I recently had the pleasure of attending the Nation Council of Teachers of Mathematics (NCTM) Annual Meeting and Exhibition in Washington, DC. This was my first big math conference. I attended some great presentations. One message that I heard reiterated in a number of presentations and one that resonated with me was about rich tasks. The message was that having a rich task is only a starting point for effective mathematics instruction. A rich task in math class is like being dealt a great hand of cards in Poker. It makes winning easier but it still takes a seasoned player with solid understanding of the complexities of the game to win a big pot.
Full Stack Lessons
Dan Meyer presented a session called "Why Good Activities Go Bad" in which he discussed a math task called Barbie Bungee. After giving summary of the task he interviewed three different teachers on their use of the task and their students' experiences. Dan asked us to think about what makes a task engaging and productive and what might make it fall flat. He talked about "full stack" lessons and how the mathematical task itself is just one component of a fully developed and presented lesson.
Sara VanDerWerf, in her presentation ‘Engaging Students in Seeing Structure’, talked about her overarching goals when lesson planning. Using routines such as Notice and Wonder and Stand and Talks, Sara supports her students to see and talk about math concepts before they are formalized. Students have a chance to engage in the mathematics and build conceptual understanding.
These types of routines which allow students to be curious about math and ask questions are important elements for getting the most out of a rich math task.
Super (Secret) Mathematics of Game Shows
One of the most engaging sessions that I went to at NCTM was presented by Bowen Kerins. He had a fun presentation called Super (Secret) Mathematics of Game Shows. A few elements of his presentation that stand out:
Shortly after returning from NCTM, I saw these tweets above from Fawn Nguyen and from Cathy Marks Krpan. These thoughts sound like they reflect many of the messages that I heard in Washington, DC this year. This morning, I also saw John Rowe's blog post "The Secret Sauce of Great Lessons." It looks like he attended several of the same sessions that I did and had a similar reflection.
My Lesson Planning Challenge
One the first slide of my presentations, down in the notes, I often write, "The essential components of a presentation: a clear focal point, a strong flow and structure, a beautiful design and a compelling delivery." (I picked this quote up here). It serves as a reminder to stay focused and think about the structure of my presentation (or blog post for that matter). I need to create a similar reminder for planning lessons to focus on more than the task itself. I need to consider how that task will be implemented to make it as engaging and productive for students as possible.
Personal, professional and financial aspects of my life have come to a rare convergence which will allow me to attend the National Council of Teachers of Mathematics (NCTM) Annual conference this April in Washington D.C. This is the first time that I've had the opportunity to attend a conference like this. I've registered, arranged transportation and lodging, double checked my passport and I'm almost ready to go... just a few more steps.
Step 1 - Math Convention Carry
Packing my pencil case is something I put far too much thought into. This is what I currently have packed.
Step 2 - Pick Out Too Many Sessions
On my first pass through the list of sessions, I just pick out all the sessions that I'd like to attend. It turns out, there are a lot of sessions that I would really like to attend. Now to make some hard choices.
Step 3 - Fine Tune My List of Sessions
Step 4 - Listen to Good Advice
Speaking of advice, I was talking to a colleague yesterday about the NCTM conference. She said to not run from session to session for the whole conference. She said to slow down and talk to people. The networking and discussions between sessions can be very valuable. Returning with a few really good ideas can be better than returning with dozens that get lost in the shuffle.
If you have any good advice from a first time NCTM conference attender, please let me know. I'm moving right along and perhaps I'll see you there!
Have you ever had a student look at you like you're talking in a foreign language during a math lesson? It happens. Sometimes there are gaps in students' prior knowledge. Sometimes students need more time to process a new concept in order to construct and develop their understanding. Sometimes I haven't explained something clearly and I need to think of a new approach to tackle this topic. When I encounter those blank stares, I think, "That's Numberwang."
Numberwang is a skit from That Mitchell and Webb Look, a British sketch comedy show from 2006. If you've never seen it, take a two minutes to watch a video of this skit. The premise of the skit is that while the presenter and contestants seem to understand the rules perfectly, they are completely inscrutable to the viewer. We're left scratching our heads in confusion just like our students sometimes do in class.
