It is not that I am good at it: I just know how to learn

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In the Spanish educational system (at least when I studied) we spent years studying English..., without learning it. We work hard..., work very hard even, but we do not work well. When I moved to France, I learned French and now in Austria, I am learning German. I tell you, I do not feel I have a special gift for languages, but now I am a much faster learner than before, and not only that: I do not work even a tenth so hard as I did. I understood that I had to enjoy learning German if I really wanted to master the language. It is not that I am good at it: I just know how to learn; what works and what does not work.

And it is the same for any other discipline: there are methods in which one learns and there are other methods that, despite putting in a lot of time and hard work, the effectiveness is very low: it is not that you cannot learn, it is that you do not know how to learn.
Of course, I am not saying that learning does not require effort. What I am saying is that it requires the right effort.
And that is what I want to teach to my students. 


I taught again the exercise class for the STEOP (the bridge course for new students who want to study mathematics at University). The students must prepare some exercises beforehand and then present their answers on the blackboard.
It is a challenging course, mostly because it is the first time that they are studying mathematics (at the university level). They have never experienced that level of abstraction and logical rigor and also, they have not seen mathematical proofs before.
It is tough because they have to acquire many skills and learn many things at the same time: understand the mathematical concepts (they need to understand their meaning but they also need to have them solidly in their heads so that they can work with them), remember the mathematical notation, see the logical structure of the argumentation, and write mathematics. All the above are necessary to be able to do problem-solving, but I feel that writing mathematics tends to be the skill that students focus on the least, but it is essential to progress faster in mathematics, to learn it properly.
I am currently thinking of ways of breaking up this process so that students can focus on just one difficulty at a time. It is not so obvious, though, how to do this.


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