In my last post, I summarized the overall experience of Twitter Math Camp 2013 at Drexel University. Following is my recap of the sessions that I attended. This conference was unique in that I learned something significant in each session.

**Geometry Break-Out #1, Megan Hayes-Golding @mgolding, GA & Tina Cardone @crstn85, MA**

After the opening greeting, the first morning session was a choice of break-outs according to course (Algebra 1, Geometry, Stats etc). These were intended to be open-ended discussion/work sessions. In the Geometry session, there was an overwhelming need by the group to wrap their heads around the Common Core Geometry Standards. Megan & Tina wisely went with the flow, and had us jigsaw the standards in pairs and share out. It was enormously helpful for everyone. I was already very familiar with the standards, but I still learned something about the CC standards on constructions. Specifically, the standards not only call for the four basic constructions plus those involving parallel and perpendicular lines, but the students are expected to construct a square, equilateral triangle, and hexagon as well. This was time well spent, with the bonus of getting to know Edmund Harriss @Gelada, Jessica @algebrainiac1 and StephReilly @reilly1041.

Through out the weekend, I had extended conversations with Edmund from which I learned a great deal. Mostly because Edmund is a math professor and as he spoke of his work with the mathematics of tiling patterns, I felt my IQ rise just by listening to him. Much of our discussions centered around the American education, though. Edmund had an interesting perspective, because while he teaches at the University of Arkansas and also leads special math programs for gifted children, Edmund is British. From that experience, he had a great deal to share about “how to run standards based education correctly.” I hope he blogs about that soon.

**“I Notice & I Wonder,” Max Ray @maxmathforum, PA**

Max Ray is the “Professional Collaboration Facilitator” at the Math Forum at Drexel. In essence, he teaches teachers how to teach problem-solving. I had heard before of starting lessons with “What do you notice? What do you wonder?” This phrase, which was originated by Annie Fetter @MFAnnie, is intended to initiate student thinking on a rich and robust task. That seemed pretty simple, so I wasn’t anticipating much new learning here … Boy, was I wrong! Max started with a picture of 3 glasses and the phrase “What do you notice? What do you wonder?”

We were asked to ponder for a moment, then share our thoughts with our neighbors. (Think-Pair-Share). “I notice they have different shapes. I wonder if they have the same volume. What kind of drinks go in each one?” Then he posted the picture of 4 graphs, and again posed the same questions: “What do you notice? What do you wonder?” The ensuing discussion resulted in everything from “I notice the graphs are different colors” to “I wonder if the graphs correlate with the filling of the glasses.” The thing that I noticed about this whole activity is that Max let us mull this over without offering a single number or formula. Nor did he offer a single answer to any of our wonderings. Two pictures and two questions occupied us for 15 minutes. In the era of rushing through content it was *wonder*ful to be reminded that mathematics starts with an observation and a question. Speaking of questions, my group wondered what glass shape would correlate to the fourth graph… while Max stood at the front of room silently smiling.

**“Practicing the 5 Practices,” Christopher Danielson @Trianglemancsd, MN**

Christopher Danielson is a professor of mathematics at Normandale Community College and also teaches methods courses for elementary school teachers. He shared the research published in *Five Practices for Orchestrating Productive Mathematics Discussions*. In summary, the 5 Practices are:

**Anticipating**, during planning, student responses to the lesson prompt

**Monitoring** students repsonses during the lesson activity

**Selecting** which student responses are to be discussed publicly

**Sequencing** those student responses chosen

**Connecting** the responses to each other and to the mathematical ideas

Chris emphasized that the first and last of these are the two most troublesome for teachers. Chris modeled all these principles by conducting a math lesson on fractions. He knew what the issues would be with the context. He called us specifically by name to present our responses in an order that allowed the discussion to develop from simple ideas to more complex. I was particularly impressed on how he asked us to compare and contrast the various strategies. This is where I personally saw that I needed to bolster my own efforts on connecting ideas in own my class discussions. I walked away with the understanding that while any class discussion is better than none, there truly is an art form to doing class discussion right.

**“5 Ways to Boost Engagement,” John Berray, @johnberray, CA**

I have to say that the number one way to boost engagement is to teach like John Berray. The joy that he has for the material and for his students was just bursting out of him. With that said, John had 5 other ideas on increasing engagement:

1) Turn the Mundane on its ear

2) Jump on the timely

3) Bring in the outside world

4) Unlikely objects arouse wonder

5) Spill some paint

Translation: 1) Make it fun, 2)Tie math to current events, 3) Use the internet, particularly video, 4) Be goofy, 5) Connect the material to kid’s lives.

