Tracy ends the chapter discussing equity and some different responses to mistakes she has observed from girls and boys. Watch Reshma Saujani’s TED Talk “Teaching Girls Bravery, Not Perfection” at https://youtu.be/fC9da6eqaqg . Share your thoughts on this issue.

What do you make of the distinction between mistakes and errors? Next time you’re teaching, note down mistakes you observe that reveal conceptual misunderstanding and errors that reveal students’ need to work on precision. How does distinguishing between the two affect the way you think while teaching?

Reflect on the list of teachers’ comments on page 57. What language do you currently use when students make mistakes? What language might you use going forward?

On her website, Tracy shares a link to James Tanton’s videos about thinking like a mathematician, and this is a chance for you to engage with some math yourself.

Watch part 1 at this link and try out some of the demonstrated strategies for math problems. Tell us about the experience. 

Part 1: http://www.youtube.com/watch?v=KPt1inAIs3k

Full set of videos: http://www.jamestanton.com/?p=1097

The chapter details 3 classroom examples in which the teachers’ language, tasks, and instructional strategies encouraged their students to take on challenges. Comment on one strategy, teacher move, or feedback phrasing from Heidi’s, Cindy’s, or Shawn’s classrooms that you use or aspire to use in your teaching.

Write about obedience versus risk taking in mathematics. What came to mind when you read the passage on page 31?  What are you thinking now or what questions do you have?

Look for some mathematical objects, books, videos, or experiences applicable to your grade level that might exemplify what mathematicians do (from the resources Tracy lists in the book or others you have sourced).  Tell us what you found.

What do you observe about how students use the phrase “this is easy” in your classroom? What is it effect? (You are free to choose a different word from page 11 if it is more common in your teaching, and please do remind us of your grade level in your response).

Pick out something from the vignette of Deb’s classroom that resonated with you and tell why.

[Reposted after accidentally deleted.]

The book will offer three approaches to closing the gap between “school math” and mathematics: learning about mathematicians and their habits of mind, learning from other teachers’ experiences, and engaging with math ourselves as readers.

Which approach are you most comfortable with?  Excited about? Which do you think will be most challenging for you?