LD@school presents Math Fact Fluency

The Importance of Math Fact Fluency: Evidence-Informed Classroom Practices

Written by Lara Shkilnyk, Intermediate Teacher, OCT

In mathematics education, building fluency with foundational skills is more than just helping students work quickly — it’s about freeing up cognitive space so they can tackle more complex thinking. This is especially critical for students with learning disabilities (LDs), including those with co-occurring conditions like ADHD, and other struggling learners who may face challenges with working memory and information processing. One helpful way to understand how students develop and apply mathematical skills is through the instructional hierarchy.

• acquisition – learning how to complete a skill accurately, often with support,
• fluency – performing the skill quickly and accurately with increased ease,
• generalization – applying the skill in different settings or with different problems, and
• adaptation – modifying or extending the skill for new or unfamiliar situations.

Each stage supports the next, with fluency serving as a crucial bridge between learning a skill and using it effectively in new or more complex situations.

Figure: The instructional hierarchy describes how students move from learning a new skill (acquisition), to performing it quickly and accurately (fluency), then using it in new situations (generalization), and finally adapting it flexibly (adaptation). Adapted from Haring et al., 1978.

This article focuses on the fluency stage — a stage that often requires targeted, research-informed strategies, especially for students with LDs, co-occurring conditions like ADHD, and struggling learners. Grounded in current learning science and classroom practice, it explores why fluency matters, how it supports student learning, and which instructional approaches are most effective in developing math fact fluency for all learners.

Building fluency in foundational math skills is particularly important for students with learning disabilities (LDs), who often struggle with information processing and working memory.  According to Likourezos (2019), working memory is the part of our memory system responsible for temporarily holding and actively manipulating new information for tasks such as reasoning and comprehension. For learning to be successful, this information must be processed for meaning in working memory before it can be stored in long-term memory. Once stored, it becomes part of the learner’s existing knowledge base—known as schemas—which are accessed when students encounter familiar material.

With limits on the amount of information that can be held in working memory, it is essential to build fluency with mathematical skills. Developing fluency reduces the cognitive demand on learners with LDs, as fluent skills are stored in long-term memory and can be recalled automatically. When students with LDs are able to store and retrieve information efficiently, it eases the burden on working memory and allows them to focus on learning more complex or new skills.

Fluency practice for students with LDs allows neural pathways (circuitry) in the brain to connect and strengthen for automatic retrieval of information. When practice is purposeful and well-structured, it supports the development of these pathways—much like widening and paving a major highway. The bigger and smoother the route, the more traffic it can support and the easier it is to travel from place to place.

Fluency supports the cognitive demand and stimulus that a student with a learning disability needs to remember and retrieve information. It is developed through purposeful, repeated practice that emphasizes sequence, order, and consistency—key features in neuroplasticity, the brain’s ability to change and strengthen connections through experience (Doidge, 2008). While repeated exposure in short intervals can support initial fluency, research suggests that fluency is most effectively built through purposeful, distributed practice over time. This aligns with Ontario’s mathematics curriculum, which emphasizes the development of automaticity—performing basic operations with ease—as essential for critical thinking, problem solving, and mental math.

Fluency practice also helps to alleviate the “bottleneck effect” that can occur when large amounts of new information are introduced. In these moments, working memory may become overloaded, making it difficult for students to retain or apply what they’ve learned. Structured fluency-building strategies can reduce this load by helping students consolidate foundational skills into long-term memory, freeing up cognitive resources for new learning. As Kirschner, Sweller, and Clark (2006) explain, “learning requires a change in long-term memory”—and fluency practice can support that change for students with LDs.

Fluency, in simple terms, is a combination of accuracy (answering questions correctly) and efficiency (retrieving those answers quickly and with ease). According to Binder (1996), fluency reflects both speed and correctness—but also goes beyond these two traits. True fluency also includes the ability to apply skills flexibly across contexts, adjust strategies when needed, and explain reasoning with confidence.

