Can a child really learn multiplication tables without chanting them a hundred times? Ask ten teachers and you will get ten different answers, often delivered with real feeling. Few topics in education spark as much argument as drill in mathematics, the practice of repeating exercises until facts and procedures become automatic. Some see it as the backbone of arithmetic. Others see it as the thing that makes children hate math. (Almond Nails: Shapes, Styles, and How to Care for Them)

The truth, as usual, sits somewhere in the messy middle. Drill is neither a miracle nor a villain. It is a tool, and like any tool, its value depends on how it is used, when it is used, and what it is used for.

What Drill in Mathematics Actually Means

Drill, sometimes called drill-and-practice, refers to repeated exercises designed to build fast, accurate recall of math facts and procedures. Think multiplication tables, addition facts, long division steps, or factoring quadratics. The goal is automaticity: the ability to produce an answer without conscious effort.

This separates drill from two related but different activities. Problem-solving asks students to figure out which math to apply to a new situation. Conceptual instruction builds understanding of why a procedure works. Drill sits alongside both, aiming at fluency rather than insight.

A useful distinction is between retrieval practice and passive repetition. Copying a times table ten times is repetition. Being asked to recall 7 × 8 from memory is retrieval. The research below suggests this difference matters enormously.

A Short History of the Drill Debate

Drill has been contested for over a century. Early in the 1900s, Edward L. Thorndike argued that repetition strengthens connections between a stimulus and a response, a view that supported drill-heavy arithmetic teaching. Thorndike himself later qualified this “law of exercise,” acknowledging that repetition without feedback and reward does not do much on its own.

By the 1920s and 1930s, progressive educators pushed back hard. William Heard Kilpatrick and others criticized isolated drill as meaningless, favoring projects and meaningful learning. The phrase drill and kill entered the vocabulary and has never really left.

The argument has resurfaced in every reform cycle since. In the United States, the 1989 NCTM standards emphasized conceptual understanding and de-emphasized rote computation, igniting the so-called math wars. The 2000 NCTM standards and the 2008 National Mathematics Advisory Panel report both called for balance: conceptual understanding and fluency, side by side. The pendulum keeps swinging because both sides are partly right.

What Cognitive Science Says About Practice

Modern research gives the drill debate a firmer footing. Three findings stand out, and each one complicates the simple “more repetition is better” story.

Retrieval beats rereading

Roediger and Karpicke, in a 2006 study in Psychological Science, showed that testing oneself produced better long-term retention than repeatedly restudying material. This is the testing effect. For math, it means that recalling facts from memory does more than staring at a worked example. A worksheet where students retrieve answers is not the same as a worksheet where they copy them. (Star Nails: Designs, Ideas, and How to Create Them)

One caveat: this evidence concerns retrieval practice generally, not timed arithmetic drills specifically. It supports recall, not necessarily speed.

Spacing beats cramming

A 2006 meta-analysis by Cepeda and colleagues in Psychological Bulletin found that spaced practice outperforms massed practice for retention. Translated to the classroom: five minutes of fact practice spread across four days beats twenty minutes crammed into one session. Drill works best when it is distributed, not dumped.

Mixing beats blocking

Rohrer and Taylor, in a 2007 study in Instructional Science, found that interleaving math problems of different types improved later test performance compared with practicing one type in a block. Students who drill twenty problems of the same kind often feel confident but struggle later when problems are jumbled. Mixing problem types during practice, even though it feels harder, produces better transfer.

Automaticity frees up working memory

Cognitive load theory, developed by John Sweller in 1988, argues that working memory is limited. When basic facts are fluent, mental effort can go toward understanding the problem rather than grinding through arithmetic. This is the strongest argument for basic-facts practice: fluency is not the finish line, but it clears the road to it.

The classroom evidence for a direct causal chain is mixed, but the logic holds up in practice. A student who pauses to count on fingers while solving an algebra problem is using bandwidth that could go toward the actual reasoning.

The Case for Drill

Drill has real defenders, and their arguments are not nostalgic hand-waving.

• Fluency supports higher math. Students who know their multiplication facts cold can focus on fractions, ratios, and algebra instead of basic arithmetic.

• Confidence grows with competence. A child who can answer quickly feels capable, and that feeling fuels persistence.

• Some procedures require automatic recall. Factoring, simplifying radicals, and working with common denominators all run smoother when basics are instant.

• Retrieval practice is well-supported. When drill is structured as recall rather than copying, the evidence is solid.

Practically speaking, the most effective drill is short, frequent, and focused on recall. Ten focused minutes a day beats a single long session. Feedback matters too: students need to know immediately whether an answer is right, or they may practice errors into permanence.

The Case Against Drill

Critics are not being soft. They raise legitimate concerns.

• Drill can be meaningless. If students do not understand what multiplication represents, fast recall can mask a shaky foundation. They can compute without comprehending.

• Timed tests can trigger anxiety. Some research links timed basic-facts testing to math anxiety, though findings are contested and the evidence is not settled. Treat claims in either direction with caution.

• Massed drill wastes time. Blocked, crammed practice is less efficient than spaced, mixed practice, according to the research above.

