Comparing forward with reverse (retrograde) presentation
The Danish philosopher Søren Kierkegaard famously observed that life can only be lived forwards, but can only be understood backwards. I was reminded of this last June, when I received an intriguing email from a retired professor of maths and physics (and keen Chessable user), Santo d’Agostino. Santo presented his idea in the following way, and I quote directly from his email:
“In chess tactics, consider the basic smothered mate pattern with White Q at b3, White N at f7, Black King at g8, Black R at f8, and Black Pawns at g7 and h7:
White plays 1 Nh6+ Kh8 2 Qg8+ Rxg8 3 Nf7 mate. This is a basic pattern that we all learn at some point. Now imagine a series of exercises where this basic pattern is pushed back a move, with some other preliminary move to set the pattern up, then pushed back two moves, then three moves, and so on. I have seen a few such exercises in various Chessable courses, but they are not assembled in the same place. … And of course, you can set up similar sequences for all kinds of different tactical patterns. The training idea is that once you learn a basic pattern, the sequence of exercises may lead you to be able to recognize the pattern “hidden” (“latent” is a better word) in more complex positions. You can imagine setting up an entire course with a variety of sequences of this kind. (The Chess Informant Encyclopaedia of Chess Middlegames/Combinations is not quite like this, but they have two sections, the first where the tactical patterns are more direct, and the second where they are buried a bit further after some preliminary moves.) Several research questions may flow from this:
- Is learning tactics using such sequences more effective?
- If so, when during the learning process should one be presented with such exercises – as a sort of cumulative review, or at various intermediate stages? Is such repetition-with-variation better than simple repetition?
- One can also imagine repetition-with-variation with a number of exercises all at the same difficulty level, rather than with a sequence during which the difficulty level increases. Which is better? Or are both useful in some combination?
- Could such sequences of training exercises be useful for other kinds of learning besides tactics? Endgames? Positional play?”
The subsequent further exchange of correspondence with Santo caused Karel van Delft, the Chessable Science Project Manager and me to decide to interrogate his core idea and research questions more extensively, and to bring in the thoughts and ideas of a wide range of chessplayers, chess coaches, chess authors and chess researchers—whose invaluable input we acknowledge explicitly in our final report. Central to this was the involvement of two popular and creative Chessable authors, Raf Mesotten and Alan Bester. Raf already had the germs of an idea for integrating elements of Santo’s proposal in a new course, and Alan had the most substantial track record of any Chessable author for ‘reverse-engineering’ puzzles—ie asking users to work backwards from a ‘given’ position in order to reconstruct the path towards it.
We implemented a matched samples study involving nearly 100 participants recruited from the contacts of Karel, which was designed to illuminate what, if any, differences there would be in performance outcomes for participants following a traditional forward-solving puzzle strategy (‘Find the move in the position which results in the optimal outcome’), and for those following a reversed-solving puzzle strategy (‘Find the best move to achieve a given position’). We chose deliberately to omit any ‘training’ element for either condition, in order to capture as closely as possible the naturalistic context of an over-the-board game. Since the reversed-solving condition involved first presenting a mate-in-one position, and then a mate >1-ply position from the same game (unlike in the forward-solving condition, where the positions were unrelated), we were interested to see if, in such a relation, the participants would discover/learn this relation/connection for themselves via an untutored ‘aha’ insight and apply it accordingly.
The detailed results are revealed and discussed in our report, but in a nutshell we found no significant differences between the forward-solving and reversed-solving conditions. Specifically, and perhaps a little surprisingly, the matched-nature of the puzzles in the reversed-solving condition did not lead to any gains in performance. We discuss possible reasons for this, and are at pains to point out that the fact this study showed no significant differences between the two conditions, doesn’t mean the reversed solving method has no potential applications. Conceivably, better results could be attained if participants were to receive an explicit explanation of this search method before solving puzzles (as provided in Alan Bester’s courses), and it could be significant that in a short follow-up intervention where we asked the reversed-solving participants if they had “noticed anything” when they solved the puzzles, almost all the players rated >1800 ELO had indeed noticed a connection between the one-ply and the >1-ply positions, whereas those rated below 1800 had not.
In terms of potential applications, whilst our results do not themselves justify a call to authors to incorporate a reversed-solving element in their materials, it should be pointed out that many of the most highly-regarded chess training materials already (and perhaps intuitively) employ one or more versions of a reversed-solving strategy – e.g. the Dutch ‘Steps’ training materials. One of our chief collaborators, Raf Mesotten, uses a reversed-solving strategy in his brand new course (out very soon), Tactics prior to Checkmate Patterns’, which as he outlines, ‘… teaches you how to use tactics that can lead to the very same checkmate patterns as in The Checkmate Patterns Manual. Each motif is rolled back one or more moves and is viewed from the attacker’s perspective. The task is to use tactics that can give you an advantage. And if our opponent is not careful enough, the game ends in one of the thirty checkmate patterns that are covered in The Checkmate Patterns Manual’. And should an opponent spot the specific tactical idea, s/he will end up with a disadvantageous (albeit non-catastrophic) position anyway. This is a direct link with the original training idea that once you learn a basic pattern, the sequence of exercises could lead you to be able to recognize the pattern latent in more complex positions. Our data suggest that at least weaker players could require explicit tuition in making connections of this nature, as these may not be made intuitively.
We continue to welcome ideas and suggestions from our users for improving our courses and their experience of our platform, and I personally have thoroughly enjoyed engaging with our users to this end. I am now passing on the mantle of Chief of Science in preferment of retirement and a chance to spend more time on my Chessable courses myself! My successor will be announced in early April, and I have no doubt that she will love the chance to strengthen further the place of chess science in every fibre of our platform, and to ensure that we continue to take seriously the creativity and ingenuity of our userbase. So thank you, and with a nod to our recent study, if I haven’t checked you in the past, maybe I’ll check you in advance sometime?
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