Chapter 1

Chapter 1 Entry:

The five content strands defined by Principles and Standards are:
1. Number and Operations
2. Algebra
3. Geometry
4. Measurement
5. Date Analysis and Probability

Following the five content standards, Principles and Standards lists five process standards:
1. Problem Solving
- 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

2. Reasoning and Proof
- Recognize reasoning and proof as fundamental aspects o mathematics
- Make and investigate mathematical conjectures
- Develop ad evaluate mathematical arguments and proofs
- Select and use various types of reasoning and methods of proof

3. Communication
- Organize and consolidate their mathematical thinking through communication
- Communicate mathematical thinking coherently and clearly to others
- Use maths language to express mathematical ideas precisely

4. Connections
- Recognise 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

5. Representation
- 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

The process standards refer to the mathematical processes through which students should acquire and use mathematical knowledge.

The common core state standards are:
1. Mathematical practice
2. Learning progressions
3. Assessments

There are six major components of the mathematics classroom that are important to allow students to develop mathematical understanding:

- Creating an environment that offers all students an equal opportunity to learn
- Focusing on a balance of conceptual understanding and procedural fluency
- Ensuring active student engagement in the National Council of Teachers of Mathematics (NCTM)process standards (problem solving, reasoning, communication, connections and representation)
- Using technology to enhance understanding
- Incorporating multiple assessments aligned with instructional goals and mathematical practices
- Helping students recognize the power of sound reasoning and mathematical integrity

To become a teacher of mathematics, one must have the knowledge of mathematics, is persistence, have positive attitude, readiness for change and has reflective disposition.