Common Core State Standards for Mathematical Practice

National Practice Standards in a Mathematics Classroom?

Common Core State Standards for Mathematical Practice

Icebreaker

• Compromise

• Without talking, write down the answers to the three questions presented.

Common Core State Standards for Mathematical Practice

Icebreaker

• Compromise

• What is your favorite Ice Cream flavor?

Common Core State Standards for Mathematical Practice

Icebreaker

• Compromise

• What is your favorite genre of book?

Common Core State Standards for Mathematical Practice

Icebreaker

• Compromise

• Where do you like to go on vacation?

Common Core State Standards for Mathematical Practice

Icebreaker

Compromise: As a team, compromise on one thing for each question, that your whole team can agree on.

• What is your favorite Ice Cream flavor?

• What is your favorite genre of book?

• Where do you like to go on vacation?

Common Core State Standards for Mathematical Practice

Icebreaker-Debrief

Compromise

What might be the reason we did this icebreaker?

Common Core State Standards for Mathematical Practice

Agenda/Goals

• Opening

• CCSS practices

• Doing Mathematics

• Looking at a lesson

• Closure

Common Core State Standards for Mathematical Practice

The Common Core State Standards (CCSS) were:

developed by the Council of Chief State School Officers (CCSSO) and the National Governor’s Association (NGA) Center for Best Practices

formally released on June 2, 2010 adopted by 45 states and territories

Common Core State Standards for Mathematical Practice

CCSS: A Major Challenge/Opportunity

COLLEGE and CAREER readiness expectations Rigorous CONTENT and APPLICATIONS Stress CONCEPTUAL UNDERSTANDING as well as

procedural skills Organized around MATHEMATICAL PRINCIPLES

FOCUS and COHERENCE Designed around RESEARCH-BASED LEARNING

PROGRESSIONS whenever possible.

Common Core State Standards for Mathematical Practice

CCSS: A Major Challenge/Opportunity

COLLEGE / CAREER readiness expectations

CONTENT / APPLICATIONS

CONCEPTUAL UNDERSTANDING as well as

MATHEMATICAL PRINCIPLES

FOCUS / COHERENCE

RESEARCH-BASED LEARNING PROGRESSIONS whenever possible.

Common Core State Standards for Mathematical Practice

What’s different about CCSS?

These Standards are NOT intended to be NEW NAMES FOR OLD WAYS OF DOING BUSINESS. They are a call to take the next step. It is time for states to work together to build on lessons learned from two decades of standards-based reforms. It is time to recognize that standards are not just promises to our children, but promises we intend to keep.

— CCSS (2010, p.5)

Common Core State Standards for Mathematical Practice

What’s different about CCSS?

These Standards are NOT intended to be NEW NAMES FOR OLD WAYS OF DOING BUSINESS. They are a call to take the next step. It is time for states to build on lessons learned from two decades of standards based reforms. It is time to recognize that standards are not just promises to our children, but promises we intend to keep.

— CCSS (2010, p.5)

Common Core State Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice

#1 is Detective

Common Core State Standards for Mathematical Practice

#2 is Escher

Common Core State Standards for Mathematical Practice

#3 is Debaters

Common Core State Standards for Mathematical Practice

#4 is Models

Common Core State Standards for Mathematical Practice

#5 is Toolbox

Common Core State Standards for Mathematical Practice

#6 is Compass

Common Core State Standards for Mathematical Practice

#7 is Construction

Common Core State Standards for Mathematical Practice

#8 is Fractal

Common Core State Standards for Mathematical Practice

#1-8

Can you repeat all the numbers and words?

Common Core State Standards for Mathematical Practice

How did you do?

1. Detective2. Escher3. Debaters4. Models

5. Toolbox6. Compass7. Construction8. Fractal

Common Core State Standards for Mathematical Practice

Two Types of Standards:

Mathematical Content (different at each grade level for K-8 and by content strand for 9-12)

NEW!!!…MATHEMATICAL PRACTICES (recurring throughout the grades)

Common Core State Standards for Mathematical Practice

Standards for Mathematical Practice

Describe HABITS OF MIND of a mathematically expert student

Common Core State Standards for Mathematical Practice

1. 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 mathematics

CCSS Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice

CCSS Standards for Mathematical Practice

5. 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

Common Core State Standards for Mathematical Practice

The Standards for Mathematical Practice

Take a moment to examine the first three words of each of the 8 mathematical practices… what do you notice?

Mathematically Proficient Students…

Common Core State Standards for Mathematical Practice

The Standards for [Student] Mathematical Practice

What are the VERBS that illustrate the student actions for your assigned mathematical practice?

CIRCLE, HIGHLIGHT or UNDERLINE them for your assigned practice…

Common Core State Standards for Mathematical Practice

The Standards for [Student] Mathematical Practice

Take 3 minutesto prepare a

2 minute ELEVATOR TALKexplaining your practice standard.

Common Core State Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice

Connecting the pictures to the practices

Common Core State Standards for Mathematical Practice

Detective

1. Make sense of problems and persevere in solving them.

Common Core State Standards for Mathematical Practice

Escher

2. Reason abstractly and quantitatively.

Common Core State Standards for Mathematical Practice

Debaters

3. Construct viable arguments and critique the reasoning of others.

Common Core State Standards for Mathematical Practice

Models

4. Model with mathematics.

Common Core State Standards for Mathematical Practice

Toolbox

5. Use appropriate tools strategically.

Common Core State Standards for Mathematical Practice

Compass

6. Attend to precision.

Common Core State Standards for Mathematical Practice

Construction

7. Look for and make use of structure.

Common Core State Standards for Mathematical Practice

Fractals

8. Look for and express regularity in repeated reasoning.

Common Core State Standards for Mathematical Practice

Think-Pair-Share

Imagine what a lesson would look like if it had the practices embedded.