So what do you do when you sense that students in your class are not getting it? I suggest that you invest some time to uncover your students' thinking. As Guildenstern implores in Tom Stoppard's play Rosencrantz and Guildenstern Are Dead, "Delve. Probe the background, establish the situation." Take the opportunity check in with students to determine their level of understanding. Here are some strategies you might use:
Reflect and Respond
Once you have a better picture of the misunderstandings and misconceptions that may be present in your class, you can plan your next steps. Was there really a misunderstanding or did you make assumptions about prior knowledge that weren't true? Were just a few students struggling or was it a commonly held misconception? Tracy Zager, in her book Becoming the Math Teacher You Wish You'd Had, writes, "If just a few students were confused, she could work with them individually. If there was a really interesting mistake, or patterns among the misunderstandings she saw, she could use those examples as her next teaching opportunity."
When I see those "Numberwang" looks I am reminded that even a well planned lesson can sometimes miss the mark. Reflecting on how a lesson went and how I can improve it helps me refine my teaching practice and be more responsive to students' needs. Don't let those "Numberwang" moments go by ignored. Matt Larson, in his August NCTM president's message, wrote "Making mistakes, getting feedback from our colleagues, and making iterative improvement are part of the natural process of continual growth. We should never forget that perseverance isn't just for students—perseverance also applies to us as professionals."
A couple of months ago, I posted a list of six exceptional math Ignite Talks. For those unfamiliar with the format, an ignite talk includes presentation slides that automatically advance every 15 seconds. Exactly 20 of these slides result in a 5 minute talk. Since I posted my first list, Suzanne Alejandre (@SuMACzanne) at the Math Forum has been busy posting videos from older Ignite sessions. These playlists are a gold mine of mathematical thought and reflection. Additionally, the Ontario Association for Mathematics Education (OAME) had their 2017 conference ignite talks. There are so many great talks posted recently that I felt the need to recommend an additional six talks. It will take just 30 minutes to watch all six... time well spent.
I've been working on my own ignite talk and have discovered how difficult it is to craft one. There is a lot of reflection and thought involved in refining what you are really passionate about as an educator, determining how to explain it clearly and figuring out how to make it entertaining. At this point, my talk is a still just an organized collection of notes, ideas and images. I don't have any plans to actually present this ignite talk, but I feel that the process of creation and reflection is very worthwhile.
I get so excited when my kids tell me stories of what is happening in their math classes. This is a favourite.
My youngest son (age 7, grade 2) began his story as soon as I picked him up from school.
"Mommy, did you know that if you wanted to buy, let's say some....fabric, you couldn't just like go the fabric store and say 'I'll have 20 pencils of fabric'"
I was curious where this was heading; being a mathematics consultant, I knew what grade 2's were working on at this time of year (measurement). I didn't want to steal his thunder, so I just went with it.
"Really, Michael?" I turned into teacher mode: "Can you tell me some more about that?"
He went on to explain in great detail and with loads of enthusiasm about all the trouble he would run into if he wanted to measure fabric with random objects. He actually had a lot of fun naming all of the things that would be silly to use to measure fabric. He went on for a while and wrapped up the conversation telling me there was this "thing" called a "centimeter" that we could all use and understand. You would swear he discovered the metric system himself; he took such ownership of the concept.
Keep in mind, I can't think of a time he has ever been in a fabric store (I am not the crafty type) and I am almost certain that before this math lesson, he would never have used the word fabric (cloth or material, maybe?).
So he had no previous experience with the concept but he was still engaged? Yes.
When I was at Dan Meyer's NCTM presentation (Beyond Relevance & Real World: Stronger Strategies for Student Engagement) last week, I couldn't help but think of this story from my son. I can imagine the kind of "teacher moves" my son's teacher used. She is a natural story teller, her enthusiasm is contagious and she loves to laugh. I can imagine her telling a story to the class, strategically leaving out important parts, having them experience her fabric store dilemma for themselves and brainstorming ideas with the class on how they can fix this problem!
Even if he didn't really discover the metric system, he certainly thought he did. And his teacher created those conditions. And I think that's pretty cool.