Doug Lemov's field notes

On February 10 and 11 we’ll be in Houston for something new and exciting–our first math-specific teaching workshop: Checking for Understanding in Math. We’ll discuss topics we’d cover in a typical CFU workshop–gathering data, perceiving and responding to errors–but look at them all through a math lens: What and how do we use and adapt these tools.

This is important. As my colleague Joaquin Hernandez points out, math is cumulative and relentlessly hierarchical, it requires constant switching between procedural skills and conceptual understanding, and of course it can be intimidating to some students. All of these factors should shape how we teach it

Retrieval Practice provides one example. When we “Check for Understanding,” we have to check for durable understanding…understanding can be temporary; learning is a change in long-term memory. So we should use retrieval practice in all subjects to test for and build long-term memory of concepts and ideas.

But math has some specific cases. For example one sub-category of Retrieval Practice that math requires is fluency practice. We need to go over certain foundational skills again and again and again so they are over-learned and students can execute them at no load on working memory. Only then can their minds be free to engage in more conceptual thinking.

Consider  one study–Siegler et al (2012)–which found that knowledge of fractions and whole-number division was a stronger predictor of high school algebra success than IQ, reading achievement, or family income. If your foundational skills are fluent, your working memory is free to perceive and learn more complex skills. Or another–Rittle-Johnson and colleagues (2007)–which found that when students learned a procedure fully and fluidly, it helped them deepen their conceptual understanding.

In math: over-learning of foundational concepts assists in learning complex and abstract ideas.

So in math part of our Retrieval Practice should be focused on important foundational content that needs to be practiced over and over so it’s practically automatic.

Think mad minute.

But the idea also applies in more advanced classes. Like you’ll see in this video of Bradi Bair at Memphis Rise Academy in Memphis. She’s helping her Calculus students become fluent with antiderivatives so–as she tells her students–they can use them all unit long in solving integrals.

Which is what you see her doing here. One of several repeated rounds of fast retrieval practice with a foundational skill to ensure fluidity.

It’s a great video and you can study it and a dozen more like it with us at our Math CFU workshop February 10 and 11 in Houston, TX.

Details here: https://www.tlacdevserver.com/checkforunderstanding/mathfeb2026