Common Core State Standards for Mathematical Practice

NEWTON’S REVENGE Task

Have you heard about Newton’s Revenge, the new roller coaster? It’s so big, fast, and scary that people are already starting to talk. Some people are worried about the tunnel that thrills riders with its very low ceiling.

The closest the ceiling of the tunnel ever comes to the seat of the roller-coaster car is 200 cm. Although no accidents have been reported yet, rumors have been spreading that very tall riders have broken their arms as they went through the tunnel with their arms raised over their heads. Unfortunately, due to these rumors, many tall people have stopped riding the coaster.

Algebra Connections

Common Core State Standards for Mathematical Practice

Teammates ConsultParticipants will be organized into teams… Step 1: Pencils down… individuals read

silently and then come up with ideas. Step 2: Teams discuss the problem and

develop a plan. Step 3: The team will share the plan with the

facilitator. Step 4: The team can pick up their pencils

and begin working on the problem.

Common Core State Standards for Mathematical Practice

NEWTON’S REVENGE Task

Have you heard about Newton’s Revenge, the new roller coaster? It’s so big, fast, and scary that people are already starting to talk. Some people are worried about the tunnel that thrills riders with its very low ceiling.

The closest the ceiling of the tunnel ever comes to the seat of the roller-coaster car is 200 cm. Although no accidents have been reported yet, rumors have been spreading that very tall riders have broken their arms as they went through the tunnel with their arms raised over their heads. Unfortunately, due to these rumors, many tall people have stopped riding the coaster.

Your Task: Consider how you could determine whether the tunnel is actually safe for any rider, no matter how tall. Be ready to share your responses with the rest of the group.

Algebra Connections

Common Core State Standards for Mathematical Practice

Discuss the Standards for Mathematical Practice that were employed as you worked

through this lesson…

Common Core State Standards for Mathematical Practice

Balancing Procedure and Understanding…

Content standards that begin with “UNDERSTAND” connect practice to content.

Lack of understanding prevents students from engaging in the mathematical practices.

Common Core State Standards for Mathematical Practice

CCSS standards

build in complexity

and provide more clarity

for expected student

performance.

Common Core State Standards for Mathematical Practice

If your goal truly is only to get the answer, then the ‘butterflies have it’…

Common Core State Standards for Mathematical Practice

Butterfly Method:

Common Core State Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice

Now try using butterflies on this TIMSS* item…

1/2 + 1/3 +1/4 =

*Trends in International Mathematics and Science Study

Common Core State Standards for Mathematical Practice

Walk and Talk…

• What are the implications of teaching strategies like “the butterfly method”?

• How will implementation of the Practice Standards impact our teaching?

Common Core State Standards for Mathematical Practice

Let’s see what you remember…

• Turn to your elbow partner. See how many of the practices you can remember without looking at the posters.

Common Core State Standards for Mathematical Practice

CCSS Standards for Mathematical Practice

1. MAKE SENSE of problems and persevere in solving them.

2. REASON abstractly and quantitatively.3. CONSTRUCT VIABLE ARGUMENTS/ critique the

reasoning of others.4. MODEL with mathematics.5. 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.

Common Core State Standards for Mathematical Practice

Looking at a lesson

• Take the lesson that you are given. Go through the lesson, citing all practices that students are expected to be engaged in. Make sure this is written down.

Common Core State Standards for Mathematical Practice

Jigsaw/Table Carousel

• All participants with the same lesson gather at the same table. Put your citations together with the lesson you were using. Pass the papers to another pair to give feedback on what you found. The feedback should be written on post-its and put on the back of your paper. Repeat, if time.

Common Core State Standards for Mathematical Practice

The Standards for Mathematical Practice

will be assessed…

Common Core State Standards for Mathematical Practice

So What’s Different About the CCSS?

• Accountability

• Accountability

•Accountability

Common Core State Standards for Mathematical Practice

Implementing CCSS: Where NOT to start

Do not begin by aligning CCSS standards grade-by-grade with existing mathematics standards.

Do not start by focusing on teaching “a” standard.

Common Core State Standards for Mathematical Practice

Implementing CCSS: Where TO start

The Eight Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice

Implementing CCSS: Where TO start

There is research on PD practices that are most

effective in supporting teacher learning; use it!

Pres. J. Michael Shaughnessy,NCTM Summing Up, 12-2011

Common Core State Standards for Mathematical Practice

Implementing CCSS: Where TO start

Target a few selected practices to address in depth.

These practices must be embedded in discussions about content.

Pres. J. Michael Shaughnessy,NCTM Summing Up, 12-2011

Common Core State Standards for Mathematical Practice

Implementing CCSS: Where TO start

Avoid a fragmented menu of varied professional

development offerings! Pres. J. Michael Shaughnessy,NCTM Summing Up, 12-2011

Common Core State Standards for Mathematical Practice

Implementing CCSS: Where TO start

Include a variety of stakeholders in whatever PD is offered –

don’t compartmentalize it; bring groups together.

Pres. J. Michael Shaughnessy,NCTM Summing Up, 12-2011

Common Core State Standards for Mathematical Practice

Common Core State Standards for Mathematical Practice