The highlight of the session was John showing how to make a textbook problem more exciting (a textbook makeover). The sample problem asked how many ways are there to take a 10-question true-false test (assuming all 10 question are answered). John asked us, “Who wants a shot at the glory?” and offered $5 to anyone who can match his answer key exactly. We were all prompted to number our papers #1-10 and choose T or F randomly for each. Once we all had our answers to this hypothetical 10-question True-False quiz, we were all asked to stand up. He began to display 10 questions, one at a time, about the participants at the conference. This offered humor and another level of engagement, as we were all trying to guess correctly, even though we had predetermined answers. After the first answer was revealed, all those who answered wrong on the paper had to sit down. We were asked to notice how many were still standing. This routine continued as we went through the entire list. Nobody won. The obvious question is, “How many people would we have to do this with in order to expect a winner?” He had just turned the mundane on its ear.

**Geometry Break-Out #2**

Our group reconvened with a few new people joining in. It was especially nice to See Peg Cagle @pegcagle after so many years. While the first day was a working session, this day was all about discussion. The group really wanted to talk about how to teach all the standards we listed in the previous sessions, while instilling the CCSS Practices. Teachers shared their various ideas, experiences and techniques. There was also a question on grading practices that revealed the dark side of the MathTwitterBlogosphere … We can be a very opinionated bunch. The hot topic for us was standards based grading. This turned out to be a benefit to the new teachers in the room or to old teachers with open minds, because quite a variety of ideas and positions were shared. It was an engrossing conversation, because no matter the positions taken, they were all shared with a passion for teaching students rich mathematics. The end of session came way to soon.

**“Still Keeping it Real,” Karim Kai Ani & Team Mathalicious, @Mathalicious, VA**

Mathalicious offers engaging, innovative math lessons with a focus on “real-world” applications. Karim @karimkai led us through two Mathalicious lessons that were solidly based in mathematics and loads of fun. The first, *Datelines*, tied the age of potential dates to systems of inequalities. The age gap on a date becomes less of an issue as people get older. For example, a 24-year old dating a 20-year old is less awkward than the 20-year old dating a 16-year old. This is an engaging topic for teenagers that Mathalicious sets to a graph and poses critical questions according to a given rule on dating ages. Like I said … solid. The second lesson, *Prisn*, used Venn diagrams to analyze the probability of being wrongfully flagged by the governments PRISM program for mining data. This lesson was about as relevant as any can get. It allowed for rich non-partisan conversation on how much error the public will accept. As I told Karim, these lessons are sexy, but have a lot of substance. At the conclusion, he generously gave the TMC participants a free trial subscription to Mathalicious. I intend on checking out more of their work.

**“Getting Students to Think Mathematically in Cooperative Groups,” Lani horn, @tchmathculture, TN**

This one was very special for me, because Dr. Ilana Horn was such an influence on the teacher collaboration model that we have implemented at my high school for the last 9 years. Back in 2004, I was about to be the Math Department Chair for a new high school and was speaking with Jo Boaler about collab models for teachers. She told me that the person to contact was Lani Horn at the University of Washington (She is now at Vanderbilt in Tennessee). A week later, I happened to be vacationing in Seattle, and Lani was kind enough to give up time to a stranger and talk about her doctoral research. She was gracious as well as knowledgeable.

So I was excited to see her again and share how her information helped lead my crew back home to be one of the highest performing schools in the county. She was pleased to hear the news. Her session this time was on student rather than teacher collaboration. The specific model she shared is known as Complex Instruction (CI), in which students are grouped heterogeneously, with intentional methods to have all students participate. The focus of Lani’s session was on how academic *status* affects student engagement during group work. She was very intentional in telling us that participation is hindered by this *perceived* status about *smartness*, which is too often defined in math class as “quick and accurate.” To help make it safe for everyone to participate, the teacher needs to redefine smartness by acknowledging and rewarding “good questions, making connections, representing ideas clearly, explaining logically, or extending an idea.” Lani shared a video of a group of students working on a math problem, and asked us our thoughts regarding each students level of participation. She also asked us to analyze the teachers interaction and prompted us for alternative responses. This analysis of the work done by each student debunked the conventional wisdom that non-participatory children are lazy, stupid or shy. I had learned as much from Lani Horn on this day as I did in our first encounter.

Due to another engagement, I had to fly home early from the conference so I did not get a chance to attend the last session on Friday or any on Saturday. I heard I missed some great stuff, which I don’t doubt.