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This post is about Tracy Zager's most excellent book, Becoming the Math Teacher You Wish You'd Had.

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I actually finished reading it back in January, and I The process culminated with this tweet:

That's what I thought about it at the time, but I haven't sat down to organise my thoughts on it. Until now.

I was first drawn to the book based entirely on its contents page. Check this out:

• Chapter 1: Breaking the Cycle
• Chapter 2: What Do Mathematicians Do?
• Chapter 3: Mathematicians Take Risks
• Chapter 4: Mathematicians Make Mistakes
• Chapter 5: Mathematicians Are Precise
• Chapter 6: Mathematicians Rise to a Challenge
• Chapter 7: Mathematicians Ask Questions
• Chapter 8: Mathematicians Connect Ideas
• Chapter 9: Mathematicias Use Intuition
• Chapter 10: Mathematicians Reason
• Chapter 11: Mathematicians Prove
• Chapter 12: Mathematicians Work Together and Alone
• Chapter 13: "Favourable Conditions" for All Maths Students

Is this not awesome? Here was a list articulating things about maths that I know are important and yet that I've struggled to articulate all my life as a mathematician and maths educator. Many of them cut straight to the heart of the difference between how I experience mathematics and how it usually is experienced in a classroom.

• "Mathematicians use intuition" you say? Well, yes. Yes we do.
  But many a maths classroom is about following rules and avoiding the need for intuition.
• "Mathematicians work together" you say? Well, yes. Yes we do.
• But so many students think maths is only a solitary activity.
• "Mathematicians make mistakes" you say? Well, yes. Yes we do.
  But mistakes are feared and avoided in most maths classes.
• "Mathemaicians connect ideas" you say? Well, yes. Yes we do.
  But so many maths curriculums are just so many piles of disconnected procedures, even here at my own university.

The contents page promised a book about the most important aspects of mathematical work and thinking, and a hope that it would give ways to bring these into the experiences of students in all maths classrooms.

And the hope was made real.

Each chapter starts out comparing how mathematicians talk about what they do and what students' experience of it is. Then it moves on to detailed examples of the aspect of maths thinking in action in real classrooms, as well as strategies to encourage it both in your students and in yourself as a teacher.

I didn't expect to see this last point about encouraging these attitudes and thinking in yourself as a teacher. Yet it is the most compelling feature of the book for me. Indeed, I don't think the book would have had nearly the impact it had on me (or the impact I see it having on others) without this constant message that to help your students experience maths differently, then you yourself need to experience it differently too. More than this, Tracy doesn't just make this need clear, but actively and compassionately empowers us to seek out ways to fill it.

These comments were left on the original blog post:

Tracy 10 May 2017:

Misting up over here, David. You’ve cut right to the heart of it. Thank you so much. I feel incredibly lucky to learn with you.

David Butler 10 May 2017:

And I am lucky to have been able to sit and talk with you by reading your book. I really felt like you were there with me, encouraging me to be more.

Susan Jones 10 May 2017:

I’m still reading it. Your post makes me realize my privilege in not majoring in math 🙂 I never did lose the “play with the numbers” thing.

David Butler 10 May 2017:

Sadly, you don’t have to major in maths to lose the play-with-numbers thing. A good dose of standard high school maths teaching can safely banish that tendency, as Tracy described in the first chapter of the book!

For me, my maths university degree is what actually freed me to play. I took Discrete Maths II in second year of university and it felt like all we were doing was playing with these ideas, and it was play encouraged by the lecturer.