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Retrieval, Spacing, and Interleaving: How to “Learn”

We give students homework and practice and tasks, but do we really know how “learning” takes place, and the best methods to engage in that process?

By Michael Shirey, Mathematics Product Manager at McGraw Hill

For the past six plus years, I have been observing classrooms from coast to coast. I’ve executed Field Tests, hosted Teacher Advisory Boards, and interviewed more teachers than I can count. I have witnessed a change in teacher landscape (less experience and training in some cases), to traditional teaching practices. Homework is one example. Many schools are giving up on assigning homework altogether because either their students will not do it, or the schools have decided it is not as useful as previously thought. In some cases, the “homework” is a digital task and not all students have access to the tools they need when they’re at home. If there is one thing that is consistent, it’s that homework is inconsistent.

What if we had a better understanding of how humans learn best? We know that our students need to “practice” in order to get better, but do we have a good understanding of how often a concept, or a list, or a problem type needs to be practiced before the student can truly work independently?

The Good News

What is different now from 25 years ago — when I first entered a high school mathematics classroom as a teacher — is that we have digital platforms that can help the student remember to practice. Because it’s digital, it’s easy to track. If we can track it, then we can provide timely course correction, and we can track efficacy.

Before embarking on some research, I pondered back to sitting on the living room stairs as a youngster and getting quizzed on the “times tables” with my math professor father. His method was very precise, and you learned quickly what the rules were…like them or not.

  1. Show the problem
  2. Wait one second for the answer
  3. If incorrect or no answer, show the answer
  4. Put card randomly somewhere in the deck
  5. Wash, Rinse, Repeat for a while
  6. Stop and do the same thing the next day

Each step is important, although they don’t have to be executed in precisely this manner. But there was a method to his madness in the learning process that I found during my research into the basics of Learning Science.

Retrieval Learning: Answering the Question without Looking Back

This is one of the most important steps in the learning process. The act of retrieving the information that you are learning is known as “Retrieval Learning.” It is any method that requires you to think of the information that you are trying to learn and bring it to the forefront of your mind. There are many ways to retrieve the information. Homework, a quiz, a test, flashcards, mentally reviewing a list.

We all do this on a regular basis. Think about a presentation that you’re going to be giving in front of a room full of people. For as many times as you might go through your presentation, you spent many more times mentally reviewing it and silently practicing and re-writing while driving to work. You are retrieving the information in order to know it better.

There are several common errors that students tend to make when practicing with flashcards. Teachers can help their students improve the deepness of their learning by helping them to avoid these mistakes:

  1. Mistake One: Often, students will look at the front and THEN the back. The “answer” is familiar to them…so they think they “knew” the answer, when in fact they were just prompted with it.
  2. Mistake Two: Frequently, students believe that the act of creating their flashcards is what the “learning” process is. Once they make the flashcards, they do not look at them anymore. Their confidence in knowing the information is a brain-trick. Our Learning Scientists have discovered the students who practice “Retrieval” on a regular basis performed far better on testing of the information than those who just created the flashcards.
  3. Mistake Three: Much of the time, students feel that they have learned the information once they’ve made it through a set of cards accurately. Then they stop.

Making your students aware of these misconceptions can help them avoid them. Of course, students often like to have their own proof of what is effective and what is not. Some teachers have held experiments with their students where they have applied different methods across various student groups in an effort to demonstrate the methods that work best.

Spaced Learning

Our brains can only handle so much information at a time. If you’re trying to “learn” a list of ten things, you will likely remember about four or five on your first try, then forget most. Then try again the next day, and only remember one. Then try again later and remember three. Then try again the next day and remember six. And so on. Eventually you remember them all…for a while.

Practicing something ten times in a row will not help us remember the list of ten items as well as practicing ten times with time spaced in between. . Hundreds of experiments have been conducted on Spaced Practice versus Massed (or Blocked) Practice, and the results are impressively in favor of the Spaced Learning process.

Blocked Learning versus Interleaving

Blocked Learning is when you practice items of the same type all at the same time, then move on to the next problem type. This is traditionally how math practice begins.

Interleaving is when you mix up the “types” of things you’re trying to learn. This forces the brain to focus with more precision and to be more thoughtful. It avoids the illusion of learning something because you’ve learned a pattern instead of an actual answer.

When my father wouldn’t shuffle the flashcards, it would allow me to remember that the next answer was “35” just because the previous answer was “30.” Our digital assessment system can be used to provide this experience. If a student works the same set of ten problems multiple times, the order of those problems can be randomized. While not as preferable over problems with entirely new values, it does remove the “memorization of pattern” for the student, allowing them to practice the problems in a new order.

This forces the brain to focus with more precision and to be more thoughtful. It avoids the illusion of learning something because you’ve learned a pattern instead of an actual answer.


When I began my research into the science of learning, I had many moments where I thought, “Well yeah, of course.” Many of the methodologies are ones that as educators we already know and implement within our classrooms. In my case, I just didn’t realize I was doing it. But I was also implementing them inconsistently.

The good news is that educators are beginning to embrace the ideas behind the effectiveness of learning through Spaced Practice and Retrieval Learning. More educators are deliberately implementing these concepts into their classrooms, and there is a lot of information available online to help. In many cases we are finding that teachers have innately been using these methods without even realizing it. The concepts are all around us. We just have to look for them.

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.

Spaced Practice is one of the fundamental pedagogical aspects of our award-winning curriculum, Everyday Mathematics. Learn more about how it works below.



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