Interleaving and Calculation Training

I recently read an interesting book called Make It Stick, subtitled ‘The Science of Successful Learning’. In it, the authors expound a number of ideas about effective learning, most of which are not particularly common practice, and discuss the science behind these ideas. Some , such as spaced repetition, I was already familiar with. Others, like ‘interleaving’ (the topic of today’s post), were new to me.

Interleaving means mixing up the practice of different types of problem in a single session. The first study cited is of children learning to throw beanbags into a bucket three feet away. One group’s practice is confined to a bucket three feet away; the other group practises throwing into buckets which are two and four feet distant (but not into a three foot bucket). In the test, which features only a bucket at three feet, the second group does markedly better, despite never having practised at that distance. Whilst this may be surprising, it is hard to see what relevance it might have for chess study.

In the second, more pertinent study, students were taught to calculate the volume of four different three dimensional shapes. One group practised solving all the exercises for one type, before moving on to the next type, solving all those exercises, and so on. The exercises for the other group were ordered randomly, so that a student could, for example, find herself solving one exercise for shape A, then one for shape C, then one for shape B and so on. Intuitively, I suspect most people would expect the first method to be more effective; it seems that it would allow the student to really master solving one type of exercise before turning her attention to the next type. Indeed, during practice the first group fared better. However, on the final test a week later, the first group averaged only 20%, while the second group eclipsed that score with an average of 63%. A possible explanation is that the effortful recall involved in remembering how to solve a particular type of exercise was very effective at strengthening the neural pathways for that particular skill; clearly this is something the second group had to do much more of during practice. The book goes into more detail, for those interested.

Another interesting book I own, but have yet to read very much of, is Calculation, from Jacob Aagaard’s highly acclaimed ‘Grandmaster Preparation’ series. In it, a few hundred difficult calculation exercises are presented, divided into themes such as ‘Candidate Moves’, ‘Comparison’ and ‘Elimination’ according to the calculation method most useful in solving them. Each theme has an explanation, which is followed immediately by exercises designed to reinforce that explanation in the student’s mind. I would imagine that Jacob intends students to read the book from start to end, following the same method as the first group in the volume calculation experiment presented above. I intend to use the second group’s method instead, and have used this tool to order the problems randomly. My hope is that the greater amount of effortful recall involved will result in far better retention of all methods after finishing the book, but of course with myself as the only experimental subject I will not be able to prove that it has worked. If any chess teachers out there would like to try an interleaving experiment with their students I would be very interested to hear the results!

P.S. For those of you coming here to read my ‘T-40 Review’, I have postponed this by a week and will be presenting a ‘T-39 Review’ next Sunday instead.

2 thoughts on “Interleaving and Calculation Training

  1. I don’t have the book but “Practical Chess Exercises” by Ray Cheng sounds similar to interleaving.

    If interleaving is better than sequential learning it should be applied as much as possible.

    The shortest distance in learning apparently is not a straight line

  2. I love learning theory, spaced repetition is fantastic, but i hadn’t heard about interleaving either, good to know. Sounds like a great idea to apply it to the calculation book! Good luck!

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