What Is Math Fluency?
Fluency is the ability to understand and apply something effectively. We talk about fluent readers who can look at a word, instantaneously know what it says, and understand whether there is a deeper meaning in the context of the whole. Math fluency is a very similar concept.
Math fluency is the ability to use different computational strategies to reach solutions quickly and effectively. This means that kids can assess a problem and predict which method would be the easiest to calculate the answer.
Many people drill their kids with flashcards, driving their kids to memorize the facts. While this gives the same quick response as fluency, it lacks the diverse and flexible thinking skills that define fluency.
Why Is Math Fluency Important?
I am a bit bitter about my subpar math education from elementary through junior high school. I, like many parents who are struggling with Common Core Math, lack fluency. While we may be able to quickly fire off the sum of 19 and 23, this is a hollow shell of fluency. We simply lack the flexibility in computational strategies that is the hallmark of fluency.
This study found that fluency was an accurate predictor of mathematics success in the long term. This study is not unique. Researchers and teachers alike have noticed a strong correlation between fluency and success in math and related areas for decade. Researchers have even noticed that the brain changes in response to fluency. Which makes sense, because researchers have noticed that those who are fluent pull information from a completely different area of the brain than non-fluent people. During the high school years, activity during calculations in the area of the brain linked to insufficient math fluency was also linked to lower PSAT scores.
Fluency is about understanding numbers in a deep way that allows you to work the same problem many different ways. This flexibility is the key to being confident in problem-solving. When children are not intimidated by simple calculations, they have more mental labor available for wrestling the deeper part of the problem.
Imagine how children learn to read. At first, all their focus must be aimed at sounding out the words, and it is difficult for them to understand the meaning of a complete sentence. As they grow older, they are able to immediately recognize more and more words, allowing them to consider the meaning of the whole sentence, then a paragraph, and eventually they are reading, comprehending the shallow meaning and later deeper symbolism and other literary elements.
Mathematical fluency is much the same. We must teach our kids many different computational strategies so that we can give them the tools to face each and every problem with a fresh and appropriate strategy.
Math concepts build upon one another just like reading. Multiplication is just repeated addition. Exponents are just special types of multiplication. Algebra is basically realizing that math is a puzzle, with pieces that directly relate to each other. Understanding each of these basic concepts makes it easier to understand the more complicated ones.
If we spend our time focusing on making kids just memorize facts, we are not giving them the tools to really use numbers and their relationships to each other. This will leave them high and dry when they come to a problem where they need to understand addition in the realm of a division problem, like in remainders. For example, 28/5 = 5 R 3, because 5*5=25, and you must add the remainder of 3 to get 28. A fluent way to write this would be 28/5=5R3 = 5*5+3 (see how I used addition?).
How to Build Fluency
I briefly mentioned earlier that some people focus on memorizing math facts as a way to gain mastery, help free up mental labor, and help kids gain confidence. However, rote memorization does not mean a child or adult is fluent in mathematics. Memorization alone does not provide the flexibility in calculations that set a student up for success in higher mathematics.
This is where I start defending Common Core. So many people hate Common Core because they don’t understand why CC places so much emphasis on making kids use so many methods to solve problems and explain mathematical reasoning. Can you imagine a reading program that stopped teaching reading when the kids could just sound out words? Because that is what the old-style math taught. Parents have a hard time understanding so many CC concepts simply because parents are NOT fluent in math.
So if rote memorization isn’t the way to build fluency, what is?
Teach your kids different computational methods. Teach them to use addition to solve a subtraction problem. Does this make absolutely no sense to you? Well, I bet you do this without realizing it. Let’s say you get a coffee and the total is $1.23. Do you think about the problem like this: .23 + .02 = .25? Then .75 + .25 = 1. So your change should be .75 + .02 or $.77. To put it in other words, I am using easy addition problems to solve a subtraction problem. You may have seen a meme like this:
This comparison is meant to show the simplicity of the place value based subtraction (“The Old Way”). “The New Way” is meant to look complicated. But “The New Way” makes mental computation much easier and demonstrates the mental flexibility characteristic of math fluency. “The New Way” simply uses easy addition problems to find the difference.
This meme is used to make people think that CC is unnecessarily complicated, but the CC way is only complicated if you don’t truly understand the relationship between addition and subtraction.
Teaching Fluency If You Aren’t Fluent
If you are realizing that you are not fluent, all hope is not lost if you want to raise kids who are fluent in mathematics. You also don’t need to enroll them in school, either. It is all about your resources. Now, I am going to review one of the best resources for promoting fluency I have ever seen.
