Implementing the Third Mathematical Practice by using Argumentation
This paper examines the current research and theories that can help those teaching the third Mathematical Practice in the Common Core State Standards of Mathematics. Driven by a Constructivist approach to learning, the two existing design models of Problem-Based Learning and the Hypothetical Learning Trajectory could be helpful for teaching this Mathematical Practice. In addition, the idea of developing argumentation as a way to promote student learning becomes most suitable for this kind of lesson content. However, this poses a challenge to teachers to consider multiple aspects of the classroom during teaching. When using the concepts of argumentation research, focusing on class norms could help teachers keep the classroom running smoothly. Other research on the structure of argumentation provides valuable insight into how to evaluate argumentation as a learning product. This paper analyzes how Problem-Based Learning and the Hypothetical Learning Trajectory can help teachers design feasible lesson content for teaching this Mathematical Practice and the role of the teacher during instruction. It finally discusses ways to help students develop strong argumentation skills, and investigates ways to assess argumentation.