What Is Math Fluency?
You have probably heard of math fluency a lot, especially if your kids have gone to school but what exactly does it mean? Well, the definition has changed a bit since I was in elementary school. Math fluency used to be very simple, knowing your facts. It was achieved through constant repetition and memorization. It was assessed through fact quizzes often done in one minute. It focused primarily on learning the times tables in third grade but it included addition, subtraction and division as well. High importance was placed on knowing your facts with automaticity so you did not waste time solving a problem by counting, drawing or any other slow method.
Today, when we define fluency
it still includes accuracy, rate and automaticity however, there is a much stronger focus on flexibility and efficiency. Fluency still means answering questions quickly and correctly but we are reaching that level through a deep understanding of concepts. This understanding allows children to be flexible with their problem solving and critique strategies for efficiency.
The goal is not for children to achieve accuracy and automaticity through rote memorization
as this does not show any conceptual understanding and therefore, cannot be applied or generalized to other problems. The relationships between numbers are being ignored and they are memorizing questions and answers the same way they might memorize a series of unrelated pictures for later recall. This strategy is not efficient for its lack of usefulness but also because many people do not have a strong visual memory. The majority of our students are relegated to counting on their fingers or drawing a problem out to solve it, two methods that are inefficient, as they lead to errors and slow work.
So, what does it mean to be flexible when problem solving?
Once kids have a really strong foundation in numbers they are able to see that there are several ways to solve a problem. This starts with very simple problems and is applied to all four math operations. Here is an example of a kid with a strong foundation in number sense:
The problem: 9+6
Kid knows: 9 is one less than 10, also 10+ any one-digit number that digit replaces the 0 so, 9+6 would be same as 10+5 because you can take one away from the 6 and give it to the 9 making the answer 15.
As other kids share the way they solved this same kid is able to understand their line of thinking and critique them all to choose the most efficient strategy.
When another kid shares: 9+6 is same as 9+1+5 because they broke the 6 into a 1 and 5 it makes perfect sense to the first kid.
When kid 3 shares that she broke the 9 into a 4 and 5 and knew 4+6 made a 10 so 5 more was 15 it also makes perfect sense to kid 1.
The kids enjoy evaluating each other’s strategies and critiquing which one would reliably get them the answer correct and fast.
We can build fluency and efficiency in kids from an early age
Notice, I am not recommending flashcards, quizzes, minute assessments and shaming kids who are not memorizing their facts. Simply, giving kids one problem to analyze is enough to make a valuable math lesson. This example could have included much more difficult numbers, subtraction, multiplication or division, fractions, decimals, percentages, or money.
The best way to assess mathematical fluency is not through quizzes but rather conversation
It is often difficult to ascertain how students got an answer if they are simply writing it in. Many workbooks today require kids to write out the process which is time consuming and defeats the purpose of the skill. The skill is to become quick, automatic and it relies on mental math practice. If we require kids to transcribe their mental math practice every time they do it we are laboring something that should be fun. I’m not saying there is no value in kids explaining their thinking however, I think the ability to do so in writing takes a certain maturity that most have not achieved in elementary school. I also think it steals some of the joy of math.
For teachers, if you want to know how fluent your students are you need to work with them in small group
Ideally, you would also give math interviews individually a few times a year to assess where they are at. Sure, giving fact quizzes will allow you to see how accurate and fast they are at solving but you will have no idea of their flexibility and ability to critique efficiency. You will also add an element of pressure and anxiety that will turn many kids off to math.
Let’s preserve the fun in math
and not spoil it with paper and pencil, quizzes and anxiety provoking practices that lack in merit anyway. Too many people hate math when it should be loved and celebrated. Math is an amazing subject that allows for tons of creativity and exploration as well as real-world application and hands on learning. It has all the components of fun yet, schools have found ways to make it awful for so many. It’s time for a change!