National Mathematics Standards Categorized by process, knowledge, attitude, and perspective:

PROCESS and INQUIRY KNOWLEDGE

Or

Practices and process skills:

the system of actions and procedures used to create knowledge in the subject or discipline.

Or the practices of the discipline.

 

Problem Solving

  1. build new mathematical knowledge through problem solving;
  2. solve problems that arise in mathematics and in other contexts;
  3. apply and adapt a variety of appropriate strategies to solve problems;
  4. monitor and reflect on the process of mathematical problem solving.

Reasoning and Proof

  1. recognize reasoning and proof as fundamental aspects of mathematics;
  2. make and investigate mathematical conjectures;
  3. develop and evaluate mathematical arguments and proofs;
  4. select and use various types of reasoning and methods of proof.

Communication

  1. organize and consolidate their mathematical thinking through communication;
  2. communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
  3. analyze and evaluate the mathematical thinking and strategies of others;
  4. use the language of mathematics to express mathematical ideas precisely.

Connections

  1. recognize and use connections among mathematical ideas;
  2. understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
  3. recognize and apply mathematics in contexts outside of mathematics.

Representations

  1. create and use representations to organize, record, and communicate mathematical ideas;
  2. select, apply, and translate among mathematical representations to solve problems;
  3. use representations to model and interpret physical, social, and mathematical phenomena.
CONTENT KNOWLDEGE - the ideas (facts, concepts, generalizations, conjectures, theorums, and proofs) that are created by doing the subject.

Number and Operations

Algebra

Geometry

Measurement

Data Analysis and Probability

PERSPECTIVE - the relationship of the different dimensions of a subject or discipline to its other dimensions and to its whole as well as the subject's or discipline's relative significance for explaining and understanding the world.

Connections (connections are included in both the perspective and process skills categories. The ideas expressed in these statements describe perspectives of mathematics and are written as skills in their identification and use.

  1. recognize and use connections among mathematical ideas;
  2. understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
  3. recognize and apply mathematics in contexts outside of mathematics.

ATTITUDE - The diposition and values that people have that increase their likelihood of success in the subject or discipline.

The inclusion of disposition and value statements in the principles, beliefs, and other supporting information in the standards. Such as, become independent learners with a disposition and capacity to engage in and value mathematics in their everyday lives.

Dr. Robert Sweetland's notes
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