In the Ontario mathematics curriculum (2020, 2021), fluency is recognized as an important part of mathematical thinking. While it includes accuracy and efficiency in basic fact recall, it also supports students in solving problems and estimating reasonably—without overwhelming working memory. In particular, math fact fluency develops through focused practice that builds automaticity.

Math facts refer to basic arithmetic computations involving the four fundamental operations: addition, subtraction, multiplication, and division. These are often single-digit combinations (such as 6 + 3 or 8 × 2). These are sometimes referred to as basic number combinations.

Knowing math facts fluently allows students to approach more complex tasks with greater ease. For example, recognizing that 7 × 6 = 42 can help a student quickly identify 42 as a multiple of both 6 and 7 when factoring or simplifying fractions. Without automatic recall of these facts, students may become bogged down in computation, limiting their ability to engage in higher-level problem solving. As such, math facts form the building blocks for more advanced learning in areas such as fractions, algebra, and proportional reasoning.

1. Increased Opportunities to Answer Questions

The more opportunities students have to answer questions correctly, the more likely they are to increase their speed and accuracy. This reflects the idea that practice builds fluency—the faster a student can respond accurately, the more opportunities they have to apply and reinforce their learning. The more correct responses a student produces, the more fluent they can become with math facts.

Increased opportunities are particularly important for students with LDs because each correct response supports the encoding of information into long-term memory and strengthens retrieval. A useful comparison comes from sports: the more often an athlete practices a targeted skill correctly, the more likely it is to become embedded in muscle memory. The more accurate the muscle memory, the easier and more natural the skill becomes to perform.

2. Rate of Reinforcement

As students become more fluent (or automatic) with math facts, the rate of reinforcement increases. Educators should give consistent positive feedback when students answer questions correctly. This positive reinforcement builds student confidence. When students feel successful in skill development, it increases their motivation toward the subject area—in this case, math fact fluency (Poncy, Fontelle, & Skinner, 2013).

Students with LDs—and those with co-occurring conditions like ADHD, as well as struggling learners—may experience anxiety in learning environments where tasks require rapid recall or sustained mental effort. Like all learners, students with LDs benefit from clear instruction, meaningful practice, and frequent feedback. They particularly benefit from direct, specific instruction that breaks down skills into manageable steps and reinforces progress. While they may need more time or repetition to consolidate new information, with the right supports, they can build strong, lasting skills. The concept of “rate of reinforcement” highlights the power of frequent, encouraging feedback. When students consistently hear that they are capable and making progress, their belief in themselves grows—and so does their willingness to persist. For students with LDs, this kind of feedback can be affirming.

3. Holding Knowledge and Reducing Cognitive Load

Students need to be able to hold learning and knowledge in memory. When foundational skills are stored in long-term memory, the rate of learning increases. The brain is filled with circuitry; by creating automaticity with foundational skills, this circuitry is strengthened, enabling students to recall information more efficiently. When students no longer need to consciously focus on basic procedures, they can direct their attention to learning more complex concepts and strategies (Schutte, 2015).

Students with LDs often benefit from additional practice and exposure to foundational skills, particularly when working memory is taxed. Fluency supports more efficient learning by reinforcing neural connections that enable automatic recall and reduce the burden on working memory.

4. Skill Generalization

Once students can automatically recall a skill, it becomes easier to learn related or more advanced skills. This reflects the next stage in the instructional hierarchy—generalization—where students begin to apply learned skills in new contexts. Mathematics learning is cumulative and hierarchical, and because of this structure, skill generalization is essential.

Skill generalization supports the transition between procedural and conceptual understanding. These two types of understanding work together to help students make meaning of mathematics. Students with LDs need strong foundational skills to access this stage of learning. When those foundational skills are stored in long-term memory and can be retrieved efficiently, students are better able to transfer their knowledge to multi-step problems and more complex mathematical tasks.

5. Considering Timed Components in Fluency Practice

Some fluency-building strategies include a timed component to promote automaticity to track growth. While concerns have been raised about the connection between timed tests and math anxiety, it’s important to differentiate between high-stakes testing and low-stress, formative practice.

