Common Core State Standards for Mathematical Practice National Practice Standards in a Mathematics...

Common Core State Standards for Mathematical Practice

National Practice Standards in a Mathematics Classroom?


Icebreaker

• Compromise

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


Icebreaker

• Compromise

• What is your favorite Ice Cream flavor?


Icebreaker

• Compromise

• What is your favorite genre of book?


Icebreaker

• Compromise

• Where do you like to go on vacation?


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?


Icebreaker-Debrief

Compromise

What might be the reason we did this icebreaker?


Agenda/Goals

• Opening

• CCSS practices

• Doing Mathematics

• Looking at a lesson

• Closure


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


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.


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.


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)


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)


#1 is Detective


#2 is Escher


#3 is Debaters


#4 is Models


#5 is Toolbox


#6 is Compass


#7 is Construction


#8 is Fractal


#1-8

Can you repeat all the numbers and words?


How did you do?

1. Detective2. Escher3. Debaters4. Models

5. Toolbox6. Compass7. Construction8. Fractal


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)


Standards for Mathematical Practice

Describe HABITS OF MIND of a mathematically expert student


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



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


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…


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…


The Standards for [Student] Mathematical Practice

Take 3 minutesto prepare a

2 minute ELEVATOR TALKexplaining your practice standard.


Connecting the pictures to the practices


Detective

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


Escher

2. Reason abstractly and quantitatively.


Debaters

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


Models

4. Model with mathematics.


Toolbox

5. Use appropriate tools strategically.


Compass

6. Attend to precision.


Construction

7. Look for and make use of structure.


Fractals

8. Look for and express regularity in repeated reasoning.


Think-Pair-Share

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


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


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.


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


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

through this lesson…


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.


CCSS standards

build in complexity

and provide more clarity

for expected student

performance.


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


Butterfly Method:


Now try using butterflies on this TIMSS* item…

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

*Trends in International Mathematics and Science Study


Walk and Talk…

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

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


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.



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.


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.


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.


The Standards for Mathematical Practice

will be assessed…


So What’s Different About the CCSS?

• Accountability

• Accountability

•Accountability


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.


Implementing CCSS: Where TO start

The Eight Standards for Mathematical Practice



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



Target a few selected practices to address in depth.

These practices must be embedded in discussions about content.




Avoid a fragmented menu of varied professional

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



Include a variety of stakeholders in whatever PD is offered –

don’t compartmentalize it; bring groups together.


Common Core State Standards for Mathematical Practice National Practice Standards in a Mathematics...

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