The other day I received a text from a school district I serve. It read, “On a scale of 1-10, how important is math fact fluency?”

My answer: 11

In a follow-up text, they asked for my thoughts on fluency instruction, fluency practice, and whether there are any online apps to support the development of fluency. I thought I’d share my thoughts for all to read.

There are a bazillion online apps claiming to develop fluency, but first let’s describe what – exactly – fluency is.

For most people, math fact fluency means the quick and accurate recall of basic math facts in addition, subtraction, multiplication, and division. This is a correct, but incomplete, definition of fact fluency.

## What is basic math fact fluency?

Basic math fact fluency requires the presence of FOUR critical components:

- Efficiency
- Accuracy
- Flexibility
- Appropriate choice of strategy

For decades we have focused on the first two components – efficiency (fast) and accuracy – while under-developing our students’ ability to think flexibly about the numbers and select an appropriate strategy for arriving at the answer if the answer does not immediately come to mind.

When we use this broader vision of math fact fluency, it suddenly calls into question our use of flashcards and online apps that merely provide some sort of naked problem (like 6 x 8) and feedback based on the student’s answer (happy bells for correct answers and buzzers for wrong answers). This is because flashcards and most online apps only focus on speed and accuracy, while completely ignoring flexibility and appropriate choice of strategy.

## How do we develop math fact fluency?

We develop math fact fluency by guiding students through three stages in order:

### Stage 1: Conceptual Learning

We begin by teaching the meaning of the operations so students truly understand them. Students in early grades begin by understanding that addition and subtraction mean join together and take apart. In third and fourth grade students need to learn that multiplication and division means joining and separating equal groups. To reinforce the meanings of each operation, students must be given ample opportunities to use lots of concrete manipulatives and pictorial models.

### Stage 2: Learn Fact Strategies

Rather than merely focusing on memorization of facts, teachers need to explicitly teach strategies for deriving answers. For addition and subtraction examples of these strategies are make a ten, doubles, add a friendly number, etc. In multiplication and division strategies might include doubling and halving, distributive property, multiply by a friendly number, etc.

Students need to be provided with lots of opportunities to practice and apply these strategies, while emphasizing relationships and connections between the numbers and recognizing which strategy is more efficient than the others. Students are still expected to use lots of manipulatives and models, but now it is to develop deeper insight as to WHY the strategies work and to justify why they used a particular strategy.

### Stage 3: Memorization of Basic Math Facts

Students are finally ready to begin putting their facts to memory through a variety of practice. This might be in the form of games, flashcards, online applications, etc. Whatever form of practice you choose for your students, keep it fun! Your target is for students to recall a fact within 2 to 3 seconds. Ideally, students will be given math facts to remember through an approach called spaced repetition, in which students are shown facts they are most likely to forget thereby ensuring all problems reach long-term memory.

By the time students have reached Stage 3, many of the facts will already be in long-term memory simply through the repeated efforts of Stage 1 and Stage 2. Essentially, students are REMEMBERING their facts more than they are MEMORIZING them.

This finally brings me to those online applications that schools and districts pay so much money for. Tools like **Reflex Math** and **Xtramath** focus nearly exclusively on speed and accuracy while ignoring flexibility and appropriate choice of strategy.

Case in point:

Reflex literally says they focus on a single strategy: fact family.

https://reflex.explorelearning.com/about/why-math-fact-fluency-matters

While Xtramath is even more candid, explicitly saying it does not teach strategies…

https://home.xtramath.org/support/how-does-xtramath-work

Since Reflex and Xtramath (and online apps like them) only focus on speed and accuracy, students generally continue using what limited repertoire of strategies they already have (this is almost exclusively finger-counting) and merely attempt to get faster at that limited repertoire. Unfortunately, students do not develop more efficient strategies that will lead to long-term math success.

For example, both Reflex and Xtramath allow (even encourage) students to continue using finger-counting strategies during addition and subtraction, failing to introduce students to more sophisticated strategies that will also prepare students for multiplication and division.

## A hopeful alternative

I was recently introduced to an online tool called MathFactLab. This online tool focuses on teaching students a variety of strategies and models as integral components of mastering basic math facts.

If you are looking for an effective fluency tool, consider checking out MathFactLab.

Another fantastic online tool for mastering multiplication facts is Multiplication By Heart. MBH introduces students to a variety of models for students to use to answer questions. MBH also employs manages the spaced repetition automatically so you don’t have to.

### In conclusion

Online tools like Reflex and Xtramath might be reasonable tools to use for practice and progress monitoring, but only AFTER students have already been fully immersed in strategies, concrete models, and pictorial representations and have had plenty of offline practice developing flexibility with those strategies.

If Reflex or Xtramath are tools your district is already using, please consider how students might access ALL FOUR components of math fact fluency: efficiency, accuracy, flexibility, appropriate strategy use.

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I totally agree!

Our third graders are currently using MathFactLab and are doing very well. I love that it doesn’t stop with basic facts but contiiues on to more difficult math problems using all 4 operations.

We also used the Multiplication by Heart online and I even had a parent donate the physical Multiplication by Heart flashcards. My scholars love the whole Mathigon website! The Polypad is phenomenal!

I am so glad to hear that your students are benefiting from MathFactLab! It looks like a wonderful resource. I need to find some teachers in my area who are willing to give it a try.