The Importance of Being Fluent, Part II

Child sitting test

At the end of my previous post, I hinted at another reason why fluency is important for students and how they can “go even faster…”.

Fluency is not only the ability to recall effortlessly and accurately, but also the ability to recognize patterns and to apply shortcuts and ‘tricks’ correctly. For example, in teaching data analysis units, some students have problems with finding means– either forgetting to divide, or more usually, making a mistake in the addition of the set of numbers and getting an unending decimal when they try to divide. For example:

Find the mean of the following numbers:
5 + 9 + 4 + 3 + 2 + 8 + 6 + 7 + 1 + 10= ? (this equals 55!)

To a student who is not fluent in addition, this looks hard! The student thinks, “Too many numbers to add up. Then I have to divide. And I’ll probably get a decimal that doesn’t end…” The student has no confidence in themselves, and will not want to apply the effort to add all the numbers.

However, you may have seen it quickly because you are fluent in adding 1-digit numbers:

8 + 2 = 10          7 + 3 = 10             6 + 4 = 10               9 + 1 = 10  

What’s left? 5 and a 10.  Obviously, much easier to add 10 + 10 + 10 + 10 + 10 + 5 = 55.

I understand that this is a specific, made up example to illustrate my point, but the fact the fluency allows us to instantly see ‘groups’ of 10’s makes the addition go much faster and easier.

What about multiplication? Teachers, have you seen this? (I did in 7th grade):

x 200 

as opposed to this:

  x 200

or even this: “I know that I can just add two zeros at the end since I am multiplying by 200. And since 4×2=8, 1×2=2, 3×2=6, the answer is 82,600”

The problem with this multiplication problem is writing down way too much information (then consider how bad some handwriting can be, especially boys!)– which can introduce mistakes not related to actual multiplication– but to organization. Forgetting to add a place holder 0, or lining up the columns correctly, OR actually multiplying incorrectly. And this example does not have any carry values.

The second example is a lot less writing and computing, so there is a lot less chance for error. The last example there is only single-digit multiplication.

I am all for students to learn ‘tricks’ and shortcuts…ONLY after I know they have mastered basic addition and multiplication. One of the problems that occurs when students learn a trick before mastery and understanding is that they will apply the shortcut incorrectly. Teaching tricks and shortcuts over process can lead to confusion on the student’s part.

So, the importance of being fluent is that it allows students to go faster, make fewer mistakes, and be more accurate. Under the pressure to perform well on standardized tests, I firmly believe students who are fluent have a huge advantage of those who still have to compute 5 + 9 + 4 + 3 + 2 + 8 + 6 + 7 + 1 + 10.

The Importance of Being Fluent (Part 1)


During my teaching career I taught 7th grade math, from below grade level through two years above grade level. I truly believed each student could learn the math concepts that were being presented, especially at the 7th grade level. So why didn’t all my kids learn? Why didn’t all my kids exceed on standardized tests?

There were many factors of course, but I put them in these categories:

  • Lack of Effort (this is the biggest one!)
  • Lack of Confidence in themselves (second biggest issue!)
  • Lack of Proficiency in fundamentals

However, it wasn’t until I “saw the light” on fluency, that I added a new category:

  • Lack of Fluency (which is closely related to fundamentals)

In my previous post, I referenced this statement concerning math fluency:

Educators and cognitive scientists agree that the ability to recall basic math facts fluently is necessary for students to attain higher-order math skills… If a student constantly has to compute the answers to basic facts, less of that student’s thinking capacity can be devoted to higher level concepts than a student who can effortlessly recall the answers to basic facts.”1 Computational Fluency is part of an essential foundation for more advanced performance.2

As I mentioned, this paragraph changed my view on why fluency is so important.

The sentence made perfect sense to me– “If a student constantly has to compute the answers to basic facts, less of that student’s thinking capacity can be devoted to higher level concepts…”

“Compute” is the key word here, and I compare that to “Recall”. If a student spends so much mental energy on computing 6×8, 9×7, or 3+9+7+1, and etc., then there will be less mental energy to work through word problems or process-oriented calculations such as:

  • Operations with Fractions
  • Long Division
  • Finding Means/Averages
  • Word Problems
  • Solving Equations

But, if the basic operations and skills are automatic (fluency), then there literally is no mental energy spent on that part of the problem because the values are memorized, and students can devote all of their thought processes to solving longer and more complicated problems. This also leads them to know when a solution is incorrect or (probably) correct, the ability to check their work, and the ability to communicate their thought processes to others.

What else results from this? If students realize that they are ‘getting it’, that builds confidence in themselves. They are more willing to tackle the next math topic, which makes learning easier for them. Which in turn means they are more willing to apply effort.

And that makes it much easier to teach students!

In the next post, I’ll discuss another result of fluency, and how students can go even faster…