Session 1. The Process Standards
This session introduces the course content and structure, providing examples of all the activities in the course. The five-part structure of each session — Observe, Explore, Define, Apply, and Evaluate — is explained in detail. Go to this unit.

Session 2. Communication
Discover the role that communication plays in your teaching and in your students' learning. Topics covered include effective questioning, helping students understand and use precise language, and using writing assignments and presentations to help students clarify and deepen their thinking. The session also includes content and activities designed to help you better assess your personal formal and informal mathematical communication. Go to this unit.

Session 3. Problem Solving
Explore problem solving as a key means to introducing new material and building conceptual understanding in your students. Topics include problem selection and how to help all students develop a problem-solving disposition. A range of approaches and strategies to solving problems is introduced, as is advice on helping students identify and solve problems in contexts beyond the mathematics classroom. Go to this unit.

Session 4. Reasoning and Proof
Investigate how reasoning and proof provide the foundations of mathematics, at all levels and in a broad context. Topics include ways to integrate the concept of deductive proof and reasoning into instruction, particularly in subjects beyond geometry. Help students understand how mathematical arguments work and the meaning of concepts like deduction, induction, validity, and conjecture. This session also introduces types of reasoning and how mathematical proof relates to and differs from proof in other subjects. Go to this unit.

Session 5. Representation
Discover how mathematical representations connect concepts and prompt problem solving and communication. Topics include how to help students understand and move fluently among representations, refining informal models, and understanding when and why to move to standard representations. Activities that demonstrate how to use mathematical representations to model real-life phenomena are included as well. Go to this unit.

Session 6. Connections
Explore the interrelated nature of mathematics in this session. Topics include information on how to connect concepts within mathematics to related science, engineering, technology, and non-technical topics. The session includes exercises designed to help you see how mathematics builds as a coherent, connected whole, both from grade to grade and across subject areas. Go to this unit.