Opinions are divided on whether students should be expected to memorize their basic math facts or given timed math fact fluency assessments. While the research supports the benefits of fact fluency, many schools have pivoted toward a greater focus on higher-level math skills instead of fact practice.
I firmly believe that computational fluency, or the ability to quickly and accurately compute the answer to a given number sentence, is a cornerstone of math success and a precursor to being able to efficiently solve challenging multistep word problems. Being able to quickly and easily recall the answers to basic facts is one piece of this process.
While the pendulum has currently swung in favor of those opposed to math fact practice and timed tests, I fully believe that math facts should be a core component of any math block.
But before I dig in too deep on why I hold this belief, let's start with the basics.
What is math fact fluency?
Math fact fluency is the ability to quickly and accurately recall the answer to basic math facts. This is typically the result of repeated practice that results in the fact being committed to long-term memory, allowing it to be instantaneously recalled.
To be considered fluent, students should no longer need to rely on strategies such as counting on their fingers or drawing models to compute.
Is fact fluency the same as computational fluency?
Kind of. Depending on who you ask, computational fluency can be synonymous with fact fluency or it can be something a little different.
Computational fluency is the ability to quickly and accurately solve math problems. While it requires the application of basic fact fluency, it can go beyond simple computation. For example, being able to quickly get the right answer to an addition equation requiring regrouping would be a sign that a student has developed computational fluency.
The path to fact fluency
Based on the hierarchy of learning, we know that students must acquire a conceptual understanding first. For basic facts, this means using strategies like counters to compute sums and differences.
Stage 1: Skill Acquisition
At this early stage, students need to see how the solution is formed. This means they need lots of hands-on experience putting groups together for addition or taking away to subtract. Visuals are a huge help when students are at this stage of learning, which is why you commonly see pictures on kindergarten and first grade math worksheets.
As students progress, we introduce many different strategies to help them find the ones that are most efficient for them. Making a ten, counting on, repeated addition…the list goes on and on. The goal at this initial stage is accuracy not speed.
Stage 2: Fluency Building
Once students have a strong foundation and conceptually understand the computation process for basic facts, they can begin to transition from toward fluency building.
At this stage, students should begin to memorize their facts as a result of repeated practice. For some students this begins to naturally occur through their exposure during the early phases of learning.
For other students, this requires a concerted effort and possibly some “tricks” or mnemonics. It might even mean they still bust out their fingers to help them compute when necessary. There is nothing wrong with this. It is all a part of the fluency building stage.
Stage 3: Application
The major goal of the fluency building stage is moving from accurate to automatic. A student who is fluent with their math facts no longer needs to think about the answer to 2 + 2. This means their mental resources are freed up for more complex mathematical thinking and problem solving.
Why is math fact fluency important?
There are numerous benefits to math fact mastery. In fact, there is a plethora of research supporting its importance. Here are a few highlights:
Fluency in math saves mental resources
Research on cognitive load supports the idea that we all have a limited cognitive capacity at any given moment. In other words, we are working within the limits of our brainpower.
By memorizing their facts, students can use the mental resources they would've spent on trying to figure out 6 + 9 to actually do some real mathematical thinking.
If a struggling student is using all their mental energy just to solve the basic facts, what is left for problem solving or determining whether their solution is reasonable?
This is why we see many struggling students frustrated and overwhelmed when asked to check their work. They've used all their resources just to get to this point, and we are asking them to go back and work it again from an empty tank.
That being said, mental math strategies can be a useful tool. This is because the goal of these strategies is to make the computation process easier and reduce the cognitive load.
It improves the likelihood of success on state testing.
If you've looked at any practice tests, you'll notice that there is a growing trend toward problems where students are asked to pick the right answer with an explanation. They look something like this:
A. 43, because if you subtract 55 from 98 you are left with 43 apples.
In this type of problem, three of the answers have computational errors. When students struggle to compute, these questions become another obstacle to good performance.
For students who have developed computational fluency and know their facts, these are basically free score boosters.
It saves student's time.
All those strategies we are teaching students are meant to help them. However, they are all meant to be short-term bridges toward an end goal of computational fluency.
If a student has to draw a picture or make a number line each time they need to add or multiply, it is only a matter of time before they begin to struggle to keep up.
With more and more algebraic reasoning skills being pushed at elementary, students who aren't fluent in math are more likely to develop an aversion or dislike for the subject.
The challenge of balancing problem solving with fact fluency
Education today is a barrage of standardized assessment. In math, the focus is on story problems and multistep problem solving. The vast majority of state math assessments are page after page of word problems.
This means we need to give our students exposure to this type of problem solving. The fear is that if we don't give them enough practice with the types of problems they'll be asked, they won't be successful.
So we find ourselves pushed to make more and more of our math block focus on work problems. As spring approaches, this push moves from a gentle wind to a full-on hurricane force storm.
As a result, there are some who would argue that if a child can find a way to get the answer to a math problem that is good enough. They argue that as long as a child has a strategy, they can be good problem solvers.
While this is true for some students, if you look at the majority of struggling math students you find the same gaps in basic skills. They don't know their facts. While some can compute them, others are missing even the conceptual understanding of the foundational skills.
Even those who are semi-successful in math often use inefficient strategies that take time and are mentally tiring leaving them with incomplete or partially done assignments. These students are treading water, but as the rigor increases they are sure to begin sinking.
While I think having a strategy is a good band-aid, it fails to consider the big picture of the progression of mathematical skill building.
This is especially true considering there are so many easy and inexpensive ways to build math fact practice into your classroom routine beyond just flash cards and timed tests.
Should problem solving be a major focus in math?
However, we need to find balance between skill building and application if we want to give students the best chance for long-term success.