Centering Student Reasoning in Conceptual Understanding and Procedural Fluency

Room to Grow - a Math Podcast

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 [email protected] . Be sure to connect with your hosts on X and Instagram: @JoanieFun and @cbmathguy.