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.

Here we go…

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 underdeveloping 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.

The secret to developing fact fluency

Lemme put it simply: Students using a strategy-based approach for fluency development by means of instructional tasks emphasizing strategies and conceptual understanding increase fact fluency, with a greater degree of consistency, than students using a drill-based approach emphasizing repetition and memorization.

How do I know? Here are two PDFs that I’m drawing upon:

This PDF is general and includes discussion about both addition AND multiplication facts.

https://drive.google.com/file/d/1A_VRYvyBex_GIV9hgEFw9zM40E74FXe-/view?usp=drive_link

This PDF is specific to multiplication.

https://drive.google.com/file/d/1kXQpWyqg8awl3wHPyafg4LgOBuvNqGv8/view?usp=sharing

At little less formal than the two prior resources, here is a nice article that I use in my training:

https://www.edutopia.org/article/how-decreased-practice-time-plays-into-historic-math-declines/

How do we develop math fact fluency?

In general, we all agree on the WHAT: students need to be fluent with math facts. 

It is the HOW, however, that gets sticky. Students need to be taught how to visualize the numbers and also need to be taught specific strategies for “getting the answer” that will eventually lead to procedural fluency and automaticity. Using drill-and-kill software that focuses merely on memorization without including a huge emphasis on conceptual understanding and strategies is likely to be a waste of everyone’s time.

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.

What might this look like in an after-school setting?

Teachers need to do stages 1, 2, and 3 within their classrooms. Perhaps flashcards can assigned as homework…assuming both students AND parents are clear that the purpose of the flashcards is to build understanding and not necessarily speed.

Invariably, however, you will also need to consider some sort of extended learning opportunity with the math facts. What might this look like in an after-school setting?

• An adult might work with a small group of students to provide direct instruction on specific addition and/or multiplication strategies.

• • Addition strategies (Here is a blog I wrote)

• • • Count on by 1 or 2
    • Make a ten
    • Doubles and near doubles

• • Multiplication strategies  (Blog post 1)   (Blog post 2)

• • • Adding or subtracting a group
    • Halving and doubling
    • Decomposing a factor

• Concrete manipulatives are used to support number sense.

• • Ten frames
  • Number lines
  • Numicon
  • Grid paper

• Students make their own flashcards to practice

• • FRONT: the number fact without the answer
  • BACK: the answer along with a drawing to represent the strategy the student wants to use for that number fact.

• Occasionally students will do timed activities to measure progress towards automaticity

• • This should NOT encourage students to race or “go as fast as they can”.
  • Students track their own progress on a chart.

To my knowledge, there are not many fact fluency software programs that align with all the research for best practice. Existing software largely focus only on memorization and speed without building conceptual understanding. Two notable exceptions are MathFactLab and Fluency By Heart.

I hope this gets you started. Let me know if you need more information!

.

.

.