Bridging Math and Cognitive Science

Mathematics is more than numbers—it’s about thinking, problem-solving, and making connections. In Part 2 of the Staircase Problem on the Tier 1 Interventions podcast, we explored how structured problem-solving builds both math fluency and executive function.

Why the Staircase Problem?

The Staircase Problem is more than a simple counting task; it’s a foundational exercise that scaffolds students’ understanding of number sense, patterns, and problem-solving. It’s one of the 12 reference tasks that can be adapted for students at all grade levels, reinforcing the power of repeated exposure and gradual complexity.

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The Goldilocks Principle: Finding the “Just Right” Challenge

Every student learns at their own pace. The challenge for educators is differentiating instruction to match each student’s “just right” learning zone. Rather than isolating students into different groups, whole-class differentiation allows all students to engage at their appropriate level while working on the same task.

The Intersection of Math and Executive Function

Cheri and Jonily emphasized that learning isn’t just about content—it’s about cognition. When students are engaged at their optimal level, the brain shifts into a learning state where focus, flow, and automaticity take over. This balance prevents frustration while maximizing growth.

Strategies for Making the Staircase Problem Accessible

  • Use Concrete Materials: Blocks, sponges, or other tactile tools can make the problem more tangible.
  • Leverage Grid Paper: Adjusting line thickness and square size supports students with fine motor challenges.
  • Encourage Exploratory Thinking: Instead of giving immediate answers, guide students toward discovering patterns themselves.
  • Mix Explicit and Inquiry-Based Learning: Sometimes, direct instruction is needed to establish rules; other times, open-ended exploration fosters deeper understanding.

Final Thoughts

The Staircase Problem isn’t just a math exercise—it’s a pathway to deep conceptual learning, executive function growth, and full classroom inclusion. Whether you’re a math teacher, occupational therapist, or intervention specialist, understanding how to scaffold and differentiate this task can transform student engagement and success.

Want to learn more? Listen to the full episode now!