How to Engage Students in Meaningful Math Discussions
As middle and high school math students talk through problems, they build camaraderie and gain greater conceptual understanding.
Before I stepped into the classroom as an educator for the first time, I had fantasized about what it would be like. I would lecture from the front of the room while all students diligently hung on my every word, eager to learn what I had to share. Students would have pencils to paper for the entire 90-minute block and would readily digest the material.
Anyone who has been in a classroom, especially a sixth-grade one, can easily find fault with my fantasy—there are very few students who want to be passively lectured at and fewer who plan on silently absorbing information for a full 90 minutes at a time. While I recognized that my fantasy was a bit of a stretch even before I began, I very quickly realized that I needed to make some major adjustments to my instructional planning to create the type of highly engaged and high-performing classroom I wanted.
Over the past three years as a sixth-grade math teacher, I have developed a number of strategies that have catapulted my classroom from the rigid and dry lecture halls of my imagination to the highly engaged and passionate places for deep exploration that they are today. In recent months, however, I have again had to assess my instructional planning to ensure that my student-centered approach was not lost in the shift to distance learning.
While distance learning has certainly altered the way in which I carry out my instructional strategies, I have continued to employ the below outlined strategies to ensure a high level of student engagement through discussions. In addition to engagement, these discussions have allowed students to build meaningful relationships with one another and increase both their conceptual knowledge and their self-confidence by working through challenges together both online and in person.
Strategy 1: What Do We Think About That?
When a student provides the correct answer to a posed question, it is easy to simply respond with “Yes!” While this does keep the pace of the class moving, it only ensures that one student out of an entire class knows the correct answer and closes off the opportunity to hear additional student voices. Instead, we as teachers can respond with “What do we think about that?” in response to a given answer. This generates an open-ended question, which allows multiple students to weigh in on the given answer: agreeing, disagreeing, providing additional evidence, etc.
This strategy can easily be applied during a synchronous session of distance learning in the same way as in person. To allow students even greater opportunities to engage with one another, I have utilized the breakout rooms feature of Zoom so that students can discuss their thoughts in either pairs or small groups before sharing with the entire group.
To employ this strategy in an asynchronous session of distance learning, I have utilized Google Docs to pose a question on a collaborative document and required students not only to add their own individual response but also to assess the responses of their classmates by using the comments feature. Additionally, I have utilized Flipgrid to allow students to record themselves providing responses to questions. Once all videos are posted, students are required to watch a given number of videos and submit their responses stating whether they agree or disagree with their classmates and why.
Strategy 2: What Do You Mean I’m Wrong?!
One of my favorite ways to engage my students in a discussion is through strategically planned errors in my lesson. Once I have introduced a topic and am confident that my students understand the solving process, I will guide them through a problem and intentionally make common errors. I will then wait for students to point these out. However, I will not immediately accept that they are right. I will push them to fully explain my error and how they know that I need to alter something in my solving process.
To employ this strategy in a synchronous session of distance learning, I have utilized the whiteboard feature on Zoom as well as shown images of completed problems that have specific mistakes. Once students are able to see the work, they are able to openly discuss mistakes and how to fix them.
In an asynchronous session, I have utilized Google Docs in order to show students an incorrectly completed problem and have asked them to identify and correct the errors using the comments feature. Additionally, I have employed this strategy by posting a video of myself solving a problem incorrectly and have asked students to identify the mistakes and provide the necessary corrections to reach the appropriate answer. I have relied on the platform Edpuzzle to accomplish this. It allows me to post videos with embedded questions, so that students can either respond in a short answer at the end of the video to assess my entire solving process or respond to questions throughout the video to state whether they agree or disagree with each step and why.
These strategies provide a starting point for any teacher to begin to implement a more discussion-based approach to teaching mathematics. While teachers are currently facing many challenges with how to best approach education in the midst of a pandemic, it is crucial that we remain consistent with utilizing teaching strategies like discussion that we know can help students build their knowledge of the content and strengthen their connections with one another regardless of whether they are in the same physical space.