Research on math anxiety, including a recent 2024 study by Maki, Zaslofsky, Codding, and Woods, suggests that task complexity—not timing alone—has a greater impact on anxiety levels. In their study, students showed similar anxiety levels across timed and untimed conditions when tasks were simple, but anxiety increased for complex tasks, particularly under covert timing.

For students with LDs, the goal is always to build fluency in a way that supports confidence, not pressure. Timed elements, when used as part of a supportive, feedback-rich environment, can help some students track progress and experience success.

Targeted fluency practice can play a meaningful role in supporting students’ success in mathematics. Research shows that fact fluency is most effectively developed through purposeful, consistent practice (Duhon & Poncy, 2022). When introduced at the right time, this kind of practice strengthens memory, supports generalization, and helps students apply skills with greater ease.

Because mathematics builds over time, fluency supports students in accessing more complex learning. When fluency instruction is sequenced thoughtfully and grounded in understanding, it can enhance students’ confidence, automaticity, and mathematical readiness.

First, educators need to think about the Instructional Hierarchy: Acquisition, Fluency, Generalization, Adaptation. If this is a new concept that needs to be defined, perhaps refer to the framework

1. Does the student know how to complete the math fact without teacher assistance?
2. Does the student identify the math fact correctly?
3. Can the student consistently recall the fact over spaced practice?
4. Can the student recall the math fact independently?
5. Does the student complete mastery level fact fluency for the specific grade level?

In this context, “mastery” refers to a student’s ability to recall math facts accurately, consistently, and independently—hallmarks of the fluency stage in the instructional hierarchy. If the answer to most of these questions is ‘no,’ the student is likely still in the acquisition phase.

These questions guide educators in determining the student’s current stage and planning appropriate next steps. Students who are still acquiring a skill benefit from explicit, scaffolded instruction. Those who have reached the fluency stage are ready for targeted interventions to build speed, confidence, and automatic recall. Before beginning any intervention, baseline data should be collected to determine which facts have been taught and retained, and which require further practice or consolidation.

Cover, Copy, and Compare is a structured routine that supports purposeful practice by combining repetition with self-monitoring. It helps students focus on accuracy and automaticity while actively engaging with math facts.

Procedure:

1. The teacher starts a 2-minute timer and prompts students to begin working on their math facts. Students follow the worksheet row by row, moving to the next line only after completing the current one.
2. Students read the math fact aloud or silently to themselves.
3. They cover the entire math fact (including the answer) with their fingers or a piece of paper.
4. They write or say the problem and the answer from memory.
5. Students uncover the original fact and check their response for accuracy.
6. If the response is correct, students move on to the next item. If it is incorrect, they repeat the problem until they respond correctly.
7. Students continue working through the row, then proceed to the next one.

Materials required:

• Pencil
• Worksheet with math fact problems (addition, subtraction, multiplication, or division)
• Timer

This strategy provides immediate feedback and reinforces accurate recall, making it an effective option for students who have already developed conceptual understanding and are working toward fluency.

Incremental Rehearsal is a research-based strategy that supports purposeful practice by balancing new learning with review of mastered content. It is particularly effective for students with LDs because it builds confidence, minimizes cognitive overload, and strengthens retention through structured repetition.

Procedures:

1. The teacher uses diagnostic data to determine which basic facts the student has not yet mastered.
2. The teacher prepares a set of 10 flashcards for the student.
3. This set includes 9 facts the student already knows and 1 new fact to be learned.
4. The student reviews all 10 flashcards three times. This can be done with the teacher or a classroom partner.
5. Once the student demonstrates mastery of all 10 cards, the teacher replaces one known fact with a new, unknown fact (Burns, 2005).
6. This process continues until the student has mastered all facts within a targeted domain (e.g., addition, subtraction, multiplication, or division).

Materials required:

• Domain specific Flashcards

By spacing new learning within a high ratio of known material, Incremental Rehearsal helps students stay motivated while systematically moving toward fluency.

