A Randomized Controlled Trial of Interleaved Mathematics Practice [pdf]
uweb.cas.usf.edu
uweb.cas.usf.edu
In the same way that muscle need to rest to grow, knowledge need to rest to stay with you. Even if subjectively seems that nothing has been learned the first time that you are in contact with a subject, that is hardly ever truth. Even if only the name of the concepts are familiar that's some progress from where it's possible to build solid knowledge.
The big ideas in any Mathematics subject are usually very few. They can be covered at a high-level in a few classes before going into them in detail. This also gives you a broader context for you to place the details as you come across them.
Problem? ... It's not very fun. You always feel frustrated and dumb because you don't understand it. So you'll eventually stop practicing at all because you feel like you don't make any progress.
Same thing with chess; play only with Grand masters (if you can find them) and after a few years of getting your ass kicked, you'll eventually get good. (Disclaimer: I only skimmed the article)
Wouldn't the grand masters not enjoy beating you over and over again? That's why Go has a handicap system and why online games have matchmaking systems. I think it would be more courteous to try and play with people that could potentially learn something from you, instead of you only learning from them.
I mean, a couple times maybe? At some point I feel like they’d think this is a waste of time.
I doubt that this would work. It would be like trying to learn math just by reading cutting edge research papers and trying to solve major open conjectures. The gaps between your current level of skill and knowledge and what is needed to comprehend anything from the material you are trying to learn from would be too big.
Yes, you learn best with challenging material, but it needs to be sufficiently close to your current skill level that you can at least partly understand it.
There used to be a chess club that met weekly in the '80s in Sunnyvale, CA, at the Lockheed Employees Recreation Association facilities. Not many people actually went to it to play chess, because a regular attendant was Richard Shoreman, a well known chess teacher and coach. If you brought the score from one of your recent tournament games, Shoreman would play over it and annotate it for everyone, and give you suggestions on how to improve.
His specialty was getting people whose progress had gotten stuck, typically in the 1800-2300 USCF rating range, unstuck, although he was also good at getting lower rated players to rapidly improve.
The #1 reason people got stuck, especially around the 2000 rating neighborhood, was they were spending too much time studying GM games and trying to play like GMs. This doesn't work because, to paraphrase Shoreman (because I don't remember the exact statement), GMs play good chess, and before you can play good chess, you have to get good at playing bad chess.
Good chess is what GMs do--deep subtle positional play and a thorough opening understanding. Underpinning all of that good chess, though, is tactics. Every positional thing ultimately is either to enable or prevent some tactical thing from happening, and to really play positional chess well you have to have a good tactical understanding.
So what Shoreman did with these stuck 1800-2300s was get them to set aside their opening repertoires that they had copied from their favorite GMs, and get them play aggressive tactical openings. It is important to note that these openings were NOT required to sound--the important thing was to get into a tactical game. You are playing for a knockout here, not for a slightly superior pawn endgame. If you can get a good attack from a sacrifice, but can't calculate it out for a win--go for it! I think I recall Shoreman saying to always play the most aggressive move that you cannot see an outright refutation for, or something to that effect.
That kind of chess is what he meant by bad chess. Once you really understand that bad chess, you can then start to understand good chess.
That sounds suspiciously like one of those surface leval optimal solutions which don't survive reality. I imagine the best way to improve is like the best way to diet or exercise. The flawed system you can sustain is better than the optimal system cannot.
Playing against the pinnacle of a sport as an amateur is likely sustainable for neither the amateur nor the master. The amateur will quickly tire of never feeling like they have a chance, and not seeing a real improvement when measured against the vast gulf of ability compared to the master. The master will be bored and unchallenged.
I think a close to optimal path to improvement for real people would be a club of people all dedicated to improving, with enough competition between them all that none can be complacent, and a mentor with enough skill to provide useful advice at all skill levels. Martial arts schools in the Eastern tradition, for example.
Now I'm wondering what the world would be like if every GM ran their own chess dojo. :)
I would strongly recommend the course to anyone interested in learning and who doesn't have a good learning process, because that's all that it ultimately is: a set of steps that you use to train your brain to remember a body of knowledge.
Anecdotally, after reading a paper on this, I made a Python script to drill guitar pieces, chords, progressions, etc. in an interleaved fashion and I believe it has helped me become a better player. Before doing this, when I would practice, e.g., scales, I might start in A then B, C, etc. but what I noticed was after doing the first scale, the rest were just minor variations so my training went from deliberate to auto-pilot. Now, with interleaving, I have to give some brief thought not just to how to mechanically perform the piece but what exactly the piece being asked for is. Consequently, during a performance, my ability to go from an intention of doing something on the guitar to actually plucking the first string is much more comfortable and faster.
My rationale was the same as in this paper: I wanted to handicap myself from knowing the "type" of question I was trying to answer and force myself to think, "Ok. Where is this question 'located' on the map of everything I've been taught? And once I know its location, where do I need to go to get to its answer?"
So, I hand-entered every question I could get my hands on and I had the computer throw random problems/questions at me before an exam.
The problem w/ my approach was that I had to hand-enter problems from my textbooks, so there was a decent chance that I would still remember the type of question simply from the act of typing it into my 'database.' But it was the best I could do.
I teach some college chemistry now and I think interleaving would be helpful to my students. I say this because one of the biggest issues on exams is that the students will have no idea what _type_ of problem they are looking at. If they correctly determine the type of problem, the remaining work is relatively easy. And I think the problem stems from students practicing the work by answering multiple problems that belong to the same category.
I don't see anything controlling for that in the setup:
"The present study examined interleaved practice in a large number of classes at multiple schools over a period of five months, and all instruction was delivered solely by teachers who had no prior association with the intervention or the authors."
Spaced repetition is not the same as interleaving, but the apps will force you to interleave knowledge anwyay.
Effective at what though. Just passing the test?
Do the students actually understand the material? Can they apply it to novel (to them) situations?
When I was studying physics ('74-'77) a significant number of students who all had just as good test results as I did in senior high school dropped out after the first term because they just couldn't manage the material. They had learnt enough to pass the exams (British A-levels) but had not really understood and had not practised enough. I suspect that rise of modular courses might make this situation even worse but that might be prejudice on my part.
Everyone has sat through 12 or 16 years of school. That can lead them to think they know all about it. I've been teaching since 79 and I'm still learning a lot,all the time. It ain't obvious.
It always comes down to time though, it seems like you can use all these ideas and teach for mastery, but it costs about 30% in terms of forward motion through the material. I'm lucky in that that I can just decide to pay that price, but it would be a real stretch to put all this into practice in a place where you have a coverage deadline that's already hard to hit.
Now we have some evidence that it is probably true; we still need a bunch more studies to make sure this is reproducible and robust for a variety of circumstances. Yay science !