What Is Math Fluency? - Definition & Components

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this lesson, you will understand what it means to be math fluent. Learn that it's not just about memorization, but about understanding, and smoothly and quickly applying math concepts.


This lesson is about math fluency. We define math fluency as the ability to perform mathematical problems accurately and quickly. For example, a child is fluent in addition within 5 numbers if she is asked to add 1 + 3 and she immediately blurts out 4! A child is not fluent in addition within 5 numbers if he is asked the same 1 + 3 question and he blurts out 5 with an unsure tone and then continues to count with his fingers.

Mathematical fluency is a required component in state educational standards as well as in common core standards. This math fluency has four parts to it: accuracy, automaticity, rate, and flexibility.

Let's look into each of these components in detail.


Accuracy involves solving problems using an appropriate method by following the right steps in the right order to arrive at a correct answer. Ok, that's a long way of saying that if you are accurate, then you know how to use the various mathematical methods available to you. You know how to use them, you know the steps you need to take, and you know the order in which you need to take those steps.

For example, if you are asked to find the area of a circle, you'll know the formula you need to find a circle's area, and also know how to use that formula to find the correct answer. You'll know what numbers to plug in to the formula along with where those numbers go. Finally, you'll know how to follow the order of operations to evaluate that formula.


The next component of fluency, automaticity, can also be referred to as a reflex. Automaticity means that you have performed the mathematical operation so often that it's almost automatic for you. For example, you've practiced your multiplication table so well that every time you see a multiplication problem, you automatically replace the multiplications with their respective answers. Like, when you see 5 * 6, you automatically replace it with 30.


The rate component is about being efficient. If you think about it, if you are fluent in speaking a language such as English, then you can efficiently speak in coherent sentences that convey your thoughts. You don't need to pause to think about what word to say next. You are efficient in speaking English. The same goes for math fluency. If you are fluent in math, then you can efficiently solve math problems. For example, when solving 7x - 4 = 10 for x, you won't need to pause to figure out what next step to take. You'll know that after adding the 4 to both sides, the next step is to divide both sides by 7. You won't need to pause to think about what operation and what number to use next.

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