As you might know, fractal structures appear in a variety of natural situations and have found many technical applications (see Wikipedia for more information and examples). In this short article I want to ask the question, whether it makes sense to structure various activities according to a 'fractal timetable'?
When you have to clean a flat or a house you probably you have seen a list like this before. There are some tasks that one needs to do every day, others come along only once a week or once a month. Aside from those main cleaning tasks, there will be many small things you do several times during a day, like throwing something into the trash bin or washing your hands.
If you analyse the structure of this behaviour, you will find that it looks similar to a one dimensional fractal (compare with the various layers in the construction of the Cantor set, for example).
Most schools that I am familiar with use periodic arrangements for the teaching. You have a weekly timetable and at the same time every week you have the same subject for a whole year. This makes sense from the point of view of teacher and room allocation, but is this the best structure for optimal learning?
My own experience suggests that the quality of my memory strongly depends on my understanding. If I take the time to understand everything, I will remember those things for years and can even reconstruct lost knowledge by using intuition and logical deduction. If I learned something poorly, on the other hand, I sometimes forget it completely in a matter of hours.
Understanding is usually gained by a deep involvement with the topic for a longer period of time. I also find it much easier to learn something if I can focus on it for a certain period of time and examine the object/concept in detail without being disturbed by other matters.
What if the best way of teaching school mathematics (for example) would be to have a 3 week long intense workshop once a year with some other 10 one day sessions allocated once a month and small homework problems evenly distributed throughout the year? The same could be done with the other subjects to fill the full school year.
Our motivation, health and available time fluctuate widely, but most jobs require a periodic commitment. This might be OK for mechanical jobs, but for professions with a substantial amount of creativity and cognitive demand one certainly can do better by playing around with the time/work distribution. (Here is an interesting TED talk about a 'year off'.)
Similar problems/opportunities arise in fitness, personal development and relationships.
I don't know, whether there are any existing studies on this topic. A superficial Google search didn't reveal anything interesting. I also would like to know, whether you had similar or contradictory experiences? Maybe I am an exception when it comes to this type of learning.
Do you think that adding the mathematical model of a 'fractal' makes this approach more intuitive/useful or whether 'flexible time management' captures enough of the structure of the problem?
No, it doesn't. While the current structure of mathematics curricula might not be ideal, the solution won't be found by the means outlined in this post.
It is clear that spaced repetition makes learning material much easier. Start there.
I am not sure, whether we actually have a disagreement here.
Spaced repetition is a special facet of the idea that I outline in this article and I am currently experimenting with it exactly for the reason to test my "theory" above.
I have similar thought and experience. and I was glad when I found your post through searching google.
My first experience was from computer program.
I would like to talk together more about this topic here and by email :)
Nah, the main benefit you get from organizing your time as a fractal is easier enjoyment; splurge on icecream bigtime one day, but take smaller nibbles at other times...
ok, MAYBE doing a 2 or 3 level cantor set for time management might be useful (anecdotal evidence: my performance on piano pieces would occasionally improve if I left it alone for a week), but you can only handle so big a gap before the knowledge just simply starts decaying.
As a mental shorthand, whatever works for you, but I don't think fractals would be useful in any kind of formal treatment of the problem.
It vaguely matches my own intuitions on the subject, just not closely enough.