• Motivation can suffer. Endless worksheets can convince students that math is a chore rather than a way of thinking.

The most common mistake teachers and parents make is treating drill as a substitute for understanding rather than a partner to it. A second common mistake is drilling one skill in isolation for too long, which builds short-term performance but weak long-term retention.

Drill vs. Discovery: A Practical Comparison

The table below sums up how the two approaches differ and where each shines.

Feature	Drill-and-practice	Discovery and problem-solving
Main goal	Automatic recall and fluency	Conceptual understanding and transfer
Typical activity	Retrieval exercises, flashcards, mixed problem sets	Investigations, open problems, discussion
Best for	Basic facts, procedures, speed	New concepts, reasoning, application
Main risk	Boredom, anxiety, shallow understanding	Slow fluency, gaps in basics
Research support	Retrieval, spacing, interleaving	Conceptual change, transfer
Ideal use	Short, spaced, mixed, with feedback	Extended, guided, with reflection

The smartest classrooms do not pick a side. They drill the basics briefly and regularly, then spend the bulk of time on reasoning and application. The two reinforce each other.

How to Make Drill Work in Practice

If drill is going to happen, it should be done well. These steps reflect what the research and classroom experience suggest.

• Keep sessions short. Five to ten minutes of focused retrieval beats a long worksheet session.

• Space it out. Distribute practice across days and weeks rather than cramming.

• Mix problem types. Interleave related skills so students must choose the right approach rather than repeat a pattern.

• Use retrieval, not copying. Ask students to recall answers from memory rather than reread notes.

• Give immediate feedback. Correct errors quickly so they do not become habits.

• Pair drill with meaning. Briefly explain why a procedure works before or after practicing it.

• Watch for anxiety. Keep timed elements low-stakes and optional where possible.

A parent helping at home can apply the same ideas. Five minutes of multiplication recall at breakfast, a few mixed problems after school, and a short review on the weekend will do more than an hour-long Sunday session. The same principle of short, regular, focused practice applies to many skill-building routines, whether it is math facts or a weekly hair mask routine that works through consistency rather than marathon sessions.

What the International Comparisons Really Show

Drill-heavy approaches in some East Asian systems are often cited as proof that repetition works. Researchers caution against the easy conclusion. Performance differences in international studies reflect curriculum, teacher training, culture, parental expectations, and more. Drill alone is not the cause. It is one ingredient in a complex recipe, and copying it without the rest of the system rarely reproduces the results.

The honest takeaway is that drill is neither the secret weapon nor the villain. It is a technique with a clear purpose and clear limits.

Where Drill Fits in a Balanced Math Education

The most defensible position is a balanced one. Drill earns its place when it targets basic facts and procedures, happens in short spaced bursts, mixes problem types, includes feedback, and sits alongside genuine conceptual work. It loses its place when it becomes the whole curriculum, when it is timed in ways that frighten students, or when it substitutes for understanding.

Educators who get this right tend to describe drill as a foundation, not a finish line. Fluency in arithmetic is a means to an end: the ability to reason, model, and solve problems with confidence. The goal is not a child who can recite tables like a machine, but one who can think mathematically without being slowed down by the basics.

Conclusion

Drill in mathematics is a tool with a long, argumentative history and a surprisingly solid research base, provided it is used thoughtfully. Retrieval practice, spacing, and interleaving all support well-designed practice. Massed, meaningless, anxiety-inducing worksheets do not. The debate between drill and understanding is a false choice; the real question is how to combine them. Short, spaced, mixed practice with immediate feedback, paired with genuine conceptual instruction, gives students both fluency and understanding. That balance is what actually works, and it is what the evidence, the history, and good classroom practice all point toward.

Frequently Asked Questions

What is drill in mathematics?

Drill in mathematics means repeated exercises designed to build fast, accurate recall of facts and procedures, such as multiplication tables or algebraic steps. Its goal is automaticity, so students can solve problems without being slowed down by basic arithmetic.

Is drill bad for students?

Not inherently. Drill becomes harmful when it replaces conceptual understanding, is massed into long sessions, or is timed in ways that cause anxiety. Short, spaced, mixed practice with feedback is well supported by research and helps students build fluency.

Does drill actually improve math performance?

It improves fluency and recall, which supports higher-level problem-solving. The strongest evidence comes from retrieval practice, spacing, and interleaving studies. The evidence on timed drill specifically is mixed and contested, so it should be used carefully.

How long should drill sessions be?

Short sessions work best. Five to ten minutes of focused retrieval practice, repeated across several days, is more effective than a single long session. Spacing practice over time improves long-term retention compared with cramming.

Should drill be timed?

Timing is optional and should stay low-stakes. Some students benefit from gentle time pressure for fluency, while others experience anxiety that undermines learning. Teachers and parents should watch for signs of stress and adjust accordingly.

How can parents support math drill at home?

Keep it brief and regular. Use flashcards or quick recall questions for a few minutes a day, mix different problem types, and give immediate feedback. Pair practice with simple explanations of why the math works so fluency and understanding grow together.