During my science education at CÉGEP, there was a lot to learn. In two years, I took five physics classes, four mathematics classes, two chemistry classes, and a biology class. This was in addition to many other complementary and language classes I had, which meant there was a lot of content to get through over the years. Consequently, there was an impetus to prioritize work by looking at whatever was coming up in the next week. Once the material was covered, it could safely be forgotten.
I’ve written about this last week, but I want to discuss something a little different today: revisiting material. This is something I don’t see being done very often. Throughout all my years at school, I don’t know anyone in particular that would revisit their old material. Of course, I may just not have noticed (as others could make the same claim for myself), but it demonstrates how this isn’t necessarily an aspect of one’s education that frequently occurs.
You may have heard that people say that re-reading a book always gives them new information or a different perspective on the story. I believe learning is much the same. If we only go through material once, there’s a fair chance that many aspects of it will be lost on us. However, if we revisit a concept many times, there’s a better chance that we will learn to appreciate all of its nuances.
Have you ever wondered why a teacher is so good at their subject? It’s usually because they’ve worked on the concepts many times over. The best science and mathematics teachers I’ve had are the ones that have been teaching the material for years. Because of this experience, they are able to recognize and solve all sorts of problems, merely due to repetition. This is the exact same thing as teaching a small child the principles of addition, subtraction, multiplication, and division. Since these are the basic operations in mathematics that are learned at a very young age, it becomes basically second-nature once one has moved on to more advanced mathematics. Therefore, one’s experience is great enough doing these operations that there is seldom a problem.
For myself, I’ve recently been brushing up on my own skills in a subject that has been a little bit distant in my mind: linear algebra. I know that I did well in the subject, but there were always ideas in the class that made me a little confused. This list includes linear transformations, Markov chains, and working with the transpose of matrices. These caused me some trouble in my classes, and until now I’ve basically ignored them. I didn’t try to forget about them, necessarily, but I also didn’t try to understand these concepts.
Now though, I understand the value of revisiting ideas that gave you trouble. Even more, one should revisit ideas that one is already familiar with. This is important because it will help you remember ideas you may have forgotten or not learned well, helping your mathematical skills in the long run.
If you’re interested in re-examining some ideas from linear algebra, I recommend starting by Grant Sanderson’s new video series on linear algebra. He makes beautiful animated mathematics videos, and they’ve helped me solidify some of my understanding which was a bit hazy in linear algebra beforehand. I also like that they are brief yet still give deep insights into the intuitions behind different linear algebra concepts. I’ve found that this is a good method for me to revisit material because it isn’t as rigorous as the first time around, yet refreshes my brain enough that I can learn some more on the subject.
As science students, many of us dread to even think about the word “repeat”. This word has a certain implication of requiring one to re-do a class, which is something no student wants to do. Therefore, we focus on doing enough to get through a class once, and then not needing to know too much about it anymore. This can be done with both good and mediocre grades. I personally did well in linear algebra (in terms of grades), yet I still did well to revisit concepts in linear algebra. The urge to forget information in favour of new information is strong during our education, which means it’s imperative to go back and look at things you’ve learned a while back in order to keep it fresh.
Don’t do things once and then move on. Make sure you take the time to look back at the material from time to time in order to stay sharp.