Making Math Moments That Matter Math Rules That Expire: Rethinking Math Tricks & Shortcuts for Long-Term Understanding
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This episode explores the concept of “expired math rules or math tricks”—rules, tricks, and shortcuts commonly taught in early mathematics that become problematic as students advance in their learning. Based on the article 13 Rules That Expire by Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty, the discussion highlights how overgeneralizing strategies, using imprecise vocabulary, and relying on procedural tricks can lead to misconceptions. The conversation emphasizes the importance of fostering deep mathematical understanding rather than rote memorization of rules that don’t hold true in all contexts.
Key Takeaways:
- Many tricks (e.g., “you can’t subtract a bigger number from a smaller one”) work in early math but break down with more advanced concepts like negative numbers.
- Teaching why math works builds deeper understanding and helps students apply knowledge flexibly, rather than relying on rules that later fail.
- Imprecise wording (e.g., "always move the decimal when dividing") can cause confusion when students encounter different representations of numbers.
- Encouraging reasoning and sense-making allows students to adapt their thinking to new problems, rather than getting stuck when a memorized rule no longer applies.
- By recognizing these expired rules, educators can modify instruction to prioritize reasoning and problem-solving over rote tricks.
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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.