The end of the math wars?

Memorization or thinking strategies? It's both in the right dosage, argues a new paper

Welcome back, Bell Ringers! Today’s newsletter is a great one—Part 3 of Raising the Bar: What it takes to raise math achievement. It follows Part 1, on whether states will invest in LETRS-like training for math teachers, and Part 2, about what courses future math teachers take (and don’t take) in their training. Continuing the theme of this series—that teacher knowledge is a crucial piece to higher math achievement for students—today’s topic is the war over whether to emphasize procedural knowledge or conceptual understanding when teaching early math. 

Read the first Bell Ringer Open Thread on what teachers learned (and didn’t learn) in their training. You’re going to be reading a lot more about this topic beginning this fall, but in the meantime I want to hear from as many educators as I can. I’m looking for specifics: what courses did you take? What did you take away from your training that helped you in your new classroom? What did you realize you *didn’t* know when you started teaching? Leave a comment, or email me privately about your training: holly@hollykorbey.com

Our first book club is launching in just a few weeks. We’re not only going to read and discuss the role knowledge plays in learning by reading the free, downloadable Developing Curriculum for Deep Thinking: The Knowledge Revival, you’re going to get a chance to ask some questions of co-author and godfather of the science of learning, Paul Kirschner. Want to get a head start on the book? Download it here. 

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The Math Wars’ last stand 

One of math education’s biggest and most strident disagreements is how to teach the fundamental skills most students learn in elementary school. For decades (or as Tom Loveless has argued, longer than that), the pendulum of thought has swung back and forth between two main ideas: arithmetic skills like addition, subtraction, multiplication and division should be taught by focusing on the procedure and memorizing math facts; or arithmetic skills should be taught by focusing on the concept behind the math, making connections and “thinking strategies.” 

In a lot of my reporting on math, researchers and experts have said that there’s a “bi-directional relationship” between memorizing math facts and thinking strategies—that the two should work together and inform each other. But this doesn’t give teachers a solid way on how to teach the two processes, a new paper from a group of psychologists and cognitive scientists argues. 

“We've had people saying ‘it's both’ a lot and there's a lot of analogies to reading as well, where it's like balanced literacy. What is the balance? Telling us that it's both isn't actionable,” said Notre Dame professor and cognitive scientist Nicole McNeil, lead author of the new paper “What the Science of Learning Teaches Us About Arithmetic Fluency.” The paper’s authors, which include researchers Nancy Jordan and Daniel Ansari, propose evidence-based ideas for teaching students arithmetic that rely on both methods.