Balancing Explicit Instruction with Inquiry-Based Math

In this episode, Drew Perkins talks with veteran high school math teacher and author Kristen Smith to discuss her evolution from a more traditional approach to math teaching, in the style of Teach Like a Champion, to one that might best be described as "teacher-led inquiry". We explore her "Inquiry Sandwich" methodology—a balanced pedagogical framework that leverages explicit routines to build fluency while creating space for deep, conceptual exploration.

Links & Resources Mentioned In This Episode

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Key Takeaways

• The "Inquiry Sandwich" Methodology: Learn how to bridge the "math wars" divide by blending explicit instruction with inquiry-based learning. This structure—starting with retrieval practice, moving into conceptual inquiry, and concluding with formal explicit instruction—allows students to build fluency while developing deep mathematical understanding.
• Disrupting the "Not a Math Person" Narrative: Math anxiety is often a result of rigid instruction. Discover how to engineer classroom experiences that prioritize consistent student success, clear modeling, and structured problem-solving to help students see themselves as capable mathematicians.
• Moving Beyond the "Geometry Sandwich": A critique of traditional fragmented course sequences (Algebra 1 → Geometry → Algebra 2). We explore the benefits of integrated mathematics pathways and the importance of allowing student choice in elective courses like financial math during the 11th and 12th grades.
• Bridging the Research-Practice Gap: Why relying on "laboratory" research can hinder classroom reality. We discuss the necessity of pedagogical synthesis—taking the best of structured classroom management and blending it with conceptual inquiry—rather than strictly adhering to one "side" of pedagogical theory.
• The Realities of PBL in Mathematics: While Project-Based Learning (PBL) is valuable, the hierarchical nature of math standards makes it difficult to implement in every unit. We discuss strategies for when to use PBL (e.g., specialized financial math courses) versus when to prioritize standards coverage and scaffolding.

Episode Highlights & Timecodes

• [00:04:08] Background and Teaching Experience: Kristen shares their journey from finance into education via the Math for America program and their reflections on high-quality teacher preparation.
• [00:11:29] Addressing Math Anxiety: Insights from Kristen's book, Cultivating Math Confidence, on disrupting the "not a math person" narrative.
• [00:15:56] Math for the Real World: A discussion on why high-level math education is essential for developing transferable problem-solving and modeling skills.
• [00:23:06] Rethinking Math Pathways: Why moving away from the traditional "Geometry Sandwich" and toward integrated math pathways supports better student engagement.
• [00:29:09] The "Easter Egg" Pedagogical Model: How Kristen blends the structured "I do, we do, you do" explicit instruction model with inquiry-based, conceptual lessons.
• [00:32:34] Influence of Illustrative Mathematics: The origin and philosophy of the problem-based curriculum designed to uncover mathematical meaning.
• [00:44:04] Inquiry vs. Procedural Fluency: The "both and" approach—why students need conceptual inquiry and fluency in prerequisite procedures to succeed.
• [00:51:37] The "Inquiry Sandwich" Methodology: A breakdown of Kristen's lesson structure: warm-up/skill-builder, inquiry experience, and concluding explicit instruction.
• [01:01:34] The Challenges of PBL in Math: Why Project-Based Learning can be difficult to implement in math courses due to the hierarchical nature of standards.
• [01:07:14] Closing & Resources: Where to find Cultivating Math Confidence and The Confidence Interval newsletter.