I attended the Teachers Teaching with Technology (T-cubed) International Conference this past week in Chicago, and my four days were chock-full of thought-provoking sessions and conversations. As expected, there was much talk about technology in math and science classes, but there was also a great deal of discussion concerning thinking about teaching and learning in math and science classes. Here are some of my take-aways:
1. Get out of your comfort zone into the “learning zone.” In order to learn something new, get out of established routines (about doing math, about teaching math) and try another technique or perspective. I pushed myself to learn about topics that are not my specialty, things I might have otherwise avoided. I tried coding some calculator programs, tackled STEM/engineering design projects, learned a bit of 3D graphing, and brushed up on statistics. Some things came easily, and other new skills were quite difficult. At one point in a STEM session, I declared that the project was “really hard”, and sat back to watch others. I was urged to continue by the presenters and fellow participants, and we worked together to complete the task. I gained confidence because they had confidence in me, and was able to achieve something I thought might be beyond my abilities. I was really glad I persevered in the task, and had acknowledged that it was “hard” but not “too hard.”
2. Productive struggle takes time. One of the eight Mathematical Teaching Practices in NCTM’s Principles To Actions (2014) is to “support productive struggle in learning mathematics.” In one of the sessions, presenters Jennifer Wilson and Jill Gough had us work on a difficult geometry problem, asking us to:
- Allow for “individual think time.” Please don’t steal another student’s opportunity to think by talking too soon.
- Go beyond getting the answer. What can you show about how you make sense of the problem?
- Work with it some more. Can you find another way? Can you relate your solution methods to each other, or to another person’s method?
I was surprised by two things that happened in this session. First, as the presenters circled around the room reviewing our progress, they didn’t evaluate our work or tell us if we were on the right track. When Jennifer suggested that I keep working—which I interpreted to mean that I had made an error in my reasoning—my solution was actually correct. I realized later that taking more time to work had been advantageous and it had spurred me to find alternative methods. A teacher saying to a student “work on this some more” is not the same as “you’re doing it wrong.”
The second big surprise was how long the process of struggling toward a solution took us. I thought perhaps we had been working for ten or fifteen minutes (we are math teachers, after all, so I expected we would find solutions quickly). In fact, we had been working for 35 or 40 minutes, which was astounding to me. Time had seemed to slow down, and there wasn’t any race to finish up. I was able to really make sense of my multiple solution methods, and enjoyed pursuing more ways to solve the problem.
So if “promoting productive struggle” is a goal for your classroom, consider how to encourage it with your messages to students. Think carefully about implementation: you need to invest ample time, but you will reap rewards in terms of the variety and depth of math concepts your students will uncover.
3. Be responsive to your professional peers. In his keynote, Timothy Kanold spoke about the professional community that exists in a school, and how a robust collaboration enhances the success of all students. When teachers engage with each other, sharing best practices, kids experience similar (high-quality) learning environments even if they have different teachers. When teachers operate independently, there can be substantial inequity between what students in different classrooms receive.
How might we apply this in our school settings? If there is a great activity you use in one of your courses, perhaps share it with colleagues teaching the same course. If you employ technology to build mathematical understanding, try to make sure others have access to it as well. You will benefit too: discussing a lesson or teaching practice with a colleague will make your teaching repertoire more robust. Attempting something new and different is easier when you have a like-minded peer who can give feedback (or possibly observe your lesson in action).
So what are my next steps? Returning home after an exciting professional conference always involves catching up and getting back to my regular teaching routines. But Jennifer and Jill commented that “closure” is not simply packing up at the end of class; instead I need to reflect on what I’ve learned, and thoughtfully consider how to put it into my practice. I invite you to join me: take a risk, plan to do something new in the next few weeks, and find a colleague to collaborate with you as you move into the learning zone.
NOTES & RESOURCES:
There is a full set of coding lessons and teacher guides available on the TIcodes section of the TI website.
The “Learning Zone” idea is related to Vygotsky’s “Zone of Proximal Development” (1978). For more on scaffolding and ZPD, see Middleton, J. A. & Jansen, A. (2011). Motivation Matters and Interest Counts: Fostering Engagement in Mathematics. Reston, VA: NCTM, chapter 9 “Providing Challenge: Start Where Students Are, Not Where They Are Not”.