Guiding Students to Learn Math Facts—Without Timed Tests

When I was younger, math facts were my jam. I had an almost photographic memory for numbers. I could memorize phone numbers, birthdays, and—you guessed it—math facts. I loved playing classwide games that tested our speed and getting to be in the final rounds to prove I was the fastest of my peers. It made me love math.

While speed is not as important as I once thought, in teaching fifth grade for many years, I’ve seen how much students in the upper grades struggle when they don’t have a solid foundation in math facts. I’ve also worked as a Section 504 coordinator and learned how executive functioning, especially working memory, can be impacted by dyslexia, ADHD, and other learning differences, which can cause memory deficits related to learning math facts. And as an instructional coach, I worked alongside teachers who were wrestling with what math fact mastery should look like; they found a conflict between the strategies that had worked for them as learners and what current research recommends.

Now, as a math coordinator tasked with finding a research-based, systematic approach for my district, I have read research, observed hundreds of teachers and students, and looked at countless pieces of student work from kindergarten to fifth grade to gain an even wider perspective.

All of these experiences have challenged and refined my thinking, sparking a deeper curiosity about what it truly means to be fluent in math facts. The most significant thing I’ve learned is that we all want students to be fluent with their math facts, but the journey to get there and the vocabulary we are using are not always aligned.

The Difference Between Memorizing and Being Fluent

Rote memorization is the recall of facts with repetition, without necessarily understanding. Fluency is the combination of accuracy, efficiency, and flexibility, and if a student is fluent, they understand the number sense behind math facts and can choose a strategy based on what numbers are presented.

Rote memorization aligns with low levels of learning, while fluency more closely aligns with the real-world skill of problem-solving.

How Students Become Fluent

After fully learning how to count, students progress to using strategies or the logic behind how they solve the fact. They then understand the fact through exposure and practice.

When students are building a foundation for math facts in addition and subtraction, they first count by ones forward and backward. Then they start to subitize and notice patterns that grow more and more complex: +/- 0, 1, and 2; combos for 10; making 10; counting on and back; doubles; near doubles; and others.

When students are learning multiplication and division, they’re building on a foundation from addition and subtraction, becoming fluent in their 2s, 5s, and 10s from skip counting in the primary grades, which transforms into foundational multiplication understanding. This leads students to be able to master more difficult facts through strategies like adding or subtracting a group, doubling, and using the facts they know to get to the ones they don’t yet know.

Once students have practiced the strategies, they gradually become a habitual way of thinking, ensuring fluency. Assessing students to figure out which facts they know and which ones they don’t can be helpful to determine where to focus students’ practice and your explicit instruction. One helpful assessment is math running records, interviews you can do with each student to gain an understanding of their path to math fact fluency.

Teaching Students Effective Strategies

Practicing math facts with flash cards or on a math fact platform doesn’t promote true fluency unless students are taught how to use strategies first. And there are more enjoyable ways to get students to practice exponentially more.

Research highlights the fact that timed tests can negatively impact students. There are ways to teach and assess math facts that are much more productive. But avoiding timed tests doesn’t mean that learning math facts isn’t essential.

Moving from counting to using strategies is where I witness both students and teachers getting stuck and then wanting to skip that phase entirely. Instead, we have to understand how students progress into new habits and how to support them in this uncomfortable phase of learning.

For example, let’s say a first-grade student is solving this problem: “Javion was at the arcade and won eight tickets on the first game he played. He won seven tickets on the second game he played. How many tickets did he win?”

Let’s say the student draws dots on double ten frames to represent the tickets Javion won. Once they finish drawing the tickets, they start counting from the top row of the ten frames to see how many tickets. Instead, we can tell the student to pause and prompt them to think about the strategies they know. Here are some different ways to prompt students.

• “Pause. What strategy do you know that would help you to solve this problem quickly?”
• Show the student an anchor chart with the strategies they know that would work. “Which strategy from here could you use instead of counting from the beginning so you can be efficient and accurate?” (You could cover some strategies to give fewer options or create an anchor chart that only has the grade-appropriate options.)
• “Pause. Would this be a time you could make ten or use your doubles facts to become more efficient and accurate?”

For multiplication, a typical problem might look like this: “A bakery made seven packages of muffins for breakfast. There were eight muffins in each package. How many muffins did they bake?”

The student uses their fingers to start to skip-count the groups of eight. Some prompts that can work here are similar to the ones suggested for addition above.

• “Pause. What fact do you know that would help you get to 7 x 8?” If the student doesn’t know, you could prompt them further: “What is five groups of eight? Then what is two more groups?”
• You could show them an anchor chart with the strategies they know that work for sevens or eights.  Let them pick the strategy they want to use. 
• “Pause. Would this be a time you could use the double-double strategy for eights or the break-apart strategy for sevens to become more efficient and accurate?”

Teach students to coach each other in this same way by modeling it and praising when you hear it happen between peers. The first step in helping students master their math facts is for teachers to fully understand the strategies themselves and create a clear plan for explicit instruction, engaging and meaningful practice, and intentional assessment.

When we design fact fluency with deep learning in mind, we ensure that mastery is purposeful and not left to chance. Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention, by Jennifer Bay-Williams and Gina Kling, is a must-read for any teacher who wants to understand the progression of how students learn math facts and what each strategy entails. The companion website has free, easy-to-implement games and assessments to use with students.