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I came across the idea of mixed up practice in Benedict Carey's book, How We Learn, in a chapter on the benefits of interleaving, particularly for learning Maths.

For instance, in "blocked practice", students might work on Maths problems in order, e.g. Problem A, then Problem B etc. following a pattern like AABBCCDD. In mixed up or "interleaved practice", the order of problems is varied, forming the pattern ADCBCDBA.

Carey also cites several studies showing how interleaved practice outperforms blocked practice in skills outside Maths, from badminton to piano playing. These insights are fascinating, as he says "the science suggests that interleaving is, essentially, about preparing the brain for the unexpected."

However, many psychological experiments seem artificial and contrived so I was happy to find a 2015 article in Scientific American that went a bit further:

"Over the past four decades, a small but growing body of research has found that interleaving often outperforms blocking for a variety of subjects, including sports and category learning. Yet there have been almost no studies of the technique in uncontrived, real world settings—until recently."

They mention one study in particular:

"The three-month study involved teaching 7th graders slope and graph problems. Weekly lessons, given by teachers, were largely unchanged from standard practice. Weekly homework worksheets, however, featured an interleaved or blocked design. When interleaved, both old and new problems of different types were mixed together. Of the nine participating classes, five used interleaving for slope problems and blocking for graph problems; the reverse occurred in the remaining four. Five days after the last lesson, each class held a review session for all students. A surprise final test occurred one day or one month later. The result? When the test was one day later, scores were 25 percent better for problems trained with interleaving; at one month later, the interleaving advantage grew to 76 percent."

That's a big difference.

I have two questions:

  1. How widely is interleaving used in your classrooms whether primary, secondary or college/university?

  2. More broadly, do you know of any studies where interleaving has been rigorously tested in more real world settings?

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    $\begingroup$ Probably most here already know the following, but for those who don't, this "interleaving method" is incorporated in the Saxon math texts, and thus one should be able to find many discussions archived on the internet concerning both positive and negative aspects of this method. $\endgroup$ Jul 21 at 21:09
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    $\begingroup$ (To me, interleaving sounds great, but many people have issues with Saxon, for other reasons. I'd expect it to be hard to tease out this aspect from the rest.) $\endgroup$
    – Sue VanHattum
    Jul 22 at 2:17
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    $\begingroup$ @Sue VanHattum: I was thinking about saying something regarding the controversies with Saxon's books, but I was a bit lazy and also felt that most anyone aware of Saxon would know this and others interested would quickly learn this. However, your point, which I'll paraphrase as being able to tease out unbiased information about the interleaving method from the strongly pro-Saxon discussions and the strongly anti-Saxon discussions (which together heavily dominate Saxon discussions) is a good point and much more relevantly specific here than what I was thinking of adding to my comment. $\endgroup$ Jul 22 at 9:14
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    $\begingroup$ "How widely is interleaving used in your classrooms" makes this sound like an opinion-based/discussion question. Wish that could be refined more. $\endgroup$ Jul 23 at 9:55

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In an answer to question 2, a few references I am familiar with are brought up at https://www.learningscientists.org/blog/2016/8/11-1. I was made aware of interleaving through this website. I will copy-paste their references here for access:

(1) Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics problems improves learning. Instructional Science, 35, 481-498.

(2) Rohrer, D. (2012). Interleaving helps students distinguish among similar concepts. Educational Psychology Review, 24, 355-367.

Two other studies from the comments:

(3) Rohrer, D., Dedrick, R., Burchess, K. (2014). The Benefit of Interleaved Mathematics Practice Is Not Limited to Superficially Similar Kinds of Problems

(4) Rohrer, D., Dedrick, R., Hartwig, M. K. (2020) The Scarcity of Interleaved Practice in Mathematics Textbooks

In an answer to question 1 which is more personal, I have incorporated interleaving deliberately in both high school and in college level instruction.

Generally when I assign practice problems at any level, I make an effort to alternate the problem type, even while moving from "easy" to "hard." Too many of the same problems in a row lead to student complacency. When learning about the chain rule, for example, it is sensible to include some problems which should not use the chain rule, and ask students to evaluate for multiple problems "Is the chain rule appropriate here, or not?"

At the high school level, when learning about trigonometry in high school geometry, we begin by learning to solve for missing sides of right triangles. Instead of grouping the problems where you solve for a leg and the problems where you solve for a hypotenuse together, I randomly alternate solving for leg and solving for side in their problem sets. This way, students have to contemplate the setup of their equations. Once we learn to solve for angles, the problem sets begin to interleave 'solving for side' and 'solving for angle' as well, and even some where you don't even need to use sine and cosine (and you can return back to the Pythagorean Theorem!).

I motivate students to follow these forms of assignments by reminding them that in exams and in real life, you are not told what type of problem you are solving: determining whether you have the tools to solve a particular problem, and/or whether the tools you have are appropriate, is an important part of learning how to problem-solve.

A place of common availability of mixed practice problems are websites such as IXL (https://www.ixl.com/). These sites have batched practice and mixed problem sets. When assigning problems through these websites, I prioritize including the mixed problem sets. Other software has also always included this as an option (e.g. kuta software https://www.kutasoftware.com/ gives the opportunity to scramble problems within the set and between sets). I just downloaded the free trial to verify this. Personally, I currently assign homework through WebWork, which requires more manual attention to this detail.

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  • $\begingroup$ After you mentioned Rohrer, I also found an interesting looking RCT: Rohrer, D., Dedrick, R. F., Hartwig, M. K., & Cheung, C.-N. (2019, May 16). A Randomized Controlled Trial of Interleaved Mathematics Practice. Journal of Educational Psychology. Advance online publication. dx.doi.org/10.1037/edu0000367 PDF available $\endgroup$ Jul 22 at 18:01

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