I am back home after an exhausting and completely wonderful experience at the NCTM Annual Meeting in San Antonio. I was so wiped after yesterday that I sat around my apartment doing nothing for the rest of the afternoon; obviously, I needed a little time to process everything I had learned over the past 3 days. Today, I have a fresh perspective and some final thoughts on the last day as well as on the conference as a whole. Day 1 and Day 2 were pretty awesome, so the last day had some big shoes to fill. Luckily, it didn’t disappoint.

I started Day 3 by going to a “celebrity” session by Dan Meyers. He might not be well-known to the wider population, but his talk was held in the theater (the largest meeting space), which is also where John Urschel (a Baltimore Raven and current PhD student at MIT–an actual celebrity) had his talk during the conference. And given the number of people at Dan Meyer’s talk, he was definitely a celebrity at NCTM.

His talk was on creating intellectual need in students. Most of the time, when students ask us, “why do I have to know this?”, we tell them one of two reasons: 1. so they won’t fail the test/class/grade, or 2. so they can get a good job in the future. We are hoping that the students feel a social need (don’t want to fail the class) or an economic need (want a good job), so they will feel obligated to learn what we are teaching them. Well, that just don’t work for some students. And they aren’t very good reasons anyway.

He suggested creating an intellectual need for the students to learn the material. Instead of posing a “problem”, pose a “puzzle”, and they need some additional knowledge in order to solve it or solve it efficiently. For example, Dan put a bunch of dots on the screen and asked one audience member to describe the location of a dot that she had chosen to another audience member. It didn’t go very well. Then, he put the dots on a coordinate plane. The audience laughed. It was so much easier to explain the dot’s location. He created a communication need, giving us (and our future students) an intellectual need for knowing how to use a coordinate plane.

With all of the talk that I heard about posing good problems in class to get students engaged and thinking (and hopefully writing), I thought this was a perfect tie-in with that. Create a problem that they can’t solve without the next math content. This creates a personal incentive to solve the puzzle. And the math is a superpower that makes it all possible. I love this idea.

Then I went to a session about mathematical argument. We watched some videos of classrooms in action (I love when they show classroom videos because it makes it so much easier to see what this would look like in an actual classroom). They give us a step-by-step method for implementing this, which I also love. It’s nice to leave a session with an actual plan, not just a vague notion. The idea is that students look at some examples and try to make generalizations about math using these examples. Then, they talk about it with their classmates and make their generalizations as specific as possible. They even test it out with “nonexamples” to see just how *general* it really is.

I like the idea of introducing making generalizations and conjectures in elementary school, because the students will need this skill a lot in high school (think proofs in geometry). Also, it gets them *creating* math concepts–how very inquiry-based–instead of having the teacher just tell them the concepts. Then, they can use the concept really understanding it and its limitations.

My last session was about connecting fraction work in elementary school with ratio and proportion work in middle school. As a 5th grade teacher, I love these kinds of sessions because I am trying to prepare my students for middle school, and it is nice to get an idea of how to do that with at least one concept.

We spent a lot of time talking about the differences between fractions (comparing part of a whole) and ratios (comparing part to a a part or part to a whole). This discussion really made me think about how similar yet different they are and how knowing fractions well can make working with ratios confusing. This was especially evident when looking at equivalent ratios and fractions, as seen in this picture:

For equivalent ratios, you actually increase the number of “objects”. In equivalent fractions, you just cut the pieces differently. I enjoyed getting to dig deeply into this topic, especially because my curriculum introduces ratios in 5th grade (even though the Common Core doesn’t introduce them until 6th grade). Plus, we got to watch a few classroom videos.

The closing session was a talk about a British science writer who writes about math in the Simpsons. It was interesting to see just how much math is hidden in the show by it’s math- and comedy-loving creators and writers. This picture shows a taxicab in the show Futurama (similar creators and writers) that has a “taxicab” number as the number of an actual taxicab.

All in all, it was an amazing experience; one of the best professional development experiences I have ever had. It was fun to walk through the Expo and see all of the materials, books, and activities for math teachers and their students. I enjoyed getting to talk to educators at different levels from all around the country. I learned so much from my presenters, whether they were math celebrities, college professors, or classroom teachers. I learned about some content (fractions, ratios, order of operations) and some concepts (argumentation, intellectual need, writing, play, formative assessments), all related to my favorite subject. I am excited to try out my learning in my classroom tomorrow. While it was nice to get a break and spend time with other educators, I miss my students, and I am ready to get back to the work that took me to NCTM in the first place: teaching.

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