Can just changing the order of homework problems transform a C math student into an A math student? Under the right circumstances, the answer seems to be yes.
Everyone knows that to get better at something we have to practice it. But we can practice in a lot of different ways. How we practice has a profound effect on what we learn.
Interleaved practice is a way of re-arranging the activities of a practice session to promote enduring, flexible learning. It’s the opposite of the more traditional “blocked practice”.
In blocked practice, we focus on one concept, one problem type, or one physical movement for a while. Then we move on to the next one. Then the next one. It’s as if we’re collecting skills. I practice solving problems that require the quadratic formula for an hour. Now I know how to do that. I’ll practice algebraic word problems for an hour. Now I know how to do that.
But this isn’t the right way of looking at things.
What is interleaved practice?
To understand interleaved practice, we have to think about how we structure a single practice session. This session could be a set of homework problems that we solve. It could be an hour of basketball practice. It could be twenty minutes trying to identify bird calls.
Let’s go with bird calls. Suppose I’m learning about three different types of bird calls: A, B, and C. And the ultimate goal is for me to be able to identify the bird calls I hear. We can think about structuring a practice session in one of three ways:
Another misconception comes from thinking that blocked practice is never useful or helpful. That’s not right: students need some blocked practice to get familiar with a new idea or procedure. But after they’ve gained that familiarity, it’s interleaved practice that will accelerate their learning.”
There’s several proposed explanations for why interleaved practice beats blocked practice. And there’s some evidence for all of them.
The first explanation is our old friend spaced practice. Interleaving naturally involves spacing out the learning of specific problem types (or conceptual categories or motor skills). An order like A-B-A-A-B-A-B-B just naturally spaces the learning of A and B over a longer period than an order like A-A-A-A-B-B-B-B. The spacing encourages students to (partially) forget things and remember them again, strengthening their memories. There are some cases where the advantage of interleaved practice over blocked practice can be almost entirely attributed to spacing out the learning sessions. But there are many other cases where more seems to be going on.
The second explanation is that interleaved practice helps people distinguish between similar-looking things (the “discriminative-contrast hypothesis” if you want to get fancy). Suppose I’m learning bird species. A big part of what I need to do is to distinguish between birds that look a lot alike, but come from different species. With interleaved practice, students simply make more comparisons between different categories. After seeing one species, I’m likely to see a different species right after, which emphasizes the differences between them. The same is true with math problems or even motor skills.
A final, complementary way of understanding the benefit of interleaved practice is to think about what students are (and are not) actually practicing during different kinds of learning sessions. One goal of mathematical fluency is to be able to solve math problems with knowledge of math equations. This requires two fundamental skills: recognizing which equations are appropriate, and using those equations in the right way.
With blocked practice, students practice using the equations: they plug in the numbers, run through the procedural steps, and come up with an answer. But they rarely practice recognizing which equations are appropriate. They already know that this set of problems is about rectangle perimeters and that set of problems is about rectangle areas, and that other set of problems is about the areas of circles. Interleaved practice provides practice at actually figuring out what the problem is about, rather than just running through the procedural steps.
A baseball analogy is helpful. It’s batting practice. Each batter hits twelve pitches. Do you, as the batting coach, a) give each batter four fastballs, four curve balls, and four change-ups? Or, b) randomize which pitches the batter sees? The more realistic scenario is definitely (b). Pitchers don’t tell batters what they’re going to throw. Batters have to be prepared for variety, so (b) is the way to go, at least if your batters already have a little familiarity with the pitches.
Ultimately, interleaved practice is another kind of “desirable difficulty”: something that makes the practice sessions more challenging, but results in more durable learning in the long-run.
Students make more errors during interleaved practice. But their learning ultimately improves.”
Unlike a lot of other learning science principles, research on interleaved practice began in the sports world. Sports researchers were interested in knowing how to effectively structure practice sessions, and interleaved practice was one of the findings coming out of this research.
Since then, research on interleaved practice has covered three different domains:
- Kinds of physical action — badminton serves; baseball pitches (a curve ball, a change-up, a fastball), surgical skills
- Conceptual categories — bird species (robin, cardinal, thrush, etc.); artist styles (a Rembrandt, Matisse, Monet, etc.)