Timed activities can be used as a low-stakes tool to help students track progress toward fluency, but should be implemented with sensitivity—particularly for students with LDs who may experience anxiety with time pressure. The goal is to build confidence and automaticity, not to test or compare.

Procedures:

1. The teacher provides a worksheet or digital tool for students to practise math facts.
2. The student is given 1–2 minutes to complete as many facts as possible, with a focus on accuracy first.
3. The student records their accuracy score after each timed activity.
4. Progress is tracked visually, such as through a graph, to celebrate improvement over time.

Materials:

• Worksheets or digital platforms (e.g., FactFreaks, or Reflex)
• Pencil
• Timer (optional)

Teachers should monitor how students respond to timed activities and offer alternative formats or remove timing entirely if it increases stress. The focus should remain on purposeful practice and developing confidence.

Fact families help students build fluency by reinforcing the relationships between numbers and operations. This approach supports both conceptual understanding and procedural skill, making it a strong example of purposeful practice.

Procedures:

1. The teacher provides a fact family flash card (three numbers that are part of the same fact family).
2. The student identifies all equations that can be formed using those numbers (e.g., 3 + 4 = 7, 4 + 3 = 7, 7 – 3 = 4, 7 – 4 = 3).
3. The educator provides corrective feedback as needed.
4. The student practises the corrected response to reinforce accurate recall.
5. The teacher continues presenting new fact family flash cards. Optional timing can be used for engagement (e.g., how many families can you solve in 1–3 minutes), but only if appropriate for the learner.

Materials:

• Flash cards with fact family groupings

This strategy encourages students to recognize inverse operations and number relationships, supporting flexible thinking and fact recall.

For educators looking to extend fluency work in the classroom, the following tools offer evidence-informed strategies aligned with the instructional hierarchy and the development of conceptual and procedural fluency.

M.I.N.D. (Measurement and Intervention for Numeracy Development)
A research-based framework offering structured, tiered fluency interventions (whole class, small group, and individual). Developed by Dr. Brian Poncy and colleagues, M.I.N.D. emphasizes daily, purposeful practice grounded in the Instructional Hierarchy.
M.I.N.D. Website – Facts on Fire

Incremental Rehearsal: Multiplication Facts
A short demonstration of an evidence-Informed flashcard intervention that helps build retention and automaticity by gradually introducing new facts alongside known ones.
Watch the video

Note: These resources are most effective when used alongside classroom instruction that builds conceptual understanding and supports students’ movement from acquisition to fluency, generalization, and adaptation.

Math fact fluency is not about speed for speed’s sake — it’s about building the foundational automaticity that allows all students, especially those with learning disabilities, co-occurring conditions like ADHD, and other struggling learners, to engage more deeply with mathematical thinking. When fluency practice is purposeful, responsive, and introduced at the right stage of learning, it becomes a powerful tool for promoting confidence, independence, and long-term success.

Lara Shkilnyk is dedicated educator with a passion for literacy and mathematics instruction. Her current role is as a Resource Consultant. Lara loves learning about and using research and evidence based instructional practices. She feels strongly about implementing learning science in her daily classroom routines and practices.

This article is being featured on the LDAO website to highlight the high-quality educator resources available through its LD@school initiative. For more evidence-informed strategies, articles, and tools, please visit LD@school.

Looking for similar resources in French? Visit TA@l’école to explore articles and strategies designed for French-language educators.

This article was reviewed and edited by LD@school, a signature initiative of the Learning Disabilities Association of Ontario (LDAO), a registered charity and provincial leader in inclusive and accessible education.

For over 60 years, LDAO has supported children, youth, and adults with learning disabilities (LDs) and related conditions such as Attention-Deficit/Hyperactivity Disorder (ADHD).

Designed for educators, LD@school provides evidence-based and practice-informed resources, along with classroom-ready strategies to help Ontario teachers create equitable, accessible learning environments for students with LDs, ADHD, and other learning differences.

LDAO also offers other signature platforms, including TA@l’école (for French-language educators), LD@home (for families), and LD@work (for adults and employers), supporting the LD community across the lifespan.

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