CMP—A 40 Year History

17th Annual CMP User’s Conference February 21-22, 2014

Elizabeth Phillips

Michigan State University East Lansing, MI

#CMPusers14

Overview

§  The Past—Brief History of CMP §  The Present—CMP 3 §  The Future

The Past

1972-1980—’Back to Basics’ ERA

• Glenda, Betty, and Bill meet at MSU

• Reaction against New Math • Remedial math at the college level

• Preservice teachers on a decline

• Concern about basic skills—backlash • Doom and Gloom Reports—A Nation at Risk • Several NSF Projects to investigate and

change classroom environment

1980-1990 A Reaction to ‘Back to Basics’

• MGMP Middle School Leadership Workshops

• An Agenda for Action—Problem Solving • MGMP— a Classic

• NAEP and TIMSS Report—Doom and Gloom

• 1989 NCTM Standards and Evaluation

• NSF’s call for curriculum proposals

1990-2000

• 1996 1st Getting to Know CMP • 1998 1st CMP Users’ Conference • 2004 1st CMP Leadership Conference

• 1990 The Connected Mathematics Project is funded (Jim and Susan are on board)

• 1995 Connecting Teaching, Learning, and Assessment (NSF funded CMP professional development grant)

• 1996 CMP1 is published & surprisingly successful

2000—2010

• 2000 NCTM Principles & Standards • NSF solicits more curriculum projects. • CMP2 is funded and has a 2006 copyright. • CMP2 is even more successful!

Development of CMP CMP 1 was guided by our experiences and vision of a curriculum that would engage both teachers and students around significant mathematics.

CMP 2 was guided by the same vision and experience from the field and by the NCTM 2000 Principles & Standards,

BUT

• The “math wars” Ø Rhetoric of the mathematics and

mathematics education communities Ø International tests

Forces  outside  of  our  control  

•  No Child Left Behind Act Ø Performance assessment items eliminated Ø Diversity in state frameworks Ø Common Core State Standards and national

testing

ØIncrease in special education ØIncrease in differentiated classrooms

ØIncreased focus on English Language Learners

ØTracking and the power of the gifted community

ØMobility of administrators and the decline in numbers of mathematics coordinators

Forces within schools

Standards—Chaos?

The Present

CMP 2 is/was a Success!

CCSSM is the new kid on the block.

CMP 3 takes up the challenge.

CMP 3 maintains the CMP philosophy. and

CMP 3 is fully aligned with the CCSSM.

The CMP3 Development Process— similar to that for CMP1 and CMP2 §  Gathered feedback from the field

§  Used research from many areas §  Identified and located CCSS for each grade

§  Used feedback and CCSS to guide the revision

§  Field-tested each unit

§  Revised based on teacher input

§  Final production

2013-14 CMP3 is in Schools!

The CMP Philosophy is intact

Overarching Goal of CMP

All students should be able to reason and communicate proficiently in mathematics. They should have knowledge of and skill in the use of the vocabulary, forms of representation, materials, tools, techniques, and intellectual methods of the discipline of mathematics, including the ability to define and solve problems with reason, insight, inventiveness, and technical proficiency.

CMP: A Problem-Centered Curriculum Important Mathematical Ideas

Reasoning

Communicating

Connecting Patterns Understanding Relationships

Skills Mathematics

Launch

Explore

Summarize

Problems

Guiding Principles CMP Curriculum §  Is problem-centered—mathematics is

abstracted from the context

§  Identifies big ideas and goes for depth

§  Has coherence—builds and connects from problem to problem, investigation to investigation, unit to unit and grade to grade

