Welcome Back Friends!
Last month I was so excited to attend this year’s annual NCTM math conference. The best part—it was in San Antonio, Texas (about 100 miles from me)! Now, while some of you are thinking, “What’s so exciting about that,” I’m thinking 1.) It was a mini-vacay in the middle of the spring semester (Raise your hand if you could use one of those!); 2.) I got the chance to spend time with professors and colleagues who I hardly ever see; 3.) I got to share the same space with some of my math idols. Yes, I totally know that I am a math geek, but I thought that’s what you loved most about me!!
All kidding aside, attending this conference is a big deal. It’s an opportunity to learn from math teachers and authors across the country. Sessions are filled with presentations by people like Jo Boaler, Dan Meyer, Graham Fletcher, Kathy Richardson, and many others. It’s also a unique experience and a chance to hear what other teachers are doing to create strong mathematicians from states across the nation. With this in mind, I want to take this opportunity to share five of my biggest take-a-ways with you.
1. My first Friday morning session, which was my first day of the conference because I was unable to take-off from work on Thursday, started the conference off with a bang! The session was focused on selecting “quality tasks” to help bridge the gaps in student understanding. The presenter, John SanGiovanni, had a profound idea—“Games are quality tasks if we do something with them.” It seems silly that he said that, but believe it or not, some teachers see games as a way to engage their students but do not view them as a real opportunity to teach content. In the session, we played several simple dice games and debriefed the games with discussion questions about how to build on the game experience. For example, using the graphic below and a dice, we rolled the dice up to five times, created 2 two-digit numbers (with the option of one discarded roll), and placed the numbers one-at-a-time in the boxes to get as close to 100 as possible.
Afterward, we discussed some extensions, such as creating a human number line with the sums or having students pair up with someone and find the sum or difference of their total sum from the game. You might even have students pair with someone whose sum will get them closest to 200 without going over. Then we played the same game but with a target of 50 and discussed which target sum was easier to achieve, 100 or 50. The possibilities are endless! You can adjust the template for decimals or even fractions, using fraction dice or creating fractions with regular dice.
The concepts seem so simple, but I really walked away thinking about how to extend my games so that I can get the most from the learning experience.
2. After my initial session, I scheduled some time to visit the exhibit hall and just happened upon a quick 10-minute chat with Elham Kazemi, one of the authors of Intentional Talk. The session was quick, but she offered two additional strategies for debriefing during math talk. She talked about looking at the strategies through a lens of “elegance and efficiency” to discuss which strategies are the best and why– analyzing strategies to determine which ones are most effective and which ones are most efficient is another way to help students make sense of the new learning before adding it to their toolbox. Ms. Kazemi also talked about looking at the strategies through the lens of exposing students to a new representation or tool and providing clarification on how and why the strategy is useful.
3. Okay—I’ll admit this next one is still rolling around in my head as I try to make sense of this new piece of learning. I’ve always defined a fraction as “part of a whole,” the numerator as “the number of parts being considered,” and the denominator as “the number of parts in one whole.” If this is how you defined it, get ready to have your world rocked. Fractions is a major topic of interest for me, so I usually attend several sessions on fraction understanding when I attend big conferences. This session was about understanding the division of fractions and was presented by two college professors. They shared that instead of saying a fraction is “part of a whole,” it should be described as “a number.” Furthermore, they described the relationship between the numerator and the denominator as shown below.
Initially, I was scratching my head, but as I review my notes from the session some three weeks later, I begin to understand the definitions differently and appreciate how they widen the way we describe fractions. I know many teachers define the numerator as “the number of shaded parts” which doesn’t seem to fit when you are working without pictures or are referring to fractions in a way that does not suggest a pictorial model, such as saying someone ran three quarters of a mile or worked on homework for five-thirds hours. This way of looking at these definitions widens the way students will understand fractions, but boy, change is hard!
4. One of my favorite sessions was titled, “Math Workshop: Guided Math & Beyond” and presented ways to structure math workshop and develop the routines needed to make it successful. As a teacher who has always been on the search for ways to maximize my students’ learning time, I appreciated the three learning structures she presented and how they could be used at different times in the unit cycle. She introduced a Task & Share model that would be great when exploring a non-routine problem related to the content you are teaching, a Whole-Small-Whole model that would be helpful when you need to teach a mini-lesson but allows you time to work in small groups as well, and a Small Group with Stations or Task model where students are able to complete independent practice or review activities in small groups. This was a really cool session and I am planning to use these models to dig a little deeper into structuring math learning time later this year. Until then, use the link below to download the presentation and the handout using the session title above.
5. The very last session I attended was titled “Is Carrying a ‘9’ Heavier than Carrying a ‘1’?” In this session we discussed the importance of using precise language to describe mathematical content and skills. You’ve probably heard some of these before, but here are a few of the math errors we sometimes use in instruction:
- Using the word “borrow” when we really mean to “trade.”
- Using the word “carry” when we really mean to “regroup.”
- Using “plus” instead of “add.”
- Using “minus” instead of “subtract.”
- Using “times” (you times it) instead of “multiply.”
- Using the term “reduce” (like reducing fractions) instead of “simplify.”
The presenter was humorous in how she presented these and many other math faux pas but these mistakes can make math very confusing for our students. It’s imperative that we examine the way in which we communicate with our students so that we do not send the wrong message and confuse the learning process.
Wow! That’s a lot of new learning! Attending the national conference is a very valuable experience and I encourage all teachers of mathematics to attend. I’ve been fortunate to attend for the past two years and I had a blast! Next year, the conference moves to Washington, D.C.—an experience that I’m sure will be unforgettable!
One more thing—That super cool guy named Dan Meyer created a program to collect all of the conference handouts in one location. He wasn’t able to capture everything, but he got really close! Check out the following website to peruse the session handouts. Happy Hunting!
Dan Meyer Website: http://s3.amazonaws.com/conference-handouts/2017-nctm-san-antonio/index.html
Sound Off! What type of professional learning most interests you?