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Maths and YouTube

We’ve met with some friends today. At some point we started talking about kids and education. One couple came from a country where one’s allowed to homeschool their children. I’ve heard that in Germany homeschooling is forbidden as it can supposedly limit child’s opportunities in life. I see cons and pros for both approaches, and I don’t know which is best. It’s sad not to have an option though.

At school and later at university, I always went for the highest marks. It didn’t matter what subject it was or if I like it or not, I always wanted to get an A grade. As a result, I’ve received a golden (unfortunately, it’s only the color) medal when graduating from school and a red diploma after my last year in the university. These are the things schools would give to their students for their excellent academic performance. It felt like I’ve achieved the goal.

Only later, when thinking more about it, I realised the mistake I’ve made. The color of my diploma meant nothing in the real world. But I wasted so much effort to get it. I would be better off learning the things I like and find interesting. Instead, I’ve studied them very superficially, on a level that’s just enough to get the grade I wanted, and then moved on to the next subject.

After finishing my formal education, I was very ashame of my shallow knowledge. For example, I knew about derivatives from maths, but I never understood what they really mean. Well, I knew how to use the formulas, and I could probably recall the formal definition, but I didn’t understand what derivatives represent in the real tangible world. And why, for example, a derivative of speed is acceleration?

Only when I started to address my shame, my wife sent me a link to the Calculus One online course from the Ohio University. Author of this course went leaps and miles to make sure students understood what exactly a derivative represents in the real world. This course isn’t loaded with heaps of repetitive exercises (unlike in my formal education), but it’s full of creative visualizations with the emphasis on explaining the concepts.

I felt a huge amount of relief after finally understanding what a derivative is. I finally felt like I wasn’t dumb after all.

My wife was doing a remote course on statistics last year. I’ve watched how she learned calculus. Whenever she didn’t understand a concept, she would go on YouTube and watch a video after video, from different authors, with different styles of explanation and different examples. Khan Academy does an excellent job on this front. My wife would not stop until she understood the concept. I think this is way superior when compared to a usual class at the university, when you have to be at a lecture at a certain time and being taught by the same teacher. It doesn’t matter if you had enough sleep or not, if you’re sick or having a headache, or if you like the teaching style — you had to take it. Or perhaps you could read a book. Math books I could ever get hold of were very dry.

When compared to learning mathematics online, sitting in a class seems not only like a waste of time, but something what can potentially have a negative influence on one’s motivation to learn.

I don’t think that the usual school like we have it today is all useless. It certainly has positive sides.

I think one should always assess if they are learning what they enjoy, if they enjoy learning at all, and make corrections if a point of dissatisfaction is met. And never stop learning a concept until the level of understading is reached. Good indicator is that one can explain the concept in several different ways using their own words.

Last edited on Jan 12, 2019