How Were They Developed? How Can We Use Them?
Reusser (1986)
What is this reform about?
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The Process of Developing Principles and Standards
Data Analysis (Coding the Responses)
Challenges
Initial Decisions
Categorization Scheme
Categorization Scheme (cont.)
Sample Coding
Issue Clusters
Overarching Issues
Structure of Document
Content Issues
Issues Related to Learning
Issues Related to Equity
“With this, NCTM has established a model, heretofore all too rare, of how to stage civil, disciplined, and probing discourse among diverse professionals on matters of mathematics education.” (p.xv)
National Research Council:
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Principles and Standards for School Mathematics
Document Structure
Features
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Principles
Statement of Principles
Statement of Principles
Choose a Principle
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The Standards
Number and Operations Standard
Number and Operations Standard: • Compute fluently and make reasonable estimates
Geometry Standard
Geometry Standard: • Use visualization, spatial reasoning, and geometric modeling to solve problems of two- and three-dimensional geometric shapes and
Reasoning and Proof Standard
Emphasis Across the Grades
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Computational Fluency
Toward Computational Fluency
Hiding a Ladybug
Ladybug Rectangles
Ladybug Mazes
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An Example of Computational Fluency
Problems That Require Students to Think Flexibly about Rational Numbers
Resourceful Problem Solving
One Student’s Solutions
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Flexible Use of Rational Numbers
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Interplay between Algebra and Geometry
Student Responses
Dynamic Pythagorean Relationships
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Flexibility in Analyzing Data
Box Plots of Airplane Data
Modeling with Algebra
Modeling with Algebra
Transforming Algebraic Expressions
Reasoning in Geometry
Reasoning in Geometry
Reasoning in Geometry
Reasoning in Geometry
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Eighth grade algebra:
How much mathematics:
About teacher knowledge:
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About technology:
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About arithmetic computation:
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About proof :
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Initial Press Reactions:
Notices of the AMS:
PSSM begins to recognize the synergy between rote training and conceptual learning….our community has a long way to go to get the balance right.
PSSM explicitly corrects the lesson taken by many from the 1989 standards that ability actually to do arithmetic does not matter…..This does not mean that PSSM is a perfect document.
MAA Focus
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What do teachers need?
What do teachers need?
What do teachers need?
What Does It Take?
Some next steps:
Principles and Standards Web Site
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