Math Wars: Why Conceptual vs. Procedural Is the Wrong Math Debate

The math wars often focus on conceptual understanding versus traditional algorithms. Jon Orr and Yvette Lehman explore a deeper challenge: understanding the prerequisite mathematical ideas students need to access new learning.

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In this episode, Jon Orr and Yvette Lehman explore what changes when we stop debating how math should be taught and start examining the knowledge students need to access today’s learning. Mathematics is cumulative, and those prerequisite ideas may be far more complex than the curriculum progression suggests. 

In this episode, you'll explore:

• Why the conceptual-versus-procedural debate may be missing the bigger issue
• What it means for mathematics to be “ruthlessly cumulative”
• Why grade-level curriculum progressions don't always reveal true prerequisite knowledge
• How specialized content knowledge helps teachers respond to student misconceptions
• What multiplying fractions reveals about factoring, scaling, ratios, and proportional reasoning
• Why high-leverage visual models can help uncover the mathematics beneath an algorithm
• How teachers can build their mathematical knowledge one concept at a time
• Why strengthening teacher capacity needs to be a long-term system priority

Choose one concept you're teaching and look beneath the expectation: What does a student actually need to understand to access this idea? Try representing it with an area model, ratio table, or double number line and see what prerequisite ideas become visible.

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Are you wondering how to create K-12 math lesson plans that leave students so engaged they don’t want to stop exploring your math curriculum when the bell rings? In their podcast, Kyle Pearce and Jon Orr—founders of MakeMathMoments.com—share over 19 years of experience inspiring K-12 math students, teachers, and district leaders with effective math activities, engaging resources, and innovative math leadership strategies. Through a 6-step framework, they guide K-12 classroom teachers and district math coordinators on building a strong, balanced math program that grows student and teacher impact. Each week, gain fresh ideas, feedback, and practical strategies to feel more confident and motivate students to see the beauty in math. Start making math moments today by listening to Episode #139: "Making Math Moments From Day 1 to 180.