I found concepts related to relative velocity quite challenging when I first encountered it in a physics course. Because I struggled with this topic, I avoided it. The consequence was that I never gained competence in that area.
This changed when I had to teach these concepts to students.
Many moons ago, I was teaching some courses to technical students. I had about a week to prepare my first lesson on relative velocity. I was well aware that this was an area of weakness for me. So, I knew I had to work. For a few hours each day, I wrestled with the material. Slowly but surely, I gained a better understanding of vectors and associated diagrams.
I worked through countless problems until I had a sense of mastery over the material. I was more or less fluent with the material when I started teaching it. But I warned the students that this was a difficult section in the course. I told them to spend extra time on it. Not many heeded my warning. Students will be students.
If You Want To Understand Something, Teach it
I wasn’t quite able to get the students to take the topic of relative velocity as seriously as I did. But the experience taught me something valuable: When we teach something, we are forced to understand it on a deeper level than when we are merely required to write a few superficial tests on the subject matter.
In tests, one might still get some marks for badly drawn diagrams and basic equations. But when you’re standing in front of a class, you need to understand things from multiple perspectives. You need to understand things on various levels. People can usually tell when you don’t have a deep understanding of something. Avoiding egg on face is a great motivator.
Teachers who cannot dive into the nuances of complex concepts usually lose credibility. “Because I said so”, isn’t a credible explanation. That said, I’ve often witnessed highly competent teachers admit when they don’t know something.
Ask Questions
Having a deeper understanding requires one to ask questions.
We learn better when we ask questions about the material. We learn better when we critically engage with procedures, methods, equations, diagrams and all the rest. Slightly straining ourselves beyond our mental comfort zone is the thing that builds capacity. As a side note, this is also why an education system that strives to make everything trivially easy is so very, very damaging to society as a whole. If everything is trivially easy, no capabilities are acquired. Ever.
Even though this doesn’t apply to all teachers, the job of the teacher is to go one level deeper than the student. Students like to learn procedures; they favour rote memorisation. This has value; there’s a place for that. But this shouldn’t be done mindlessly. And it shouldn’t be done without a clear understanding of why.
If we can ask ourselves questions about the procedures, we can gain more insight. Understanding the why is more valuable than perfect test scores. When we understand the why, we have awareness of when answers are nonsensical—more so than when we merely have formulas memorised.
Self-worth
I’ve noticed that there is a tendency to attach our self-worth to test results. I’ve noticed this when I was a student, and it became even more apparent to me as a teacher. This tendency is destructive.
I’ve often told students that doing badly in tests doesn’t mean that they don’t have the mental capacity to do well. But doing well does require you to understand where you went wrong. If we do not go through the discomfort of evaluating our own work, we impede our own ability to improve.
Over the years, my advice to all students has been this: Stoically pitch up every day and do the work. That’s all. Don’t get attached to ideas of “not smart enough,” or “this is too hard”. Rock up and do the work. Consistently. This is the mindset that yields results.
Final thoughts
One way to build mental capacity over years is to keep learning. Write down ideas. Ask questions. Keep reading. Keep thinking. Test your answers by using different methods. This doesn’t just apply to teachers and students. It applies to everyone.