Rigor for Sustained Learning

07/18/22 • 35 min

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.

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

Previous Episode

Uncovering Assumptions in Math Instruction

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.

Next Episode

Breaking the Struggle Stigma

In this episode of Room to Grow, Curtis and Joanie welcome Juliana Tapper, Math Intervention Specialist and Founder of CollaboratEd Consulting.
We start by apologizing for mispronouncing Juliana’s last name when she is introduced at the start of the podcast! Please note that her last name is Tapper, rather than Trapper. We are so sorry, Juliana!
Juliana brings her experience teaching and supporting middle and high school math teachers and math interventionists to help us consider ways to break what she calls the “struggle stigma” in math class. She grounds our conversation with powerful results from research around math anxiety, which suggest that math anxiety activates the same fear centers in the brain as seeing a snake! When teachers use this understanding, we can create more effective responses to students who are experiencing math anxiety in our classes.

Along with Juliana, your hosts discuss the importance of establishing a classroom culture that makes space all the “mathematical baggage” that students might bring with them. Providing the opportunity to talk about past experiences, positive and negative, allows students to understand that our classroom is a safe and welcoming place, where struggle becomes a normal and expected part of the learning process. Juliana has some practical tips for using instructional protocols with no math to build that classroom culture. She also shares how she established participation as an expectation rather than an option, and how those expectations along with appropriate scaffolds create small successes for students to build on.

We know you’ll walk away with some great ideas that will help you better reach more students in your classroom.

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

Juliana’s website with resources and much more information about supporting students in math www.Collaboratedconsulting.org, or email Juliana directly at [email protected].
The youcubed® article Valuing Difference and Growth Juliana refers to the findings in this paper about how math anxiety lights up the same centers of the brain as physical fear such as seeing a snake.
Juliana mentioned this The Dismantling Racism in Mathematics Instruction Course from Student Achievement Partners; the third course of the series will be available in the fall and you can take it without having taken the first two.
Juliana suggested this Good Groupwork activity for helping to build a classroom culture that supports all students’ learning from youcubed.®

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.