Designing for Mathematical Thinking — Acutely Curious

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The central question: What kind of mathematical thinking does this learning experience produce?

How this connects to the 3R Method: The Designing for Mathematical Thinking framework is the why — a shared language for what quality looks like. The 3R Method (Recognize, Reverse-Engineer, Reimagine) is the how — a repeatable process for applying these lenses when evaluating, deconstructing, and building learning experiences. These three lenses are also the foundation for using AI as a task design partner: when AI knows what you're looking for, it becomes a far more useful thought partner. Explore the 3R Method →

Further Reading

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Building Thinking Classrooms

Peter Liljedahl

Classroom structures that foster student-owned thinking

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Figuring Out Fluency

Bay-Williams & SanGiovanni (2021)

Seven significant strategies and productive fluency practice

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NCTM Process Standards

National Council of Teachers of Mathematics

Problem solving, reasoning, communication, connections, representation

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CCSS Mathematical Practice Standard 4

Common Core State Standards

Model with mathematics — the full mathematical modeling cycle

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WA State Math Learning Standards

OSPI (2025)

Fluency as efficiency, flexibility, and accuracy; modeling embedded across all grades

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Thinking Mathematically

Mason, Burton & Stacey

The investigative cycle: specializing, generalizing, conjecturing, convincing

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Mathematical Task Framework

Smith & Stein

Cognitive demand levels in mathematical tasks

This framework stands on its own — rooted in practice, not derived from these sources. They are offered as adjacent thinking worth exploring.

This is a working draft shared for feedback. If you have reactions, questions, or suggestions, I'd love to hear from you: patty@acutelycurious.com

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