Title: Connected Mathematics Project
1Connected Mathematics Project Michigan State
University
Connecting Teaching, Learning, and Assessment
2The CMP Development Staff
3Connected Mathematics Project Authors
James T. Fey University of Maryland William M.
Fitzgerald Michigan State University Susan N.
Friel University of North Carolina at Chapel
Hill Glenda Lappan Michigan State
University Elizabeth Difanis Phillips Michigan
State University
4CMP Goal1
- All students should be able to reason and
communicate proficiently in mathematics. - This includes knowledge and skill in the use of
vocabulary, forms of representation, materials,
tools, techniques, and intellectual methods of
the discipline of mathematics. - It also includes the ability to define and solve
problems with reason, insight, inventiveness, and
technical proficiency.
5CMP Goal2
- The CMP goal makes a commitment to skill, but
skill that is much more than just proficiency
with computation and manipulation of symbols. - Skill in CMP means that a student can use the
mathematical tools, resources, procedures,
knowledge, and ways of thinking that have been
developed over time to make sense of new
situations that he or she encounters.
6Instructional Themes
Mathematical Investigations The curriculum is
organized around big ideas in
mathematics clusters of important, related
mathematical concepts, processes, ways of
thinking, skills, and problem solving strategies,
which are studied in depth. Reasoning Students
grow in their ability to reason effectively with
information represented in pictorial, graphic,
numeric, symbolic and verbal forms and move
flexibly among these representations. Connections
The curriculum emphasizes significant
connections among various mathematical topics
and problems in other school subjects that are
meaningful to students. The curriculum also
offers an opportunity to revisit and deepen
understanding of ideas. Teaching for
Understanding Instruction emphasizes inquiry and
discovery of mathematical ideas through
investigation of rich problem situations. Technol
ogy Selection of mathematical goals and teaching
approaches reflects the information processing
capabilities of calculators and computers and
the fundamental changes these tools are making
in the ways people learn mathematics and apply
their knowledge to problem solving tasks.
7What Mathematical Strands Are Studied?
Number Geometry Measurement Statistics Probabi
lity Algebra (Patterns - Relationships -
Functions)
8Units by Grade1
9Units by Grade2
10The CMP Curriculum Teaching - Learning -
Assessing
In the CMP curriculum, we have taken a stand that
curriculum and instruction are not distinct. The
circumstances in which students learn affect what
is learned. The what to teach and the how to
teach it are inextricably linked. In the CMP
Assessment, we believe that assessment must be
linked to this vision of curriculum, teaching and
learning. What is assessed and how students
are assessed also affects what is learned and
how it is learned.
11Features of Student Materials
- Think About This questions
- Mathematical Goals for the students
- Investigations
- Problems
- Homework
- Applications - Connections - Extensions
- Mathematical Reflections
- Glossary and Index
12Features of Teacher Materials
- Overview of
- Big mathematical ideas of the Unit and
Investigations - Mathematical and problem solving goals
- Materials and suggested time-line for the Unit
- Teaching Notes for Each Investigation
- Instructional strategies for the
- Launch - Explore - Summarize Phases
- Appropriate ACE (homework) assignments
- Samples of student responses to questions
- Complete solutions to Investigations, ACE
questions, and Mathematical Reflections - Assessment
- Appendices
- Blackline Masters
- Family Letter
- Students work and scoring suggestions
- Additional Practice problems
- Descriptive Glossary and Index
13A Problem-Oriented Teaching Model Launch -
Explore - Summarize
- LaunchingEngaging the Students
- Teacher
- Introduces new concepts
- Reviews old concepts
- Helps students understand the context
- Issues the mathematical challenge
- Exploring the Situation
- Students
- Gather data Share ideas Look for patterns
- Make conjectures
- Develop strategies
- Create arguments to support their reasoning and
solution - Teacher
- Asks questions
- Observes individual differences
- Encourages, Redirects
- Provides extra challenges
14Assessment in the Connected Mathematics Project
- Purposes of Assessment
- For the Student
- For the Teacher
- For the Outsider
- Each of these purposes is best served by
- assessment that provides multidimensional
- information about students knowledge.
15Assessment Dimensions in CMP
- Content Knowledge
- What do students know?
- What are they able to do?
- Mathematical Disposition
- How do students respond to mathematical
- challenges?
- How do they see themselves as learners and
- inventors of mathematics?
- Work Habits
- Are the students able to organize and
- summarize their work?
- Are they progressing in becoming
- independent learners?
16Components and Assessment Dimensions
17Assessment Components
- Dailyembedded
- Applications - Connections - Extensions
- Journals
- Class Discussions
- LaunchExploreSummarize
- Surveys of Knowledge
- Mathematical Reflection
- Check-ups
- Quizzes
- Unit Test
- Unit Project
- Observations
- Students Self-Assessment
- Teachers
- Portfolio Suggestions
18Connected Mathematics and the NCTM Principles
and Standards 2000
19Connected Mathematics and the NCTM Principles
and Standards 2000
20Connected Mathematics and the NCTM Principles
and Standards 2000
21Expectations for CMP Students by the End of
Three Years of a Full Implementation of CMP
- Students will
- Carry knowledge and skills from one grade to the
next. - Deepen their understanding of concepts and
skills - over time.
- Represent and communicate their understandings
- in a variety of waysincluding the ability to
use - and make sense of symbolic statements.
- Make complete and convincing arguments to
support - their conjectures.
- Use previous knowledge to support arguments and
- to solve new problems.
- Grow in their ability and sophistication to
analyze - a problem and to develop strategies.