Guiding Principles—con’t

§  Intertwines conceptual and procedural knowledge to produce fluency

§  Develops skills and concepts as needed

§  Promotes inquiry-based instruction

§  Has high expectations for all students

Criteria for a Mathematical Task The problem supports some or all of the following §  Has important, useful mathematics embedded in it §  Promotes conceptual and procedural knowledge §  Builds on and connects to other important mathematical

ideas §  Requires higher-level thinking, reasoning, and problem

solving §  Provides multiple access points for students §  Engages students and promotes classroom discourse §  Creates an opportunity for teacher to assess student

learning

CMP3—What’s New? CCSSM and Mathematical Practices

NCTM Process Standards

1989 •  Mathematics as

Problem Solving •  Mathematics as

Reasoning •  Mathematics as

Communication •  Mathematical

Connections

2000 •  Problem Solving

•  Reasoning and Proof

•  Communication

•  Connections •  Representations

2009 Reasoning and Sense Making

Common Core State Standards Mathematical Practices

§  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

Mathematical Practices—Betty’s Version

Problem Solving 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

Connections Build on and connect to prior knowledge to build deeper understandings and new insights—

The Role of MP in CMP The Mathematical Practices come alive in the classroom as students and teachers interact around a sequence of rich tasks to

§ Discuss § Conjecture § Validate § Generalize § Extend § Connect

So that students develop deep understanding of concepts and the inclination and ability to reason and make sense of new situations.

CMP: A Problem-Centered Curriculum Important Mathematical Ideas

Problems Patterns

Reasoning

Communicating

Connecting Understanding

Concepts Relationships

Skills Mathematics

Launch

Explore

Summarize

CMP3 Mathematical Content

Issues

§  Interpretation of the CCSS

§  Staying true to the CMP philosophy

§  What will be tested?

Trying to make sense of the CCSS

CMP 3 Changes

§  100% correlation with CCSSM—(some movement of units, problem changes, one new unit)

§  Mathematical Practices permeate the curriculum (as usual)

§  Two paths through 8th grade: CCSS 8th grade

CCSS Algebra I • Fewer Problems

Organization of Student Units

Changes at the Unit Level

u  Order of units: §  Variables & Patterns in 6th grade §  Shapes & Designs in 7th grade §  How Likely Is It combined with What Do You Expect in 7th

§  Samples & Populations combined with Data Distributions in 7th §  8th grade CCSS statistics added to Thinking with Mathematical Models §  Function Junction unit added to 8th grade

u  Name changes: • Comparing Bits & Pieces (Bits I) • Let’s Be Rational (Bits II) • Decimal Ops (Bits III) • Its in the System (Shapes of Algebra) • Butterflies, Pinwheels, and Wallpaper (Kaleidoscopes, Hubcaps and Mirrors)

The CMP You Know and Love is Alive and Well!

CMP Classic Problems

§  Factor Game §  Brownie Problem §  Tuepolo Township Problem §  Orange Juice Problem §  The Henri-Emile Problem §  Mug Wumps §  The Bridge Experiment §  The Pool Problem §  And many more

What Do You Expect? Problem 3.1 One-and-One Free-Throws In the district finals, Nishi’s basketball team is 1 point behind with 2 seconds left. Nishi has just been fouled, and she is in a one-and-one free-throw situation. Nishi free-throw average is 60%. • Is it more likely that Nishi will score

0 points 1 point 2 points

• What is the probability that Nishi’s team

wins the game?

One and One Free-throws (a 60% free-throw shooter)

Hit Miss

Hit

Mis

s 1 0

2

P(0 pts) = 40/100 P(1 pt) = 24/100 P(2pts) = 36/100

Long Term Average—Expected Value

In 100 trials for a 60% free-throw shooter Score of 0 occurs 40 times Score of 1 occurs 24 times Score of 2 occurs 36 times

Total Points 40 x 0 pts = 0 points 24 x 1 pt = 24 points 36 x 2 pts = 72 pts Total points = 96pts

Long Term Average = points per trial

!

96100

= 0.96

How have they changed?

CMP 3 Student Books

Unit Organization

§  Unit Opener—Looking Ahead §  Mathematical Highlights §  Investigations (3 to 5 per unit) §  Unit Project §  Looking Back

Investigation Organization

§  Investigations form the core of a CMP unit. §  Key elements of each investigation

§  Introduction §  Problems §  Did You Know? §  Applications-Connections-Extensions §  Mathematical Reflections §  Mathematical Practices Reflections (NEW)

General Changes and Emphasis in SE

• Getting Ready’s are Gone • Boxed (Open) Questions (New) • More use of Student Thinking • More use of Which Operation? Which

Function? Which Shape? • More student metacognition questions • Mathematical Reflections are more focused • Reflections on The Mathematical Practices

occurs at the end of each Investigation (New)

What’s New?

