I first started doing number talks (also called math talks) to start class when I taught 8th grade. If you’re unfamiliar with number talks, this site by Fawn Nguyen has some great stuff to get started. My first year teaching high school (Algebra II, Precalculus, and Calculus) I stopped, opting for Visual Patterns, Open Middle, Which One Doesn’t Belong?, and a few other rotating warm-up routines. I thought that the skills involved in number talks, while useful for middle school students, were less relevant for upper high school.
I came back to number talks at the start of this school year, and I’ve been happy with the results. When I wrote a problem up on the board one day toward the end of the year, a student blurted out, “oh, I love these”. That’s just one student, but engagement was usually high. Efficient strategies for these problems often did not come easily to students, which suggests that there’s potential for learning from them. More importantly, as they became comfortable with the routine, many students who were rarely willing to share started to speak up and take more risks.
Here’s a selection of my favorite problems, many courtesy of Fawn’s site.
Picking two numbers and an operation is often insufficient for a great number talk; I’ve found that careful selection of the numbers involved to ensure a variety of strategies is worth the effort every time.
I have one lingering question for next year. Engagement during number talks seems high, and seems to engage both high-performing and low-performing students. There is clearly a need for the skills that number talks are targeting. At the same time, I don’t have any real evidence that students are learning these mental math skills. I think they are, but that’s based on my intuition and a few anecdotes. One challenge is that I tend to cycle through a variety of types of number talk problems that require different strategies. One goal for next year is to reorder the number talks I use so that I expose students to one type of problem 2 or 3 times, lead a discussion that attempts to consolidate understanding of relevant strategies and when they may be useful in the future, and then revisit that problem a few weeks later. Hopefully this sequencing will provide more robust evidence as to whether or not students are actually learning.