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National Council of Teachers of Mathematics
5 Process Standards
Problem Solving
Instructional programs from pre-kindergarten through grade 12 should enable students to:
Build new mathematical knowledge through problem solving
Solve problems that arise in mathematics and in other contexts
Apply and adapt a variety of appropriate strategies to solve problems
Monitor and reflect on the process of mathematical problems solving
Reasoning and Proof
Instructional programs from pre-kindergarten through grade 12 should enable students to:
Recognize reasoning and proof as fundamental aspects of mathematics
Make and investigate mathematical conjectures
Develop and evaluate mathematical arguments and proofs
Select and use various types of reasoning and methods of proof
Communication
Instructional programs from pre-kindergarten through grade 12 should enable students to:
Organize and consolidate their mathematical thinking through communication
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
Analyze and evaluate the mathematical thinking and strategies of others
Use the language of mathematics to express mathematical ideas precisely
Connections
Instructional programs from pre-kindergarten through grade 12 should enable students to:
Recognize and use connections among mathematical ideas
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole
Recognize and apply mathematics in context outside of mathematics
Representation
Instructional programs from pre-kindergarten through grade 12 should enable students to:
Create and use representations to organize, record, and communicate mathematical ideas
Select, apply, and translate among mathematical representations to solve problems
Use representation to model and interpret physical, social, and mathematical phenomena
HYPERLINK "http://standards.nctm.org/document/appendix/process.htm" http://standards.nctm.org/document/appendix/process.htm
Math Proficiencies
Building Blocks
Appendix 2 and 3
Understanding: (Conceptual Understanding): Comprehending mathematical concepts, operation and relations knowing what mathematical symbols, diagrams, and procedures mean.
Computing (Procedural Fluency): Carrying out mathematical procedures, such as adding, subtracting, multiplying, and dividing numbers flexibly, accurately, efficiently and appropriately.
Applying (Strategic Competence): Being able to formulate problems mathematically and to devise strategies for solving them using concepts and procedures appropriately.
Reasoning (Adapting Reasoning): Using logic to explain and justify a solution to a problem or to extend from something known to something not yet known.
Engaging: (Productive Disposition): Seeing mathematics as sensible, useful, and doable if you work at it and being willing to do the work
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