Uncovering Assumptions in Math Instruction

06/13/22 • 34 min

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.

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)

Previous Episode

Celebrating Learning with Self-Reflection

As we approach the end of the school year, this episode of Room to Grow addresses using self-reflection to celebrate the learning of the year. Our hosts use this definition: “Self-Reflection is the evaluation or judgement of one’s performance and the identification of one’s strengths and weaknesses with a view to improving one’s learning outcomes (Damore, 2017),” and start with unpacking this quote from John Dewey: “We don’t learn from experiences, we learn from reflecting on our experiences.”
In the conversation, Curtis and Joanie suggest that reflecting at the end of a lesson, unit, month or school year provides the opportunity to be energized by and to benefit from what we’ve experienced and how we use that learning to continue to improve.

After making the case for self-reflection, the discussion shifts to specific ideas for student and teacher self-reflection. Ensuring that students understand the purpose of self-reflection is integral to making the process meaningful for students, and increases the likelihood that their reflective practices will contribute positively to owning their own learning, and to building positive mathematical identities. Some specific reflection questions and protocols are discussed, giving you ideas you can apply in your own setting as we all wrap up the 2021-22 school year.

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

Dewey quote and Damore’s definition of Self-Reflection came from this post: Routines for Self-Reflection: https://thinkingpathwayz.weebly.com/routinesselfreflection.html
Journal of Practitioner Research article on reflection as a tool for continuous improvement: https://digitalcommons.usf.edu/cgi/viewcontent.cgi?article=1044&context=jpr
Edutopia article with specific ideas for engaging students in self-reflection: www.edutopia.org/article/frameworks-reflection
Tuning protocol as a way for groups of teachers to reflect specifically on student work: http://essentialschools.org/horace-issues/the-tuning-protocol-a-process-for-reflection-on-teacher-and-student-work/
Teachers and Change: The Role of Reflective Practice: https://www.sciencedirect.com/science/article/pii/S1877042812039870

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.

Next Episode

Rigor for Sustained Learning

In this episode of Room to Grow, Curtis and Joanie tackle ideas around rigor in mathematics. We start by defining what we mean by rigor, acknowledging that it’s a frequently used term that invokes different ideas and meanings! We believe that it means something different than just “difficult,” but frames a way of describing deep, robust, and applicable understanding of mathematical ideas, and we share a couple of visual images that help make sense of this complexity.

Through our exploration of rigor as an integral part of learning math, we connect it to previous conversations about productive struggle, making connections in math, and student agency and identity. Rigor isn’t just for high level math courses and high-achieving students, rigor is for everyone and may even be an unexpected approach to overcoming struggle in learning mathematics!

We believe that the best way to address rigor in the classroom is by intentional, collaborative planning, where teachers decide which obstacles they want to steer students around and which obstacles they want to steer students straight into! We hope you enjoy the episode and hear a new idea or two to consider for your own setting.

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

Definition of “rigor” from Achieve the Core: College- and Career-Ready Shifts in Mathematics
This report from the Dana Center at the University of Texas, Austin: What is Rigor in Mathematics Really?
This archived (free) blog post from former NCTM President Linda Gojak: What’s All This Talk About Rigor?
myNCTM discussion about rigor (membership required): Archived HERE

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.