The need of teaching and learning more languages

For a second, stop to think about how many languages you know. With languages, I do not mean verbal languages: rather, any means of expressing thoughts and feelings, or of expressing a dialogue. I am here do advocate for the learning and teaching of more than just one.

Our western culture is based on the verbal language – the one you can speak with your friends, read in novels, and write in essays. We educate kids in that, and yet I would argue that very few of them end up being proficient in the verbal language. Speaking a language does not make you proficient in it: that skill is a much higher level one, and involves deep knowledge of the structure of the language, exposure to thousands examples of both good and bad usage of the language, and effortful practice throughout years. Often, people who venture in learning a new language (a verbal one) do not even ever get comfortable with their mother-tongue. What I mean is that although everybody can talk in their own language, few of them have a real mastery of it. Few people, for example, are able to tell a story (and not because of lack of ideas, but for inability of structuring it), and even fewer are able to read one out loud in a way that is vaguely engaging (for example, they cannot look away from the book to the audience, and fill in any gaps in their reading my making up appropriate fill-ups).

But even if people were proficient in the verbal language, this is just one means of expression. It is barely minimum. And even though we study several different subjects at school, they are all taken across through the same verbal language. But what about other, different languages?

Musicians, on the other hand, can rarely express the feelings and the moods of a musical piece through words. They have a different alphabet, one that does not have translation to the verbal one. The fact that sometimes, some situation reminds them of a tune, or inspires them a tune, rather than words, is a clear example that the musical language is different altogether. It is incredible that we are still studying Latin and we are not all studying music.

Sports is another example where a different language is in place. The main difference between experienced and beginners in table tennis, for example, is in how they frame/live the unfolding of a point. Experienced players see a dialog in it, a conversation that ultimately leads to scoring a point. But it is exactly this sense of structure, this ability to realize how each stroke is connected and what each of them can have as consequence, that gives experienced players an unmatchable advantage. They know what is going to happen, and they know it because they are building something with that language.

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The reasons why mathematics teaching is failing

As a mathematics PhD student, I have seen a lot of mathematics teaching. I have been lucky enough to witness some (very) good teaching, but I have also been inflicted with so much bad teaching. Sometimes, I just wondered whether the people do even realize that their teaching is horrible, and I most often believe they are just unconscious about it, since most of the teaching they were exposed to was bad for them as well. I guess they just believe there is no way of making a good teaching of math, since most of it seems to be so bad.

I genuinely believe all graduate students in any subject should care about teaching. Even if you do not particularly care about teaching others, it makes your knowledge and understanding stronger. Just thinking at what matters (which is what you would teach), and how it would be best presented, forces you to thoroughly understand the topics to a deeper level. And at some point, you will just wonder: what are the essential elements of bad teaching? How can I avoid them?

#1 – Too many answers, too few questions

I am genuinely convinced that the most essential element of bad teaching is providing answers instead/without questions. Too often we go to class and we get lectured about some method, some theorem, some theory – and too seldom we get lectured about the path that actually led to that method, theorem or theory.

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