Last weekend, I joined several math teachers on a trip to Shanghai. We began a series of “institutes” that will span the next two years. The Math Specialist in International Schools (MSIS) seems to be a great opportunity to talk with other math teachers, think about my practice and find ways to improve. Presented by Erma Anderson and Steve Leinwand, the weekend focused on developing number sense and a progression through the Common Core standards.
On the first day, we spent most of the time discussing systems in the early primary years. With two girls in preK-3, my attention was grabbed as the importance of thinking more in terms of age instead of grade was repeated. I can only hope that the journeys of my daughters will be full of active exploration, manipulating models and discourse.
Rich mathematical tasks quickly became the focus of the institute. Students must engage with mathematics by grappling with problems, developing solutions, revising strategies and talking about their thinking. Have I been giving enough space for all of this to happen? My personal bank of resources has grown over the years but I soon realized how small shifts in my presentation of tasks can give massive dividends in the end.
Ease into the problem. “What do you notice?”
Build excitement. “What do you wonder?”
Turn the keys over. “What is the question?”
Invest the activated minds. “What is a value that you know is too high?”
Build skills of estimation. “What is a value that you know is too low?”
But don’t simply ask and be satisfied. Question. Have students explain their thinking. Over and over and over. This is a great way to review concepts and flush out activities. “Excuse me. You said that the object is 3D. What do you mean by 3D?”
“I’m not sure that I understand. Can you tell me more about the dimensions? The units? the…”
Finally, primed minds are released to tear the problem apart. But continue to push. Convince me. Show me. (Yep, that means providing multiple representations.) Explain.
The take home for me was to slow down and question. I need to do a better job to anticipate the reaction of students and be ready for targeted follow-up questions. How does this look? After more than a decade of teaching, I’m ready to consider creating a presentation a la .ppt. So far, I’ve done more hopping into the rich task through a video, image or description but I think that I’ve lost many opportunities in the set-up. I need to slow things down, expect communicate and question more.
The opposite bookend is equally important: presentation of the solution. My work is cut-out for me. I need to expand upon my own strategies of math talks related to solutions and student thoughts. The work of students should be more directed in the deepening of understanding and demonstration of new strategies.
Typically not one to slowly invest, my first class after the weekend focused on a rich task nestled inside a presentation. I posed probing questions to responses that I often would not at and move on. We took more time setting up the problem but the conservations were rich. When it was time to start work, the class erupted in a flurry of activity. The debrief was also richer as again I focused on asking for more explanations and stopped accepting values/comments without being convinced by the student.
A final thought: How can I shift more of my class to better scaffolded, rich tasks?
On the last day of the institute, we sat down in grade-level groups. This was the first time that I had worked with this group of teachers. In fact, introductions were the first order of business. We were then asked to put-it-into-practice: create a lesson. In a relatively short amount of time, we identified a rich task aligned with our goal and designed a scaffolded plan to work with students. What if more collaboration / professional development times were spent this way…