… you need a good math teacher!

I was talking to my daughter the other day and she told me how her impression about mathematics improved after she entered the school here in Texas, compared with the school in Brazil. I asked her the reason and she told me that here in the USA the teacher has time to dedicate to the particular needs of the student, while in Brazil the teaching is automatic, rapid and unpersonalized, the teacher explains the subject, to the student remains to understand the subject or simply to skip understanding and focusing in the next subject.

Then I remembered what happened with myself at the school. I was blessed (or cursed) with an analytic mind. An example is the image I chose to illustrate this article. This is the so called Euler’s identity. The first time I saw it (probably at the Physics course) I could not understand why Euler bothered to express it.

If fact its proof is trivial (in my opinion), we have the identity

where x is read in radians. By simple inspection one observes that the value of this quantity at 180° is real and corresponds to +1, then, for me, the identity was equivalent to stating the 1 – 1 = 0, and if you state this to any person, he or she will say it is obvious. It took me about twenty years to appreciate what is considered an expression of the beauty of mathematics.

At the fundamental school, you will probably find it strange, I initially didn’t like mathematics. The reason, now I recognize, was because I was bored. Teaching mathematics in the fundamental school is a repetition process. Fact is that most persons don’t learn so easily the mechanistic ways of mathematics and this is achieved by solving a lot of identical exercises until this mechanistic process enters the kid’s brain by brute force.

This changed some time in the seventh grade by two fortuitous events.

First, during the winter pause (in Brazil our school winter pause corresponds roughly to the month of July), for some miracle, I decided to take a look at the math textbook to see in advance what would be the subject when the lecture resumed after the pause. I remember it was the solution to quadratic roots (the quadratic formula). I remember it contained a simple deduction (in one page) of the formula (it is the same found in the Wikipedia article), and I read that and understood. I found that marvelous, to understand why a formula was the way it was, and not only to learn the formula. Of course, I went happy to the first mathematics lecture after the pause, to show what I did learn by myself, only for the teacher (an Asian lady, I don’t recall her name) to say she would skip that part because it was unnecessary.

The next fortuitous event was a test for some school Olympiad we had in that year in Sao Paulo. As I told, I was bored with mathematics, as a consequence I rarely did my homework, and, of course, this resulted in bad grades at the tests, in particular I never got a 10 (maximum note) in any math tests ever. I was considered back then an “expert” in Geography. Then this test came, and we had to do it in all subjects, since this would be considered for the school grades. To my surprise, and to the surprise of anybody else in the classroom (and the teachers included) I scored a 10 in that test.

The two events taught me I could like mathematics. I didn’t recognize back then that the reason I disliked math before was because I had very bad teachers, or at least, access to very bad teaching methods. Today I realize this is the reason why so many peoples hate Mathematics. We should have more empathy with our children.