Today I started writing a blog post on Ledger and my experience with it, but I quickly digressed into my way of learning things. Since I guess this might be interesting on its own, I decided to make a separate (albeit short) blog post on this issue. Here’s the gist: my preferred way of learning nowadays consists (roughly speaking) of reading a few tutorials first and *skimming* the manual, then actually using whatever I’m learning, and *then* carefully reading the manual. The first part is obvious: reading a few tutorials instead of one may give you better perspective, and tutorials (by their very nature) omit some things – but different tutorials may omit different things. But what about postponing studying the manual until after a few weeks or so? Well, I strongly recommend doing exactly that. If you’re learning a piece of software, a programming language, a tool etc., start using it as early as possible, perhaps with a tab pointing to StackOverflow in your browser. Then, after (at least) a few weeks, *read the manual again*. Chances are you will now appreciate (and understand) a lot more things, since by now you may have enountered some *real* problems the tool/langauge is addressing (or creating!).

Being (among other things) a math teacher, I can’t help but think about a similar attitude in case of math teaching or learning. Would it be possible to first teach some very basic notions and patterns for solving common problems, *then* make the student solve a few of them, and only *then* teach him or her the theory proper? Would this help gain deeper understanding, not only for the theorems and proofs, but for the *need* for them to exist? On a “micro” level, a similar technique might be used to teach individual proofs. Mathematical proofs are chock-full of tricks, and most students do not understand why they are there. One way to teach them this would be first to present some special case, where they don’t *need* the tricks, prove it, then show a more general case and a counterexample showing that the simple proof won’t work, and only then introduce the tricks. It would be much slower than traditional teaching, but I’m quite convinced it could result in way deeper comprehension…