In this episode of Room to Grow, Curtis and Joanie consider assumptions that we make during math instruction and how these have the potential to interfere with students’ understanding of the mathematics. Teachers know more math than their students, and as a teacher, it can sometimes be a challenge to remember what it was like before we knew and understood a math concept. This can lead us to inadvertently assuming that students are following our thinking or considering external knowledge that they actually might not yet have access to!

Our hosts get into some math content, specifically talking about the equals sign, solving systems of equations, and the standard algorithm for multiplication. In each of these examples, the common structures of instruction can lead students to an incorrect or incomplete understanding, or can force a focus on procedures without the concepts that back up these ways to doing. Curtis and Joanie had some personal “ah ha” moments during the episode as we discussed these math topics. 

Frequent listeners know that Joanie and Curtis don’t claim to have silver bullet solutions, but they suggest that slowing down when planning and teaching, regularly collaborating with other teachers, and stopping to identify assumptions can all contribute to better teaching and learning. Listen to hear more about why Joanie recommends teaching “for big circles, and not pinpricks.”

We encourage you to explore these resources, mentioned and referenced in this episode:

• Teaching Children Mathematics article (subscription required) The Equals Sign: A Balancing Act
• Elementary and Middle School Mathematics: Teaching Developmentally by John van de Walle
• Presentation of From Student-Invented Strategies to Standard Algorithms: What’s the Rush by Fran Huntoon
• Discussion about teaching algorithms on myNCTM (membership required)

Did you enjoy this episode of Room to Grow? Please leave a review and share the episode with others. Share your feedback, comments, and suggestions for future episode topics by emailing [email protected]. Be sure to connect with your hosts on Twitter and Instagram: @JoanieFun and @cbmathguy.