What Is Fact Fluency? How Does It Develop?
If you think back on elementary school math, you likely remember one key part: learning your addition, subtraction, multiplication, and division facts. And while the process for how these facts are taught has changed, the fact remains that children need to know their basic, single-digit addition, subtraction, multiplication, and division facts.
If they don't know these facts, later work in middle school math becomes unnecessarily complex for children.
But did you know that research now shows that pure memorization of these facts through flash cards and timed tests is not the best approach for helping children build fact fluency? So what is the best approach? And how can you support your child at home? In this post, we'll do a deep dive into what fact fluency means, how it develops in a child, and how parents can support at home.
What are basic math facts?
Basic math facts are the single-digit addition, subtraction, multiplication, and division facts you typically find on flash cards.
For example, a basic addition fact is one that finds the sum (total) of two single-digit numbers. 5 + 9 = 14 is a basic addition fact because two single-digit numbers are being added together. 12 + 2 = 14 is not a basic addition fact because 12 is a two-digit number. The basic subtraction facts are the subtraction facts that correspond to the basic addition addition facts. 14 - 9 = 5 would be a basic subtraction fact because it corresponds to the basic addition fact, 5 + 9 = 14, but 14 - 2 = 12 because it's corresponding addition fact 12 + 2 = 14 is not a single-digit addition fact.
Similarly, basic multiplication facts find the product (answer in multiplication) of two single-digit numbers. 5 x 4 = 20 is a basic multiplication fact, but 5 x 14 = 70 is not because 14 is a two-digit number. The basic division facts are the division facts that correspond to the basic multiplication facts. 20 / 4 = 5 is a basic division fact because it corresponds to the basic multiplication fact, 4 x 5 = 20.
These are the facts children are typically asked to memorize. In the next section, I discuss why many math programs are shifting away from the language of "fact memorization" and instead working towards "fact fluency."
What’s the Difference Between Fact Fluency and Fact Memorization?
Fact memorization refers to learning basic facts through rote memorization strategies alone. This typically looks like repetition of facts until the fact is memorized. For example, if I repeat "6 times 4 equals 24," enough times, my brain will just remember it.
Fact fluency, on the other hand, means that a child can accurately, flexibly, and efficiently come up with the answer. As the process of building fact fluency progresses, it leads to memorization, but it doesn't start there. It starts with counting, reasoning and number sense. The memorization that is built holds more meaning than rote memorization alone. The phases of building this meaningful memorization are described below.
But building fact fluency seems so much slower? Why is it better than going straight to memorization?
There are 400 total basic addition, subtraction, multiplication, and division facts. That's a lot to memorize! It's no wonder that so many people, adults included, find it challenging to remember all 400 of these facts all the time.
If, instead, we teach strategies for figuring out the fact, children always have a way to figure out that fact, even when their memory can't recall it. There's a process they can use to figure out the answer, rather than just relying on memory alone.
"The primary cause of problems with basic combinations [basic math facts] [...] is the lack of opportunity to develop number sense during the preschool and early school years." (Learning and Teaching Early Math, Clements & Sarama)
"The key to teaching basic facts effectively is to focus on number sense and the development of reasoning strategies." (Teaching Student-Centered Mathematics, Van de Walle et al. 2018)
AND!!! When children learn strategies for figuring out single-digit facts, they can apply these same principles to figure out multi-digit problems, thus increasing their mental math skills too. It's a win-win all around!
How does fact fluency develop?
"Psychologists have long known that well-connected factual knowledge is easier to retain in memory and to transfer to learning other new but related facts than are isolated facts. As with any worthwhile knowledge, meaningful memorization [fluency] of the basic combinations entails discovering patterns or relationships." (Arthur Baroody, Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them, 2006)
So we're focusing on building fact fluency—the ability to solve accurately, efficiently, and flexibly—rather than isolated fact memorization. But how do you actually build fact fluency if it's not just flash cards and timed tests?
Fact fluency develops gradually as a result of repeated practice using a variety of strategies to figure out the facts. Research from Arthur Baroody in 2006 shows that as our children's number sense grows, their understanding of the facts progresses through three stages:
Counting Strategies
Reasoning Strategies
Fact Fluency
Counting strategies are when children use the process of counting to figure out the answer. For example, an addition counting strategy for 5 + 4 would be for a child to say "5" and then count 4 more on their fingers: 6, 7, 8, 9. An example of a multiplication counting strategy for 4 x 6 would be for a child to skip count by 6s four times: 6, 12, 18, 24. In both of these examples, children are using a method of counting to figure out the answer.
After children become comfortable with counting strategies, they're ready to progress to a reasoning strategy. A reasoning strategy uses a child's understanding of number relationships and patterns (number sense) to figure out an unknown fact by relating it to one they already know. For example, an addition reasoning strategy for 5 + 4 would be for a child to recognize that 5 + 4 is close to an easier fact 5 + 5. Children often remember 5 + 5 early on because they've seen so many examples of 5 and 5 making 10 in their lives, like two hands of 5 fingers or two feet of 5 toes. A child can then reason that 5 + 4 must equal 9 because it's one less than 5 + 5 which equals 10.
An example of a reasoning strategy for multiplication is for a child to understand that 4 x 6 means 4 groups of 6, so that would be the same as 2 groups of 6 twice: (2 x 6) + (2 x 6). 2s facts are often easier for children to remember because they are doubles addition facts: 2 x 6 = 6 + 6. So a child who can see that 4 x 6 is two sets of 2 x 6 can reason that the answer must be 12 + 12, which is 24.
While these reasoning strategies initially appear much slower than if a child had just memorized the fact, the repeated practice with patterns and relationships gets more efficient with time. Over time, children will develop fact fluency that typically resembles rote memorization. The key difference is that a child with fact fluency always has a strategy for explaining how the fact could be figured out. This key difference will have a monumental impact down the road on a child's ability to do mental math with larger numbers.
How can I support my child as they’re developing fact fluency?
Now that you know how fact fluency progresses, you might be wondering how to help your child through these three stages.
Here are the steps I follow:
Watch how your child figures out an unknown fact now. Do they use some type of counting (a counting strategy) or are they using a pattern or number relationship to figure it out (a reasoning strategy)?
Engage in a conversation about their strategy. Ask them to explain to you how they figured it out so that they practice talking aloud about their thinking and you can affirm their approach. If your child is not yet able to explain their strategy, stop at this step and focus your time on helping them explain their thinking. "Can you teach me how to do what you just did?"
Show them how you would figure it out. "I figured it out a different way. May I show you how my brain thought about it?" If your child is able to easily explain their counting strategy, then you can use this time to show them a reasoning strategy. If they already used one reasoning strategy, you can show them another, which helps build flexible thinking.
Ask them to help you think of another way to figure it out. When you reach the point where you want your child to start practicing a reasoning strategy because they can easily explain counting strategies, instead of showing them how you solved, say, "Your strategy is exactly right. Can you help me think of a way someone else might have solved?" This encourages them to still practice the reasoning strategy, even though it's not their go-to approach yet.
Once your child is using reasoning strategies, the final step is just practice, practice, practice. The ongoing practice with reasoning strategies will help your child become more efficient when using them and move into fluency.
At this point, you might be thinking: "But how do I know what all the reasoning strategies are?" In this post, I talk about some helpful reasoning strategies to discuss with your child.
(And if you have a first grader working on addition and subtraction fluency, these reasoning strategies are a central component of my First Grade Math Companion program.)