data

Phase 3: Design Instruction

Video: Teacher Debriefing Student Work

Instructional Strategies and Tools

Think-Ink-Pair-Share:T: Without pencils, students think for 1‐2 minute. I: Students may then use pencil to begin working...without talking to partner. P: Students then share their thinking and answer(s) with their partner. S: Pairs then may share with larger group.

Consideration #3:

Instructional Strategies and Tools

I Spy:• One student can go around to other teams

and listen in for one minute. (without paper or pencil)

• Student reports back to the team what was learned.

Instructional Strategies and Tools

Huddle:• One person from each team (teacher’s

choice) is called to the front of the room.• Teacher gives a piece of information, checks

for understanding.• Student goes back to team to share.

Instructional Strategies and Tools

Integrating Digital Videos• Construct mathematical knowledge• Answer challenging mathematical questions• Expand student visualization skills• Mathematically analyze events in video

clips

Mathematics in Movies:Mathematics in Movies

Assessments• Explain your answer using numbers, symbols and words.• Drag tiles to… that make the statement true. There is more

than one correct answer.• Compare these statements from two students…Can both

students be correct? Explain how you know.• Are they both correct? Use the properties of operations to

justify your answer.• Which of the following statements must be true about the

model for …compared to the model you developed for …? Select all that apply.

• Drag tiles to complete the sentences and the equation below based on the results of the experiment.

Consideration #4:

Assessments• Explain your answer using numbers, symbols and words.• Drag tiles to… that make the statement true. There is more

than one correct answer.• Compare these statements from two students…Can both

students be correct? Explain how you know.• Are they both correct? Use the properties of operations to

justify your answer.• Which of the following statements must be true about the

model for …compared to the model you developed for …? Select all that apply.

• Drag tiles to complete the sentences and the equation below based on the results of the experiment.

Assessments

http://www.drawzit.com

Assessmentshttps://bubbl.us

Assessmentswww.infuselearning.com

On Common Ground with the Common Core Webinar Series

You can’t lead the change if you don’t understand the

change.-Dr. Christine Tell