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Taking Ownership Over Your Own Misunderstanding

Earlier this year I set myself a goal—a concrete challenge I wished to take on. Like a lot of us at ESM, I am often trying to learn new and exciting subjects and this was yet another instance of that. I decided to finally put some effort into learning a bit of General Relativity, beyond just the bits and pieces I picked up in my undergrad years and from popular science exposes.

So I did the normal thing and ordered a textbook to start my study. I knew that there would be stumbling blocks along the way, mostly in the mathematical background that is necessary, but it was still a bit of a shock how quickly those stumbling blocks showed themselves. I very quickly realized I needed another textbook, a math textbook, if I were to truly understand the physics. So I bought that soon after. Then, again, I realized that even this textbook was a bit short of what I needed, so I decided I would have to consult additional resources. And so it has been going. 

The last two months have been a succession of “two steps forward, one step backward” as I have had to deviate from my study in order to fill some prerequisite material in order to continue. Which brings me here.

I wanted to share some thoughts on how this process can be tackled efficiently. 

The first thing I think we all can do when this happens to us, whether it’s our own self-study or the distance learning many students are going through these days, is take a deep breath and fight that creeping sense of discouragement. It’s all too easy to become deflated when you’re trying to understand a math or science concept, but nothing is gained by this, as we all know. I’ve found it very helpful to step away for a bit (a few minutes, an hour, a day perhaps) and come back with a bit more optimism and a can-do attitude. 

Once you’re back at it, it’s time to create a plan. Let’s map out a pathway forward—one that’s sensible and well-defined. It makes no sense to charge ahead and run right back into the wall over and over. So map out the block and get a lay of the land. What EXACTLY are we struggling with? Is it the complexity of the algebra in a given formula? The fact that the topic at hand doesn’t seem to be tangible enough? Are we missing a key piece of the puzzle that the teacher is assuming we already have? Is there confusing language in the material? Any one of these issues may be hidden if we’re not willing to dig a bit. And if it’s hidden, we may not be able to truly ever tackle it.

In order to aid in this, I’ve found it very useful to have a note(s) devoted entirely to the issue at hand, separate from any highlights and/or annotations I may be making in the text or worksheet. This is merely there to collect/catalog my thoughts on what I need to look up. I’ll list topics, key terms, formulas, and anything else I feel I’m not fully confident in. And every day I will try and check one of these off. Of course, any one of these may require its own sub-note! And those sub-notes may require their own sub-notes, and on and on. Because of this, I find a software program like Evernote to be the most valuable to me: it allows me an almost endless ability to categorize and create hierarchies for my notes. Of course, if you prefer paper notebooks, post-it notes, or other physical mediums, they will work just great as well!

So yes, it can be a lot. I myself have notes upon notes already generated over the last couple of months and I’m constantly making detours as I progress. It’s far from the linear process I had hoped it to be! But there are major benefits if you can adopt a process similar to this.

  1. It forces you to truly recognize the shortcomings of your understanding.
  2. It allows for actionable steps to be taken.
  3. It encourages you to push your understanding beyond the surface level.
  4. As you progress, you can easily point out the improvements by cross-referencing your notes.
  5. Building these skills early on will pay dividends in college when the material (whether math or science) becomes a bit more abstract and not as amenable to brute force methods of learning.

Is this a highly detailed recipe for success? Of course not. Think of it as more of a rough guideline. But that’s part of the beauty: you can tailor the fine details to your liking.

The bottom-line is that we all struggle with things at times, but if we can tease apart the actual difficulties we can then begin to construct plausible solutions. Stay encouraged and enjoy the process, too. You’ll find the learning process more enjoyable if you’re actively engaged in it, instead of just running on auto-pilot!