CMP 3 Student Books Examples

What’s New?

CMP 3 Teacher Guide

Unit Teacher’s Guide u  Unit Level

§  Mathematical Background §  Mathematical Goals (Reorganized) §  CCSSM addressed in the Unit (New) §  Content Connections to Other Units §  Management Chart

u  Investigation Level §  Investigation Summaries, Overview and highlighted Goals §  Goals mapped to Reflection Questions (New) §  CCCS for the Inv. (New)

u  Problem Level §  Focus Questions (New) (what’s essential; exit slip) §  LES §  Sample Student work

Mathematical Goals

u  At the unit level • 2-3 Key ideas and essential understandings for each (New)

u  At the investigation level • Same set of goals carried over for each investigation • Understandings addressed in that investigation are highlighted

(New) u  At the Problem Level

• Descriptions provide overview of the problem and what is new • Focus Question provides further guidance

u  Goals are correlated with the Mathematical

Reflections (New)

Mathematical Goals

u  At the unit level • 2-3 Key ideas and essential understandings for each (New)

u  At the investigation level • Same set of goals carried over for each investigation • Understandings addressed in that investigation are highlighted

(New) u  At the Problem Level

• Descriptions provide overview of the problem and what is new • Focus Question provides further guidance

u  Goals are correlated with the Mathematical

Reflections (New)

Mathematical Goals—At the Unit Level Prime Time:

Factors and Multiples Understand relationships among factors, multiples, divisors, and products:

• Classify numbers as prime, composite, even, odd, or square • Recognize that factors of a number occur in pairs • Recognize between situations that call for common factors and situations that call for common multiples • Recognize between situations that call for the greatest common factor and situations that call for the least

common multiple • Develop strategies for finding factors and multiples • Develop strategies for finding the least common multiple and the greatest common factor • Recognize and use the fact that every whole number can be written in exactly one way as a product of

prime numbers • Use exponential notation to write repeated factors • Relate the prime factorization of two numbers to the least common multiple and greatest common factor of

two numbers • Solve problems involving factors and multiples

Equivalent Expressions. Understand why and how two expressions are equivalent • Relate the area of a rectangle to the Distributive Property • Recognize that the Distributive Property relates the multiplicative and additive structures of whole numbers • Use the properties of operations of numbers, including the Distributive Property, and the Order of

Operations convention to write equivalent numerical expressions • Solve problems involving the Order of Operations and Distributive Property

Mathematical Goals

u  At the unit level • 2-3 Key ideas and essential understandings for each (New)

u  At the investigation level • Same set of goals carried over for each investigation • Understandings addressed in that investigation are highlighted

(New) u  At the Problem Level

• Descriptions provide overview of the problem and what is new • Focus Question provides further guidance

u  Goals are correlated with the Mathematical

Reflections (New)

Goals—At the investigation level Prime Time— Inv 2

Factors and Multiples. Understand relationships among factors, multiples, divisors, and products:

• Classify numbers as prime, composite, even, odd, or square • Recognize that factors of a number occur in pairs • Recognize situations that call for common factors and situations that call

for common multiples • Recognize between situations that call for the greatest common factor

and situations that call for the least common multiple • Develop strategies for finding factors and multiples • Develop strategies for finding the least common multiple and the greatest

common factor • Recognize and use the fact that every whole number can be written in

exactly one way as a product of prime numbers • Use exponential notation to write repeated factors • Relate the prime factorization of two numbers to the least common

multiple and greatest common factor of two numbers • Solve problems involving factors and multiples

Mathematical Goals u  At the unit level

• 2-3 Key ideas and essential understandings for each (New)

u  At the investigation level • Same set of goals carried over for each investigation • Understandings addressed in that investigation are highlighted (New)

u  At the Problem Level

• Descriptions provide overview of the problem and what is new • Focus Question provides further guidance

u  Goals are correlated with the Mathematical

Reflections (New)

Prime Time—2.3 focus Question

How can you decide if finding the LCM is useful to solve a problem? How do you find the LCM?