- Problem types — multiplication problems vs. addition problems; perimeter problems vs. an area problems
The basic experimental set-up is almost always the same: randomize research participants into blocked practice or interleaved practice conditions, monitor their performance, and give them a delayed performance test later. These tests are usually “surprise” tests — research participants don’t know they’re coming. And, for the most part, these tests present problems in an interleaved fashion. But even when researchers present test problems in a blocked fashion, students in the interleaved condition still win.
Interleaved practice typically beats blocked practice by a lot in laboratory research. But, as is typical of most of this kind of research, when you apply it to real-world contexts the effect is somewhat diminished. Still powerful, just not insanely so.
That said, interleaved practice can have some truly striking effects even in classroom scenarios. In one experiment, students in the blocked condition received an average score of 42% on a test given 30 days after the end of the learning sessions. Students in the interleaved condition received an average score of 74%.
In some cases, re-arranging the blocking schedule can have results comparable to interleaved practice. One research study explored how to teach students to add and multiply fractions. The traditional approach has students practice adding fractions before practicing multiplying them. What if you have them learn to multiply fractions first instead? Multiplying fractions is easier than adding them (with adding, you need to find common denominators) and multiplying, at least in one sense, contains an operation fundamental to adding fractions: multiplying (or adding) across numerators. When researchers compare interleaving to the traditional approach, interleaving works much better. But when compared to the flipped ordering (multiply then add), interleaving and the flipped ordering are on par. Not all blocked practice is the same.
Other modifications to blocked practice have limited effects. Emphasizing the differences between two categories doesn’t make blocked practice as effective as interleaved practice. Reviewing the material before the exam doesn’t help blocked practice, either.
One of the hurdles of implementing interleaved practice comes from misperceptions about how much someone has learned. Blocked practice has an intuitive appeal. If you’re a tennis coach, it’s tempting to have your students practice their first serves (generally a hard, topspin serve) for a while, then have students practice their second serves (a weaker serve with a higher probability of landing in the service box). Blocked practice lets you “see” improvement over time. After 40 or 50 practice serves, students are hitting the service box more reliably. Both students and coach walk away from the practice session thinking they’ve made real progress.
But the progress that students have made during blocked sessions like this is an illusion. Almost invariably, researchers see big drops on delayed tests following blocked practice sessions.
Students make more errors during interleaved practice. But their learning ultimately improves.
Interleaved practice is a way of re-arranging the activities of a practice session to promote enduring, flexible learning. It’s the opposite of the more traditional “blocked practice”.”
As with spaced practice, there’s not that much research on how often classrooms actually use interleaved practice. Researchers argue that many textbooks encourage blocked practice: the textbook homework questions cover only the last chapter’s problems. Which leads to this basic scenario:
Interleaved practice can be fairly straightforward to implement. In the striking classroom research cited earlier, teachers literally just changed the order of homework problems to match an interleaved schedule. That’s it. No other adjustments. It’s hard to think of a simpler intervention with such profound effects.
Sometimes, however, instructors get confused when hearing about the concept. If interleaving perimeter and area problems with each other is good, what about interleaving math problems with English reading passages? What about interleaving Spanish translation questions with physics problems? This approach would take a good thing too far. When the tasks are so different, an interleaved schedule imposes significant task-switching costs.
When we sit down to work on some physics problems, we bring to mind all of the physics ideas we think we’ll need. We’re in “physics mode”. If, after a minute of thinking about physics, I have to drop all of that and pull up a completely different set of ideas (about Spanish, say), I’m spending a lot of time switching between different domains. Generally speaking, task-switching impairs learning. So it’s likely this kind of approach would impair learning, too.
These extreme task-switches also miss out on one of the primary benefits of interleaved practice: discriminating between different kinds of things. Students can already recognize the difference between a physics problem and a language translation problem. They don’t need practice at that. What they need practice on is distinguishing a conservation of energy problem from a problem involving Newton’s second law.
Researchers argue that many textbooks encourage blocked practice: the textbook homework questions cover only the last chapter’s problems.”
This is part 6 in a series on what we know about how we learn and how this knowledge should inform how we teach. The series is intended for teachers, students, and developers of education technology who want to be more informed about their practice. Parts 1, 2, 3, 4, and 5.
*This post was originally published at www.benjaminkeep.com.