When I think of learning multiplication and division facts, I instantly think of things like flashcards, timed tests, and around the world activities. I remember learning some songs to memorize my facts, along with a few tricks here and there. Honestly, I could never tell you how the tricks worked or why. Let’s just say fact fluency was not something I enjoyed. It was all about memorization.

Since then, research has come a long way. In 2006, Baroody said that students needed to go through three distinct phases in order to have excellent fact fluency– and it does not involve memorization. The old approach of memorization has been proven an ineffective method of learning the facts.

## The Three Phases of Basic Fact Fluency Mastery

**Phase 1** – In this phase students need the information to be concrete. I explained a lot about this in my post, Teaching Math so Students Get it. This is where you would practice modeling and counting. For instance, if you gave students the problem 6×4, you and your students would model 6 groups of 4 goldfish crackers (for instance) and skip-count.

**Phase 2** – Introduce students to strategies based on known facts. For instance, if a student has the problem 6×4, they can reason that 5×4 is 20 and add one more group of 4. I talk about teaching these strategies in both my post Teaching Multiplication Shortcuts and Presenting Multiplication Strategies.

Remember not to just teach the strategy and ask students to use it. That removes the reasoning. It also defeats the purpose, creating a “thing” to memorize. Instead, support students’ thinking and ask what strategy they might use. Help them see the possibilities and choose to get to the solution.

**Phase 3** – Once students arrive at this stage, they have mastered their basic facts and have come to know them from memory. They just need repeated practice. Now the problem is 6×4=24.

To increase your students’ fact fluency, you don’t want to bring in the flashcards or the timed tests. Instead, the key to effective mastery is through meaningful experiences with these phases.

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