Coaching (4): my experience of starting university

It was 2004 when I started mathematics at University. In 2004 studies were not divided between Bachelor and Master. It was just one degree and it lasted 5 years. It is my understanding that that was pretty much the case in every European country, and things changed with the "Bologna plan".

So, back in the day, in Spain, to become a mathematician, one had to study for 5 years, from which 3 years and a half were filled with compulsory subjects. Now, of course, things are very different in the study plans. But some things do not change: the transition from high school to university was tough. Very tough.

And we had to pass all the subjects of the first year (a total of 8) to be allowed to go into the second year (and you had to pay for every course that you registered to, and you could not de-register - you were given a fail -, and every time you had to repeat that subject, it became more expensive). Exams were written, at the end of each semester, and they had a fixed date.

Studying maths was very tough: I had to work a lot and many times I did not feel my efforts compensated with the marks I obtained. Mind you, getting something close to full marks was extremely hard: and we had an evaluation scaled from 0 to 100.

But enough about context. 

When we were thrown into university, we had no idea how to study mathematics. I remember I focused a lot on doing the exercises (after all, 80% of the content of our written exams was based on exercises). We had many exercises for each week, and during the exercise class, the teacher would only solve a very small percentage of them. We had no solutions, so, as students, we could only rely on each other to get the answer to the rest of the exercises. 

I was really struggling, but my breakthrough come during a lunch in the second semester. A friend of mine had had very good marks despite studying for two degrees at the same time. I asked her how she studied, and she told me that she focused a lot on the theory, even if she did not have enough time to do all the exercises (we did not have 6 exercises per week, we could have between 12 and 20 so it was super-hard to do them all). This conversation opened my eyes: I had been studying the wrong way all the way long.

I was going to class, taking notes, not understanding a thing of what the lecturer was saying, and then trying to understand something at home while attempting the exercises. From that day on, I completely changed my strategy: if there were lecture notes (many times there were not, unfortunately), I would read the lecture notes beforehand, and not take notes during the class, unless it was about new material; I would always revise my previous classes before the next one; I would find books that explained the subject in a way that suited me better. Then, I attempted the exercises and tried to relate them as much as possible to the theory. If I had no time to attempt all the exercises, I would just try to see if I understood them, and could think of how I would go about trying to solve them (or if, on the contrary, I had no idea how I would start).

This new study methodology changed everything: I started to enjoy more the theory class, I learned way faster, and I became a better mathematician.

Somehow this reminds me of an analogy: the way languages are learned in Spain. In Spain, you spend years learning English grammar. It is an arduous process that requires a lot of time and effort, and in the end you can get excellent marks in an exam..., without being able to have the simplest conversation in English. So we put in a huge effort, and we do not really learn the language. The same can happen in maths. You can work a lot, but if you do not work the right way, most of the effort is for nothing.

My first year was very tough. I think if I had received some coaching, it would have helped me enormously, so that is why I am offering the coaching sessions now. But normally, I only offer help if asked, so I will only coach and give my advice if asked.

I tell you an anecdote to illustrate how unprepared we were in our first year. We were 50 students (because at my university there were only 50 available spots, so we were all highly motivated students that really wanted to do maths), one of our first subjects was Calculus I. Only 3 people passed the midterm. Only 3 out of 50.

People were smart, people were motivated. But we were just unprepared. The gap between high school and university was huge. So it is normal if for you it is tough, there is nothing wrong with that. It is to be expected. However, make sure that you get the help that you need (tutoring, coaching, a community of fellow students) and that you adopt the right study habits.