Improving Student Learning by

Transforming Teacher Practice

K-12 Mathematics Section NC Department of Public

Instruction

Agenda

• Overview of Current Mathematical Practices in the US

• Structure of Common Core State Standards (CCSS)

• New, Better, and/or Different in the CCSS

• Getting started with the Implementation of the CCSS

Outcomes for Today

• An understanding of where the US is with mathematics teaching and practice as compared to the world

• Exploration of strategies to improve student outcomes through improving teaching practices.

• A plan to move forward in preparation of implementing the CCSS.

When you think about doing mathematics what do you think

about?

Preconceptions About Mathematics Activity

On a note card, write a preconception about mathematics.– Write one explanation of how the

preconception impacts instruction.

Preconceptions About Mathematics

• “Mathematics is about learning to compute” (Donovan& Bransford, 2005, p. 220).

• “Mathematics is about following rules to guarantee correct answers” (Donovan & Bransford, p. 220).

• “Some people have the ability to do math and some don’t” (Donovan & Bransford, p. 221).

Perception

Four Teacher-Friendly Postulates Article and Activity

Read the article

On a sheet of paper, write the statement or thought that was most profound to you.

Implementation of CCSS provides us with an opportunity to examine our instructional practices and how those practices effect student outcome.

Barbara BissellK-12 Mathematics Section Chief

“ It tells me it isn’t enough just to change the way we do things. We must also change the way we see and the way we think. We need to learn how to learn differently.”

David Hutchens

“Outlearning the Wolves”

Why is change necessary?

8 + 4 = [ ] + 5

8 + 4 = [ ] + 5

Percent Responding with These Answers

Grade 7 12 17 12 and 17

1st & 2nd

3rd & 4th

5th & 6th

Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School.

Carpenter, Franke, & LeviHeinemann, 2003

8 + 4 = [ ] + 5

Percent Responding with These Answers

Grade 7 12 17 12 and 17

1st & 2nd 5 58 13 8

3rd & 4th

5th & 6th

Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School.

Carpenter, Franke, & LeviHeinemann, 2003

8 + 4 = [ ] + 5

Percent Responding with These Answers

Grade 7 12 17 12 and 17

1st & 2nd 5 58 13 8

3rd & 4th 9 49 25 10

5th & 6th

Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School.

Carpenter, Franke, & LeviHeinemann, 2003

8 + 4 = [ ] + 5

Percent Responding with These Answers

Grade 7 12 17 12 and 17

1st & 2nd 5 58 13 8

3rd & 4th 9 49 25 10

5th & 6th 2 76 21 2

Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School.

Carpenter, Franke, & LeviHeinemann, 2003

8 + 4 = [ ] + 5

Percent Responding with These Answers

Grade 7 12 17 12 and 17

1st & 2nd 5 58 13 8

3rd & 4th 9 49 25 10

5th & 6th 2 76 21 2

Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School.

Carpenter, Franke, & LeviHeinemann, 2003

Estimate the answer to (12/13)+ (7/8)

A. 1B. 2C. 19D. 21

Only 24% of 13 year olds answered correctly. Equal numbers of students chose the other answers.

NAEP

Students were given this problem:

€ €

÷168 20

4th grade students in reform math classes solved it with no problem. Sixth graders in traditional classes responded that they hadn’t been taught that yet.

Dr. Ben Klein, Mathematics ProfessorDavidson College

Types of Math Problems Presented

How Teachers Implemented Making Connections Math Problems

Lesson ComparisonJapan and United States

The emphasis on skill acquisition is evident in the steps most common in U.S. classrooms

The emphasis on understanding is evident in the steps of a typical Japanese lesson

•Teacher instructs students in concept or skill

•Teacher solves example problems with class

•Students practice on their own while teacher assists individual students

•Teacher poses a thought provoking problem

•Students and teachers explore the problem

•Various students present ideas or solutions to the class

•Teacher summarizes the class solutions

•Students solve similar problems

22

Hong Kong / US Data

• Hong Kong had the highest scores in the most recent TIMMS.

• Hong Kong students were taught 45% of objectives tested.

• Hong Kong students outperformed US students on US content that they were not taught.

• US students ranked near the bottom.

• US students ‘covered’ 80% of TIMMS content.

• US students were outperformed by students not taught the same objectives.

BREAK

Mathematical Practices

Instructional Task I

• What rectangles can be made with a perimeter of 30 units? Which rectangle gives you the greatest area? How do you know?

• What do you notice about the relationship between area and perimeter?

Instructions

• Discuss the following at your table– What thinking and learning occurred as

you completed the task?– What mathematical practices were used?– What are the instructional implications?

Compared to….

5

10

What is the area of this rectangle?

What is the perimeter of this rectangle?

• Review the completed task• Consider the mathematical practices as

they relate to the task.• Discuss the connections you see between

the task and mathematics instruction.

Connecting Mathematical Practices and Instruction

Mathematical PracticesDiscuss the following and record responses on

chart paper:

• How will the mathematical practices impact instruction?

• How will this information impact your work with teachers as you move toward the implementation of the CCSS?

• What challenges will you face? What is a possible solution for one of the challenges?

