Tracy notes that her approach in the book is to “offer you a buffet of techniques and strategies” to use in your teaching.  What specific goal do you have going forward?  [In my personal opinion, it is easier to identify & achieve a specific goal than a general goal. Good luck!]

Read the mission statement from Clarence Stephens’s SUNY Potsdam math department on page 352. How does this statement compare with the mission of your institution?

Reflect on your experience reading and discussing the book. What ideas are resonating with you? How do you now think about creating “favorable conditions” for student learning (and how has your perspective changed since you’ve read the book)?

This 2020-21 school year has been unusual and challenging in so many ways. What strategies have you used to get your students working together and alone? What has worked? What has been a hurdle you haven’t been able to overcome?

Choose something from this chapter (Mathematicians Work Together and Alone) that resonated with you and comment.

Tracy offers this definition (p. 281): “Proving is convincing your skeptical peers that a mathematical statement is true in a way that helps them understand why.”

How do you see this process working in your teaching setting? Think about the varieties of justification/proof discussed in the chapter (pages 284–304): Measurement/Computation, Perception, Generalizing from Cases, Disprove with Counterexamples; Proving with Words, Representations, or Symbolic Notation. Which of these have you seen your students make use of?

Reflect on the section “Proof and Equity” on pages 307–309.  What changes in your thinking or practice would ensure that all students’ ideas and thinking are valued?

Choose a strategy from the chapter (Choral Counting, Visual Patterns, Number Talks/Strings, Always-Sometimes-Never, etc.) and try it out with your students. Tell us how it goes.

How do you uncover student reasoning in your teaching? Tell us about strategies you’ve used to enable students to share their mathematical thinking with you or their classmates.

Reflect on the idea of leaving the door open for revision as students learn more mathematics (pages 272-274) and how some math rules “expire” when students tackle different sets of numbers or concepts. Are you comfortable with viewing mathematical claims as subject to change?

[ If desired, check out the NCTM articles about “Rules That Expire” for different grade bands HERE. ]