Connected Math Project (CMP2)
Cindy Kostes
Director of
Curriculum & Instruction
[email protected]
Connecticut Districts Using CMP2
• Newington, Colchester, Avon, New Hartford,
Hamden, Hartford, Guilford, Canton,
Tolland, Cheshire, Greenwich, Somers,
Seymour, Windsor, Easton, Region 15,
Monroe, Westport, Stamford, New Canaan,
Southington, New Fairfield, Marlborough,
Trumbull, Orange, West Hartford, Simsbury,
Willington
The 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 proficiency.
Key Features
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Organized around “Big Ideas”
Problem Centered
Builds on and Connects
Provides Practice with Concepts, Skills,
Algorithms
• Assists in Reasoning Skills and the use of
Different Representations
• Learning is Based on Inquiry
• Research Based
History
• 1991-1997 Connected Mathematics Project
(CMP) developed a MS Math at Michigan State
University, funded by National Science
Foundation (NSF)
• 2000 Connected Mathematics 1 was developed
through a revision process; 3 cycles of reviews,
revision, field-testing, and evaluation
• 2005 latest revision, CMP2
Research
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National Research Council. How People Learn: Brain, Mind, Experience, and School.
Committee on Developments in the Science of Learning and the Committee on Learning
Research and Educational Practice. J Bransford, A. Brown, R. Cocking, S. Donovan, and J.
Pellegrino (eds.).Washington, DC: National Academy Press 2000.
National Research Council. How People Learn: Bridging Research and Practice. J
Bransford, A. Brown, R. Cocking (eds.).Washington, DC: National Academy Press 2000.
U.S. Department of Education. Before It's Too Late: A Report to the Nation from the National
Commission on Mathematics and Science Teaching for the 21st Century. Washington, DC.
Garafolo, Joe and Frank K Lester, Jr. "Metacognition, Cognitive Monitoring, and
Mathematical Performance." Journal for Research in Mathematics Education 16 (May 1985):
163-76.
Hiebert, James. "Relationships between Research and the NCTM Standards." Journal for
Research in Mathematics Education 30 (January 1999): 3 - 19.
Silver, Edward A., Jeremy Kilpatrick, and Beth G. Schlesinger. Thinking Through
Mathematics: Fostering Enquiry and Communication in Mathematics Classrooms. New York:
College Entrance Examination Board, 1990.
Silver, Edward A., and Margaret S. Smith. "Implementing Reform in the Mathematics
Classroom: Creating Mathematical Discourse Communities." In Reform in Math and Science
Education: Issues for Teachers. Columbus, Ohio: Eisenhower National Clearing House for
Mathematics and Science Education, 1997. CD-ROM.
Stigler, James W., and James Heibert. The Teaching Gap: Best Ideas from the World's
Teachers for Improving Education in the Classroom. New York: The Free Press, 1999.
Kilpatrick, Jeremy, and Martin, Gary W., and Schifter, Deborah. Ed. A Research
Companion to Principles and Standards for School Mathematics. National Council of Teachers
of Mathematics, 2003.
Lampert, Magdalene. "When the Problem is not the Question and the Solution is Not the
Answer: Mathematical Knowing and Teaching." American Educational Research Journal 27,
no. 1 (Spring 1990): 29-63.
Lampert, Magdalene, and Paul Cobb. "Communications and Language." In a Research
Companion to NCTM's Standards, edited by Jeremy Kilpatrick, W. Gary Martin, and Deborah
Schifter. Reston Virginia: National Council of teachers of Mathematics, 2003
Ma, Liping. Knowing and Teaching Elementary Mathematics: Teachers' Understanding of
Fundamental Mathematics in China and the United States. Mahwah, N.J.: Lawrence Erlbaum
Associates, 1999.
Research Development Summary
Alignment
• National Council of Mathematics Standards
for School Mathematics (NCTM 1989, 1991,
1995, 2000)
• Connecticut Mathematics Framework
• Connecticut Mastery Test (CMT)
• Region 14 Curricular Framework for
Mathematics
Recognition
• The American Association for the Advancement
of Science (1999) ranked CMP highest out of
12 programs reviewed
• U.S. Department of Education’s Mathematics
and Science Education Expert Panel (1999)
awarded “exemplary” status – 61 programs
reviewed, 5 received exemplary, but CMP only
Middle School math program
• Recommended by the Connecticut State
Department of Education
Students need to know:
• How and When to use paper-and pencil
algorithms
• Mental Computation
• Calculator Procedures
• Estimation Strategies (when is an exact answer
required or an approximate answer is sufficient)
• A Variety of Methods for finding an answer
• Methods for judging the Reasonableness of an
answer
• Communicate their reasoning, orally & in writing
Organization of Student Units
• 8 Units - each grade, an additional unit allows some flexibility
• Unit Opener - a set of three focusing questions that reflect the
major goal(s)
• Mathematical Highlights - previews the important ideas of the
unit
• Investigations - the Core of a CMP2 unit
– Launch
– Explore
– Summarize
• Mathematical Reflections - summarizing questions
• Unit Projects - at least four per grade level
• Looking Back and Looking Ahead
This feature provides a review of the "big" ideas and
connections
Investigations
• 3-5 Investigations per Unit
• 2-5 Carefully sequenced Problems per Investigation
• Exercises
– Applications - Connections- Extensions (ACE)
• students must apply an idea, strategy, or concept
• connect it to what he or she already knows
• seek ways to extend or generalize it.
Students are expected to compare, visualize,
model, measure, count, reason, connect, and/or
communicate their ideas.
Assessments
Assessment Dimension
Content
Knowledge
Mathematical
Disposition
Work
Habits
ACE
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Notebooks
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Mathematical Reflections
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Looking Back & Looking Ahead
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Assessment Tool
Checkpoints
Surveys of Knowledge
Check-ups
Partner Quizzes
Unit Tests
Self-Assessment
Project
Question Bank
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Observations
Group Work
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Class Discussions
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Students and Parents
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The Parent/Guardian Role
• Help your child to get organized
• Talk to your child about what was learned in class
and where they still have difficulty
• Provide help with homework by asking questions
that guide, but don’t tell what to do
• Encourage your child to reflect on what was recently
learned
• Allow your child to explain concepts as part of the
metacognitive process (reflecting on one's
understanding and thinking)
• Point out how math is used at home and work
• Reflect on your own attitude toward math
http://connectedmath.msu.edu/parents/
http://www.phschool.com/cmp2/
http://www.phschool.com/cmp2/parent_guide.html
Example from Prime Time
Questions and Answers