learning math effectively
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Learning Math Effectively: Why Giving More Homework Isn’t Working

While I was teaching, students and parents often asked me, “What can my child do to improve in math?” Learning math effectively is a skill anyone can develop by implementing a few simple steps.

My first checkpoint was usually homework. Were they attempting or completing it regularly? If they weren’t, I would suggest starting there. But what about the students who seemed to be doing everything right yet still did not achieve the desired grade or competence?

They listened in class. They completed their homework. They checked their answers. They studied before the tests. And yet, they still couldn’t get the grades they were working toward.

There are many factors that contribute to success in mathematics, including prior knowledge, quality of instruction, motivation, confidence, opportunities to practice, and the strategies students use to learn. One factor that doesn’t always receive enough attention is how students practice.

Two students can spend the same amount of time on math homework and learn very different amounts from it. One might spend an hour completing questions, checking the answers, and moving on. Another might spend that same hour attempting difficult questions, identifying mistakes, returning to the lesson when stuck, mixing different types of problems, and thinking about what they still don’t understand.

Both students practiced for an hour. But they weren’t necessarily learning math in the same way. This is the difference between practicing more and practicing effectively.

In this post, I’ll focus on four strategies:

  1. Consistency
  2. Breaks
  3. Focus on process goals versus outcome goals.

Learning and Practice Aren’t Completely Separate

We often talk about learning, practicing, and studying as though they happen in separate stages. First, you learn the concept. Then you practice it. Finally, you study before a test. But learning math doesn’t always happen in such a neat sequence.

What happens when you’re working on a practice problem and suddenly the concept clicks? Were you practicing before you learned it, or did the act of practicing help you learn it? Often, it’s both.

A student may begin with only a partial understanding of a concept. They attempt a problem, realize they don’t know what to do next, look back at the lesson, find a similar example, try a strategy, make a mistake, ask a question, receive feedback – and suddenly the idea begins to make sense.

The learning happened through practice.

Research on desirable difficulties suggests that learning doesn’t always feel easy when it is working well. Some effective learning strategies require students to struggle a little – such as solving a problem before seeing the solution or retrieving an answer from memory. These strategies could lead to stronger long-term learning and transfer. The key is productive struggle: a little struggle isn’t necessarily a sign that your child isn’t learning — it may be part of the learning process.

This doesn’t mean students should be expected to figure everything out themselves. Instruction does matter. The important idea is that students don’t always need to wait until they feel 100% confident before attempting a problem.

Sometimes, attempting the problem is part of how they become ready to understand the explanation.

Strategy #1: Be Consistent

Many students don’t realize the benefits of consistent practice compared with spending the same amount of time the night before a review or test day.

Math is a skill that develops over time, so consistent practice is more valuable than trying to learn everything at once. When students work on math regularly, it’s easier for them to remember concepts over the long term and develop a deeper understanding of them.

It’s also important to note that consistency doesn’t mean sitting down every night and mechanically completing a certain number of questions. It means engaging with mathematics regularly – even when you don’t feel completely ready.

One common thing I heard from students was: “I couldn’t do the homework because I didn’t understand the lesson.” I would often respond: “Show me what you tried.” Sometimes the page was completely blank. What often happened was that the student decided they didn’t understand the material before attempting to work with it. The question looked difficult. They assumed they wouldn’t be able to do it. So they didn’t even start.

This is why it’s important for students to rethink what it

means to “do their homework.”

Homework doesn’t necessarily mean getting every question correct independently. Sometimes homework means:

  • attempting the problem
  • Looking back at the lesson
  • finding a similar example
  • trying to apply that example
  • identifying where you get stuck
  • writing down a question
  • bringing that question to class

A student who says, “I don’t get this,” gives the teacher very little information. A student who says, “I understood the first two steps, but when I got to this part, I wasn’t sure whether I was supposed to distribute the negative,” has diagnosed the problem. Now the teacher’s feedback will make more sense and be more helpful.

Strategy #2: Take Breaks

Students sometimes think effective studying means sitting at a desk for two or three hours without stopping.

But more time at the desk doesn’t automatically mean more learning. Mathematics demands sustained attention, working memory, decision-making, monitoring, and problem-solving. That’s mentally demanding. Research supports taking short rest breaks during demanding math learning tasks. In a 2023 study, students who received a five-minute unstructured rest break before learning a mental mathematics strategy reported better directed attention and solved more problems on a subsequentpost-test than students who did not receive the break.

The popular Pomodoro technique uses 25 minutes of focused work followed by a short break, but there isn’t a specific magic number that works for everyone. Find a period of time during which you can work with genuine focus, then take a short break. For one student, that might be 20 minutes. For another, 30 or 40.

One way to make productive studying easier to repeat and get through is to pair focused work with an anticipated reward. Barbara Oakley, an expert in learning, recommends working in short, focused intervals, followed by a small reward. The idea is that when students repeatedly associate focused work with something enjoyable, the routine may become easier to initiate and maintain over time, forming a new habit.

The reward can be watching TV when done, playing a video game, dancing, playing your favorite song, having something sweet to eat, etc. Expecting the reward after working hard can help you develop the new habit of consistently working on the homework. Don’t be discouraged if it doesn’t work on day one. It can take a few days to create the new routine.

Strategy #3: Focus on Process Goals, Not Just Product Goals

One strategy to address procrastination when doing homework is to set a process goal rather than a product goal. For example, a process goal would be that you’ll work on your homework for 25 minutes. A product goal would be to complete every homework question. Working on one’s homework for 25 minutes seems less overwhelming and more manageable than the idea of completing every math question.

Negative feelings can surface with the second goal, as one might be triggered by anxiety about not understanding the concepts, getting stuck, and not being able to reach that goal. These negative feelings could cause a child to shut down altogether. While the goal of working on questions or re-reading the lesson for a specific time is much more achievable.

More math practice isn’t always the solution. What matters is how students use their practice time. Consistency, taking short breaks, allowing yourself to struggle a little, and setting manageable process goals can make practice more effective. The goal isn’t for students to spend more hours doing math—it’s to help them use the time they already have in ways that support greater understanding and long-term learning.

Learning Resources

If you’re interested in learning more about learning how to learn, here is a link to an online Coursera course that I took with my kids: Learning How to Learn: Powerful mental tools to help you master tough subjects. The course instructors are Dr. Terrence Sejnowski and Dr. Barbara Oakley.

To have access to the free full version of Learning How to Learn, go to Dr. Oakley’s website here: Barbara Oakley, PhD.

Interested in reading how to support your child with math homework and get a free cheat sheet? Read the post HERE.

Other posts which may be of interest to you:

Research Behind This Article

Ginns, P., Muscat, K., & Naylor, R. (2023). Rest breaks aid directed attention and learning. Educational and Developmental Psychologist, 40(2), 141-150.

Oakley, B. A. (2014). A mind for numbers: How to excel at math and science (even if you flunked algebra) (p. 336). New York: Jeremy P. Tarcher/Penguin.

Schultz, W. (1998). Predictive reward signal of dopamine neurons. Journal of neurophysiology, 80(1), 1-27.

Hi, I'm Monica!
I created this blog to help anyone who wants to learn or teach math. My goal is to simplify learning math concepts. I hope my tips and resources will help you along your math journey.

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