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Inspired Ideas

The Art of Math Practice

Building Proficiency at Home

By Michael Shirey, 6–12 Mathematics Product Manager at McGraw Hill

How do you get better at basketball? How do you get better at playing the guitar? How do you get better at juggling? How do you get better at a video game? How do you get better at math?


One of the most common questions we adults ask our children when they perform poorly on a math exam is, “Well, did you study?” “YES!!!! I STUDIED FOR HOURS!” We’ve all heard this…and likely most of us have said this in our youth.

It is not a mystery that it requires continual and repetitive practice to improve a skillset. You cannot reasonably think that it is sufficient to only practice basketball free throws the night before a basketball game without practicing any other day.

In the same vein, you cannot reasonably think that it is sufficient to only practice factoring equations the night before a test or quiz. If you have to study for hours the night before a test, then you’re already in trouble.

Conceptually, it seems fairly straight forward. Students understand this. They don’t think they can become proficient at any particular mathematical task without practice. Explaining to them that they need to practice more is not telling them something that they do not already know.

Without an innate desire to learn math, there is little motivation to practice it. Why would they want to?

Why would they want to sit down and practice math problems when they could be playing video games with their friends or skateboarding outside? Or even taking a nap? They know what they should be doing. Just as I know that I shouldn’t eat that extra bowl of ice cream, and I should be going out for a jog.

What Does It Mean to Practice?

As the Covid-19 Pandemic continues, and we are looking at uncertainty for what will happen in schools and in our homes when school re-starts in the fall, many in the education and learning science community have been thinking more about practice.

Practice is a hotly debated topic in the education community, so there are a lot of different opinions and complicated terms. This is an attempt to simplify what we’re trying to achieve. I will also reference basketball in my examples. You can replace basketball with any other activity that you like. I like to use basketball because I’m not very good at it, and I don’t especially enjoy it. But I also know what I need to do if I want to improve at it.

There are a couple of different main types and purposes of practice:

Learning Practice

Learning Practice is the early stage of practice. When you are first learning how to shoot a basketball into a hoop, it helps to have someone instruct you on what you’re trying to accomplish.

You must first learn the fundamentals of what you’re doing. You stand at a certain spot, and you throw the ball through the air into the hoop.

Simple, right?

Not quite.

It is helpful to know how to place your feet, how to hold the ball, how to steady the ball, how to line up the ball, how to lift the ball, where to release the ball, and how to follow through in order to improve your chances of getting the ball into the hoop. You often need a coach there to help you adjust your technique.

This is often referred to as “Guided Practice.” In the classroom, this is when the student has the opportunity to try, fail, ask the teacher questions, receive guidance, and learn the fundamentals of what to do and what to not do while working any given math problem.

In the new remote learning scenario, this is going to be different for every class. The fundamentals can be the same. As long as the student has an avenue for obtaining guidance, then the student can learn the fundamentals. Perhaps the most important skill in this scenario is for them to hone their skills at their own error analysis. That will require some focus and grit. Try not to yell at them.

Proficiency Practice

Proficiency Practice is about repetition. How often have you heard your child say, “I thought I knew how to do it,” for them to just find out that they drew a blank when it came time for the exam? This can be caused by a variety of factors, including the pressure of the exam and a lack of continued practice spaced out over multiple days.

Once you have learned the fundamentals of how to shoot a free-throw in basketball, you are not done practicing.

You might know where to stand, how to hold the ball, and where to release it, but that’s not going to make you consistently successful, especially during the pressure of a high-stakes game.

You have to be able to go through those motions fluidly, consistently, and without thinking about every single motion. That comes with repetition.

While I certainly will never obtain over 90 percent accuracy with free-throws like the top players in the NBA and WNBA, I am certain that if I practice even a handful of times every day, then I will improve that particular skillset. It doesn’t have to be hours every day, either. But it does need to be enough times to continually hone that skill.

What Can You, as a Parent, Do To Help?

As I stated earlier, students already know that they need to practice. What they may not understand, however, is how to approach practice.

Often students think that practice means sitting down for hours on end the night before an exam and cramming as much information into their brains as possible.

This can occur due to a misconception about how to make practice effective, or due to procrastination. I posit that when approaching practice in brief daily sprints, less time is spent on the practice activity than trying to cram for several hours on a single day. It’s certainly more effective, and it’s absolutely less stressful.

But here as some tips for parents to support their learners’ math practice:

1) Draw From What You Know, But Defer to the Experts When Needed

When it comes to guided practice, or the Learning Practice mentioned earlier, there is only so much that you can do. Middle School content is typically easier and more familiar to us as parents so we are able to help a bit at those levels. Once the content moves into more complicated Algebra or Geometry, our memories fade. You may have to have faith in the teacher and encourage your child to seek assistance directly from them when they require guidance. Obviously, there are apps and web sites that can help with providing students with the guidance they need, as well. The trick is to stop using that information during the Proficiency Practice stage.

2) Practice Different Skills in Different Scenarios

For Proficiency Practice, the student may start by practicing his or her free throws. In each lesson, there is a new concept (or extension of a previous concept) that is introduced. That concept is typically related to previous concepts. All of those concepts and skills build on each other. Think of each of those skills as a different shot somewhere on the basketball court. The goal and the motions are related, but each shot, or skill, is a bit different.

But when preparing for a basketball game, it is not sufficient to just practice the free throws. You have to practice shots from different locations. You also have to practice different scenarios.

You have to work on running…walking…dribbling…other people trying to steal your ball…as many scenarios as possible in order to improve your chances of sinking the ball into the hoop. And you have to practice almost daily.

For math practice, you have to do the same.

3) Encourage Ownership

Your child’s math lessons have been broken into sections. Each of these sections provides you with the different types of problems that your child should be able to complete. Once your child goes beyond the initial “Homework” assignment, the direct approach is for them to practice a few of these problems each day.

The key to developing proficiency is for your child to practice the problems until they can successfully solve them without having to obtain any guidance. But even once they have achieved that, your child is not done. The next step is for your child to wait a day and practice them, again. Just a few problems. Then, when your child is sure they understand it and they are bored with the problems, they should work a couple more from each section. Each day up until the exam, your child should keep taking every question type from every current lesson and practice just a couple.

Practicing in a repetitive fashion on a daily basis will have a couple of beneficial effects. One is honing skills and understanding. The other is less thought. This is when your child becomes proficient.

When I was a math tutor and math teacher, I would ask my students to try this method for just one test. That’s a two-week commitment. Just try it and see how it works out for you. If you don’t want to keep doing it, then don’t. But for two weeks, practice the way I’m telling you as an experiment. The result? I had some students who became stars…and I had some who decided they didn’t want to bother. In the end, it gave them the opportunity to take ownership of their own learning. If you want to help your child, see if you can convince them to take on short sprints of repetitive daily practice for a couple of weeks.

Give them some control over their own learning. Sometimes that can make all the difference.


Spaced Repetition Promotes Efficient and Effective Learning: Policy Implications for Instruction — Sean H.K. Kang

Michael Shirey has been with McGraw Hill since 1996 when he joined the Software Support department. Prior to McGraw Hill, he worked with under-privileged, under-performing, and at-risk students in both classroom and one-on-one tutoring settings. His focus currently centers around secondary Mathematics, but his passion has always been around helping students understand the concepts that they deem impossible to comprehend. This passion drives his never-ending quest to learn more about the science behind engagement and learning and how that knowledge can be used to help make McGraw Hill more successful. With his children all now off on their own, when Mike’s not at work he likes to work on his photography skills and try new photo-challenges, whether it is a tiny insects and spiders or photos of the moon.



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