Math is polarizing. I’ve never met the guy who says, “I don’t know how I feel about math.” No, everyone knows how they feel about math, and no one rides the fence. People either love it or hate it. If you think otherwise, you clearly haven’t gotten to calculus yet. Calculus especially makes sure you’ll either love or hate it. People who love it become accountants, engineers, or rocket scientists. The rest of us make less money.
But regardless of how you feel about math, everyone needs effective study strategies for doing math homework.
Scientists – aka, people who like math – have actually studied the way math instruction works. They’ve labeled two general strategies people use. Both involve solving loads of practice math problems, but, by the time you finish this blog, I think you’ll know which one you should use.
The Typical Math Strategy: Blocking
Most students have learned math through what we’ll call “blocking.” Blocking involves reading or listening to an explanation about solving one problem type. After this, students answer practice problems of this type. When the student can answer those problems correctly, they move on to the next type of instruction. Thus learning happens in blocks of problem types. It kind of looks like this:
a) Learn how to solve math problem type #1.
b) Solve practice problems for math problem type #1.
c) Learn how to solve math problem type #2.
d) Solve practice problems for math problem type #2.
Most students across America use this strategy. Frankly, it makes sense. When you are studying this way, you typically leave feeling like you’ve learned the problems. And, not surprisingly, you have. Blocking works, and it is the most natural way to approach math problems.
The Less Typical Math Strategy: Interleaving.
We recognize “interleave” may be an unfamiliar word for many of our readers. Don’t worry, though, as it’s a pretty simple concept. Interleaving a study session means a student studies all the material in the section before then doing the practice problems. Explanations are mixed together and then practice problems are mixed together. It might look like this:
a) Learn how to solve math problem type #1 and #2.
b) Solve intermingled practice problems for both math problem types #1 and #2.
As you might have guessed, this is the less natural feeling approach to math problems. In fact, when students get to the end of a particular learning experience using the interleaving strategy, they may actually feel less comfortable with their understanding of the problems. Answering the intermingled questions will be more difficult than answering the problems using the blocking strategy.
A Practical Example
An example should make this clear. Consider a student who must read and complete the math problems from one chapter in her Algebra book by tomorrow morning. This chapter, however, includes four different types of problems.
If she were to block the chapter, she would read the tutorial on equation one and then do all the problems pertaining to that equation. Then she would move on to equation two and answer all of the problems related to that equation. I think you can see where this pattern is heading.
Interleaving, however, means that the student will read all four tutorials first, followed by answering all of the practice problems for all of the equations in a randomized order.
So here’s the million dollar question: which strategy is better?
And the winner is…
Hands down the interleaving strategy. And it’s not even close.
A 2010 paper by Rohrer, Taylor and Sholar demonstrates the superiority of the interleaving strategy. Their paper shows that the blocking strategy actually yields better immediate results. So, if you have a test in an hour, block the material. But if you are taking a test a week or more later, consider the impact of the interleaving math problem strategy.
Students who used the interleaving approach more than doubled the test scores of those who took the initial blocking approach. We’ll call this a 40% benefit, because more experiments need to be done on this. Still, the possibility of more than doubling a test score based solely on the order in which you answered practice problems is a radical result. A another series of experiments in this area also show significant benefits, so much so that we are comfortable calling this an easy 40% increase, with possibilities of upwards of 200%.
This tells us two things. First, interleaving may be more difficult initially. You may find it harder to do, and there may be days when it doesn’t make much sense. Second, a little pain in this area is absolutely worth a 40% testing benefit in just a few short days.
Backing off the Blocking
Interestingly, most of us probably learned to do work in blocks. A significant amount of research shows that by blocking out time periods to work on one particular task – what you might call “mono-tasking” – you can actually be far more productive with your time. Your focus increases, distractions decrease, and you can make headway with a unique efficacy not found in most media-driven, hyper-connected, 9- to-nothing, multitasking worlds.
Yet the retention benefits of this approach are well worth implementing an interleaving approach to your assignments. Two simple strategies will help build this into your studies.
1. Strategically Interleave All Practice Problems
Whether or not your textbooks are set up this way, do all your practice problems at the end of a chapter (math and science especially). Additionally, mix up the order in which you do the problems. Typically, problem types are organized to help students do them in with a blocking strategy. By mixing up the order in which you do problems, you’ll force yourself to get the radical benefits of interleaving.
2. Strategically Interleave Subjects During a Study Session
Even beyond just helping students solve math problems, this strategy has far reaching implications for study sessions. One of the best things you may be able to do is change subject studied every 25 minutes or so. If you alternate between history and science, you’ll be forcing your mind to improve it’s retention of both subjects in a way that it doesn’t should you just go straight through one subject and into the other.
If you are interested in other research-backed study strategies, check out StudyRight’s student success e-book, Cracking the Student Success Code. You’ll find multiple scientifically proven strategies and simple ways to implement them.