A few months back, I attended the NCTM annual conference here in Boston. I wanted to blog about every session that I attended, and while I’m trying to catch up on a bunch of blog topics from this year, I just haven’t been able to devote the time and energy to write about every interesting idea from every session. Instead, I want to write just a sentence or two about each session. For the most part – with so much information being thrown at me – I can only absorb a couple ideas from each session anyway.

# Wednesday

**Building a Better Teacher: How Teaching Works (and How to Teach It to Everyone)**

*Elizabeth Green*

There is only one 21st century skill – being able to learn – and that is what we need to communicate to our students. This was the first instance I saw of a recurring theme: supporting teachers as learners.

# Thursday

**Improving Student Success by Spiraling Activity-Based Learning**

*Bruce McLaurin, Alex Overwijk*

More on this session coming soon. After this session, I made three important changes in my classroom.

**The Focus on Mathematics Academy**

*Shannon Hammond (with Glenn Stevens, Tracia Fung)*

NCTM sessions are way more fun when they involve doing math. Shannon had mentioned the rat problem to me before, but now that I actually did it, I understood what it had to do with polynomials and why it is such a great task.

**Adaptation: Creating Open Problems from Closed Curricula**

*Geoff Krall*

Back to the theme of supporting teachers as learners. We have tons of old textbooks at our school, and while I’m not fond of using the textbook as the curriculum, I would like our teachers to have somewhere to look for support. With Geoff’s framework, I have some concrete strategies I can use to help teachers bring out the potential within the textbook.

**Contexts for Complex Numbers**

*Michael Pershan, Max Ray*

More on this session soon. I tried out some of their activities and adapted their work for my precalculus final.

**Exhibition Center**

With a few exceptions, I found walking around the giant room full of vendors to be really boring. One of the exceptions was the MTBoS booth, where, with some great luck, I won a class set of radian protractors!

**Ignite!**

Lots of great stuff here. Two snippets stuck with me:

- At my school, we talk a lot about performance tasks and tasks that require students to do the work of a mathematician. But what exactly does a mathematician do? In one ignite talk, we got some definitions, including: “Mathematicians are people who enjoy the challenge of problem … people who see beauty in a pattern, a shape, a concept, a proof … people who share ideas.” I love that definition.
- Reading and literacy strategies are effective for making sense of word problems. We need to stop “cracking the code” and saying things like “total means add” and so on.

**Shadow Con**

Again, lots of great stuff here, but again, the two ideas that stuck:

- Lesson study, co-planning, and/or coaching cycles often involve peer observation. The observer does not have to be a silent observer – they can call a “teacher time-out” and talk to the teacher. I like how this makes the lesson implementation a collaboration and how Elham stressed that co-ownership of the lesson during the planning stages was crucial. These lessons are percolating as I think about my coaching role for the upcoming year.
- Michael Pershan talked about why our hints aren’t good enough and how they need to get better. I’ve tried to put this into action by 1) before the lesson, adding a column into my planning template to brainstorm hints and 2) after the lesson, jotting down the hints that I ended up giving and didn’t plan (so that I have them for next time).

**Desmos/Mathalicious Trivia**

I was part of the winning team: Strength in Numbers!

# Friday

**Building Student Understanding of the Mathematical Practices through IN-formative Assessment**

*Matt Mcleod*

“Using structure” seems a lot simpler in the standards than it is in practice. We talked about two different components of structure: chunking (seeing something as a single object) and hidden meaning (rewriting something in an equivalent form). The challenge is to get students to use a structural approach instead of a computational approach. While the session’s example focused on early algebra, we were given time to brainstorm for our content areas, and I found these ideas definitely translate to logarithms and trigonometry.

**With Respect for Teaching: Making Mathematics Instruction Explicit**

*Deborah Ball*

I really liked the distinction between explicit instruction and direct instruction. One of her videos inspired a new warm up activity that I’ve been trying: I give students a problem and I ask them to give me an answer that they KNOW is wrong. Then we talk about how they know that.

**Assessing Conceptual Understanding**

*Chris Chung, Adam Lavallee*

These guys were my age, maybe younger, and I looked at them and thought: I can do this … which in a manner of speaking I did at a different, much smaller conference a few weeks later. Hopefully, I will blog about that experience soon.

**Transforming Practice: Organizing Schools for Meaningful Teacher and Leader Learning**

*Elham Kazemi, Allison Hintz, Lynsey Gibbons*

After seeing Elham at Shadow Con and considering their work was primarily at the Elementary level, I’m not sure this session was a great choice. Mostly, I was just jealous of their PD structures and the functionality of their PLC and lesson-study experiences.

**My Favorite Math Fun Facts**

*Francis Su*

Lots of fun and surprising results here. My favorites were 1) a guessing game about which enormous quantity was the biggest, and 2) The Spherical Pythagorean Theorem.

**Emphasizing Experimentation and Discovery in the Teaching of Geometry**

*Matthew Chedister*

Again, sessions are more fun when I get to do math. Deductive reasoning is hard, but it is easier if we prepare with inductive reasoning aka experimentation/discovery. I learned that there are a ton of different ways to find the sum of the angles in a pentagram, and none are trivial to articulate.

**10 To-Do’s for Converting Principles to Action into Tangible Improvements**

*Steven Leinwand*

Some stuff I agreed with and some I questioned, but wow does this guy speak with a lot of energy. The most interesting piece for me: the “jump in and participate” model of coaching. He argued that you shouldn’t just take notes and talk about it in a debrief later but instead should jump in and ask a question or draw a picture. I’m not sure I agree, but it is making me question my previous assumptions.

# Saturday

**Martin Gardner and the Mathematical Practices**

*Michael Serra*

This session was just so much fun. I think a highlight was that he gave out prizes by playing the “phychological game,” where everyone has to pick a positive integer, and the lowest unique positive integer wins. I believe the winners were #1 the first round, then #9 and #5, and none of them were me.

**Strategy in Sports: Conditional Probability and Expected Value**

*Josh Tabor*

By going to a session about probability, I was trying to go outside my comfort zone a bit. I think I was disappointed because I felt so comfortable and followed the math so easily. Oh well.

**When Am I Ever Gonna Use Math in Real Life?**

*Adam Poetzel*

Adam talked about which students ask “million dollar question”?

I like how the image implies that students ask this question more often when they are frustrated or disengaged then when they are curious. Adam presented three ways to “sell” math (brainpower, opportunity, and relevant tool). I agree with all of these answers, but I worry that these responses are only good ways to answer the curious student. Soon, I hope to write more about how I try to approach these students.