How Can We Adapt Number Talks for Distance Learning? Insights from Richie Moreno
With Intro and Conclusion by Andrea Barraugh
As we move toward reopening schools, we all have many decisions to make about what is essential content and instruction in our math classes. Number talks are an essential classroom practice and, with a few adaptations, can be facilitated in-person, online, and asynchronously.
What Is a Number Talk?
For those of you who are new to number talks, here are two ways you can learn about them:
Watch this video clip where Jo Boaler explains what a number talk is: Boaler Number Talk Explanation
Watch this video excerpt of a number talk in a fourth grade classroom:
This is a fourth grade in-person number talk. Students share strategies, teacher records, and then students interact with the different strategies.
In a nutshell, number talks are a 10-15 minute math routine focused on mental math, number sense, procedural fluency, and math discourse. There are many variations but the basic structure goes like this: The teacher presents a math problem, students solve it mentally, discuss their strategies with a partner, and share their strategies publicly while the teacher listens, records their thinking, and facilitates student to student interaction. When teachers and students engage regularly in number talks, they collaboratively build a classroom culture of curiosity, flexible thinking, making sense of numbers and operations, confidence-building, and risk-taking (Boaler, 2017; Parker & Humphries, 2015; Parrish, 2010). This environment can be built in an in-person or virtual classroom.
Number Talks with Distance Learning
After exploring a variety of ways to implement number talks effectively in the distance learning environment, our network of teachers made some discoveries we think are worth sharing. In this post we will highlight an asynchronous adaptation from Richie Moreno and his sixth grade students at Innovation Middle School in San Diego, California. Mr. Moreno and his students made a discovery that extends number talks into writing math explanations and interactive student feedback cycles.
Meet Richie Moreno and His Students
Richie Moreno is a sixth grade teacher at Innovation Middle School, a sixth - eighth grade STEAM-focused school in San Diego USD with a diverse population of approximately 500 students. The ethnic breakdown of the student population is: 56 percent Hispanic, 22 percent white, 6 percent Asian, 5 percent African American, and 11 percent mixed race or other. Seventy-one percent of the students fall into the category of socioeconomically disadvantaged and 15 percent are categorized as English Learners. We worked with Mr. Moreno and his math team through the 2019-2020 school year during which time we focused on the implementation of number talks. It is important to note that Mr. Moreno is a natural at creating a student-centered classroom with a culture of safety, inclusion, and valuing student voices. He focused intensely throughout the year on integrating number talks into the classroom culture.
Mr. Moreno’s Asynchronous Adaptation
A Focus on Writing, Analysis, Feedback, and Interaction
I, like most teachers, was caught off-guard by Covid and distance learning. I knew from the start that I wanted to somehow continue our work with number talks, but I wasn’t sure how I could make it work in the new online environment. I also wanted to make sure to include as many students as possible, knowing that a portion of my students may not attend synchronous sessions.
My students were comfortable with Google Forms, therefore I chose to use Forms as a vehicle for asynchronous number talks. I decided to use an asynchronous format because, at the time, I was unfamiliar (and assumed students were, too) with video-meeting applications like Zoom. My instinct was also that students would generally be apprehensive sharing-out in a video format and that the shy, quiet kids would be even more overshadowed by the more extroverted and talkative students in that setting than they would in the classroom. It took me a few weeks of trial and error, but I eventually found a format and process that produced an asynchronous number talk experience that exceeded any prior expectations. Of course, like everything, the format and process of this asynchronous number talk will continue to evolve and improve. My hope is also that I can have input and suggestions from the math-educator/learner community.
Step 1: Post the Problem
During distance learning, my students knew to check my Google Site daily. Our asynchronous number talks spanned 2-3 days. On the first day, I posted a number talk problem on my Google Site. I gave students instructions to use mental math to solve the problem with whatever strategy they chose. I then asked them to fill-out a Google Form.
Step 2: Students Write a Response
On the Form, they entered what they thought the answer was, and then explained in words how they used mental math to solve the problem. This is where the magic happened and why I’m so excited about sharing this model of asynchronous number talks! The byproduct of doing number talks this way is that students are forced to write about their thinking, an activity which supports sense-making in mathematics (Burns, 2004; NCTM, 2000; Zinsser, 1988).
The act of writing about one's own math thinking is a metacognitive experience; students must confront their own processes, conceptions, and misconceptions. Maybe even more importantly, the process of writing slows things down, which almost always allows for deeper thinking and an appreciation for noticing nuances and patterns in numbers. William Zinsser captures this idea when he writes, “Writing organizes and clarifies our thoughts. Writing is how we think our way into a subject and make it our own. Writing enables us to find out what we know—and what we don’t know—about whatever we’re trying to learn.” Another benefit of having students put their thinking in writing is that it gives the teacher valuable information about how their students are thinking about numbers, including common misconceptions that can be addressed later.
I often find that many of my students, especially English Learners, are intimidated when I ask them to write. They seem overly worried about grammar and spelling at the expense of the content of their ideas. I find it helpful to de-emphasize spelling and let them know we are interested in their mathematical thinking. This seems to lower their affective filters and elicit higher quality responses from all students. My observations are validated in ideas put forth by Standford’s Understanding Language Project, "Instruction should focus on uncovering, hearing, and supporting students’ mathematical reasoning, not on accuracy in using language."
Step 3: Export Responses to a Google Sheet & Share with Students
I set up the Google Form so student submissions would go to a Google Sheet. During day one, as students were submitting responses, I would check the spreadsheet every hour-or-so, eager to see how my students were thinking about the problem. I was thrilled that students who were normally quiet and reluctant to share their thinking in class were writing wonderful, insightful explanations. Students were applying strategies that I hadn't anticipated to solve the problem in simple, efficient ways.
Below are some samples of student strategies from an asynchronous number talk that I did back in early April. The problem was: 4.25 x 8.
Student Sample A: Doubling and Halving
Tawika (pseudonyms used to protect student identities) demonstrates understanding that if you double one factor and halve the other, the product stays the same.
Student Sample B: Multiplying One Factor by Four and Dividing by the Other Factor by Four
Patrick used a variation of “doubling and halving.” His explanation shows an intuitive sense of inverse proportionality, as he multiplied one of the factors by four, and then to compensate, divided the other factor by four. This created a more manageable multiplication problem for him.