Evan-Moor Educational Publishers has a Building Math Fluency series, and I am reviewing the grades 4–6+ book.
The Setup
This book is set up into 8 major sections:
A teacher section: a short introduction to the book, how to use it, some reproducible tools, and a glossary of math terms.
1 each of Addition, Subtraction, Multiplication, Division (total of 4 sections): Each section includes computational strategies and practice. A double-sided cheat sheet starts each section. One side is a simple explanation of each strategy, and the other is simple examples. Then there are labeled practice pages for each strategy.
Test Your Knowledge: Short exercises or tests if you prefer to evaluate progress. These exercises can be timed to judge fluency.
Flashcards: 269 flashcards are included.
One “Test Your Skills” exercise. At the bottom, you’ll notice that there is a place for recording data to evaluate fluency.
The Good
First, Building Math Fluency recognizes the value of the diversity of learning styles and includes a page that helps kids think about how they best understand things: in pictures, in words, or in actions. Then each section has resources aimed at each of the 3 ways so that kids can practice in the way that is most valuable to them.
Second, these strategies are gold!
They are simple, easily understandable, and once you see them, you are going to wonder why you didn’t think of them yourself. For example, two addition strategies that I think everyone uses is the “See 8, Think 10” and the “See 9, Think 10.” These teach your child to add 10 then subtract 2 or add 10 then subtract 1, easy.
Some of these strategies reinforce algebraic skills, too. Like subtraction strategy “Think Addition.” I have already talked about using addition to complete subtraction problems. So instead of 29 – 13 = ? you would think 13 + x = 29. One could easily solve this problem by thinking 13 + 7 = 20, 20 + 9 = 29, so 7 + 9 = 16. This strategy shows the inherent relationship between addition and subtraction, a foundation of algebra. It makes so much more sense learning to balance equations when you understand that addition and subtraction balance each other. Same goes for multiplication and division.
There are little bubbles above each problem on some exercises, and these are for you to write the strategy best for that problem. I just feel like this is a really nice way of getting kids to think about the different strategies and keep them from becoming too dependent on one strategy.
This book also has Chock the little lizard character that adds some fun, but also asks some great scaffolding questions to get kids (and parents) thinking about the best way to solve calculations. The best part is that there is no right or wrong answers. I would encourage you to really dig deep into these scaffolding questions. Your kids’ answers will probably surprise you. If they don’t have an answer, you probably can assume you should work on those strategies more.
The Test Your Knowledge section has both long exercises and short exercises that you can time to evaluate fluency. Each exercise has a little section at the bottom where you can record accuracy and time for each exercise to track progress.
Towards the end are 269 flashcards in case your child needs to practice; there are also 2 pages explaining how to use the flashcards and the best ways to practice. You are encouraged to write down the strategy used to solve the problem on each of the printed cards to teach your child to recognize when to use each strategy. These flashcards include a set to write down summaries of the strategies to practice recalling them, too.
You also get a code to download an additional 5 practice pages to print or project via smartboard in a classroom setting.
Of course, an answer section is at the end of the book in case you need it.
The subtraction strategy pages, with explanations on the left and examples on the right.
The Bad
I really wish that this book skipped the accuracy and time recordings in the Test Your Knowledge section. While these are important for judging fluency, I would just jot a quick note somewhere else so that my kid doesn’t feel that much pressure. Connor (11) tends to panic when anything is timed, although that is an integral part of his mathematics curriculum. I guess I really just don’t like kids knowing they are being timed.
The flashcards are small, thin strips of paper, and I wish they were bigger and sturdier so I could put them on a ring. These are definitely not a set that I would take with us in the car or to an appointment. I would not take them outside to the park, either.
Some of the practice exercises are fairly long, up to 48 problems. I would probably divide these up into 2 different days just to reduce pressure and anxiety.
The flashcards
Conclusion
I have seen plenty of other programs that promise fluency but that are really aimed at just making kids memorize math facts without actually teaching them multiple strategies to solve problems, so Building Math Fluency by Evan-Moor Educational Publishers really stands out from the crowd.
Despite the things I don’t like about this book, there are clear and useful strategies to build math fluency. I highly recommend this book if you are looking to teach a child to understand math and not just imitate it.
Ali Southerland is a long term homeschool mom of many. She is zealous about education, the result of her own rigorous education. While math is not her favorite, science is. She writes all about how our science education is lacking (and how to fill the gaps) at This Addictive Mess. She also writes about teaching kids about money, how parents can save money and have a better relationship with it. When she isn’t writing, chasing her kids, cooking, or sleeping, she is probably reading about dinosaurs. #rawr