Pain + Reflection = Progress

The last three weeks have been especially challenging for me. But lets start off in the beginning. As the four Abitur exams, the finals in Germany for secondary schools so to say approached, I chose to take Mathematics as the fourth subject, knowing in the back of my head that the Maths exams in Germany in the last years were subject to various criticism by students all across the country because of their notorious difficulty; all pupils were given an extra of two points (ten percent) in the last two years.

But the alternative for me would have been to choose German, where I then had to analyze stylistic devices of a text dealing with the literature of Romanticism, a European 18th-/19th century art movement, which emphasized emotions, individualism, and the medieval. No thanks, with that in mind I can say that I prefer to analyze numbers and draw graphs... Without a doubt, there was also a bit of foolishness and thoughtlessness, as I underestimated the level of difficulty that was ahead of me, as I did pretty well in the topic we were dealing with, Analytical geometry, and it did not challenge me that much, being able to answer the questions and solve the tasks with ease and with almost no effort. Little did I know that we were just at the beginning of the topic, just scraping the surface. So I embarked on this adventure. Stormy times ahead of you, my past self, stormy times.

As we dug deeper and deeper into Analytical geometry, it came to cases where I simply did not know the answer to some issues and questions of my teacher, not being able to grasp the meaning of the numbers behind the words. This was unusual for me, had I always been among the top of the class, scoring A’s and always having the correct answer at hand. But I am a person who does not simply just accepts this fall-off. So I had to do something, that I rarely spent time on in the past: Actually spending time trying to understand maths.

First thing I had to learn: My imagination powers are limited. Before, in the mathematical area of Analysis when dealing with functions, derivatives, and integrals, I had everything I visualized in my head, no need to have a paper and to write much. With this new topic, while one might say that imagining stuff in geometry must fairly easier than in analysis, this proofed to be only partly true for me, as I had to take on new dimensions literally.

Instead of the two classical dimensions of the coordinate system in Analysis, the Analytic Geometry adds another one, ending up with a three-dimensional space with the power of modeling “real” objects and situations. This was new and much more difficult for my brain, which was used to linear, two-dimensional thinking. Also drawing it turned out to be more difficult, having to imagine a 3D-Space onto 2D-Paper as in comparison to Analysis with its two axes. I learned to work with almost painful accuracy, diligence, and cleanliness a thing unknown to a student whose handwriting became (involuntarily) famous among the teachers, some, like my ninth-grade class teacher, even saying(although in a nice way) that I have the most spiderly handwriting they have ever seen in the history of their career.

Time went by and as the Abitur was getting closer, the Abitur pre-exams approached. Taking it as the fourth subject, I did not write the Math exam along with many of my fellow students, but in Economics, Physics and English. It turned out that I got off it fairly lightly, as the pre-math exam results were so terrible that they had to be approved by the school administration, with the best in our class having a two minus. I took this as a “warning shot” for me to really learn for the math exam. But life would be too boring if it had been that easy. With problems in private life, the health condition of my single mother declined rapidly so much that she had to go to the hospital, my focus on school went down, resulting in me underestimating the (normal) math exam we wrote later, with me ending up with a two-plus only.

But mistakes are there to learn from. Standing up again, I shifted (almost) all focus three weeks before the exam date onto math. I gathered every Abitur math worksheet I could get, exams from the last years, sample papers or exercises from math books, and worked through them until I could no more. Perhaps the most important thing was not to get discouraged when I did not come up with the correct answer, even after thinking it all through. Sometimes, it is just a small miscalculation, which screws the whole thing. Does not matter, be more picky and precise in the next exercise. When it was a bigger mistake, take a deep breath first. Then analyze what you have to do to make it better next time. It may be painful to confront it at first, but in the end but learn from it. You don't need to overanalyze things, find out where you got things wrong, keep them in mind and then move on.

This is how the thing went, day after day. No day went past without fault, but I was grateful for that. Better now than in the exam, or even worse, never. It was a stressful period clearly, but looking at it backward I also enjoyed the process of learning, of finally understanding the tasks.

With that preparation, it is almost needless to say that I ended up with 15 points in the exam.

Nothing is perfect and there are always things to improve. I may therefore always choose the more challenging option for me, as from them I can learn the most. In my opinion, it's not about how intelligent a person is what determines their success, but a question of motivation discipline, and technique. So what did I learn from the math exam (besides math)?

Prepare, prepare, prepare. Shift all your focus onto your goal. If you made mistakes in the past, accept them, learn from them, because they will help you on your way over the hill.

“If you don't look back on yourself and think, ‘Wow, how stupid I was a year ago,’ then you must have not learned much in the last year. “ — Ray Dalio