Grow Your Mind

The Glue That Holds Math Proficiency Together: Building Adaptive Reasoning in Every Learner
Naomi Church Naomi Church

The Glue That Holds Math Proficiency Together: Building Adaptive Reasoning in Every Learner

Most students can follow the steps. They can execute a procedure, produce an answer, and move on. But ask them to justify their thinking, apply their reasoning to an unfamiliar problem, or explain why their answer makes sense — and the wheels come off. The National Research Council called adaptive reasoning the glue that holds all five strands of mathematical proficiency together. So why does it get the least attention? This post breaks down what adaptive reasoning actually is, why it can't develop in silence, and the practical routines that build it in every learner — regardless of grade level or ability.

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What Really Makes a Mathematician? A Closer Look at the Five Strands
Naomi Church Naomi Church

What Really Makes a Mathematician? A Closer Look at the Five Strands

It’s more than memorizing facts or following steps. This post breaks down the Five Strands of Mathematical Proficiency—productive disposition, conceptual understanding, procedural fluency, strategic competence, and adaptive reasoning—and shows how they work together to build confident, capable math thinkers. Whether you're designing instruction, planning PD, or coaching educators, this framework offers a powerful lens for supporting meaningful math learning.

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