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After completing the assigned readings for Week 6, choose two of the following response questions. Identify the numbers of the questions you answer in the initial post. Those numbers will be important when it comes to responding to peer posts.

1. Su claims, When shallow knowledge has led you astray too many times in mathematics, you begin to crave knowing things in a deeper way. When deep investigations in the past has led you to surprise, joy, or new inventions, you begin to crave deep investigation of anything valuable. (p. 109). Describe a time when shallow knowledge (in math or another subject) has led you astray. What did you take away from that experience? How has it influenced you?

2. Consider the three ideas of 1) mathematical thinking, 2) mathematical discourse, and 3) truth. How would you describe the relationship between these three ideas? In other words, do they support one another? If so, how? Do they ever act against each other? If so, how? Be sure to support your claims through examples, course readings, or video analysis.

3. This weeks readings illustrate how mathematical discourse supports both elementary and secondary students mathematical learning. Briefly describe an example from either Thompson & Gay (2020) or Hodge & Walter (2017) that illustrates how mathematical discourse also supports the development of procedural fluency, and explain why you chose it.

4.What is one criticism or misunderstanding someone may have with the idea of increasing the amount of student discourse happening in classrooms? How would you respond to this person? Come up with at least two different points you would include in your response that would clearly articulate how the role of discourse in supporting students learning.