Recently, I had an “Aha!” moment.
My colleagues and I were analyzing video from a math interview with a young student, trying to understand what he knows about number. Somewhere in the back of my mind, I vaguely recall my dad gave me an article several months ago that discussed the science behind where great ideas come from. One paragraph in the article talked about how visual information can eclipse other thought. While thinking about this, one of my colleagues commented that the boy in the video kept looking out the window. That’s when I remember the article said something about staring blankly or closing one’s eyes to reduce distractions during reflective thought. That’s when my “Aha!” moment occurred.
Here’s the video for illustration.
My “Aha!” moment only happened when I took time to “check out.”
Students will have these moments too, given a chance to reflect.
Wouldn’t we love for our students to make creative, insightful connections through thoughtful reflection? Here are some factors we might consider (not an exhaustive list):
- Atmosphere: a positive, relaxed mood can increase creativity and allow for remote connections and reflective thought. An anxious or negative mood can make only the obvious connections available (Kounios, et al., 2006). It starts with the atmosphere of our classroom. Is it a safe place? Are students having fun learning?
- Know students: do we know what our students know, and what they don’t (Steffe, 2000)? If we assume knowledge, we may expect connections to be made that aren’t possible. Telling them to “try harder” won’t help.
- Attention is not always in the eye contact: students think more deeply by reducing distractions. It’s normal to pay attention to things not in our visual field (von Glasersfeld, 1981).
- Pay attention to the pause: increase wait time — both after questions and after student solutions (von Glasersfeld, 1991). Let’s see what the pause does for them.
Even though Harvey ended up saying 24 instead of 14, his “Aha!” moment was the result of reflective thought. He connected ideas to solve a novel problem. He will get it next time, or the time after that. That is what’s awesome about mathematics.
As a teacher, you too will come across some interesting or funny examples of moments of pause during reflective thought. Feel free to share in the comment section below.