Here is the brief form of the NCTM process standards:

Instructional programs from pre-kindergarten through grade 12 should enable all students to do the following:

• 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

Instructional programs from pre-kindergarten through grade 12 should enable all students to do the following:

• 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 problem solving

Instructional programs from pre-kindergarten through grade 12 should enable all students to do the following:

• 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

Instructional programs from pre-kindergarten through grade 12 should enable all students to do the following:

• Create and use representations to organize, record, and communicate mathematical ideas
• Select, apply, and translate among mathematical representations to solve problems
• Use representations to model and interpret physical, social, and mathematical phenomena

Instructional programs from pre-kindergarten through grade 12 should enable all students to do the following:

• 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 contexts outside of mathematics

These will be the springboards for each of the following sections.

  Course Goals and Structure