Mathematical Goals

u  At the unit level • 2-3 Key ideas and essential understandings for each (New)

u  At the investigation level • Same set of goals carried over for each investigation • Understandings addressed in that investigation are highlighted

(New) u  At the Problem Level

• Descriptions provide overview of the problem and what is new • Focus Question provides further guidance

u  Goals are correlated with the Mathematical

Reflections (New)

Prime Time—Investigation 2 Common Multiples and Factors

Mathematical Goals Mathematical Reflections Differentiate between situations that call for common factors and situations that call for common multiples Develop strategies for finding factors and multiples Solve problems involving common multiple or common factors

1. When should you use common multiples to solve a problem? When should you use common factors? Explain how you can decide.

Develop strategies for finding factors and multiples Develop strategies for finding the least common multiples and the greatest common factors Differentiate between situations that call for the greatest common factor and situations that call for the least common multiple

2. a. Describe how you can find the common factors and the greatest common factor of two numbers.

b. What information does the greatest common factor of two numbers provide in a problem?

3. a. Describe how you can find the common multiples

and the least common multiple of two numbers. b. What information does the least common multiple

of two numbers provide in a problem?

Mathematical Goals

u  At the unit level • 2-3 Key ideas and essential understandings for each (New)

u  At the investigation level • Same set of goals carried over for each investigation • Understandings addressed in that investigation are highlighted

(New) u  At the Problem Level

• Descriptions provide overview of the problem and what is new • Focus Question provides further guidance

u  Goals are correlated with the Mathematical

Reflections (New)

Launch—Explore—Summarize

§  Problem Overview Focus Question (New)

§  Launch Connecting to Prior Knowledge (New) Presenting the Challenge (New)

§  Explore Providing for Individual Needs (New) Going Further Planning for the Summary (New)

§  Summarize Orchestrating a Discussion (New) Check for Understanding Reflecting on Student Understanding (New)

Providing for Individual Needs

How has it changed?

CMP 3 Assessment

Assessment Dimensions

§  Content Knowledge

§  Mathematical Disposition

§  Work Habits

Assessment Components §  Checkpoints

ACE Notebooks and Notebook Checklist Mathematical Reflections Mathematical Practices Looking Back and Looking Ahead

§  Surveys of Knowledge

Check-ups Partner Quizzes Unit Tests Self-Assessment Projects

• Observations

Group work Discussions One-on-one interactions

In CMP students expect to make sense of the mathematics

The Future Looking Ahead

Future Activities §  Identify and develop criteria for classic problems

§ Develop “Arc of Learning” for each unit

Criteria for a CMP Task The curriculum builds and connects from Problem to Problem, Investigation to Investigation, Unit to Unit and grade to grade. Each CMP Problem has some or all of the following characteristics: •  Embeds important, useful mathematics •  Promotes conceptual and procedural

knowledge •  Builds on and connects to other important

mathematical ideas •  Requires higher-level thinking, reasoning, and

problem solving •  Provides multiple access points for students •  Engages students and promotes classroom

discourse •  Allows for various solution strategies •  Creates an opportunity for teacher to assess

student learning

Classic Problem

A classic problem has most of these characteristics but has over time produced exceptionally high engagement, connections, and strategies for many students in many classrooms. These problems serve as significant cornerstones for students and teachers in their learning journey.

Position of the Problem in the Learning Sequence

Arc  of  Learning  

Introduc4on  of  Content  in  Context  

Explora4on  and    Comparison  

Analysis   Synthesis   Reflec4on  

Future Activities §  Identify and develop criteria for classic problems §  Develop “Arc of Learning” for each unit §  Series of webinars to discuss important issues §  Collect feedback from CMP 3 schools §  Face book §  Develop more classroom videos

§  Create a new website for CMP3 •  Examples of student work •  Examples of applets or technology activities •  Examples of videos for contexts •  Position Papers on important aspects and issues of CMP

Students in the CCSS era

A CMP Student

Launch

Explore

Summarize

Memorization without understanding is the tyranny of the mind…

An idea that is understood is more than half way toward

remembering and using the idea.

Youngman, 1905

The End

ephillips@math.msu.edu