Mathematical Process Categories
In addition to having knowledge of the mathematics content explicitly described in the Content Categories section, entry-level middle school mathematics teachers must also be able to think mathematically; moreover, they must have an understanding of the ways in which mathematical content knowledge is acquired and used. Answering questions on this assessment may involve one or more of the processes described in the process categories below, and all of the processes may be applied to any of the content topics.
Mathematical Problem Solving
- Solve problems that arise in mathematics and those involving mathematics in other contexts
- Build new mathematical knowledge through problem solving
- Apply and adapt a variety of appropriate strategies to solve problems
Mathematical Reasoning and Proof
- Select and use various types of reasoning and methods of proof
- Make and investigate mathematical conjectures
- Develop and evaluate mathematical arguments and proofs
Mathematical Connections
- Recognize and use connections among mathematical ideas
- Apply mathematics in context outside of mathematics
- Demonstrate an understanding of how mathematical ideas interconnect and build on one another
Mathematical Representation
- Select, apply, and translate among mathematical representations to solve problems
- Use representations to model and interpret physical, social, and mathematical phenomena
- Create and use representations to organize, record, and communicate mathematical ideas
Use of Technology
- Use technology appropriately as a tool for problem solving
- Use technology as an aid to understanding mathematical ideas