The main purpose of this web site is to help students learn about mathematics and physics, and in particular to provide guidance in how to approach your studies in a professional and effective way. I’ll be posting every week on these topics, and will also be regularly uploading various learning materials. But if there is one piece of advice that I would recommend above all others, it is to adopt the “daily work” mantra. Effective learners work daily.
When I taught at a university, I was fond of telling students a story about myself on the first day of a course to emphasize this point. The story was well-received every year, so I’ll repeat it here.
Many years ago, when I was a young and foolish second-year university student, one of my courses was Abstract Algebra. My level of mathematical maturity (and every other kind of maturity) was pretty low, and so it was very challenging for me to cope with abstraction. I made a serious mistake that I think is typical of immature learners: I shied away from my most difficult course, and left it at the bottom of my priorities, so that I quickly fell behind. At some point I realized that I was seriously behind in the course, and so I resolved to spend the entire following Saturday on this course so that I could catch up.
And I did; I devoted the entire following Saturday to studying abstract algebra, from morning to night, with breaks only for food. Unfortunately I didn’t follow up with further studies in abstract algebra in the following days, as I was busy (as are all students) working on assignments in all of my other courses. It seems that every day an assignment was due in a different course, and so each day the focus was on completing the assignment that was due the next day. By Thursday I realized that I had not spent a moment on abstract algebra since the previous Saturday’s marathon, and I resolved to devote the next Saturday exclusively to abstract algebra again.
And I did; I woke up on Saturday and sat down after breakfast to work on abstract algebra. I was astonished to learn that I had retained absolutely nothing from the previous Saturday’s marathon study session.
Nothing.
Zero.
What then was the point of my devoting 12 hours to studying a subject, if a week later I had retained nothing? What a waste of 12 hours!
I learned an important lesson that day, a lesson that I have been trying to pass on to my students over the years. This way of working is so ineffective as to be pointless. Effective learners work daily. I certainly wasn’t learning abstract algebra effectively!
Everyone knows this; at least everyone but poor little second-year me, although I learned my lesson. Think about high-school basketball practice; do you practice every day, or do you just “pull an all-nighter” the day before an important basketball tournament? The same is true of any sport, or dance, or martial arts, or learning to play a musical instrument. In any of these endeavours, if you wish to learn effectively, you practice every single day.
There is a common phrase among musicians that appears to go back to Franz Liszt, although it has been attributed to others as well: “If I miss one day’s practice, I notice it. If I miss two days’ practice, the critics notice it. If I miss three days’ practice, the public notices it.” — see Barry Popik.
If you wish to master something, you should practice it every single day. Everyone knows this deep inside, but few of us do this, because we are “busy” doing so many other things, or because we lack commitment, or because we are afraid, etc., or, more likely, some combination of these factors.
I’ll have more to say in future about this, but for now it’s worth asking yourself whether you do practice the important things in your life on a daily basis, and if not why not. Reflecting on this will be a useful exercise in propelling yourself forward to become an excellent student.
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This is part of a series of posts on how to learn; the next one is here. These posts on how to learn will all be linked on this page for easy reference.