Mathematical Practices Gallery Walk

Each group should post the chart paper with responses.

Walk around to review the responses from other groups. Note any information that you will use.

Something to Think About

• The value of the common core is only as good as the implementation of the mathematical practices.

• What if we didn’t have a requirement for math – how would we lure students in?

-- Jere Confrey

Lessons Learned

• Mile wide and inch deep does not work.

• The task ahead is not so much about how many specific topics are taught; rather, it is more about ways of thinking.

• To change students’ ways of thinking, we must change how we teach.

QUESTIONS

COMMENTS

Format and Structure

of the

Common Core State Standards

www.corestandards.org

Mathematical Practices

Grade Level

Domain Standards

StandardsDomain

Cluster

Conceptual

Categories

Standards

Common Core Resources

Glossary

Common Core GlossaryTable 1. Common addition and subtraction situations

Common Core Resources

Operations and Properties Information Tables

Property Table

Table 3. The properties of operations

Other Common Core Resources

Appendix AHigh School Pathways

Compacted Middle School Courses

NewBetter

Different

Common Core Attributes

• Focus and coherence– Focus on key topics at each grade level– Coherent progression across grade level

• Balance of concepts and skills– Content standards require both conceptual

understanding and procedural fluency

• Mathematical practices– Fosters reasoning and sense-making in mathematics

• College and career readiness– Level is ambitious but achievable

1. Make sense of problems and persevere in solving them2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning

of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated reasoning

Standards for Mathematical Practices

• Grade or course introductions give 2- 4 focal points• K-8 presented by grade level• Organized into domains that progress over several

grades• High school standards presented by conceptual

theme (Number & Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability)

Standards for Mathematical Content

Common Core Standards

Fewer

Clearer

Higher

Old Boxes• People are the next step• If people just swap out the old standards

and put the new CCSS in the old boxes– Into old systems and procedures– Into the old relationships– Into old instructional materials formats– Into old assessment tools,

• Then nothing will change, and perhaps nothing will

What can we do NOW to prepare for the implementation of the CCSS?

Development of a Team

Implementation Team NO Implementation Team

Interventio

n

Effective 80%, 3 Yrs 14%, 17 Yrs

NOT Effective

Fixsen, Blasé, Timbers, & Wolf, 2001Balas & Boren, 2000

Implementation

Establish a Professional Culture for Change

Book Studies • Who moved my cheese?

Spencer Johnson, M.D.

• Outlearning the Wolves David Hutchens

• The Prime Leadership Framework National Council of Supervisors of Mathematics

• Sensible Mathematics: A Guide for School Leaders

Steven Leinwand

Strengthen PLC’s

• Use as venues for grade level / course studies of the Common Core standards

• How is an objective in common core different from what we have been teaching?

Common Core Standards can be found at

www.corestandards.org

Strengthening Content Knowledge

• Math Matters: Grades K-8 Understanding the Math You Teach

Suzanne H. Chapin, Art Johnson

• Teaching Student-Centered Mathematics: Grades 5-8

John A. Van de Walle, LouAnn H. Lovin

• Focus in High School Mathematics: Reasoning and Sense Making

NCTM

Instructional Materials

• Look at current instructional materials and compare to the Common Core Standards

• Determine where materials can be modified and what is missing.

Changing Tasks: Low Level to High Level

Traditional Question:If you earned $380 for 2 weeks of work, how much will you earn in 15 weeks?

More Open-ended:Kate earns $380 for 2 weeks of work, how much will you earn in 15 weeks? Explain how you arrived at your answer.

Kate earns $380 every two weeks. She thinks she will earn enough in 15 weeks to pay for a used car that costs $3000. Write an explanation to convince Kate that this is or is not true.

Implement Formative Assessment

• Modules• Share and examine student work (LASW)• Book:

Formative Assessment: Making It Happen in the Classroom

Margaret Heritage

Classroom Instruction

As Cathy Seeley said:• In your math class, who is doing the

talking? Who is doing the math?

Websites of Interest

www.ncpublicschools.org

www.ncpublicschools.org/acre

www.ncpublicschools.org/stateboard

http://math.ncwiseowl.org

http://www.k12.wa.us/smarter/

“ It tells me it isn’t enough just to change the way we do things. We must also change the way we see and the way we think. We need to learn how to learn differently.”

David Hutchens

“Outlearning the Wolves”

QUESTIONS

COMMENTS

Mathematics Section Contact Information

65

Kitty RutherfordElementary Mathematics Consultant919-807-3934krutherford@dpi.state.nc.us

Robin BarbourMiddle Grades Mathematics Consultant919-807-3841rbarbour@dpi.state.nc.us

Mary RussellMiddle Grades Mathematics Consultant919-807-3618mrussell@dpi.state.nc.us

Carmella FairSecondary Mathematics Consultant919-807-3840cfair@dpi.state.nc.us

Johannah MaynorSecondary Mathematics Consultant919-807-3842jmaynor@dpi.state.nc.us

Barbara BissellK-12 Mathematics Section Chief919-807-3838bbissell@dpi.state.nc.us

Susan HartProgram Assistant919-807-3846shart@dpi.state.nc.us