In this episode of Room to Grow, Curtis and Joanie reconsider the balance of conceptual understanding and procedural fluency in math instruction. Although this topic has been discussed before, our hosts acknowledge that there is great nuance and many considerations in considering these two ideas in the teaching and learning of mathematics.

Curtis and Joanie discuss how inquiry-based, discovery-style learning opportunities are more open ended, are student centered, and are less teacher directed. They support these types of lessons in math instruction while recognizing that there are times when an explicit approach where teachers are sharing important information also has a place. Additionally, our hosts consider that teaching procedures and algorithms also provides and opportunity to cultivate conceptual understanding. When teachers help student find the conceptual understanding within the procedures, they engage in mathematical reasoning. This type of reasoning through concepts and procedures contributes to a broader and more robust understanding of meaningful mathematics.

Additional referenced content includes:

· NCTM article From Rules That Expire to Deeper Mathematical Thinking. Mathematics Teacher: Learning & Teaching PK-12 Volume 118 Issue 4. April 2025. (Membership required).

· NCTM article Teaching Is a Journey: From Rules That Expire to a Journey Aspired. Mathematics Teacher: Learning & Teaching PK-12 Volume 118 Issue 4. April 2025. (Membership required).

· Robert Kaplinski’s website and Open Middle website

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 roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy.

This episode of Room to Grow, Curtis and Joanie speak with Pam Harris. Pam is well known and loved for her website, podcast, books, and conference sessions all based on her core belief that “Math is FigureOutAble.” Today’s discussion centers on Pam’s newest publication, Developing Mathematical Reasoning: Avoiding the Traps of Algorithms.

Pam starts with three distortions about math that are common among teachers, students, and the population, and can impact how educators engage students with math in their classrooms. Next the conversation shifts to what is meant by algorithms, and how they differ from strategies and formulas. Then the discussion focuses on the potential traps to learning that can result from teaching algorithms in mathematics. All of these ideas are based on the development of mathematical reasoning, from counting strategies to additive thinking, to multiplicative reasoning and proportional reasoning, then the functional reasoning that comprises much of the math students learn in high school.

There are so many good ideas in this episode that will challenge you and get you thinking!

Additional referenced content includes:

· Pam Harris’ website, Math is FigureOutAble.

· Pam’s book, Developing Mathematical Reasoning: Avoiding the Traps of Algorithms.

· Pam’s podcast, Math is Figure-Out-Able!

· Find Pam on all your favorite social media platforms.

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 roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy.

This episode of Room to Grow brings together our 2025 series on the Mathematics Teaching Practices from Principles to Actions, an NCTM publication. After discussing each of the eight practices in isolation over the last several months, this month tackles the ideas and challenges in actually making substantive change to classroom practice.

Our hosts share ideas for engaging with others in deeper professional learning, coaching, and peer observations, as well as ideas for individual teachers to work on making change in their classrooms. They acknowledge that change is complicated, and encourage listeners to engage in small, incremental steps that add up over time.

Additional referenced content includes:

· NCTM’s Principles to Actions

· NCTM’s Taking Action series for grades K-5, grades 6-8, and grades 9-12

· NCTM’s Principals to Actions Toolkit – Professional learning and other resources for a deeper dive into the eight Mathematics Teaching Practices

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 roomtogrowmath@gmail.com . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy.