It’s the end of term, and your grade comes down to just one score: the final exam. On top of that, you’ve got a whole term’s worth of material to review! Fret not — we’ve all been there. Here’s how to make the best of it!
Organize your materials
The first step to any kind of studying is determining what to study! Especially if you’re under time pressure, you’ll want to allocate your time as efficiently as possible. Remember, work smarter — not harder!
During my undergraduate career, I often employed the following steps to set myself up for success when preparing for finals:
- Compose a comprehensive list of all topics covered. You can probably find a starting point from your syllabus or from your own class notes! Bonus points if you add some sub-lists, like “Delta-Epsilon Proof” and “Quotient Rule” under “Derivatives.”
- Draw out the connections between these topics. The reason courses are taught in a specific order is often to elucidate the connections between different topics. It’s extra helpful to draw causal connections that show what topics are the basis for others.
- Organize past materials into your diagram. It’s useful to know how problems, lectures, and readings you’ve already seen relate to the bigger concepts on your diagram. At this step, you don’t want to get caught up in “How do I do that problem again?” or “What did he say during that lecture?” and instead want to just know that the problems and materials exist.
Re-evaluating your mistakes
Now that you’re organized, you’re ready to zoom into any problem areas! Even if you’ve got your diagram down, it’s sometimes hard to see where to begin.
This is when you need to confront your mistakes. The biggest difference between self-studying a course and taking it in school or at a university is the feedback. The mistakes you made are often the most valuable learning material you have to work with! The best thing you can do for yourself is to make sure you never repeat a mistake.
One systematic way to address mistakes is to categorize them, and thereby prioritize them. From lowest to highest priority:
- The silly mistake. This is your classic “dropped a minus sign” or “miswrote the significant figures” type error that comes from carelessness, akin to a typo.
- The logical mistake. This is the type of mistake you make from logical missteps, like computing permutations when you mean to compute combinations or messing up the determinant of a matrix.
- The conceptual mistake. This top-priority mistake indicates a deeper confusion that will certainly result in more mistakes if not addressed! This is the kind of problem for which “didn’t even know where to start” or “thought you did it right, but it was much more complicated.”
With your mistakes categorized, you’re ready to revisit the materials you’ve conveniently organized in the first step, using the priority you developed here to guide your efforts.
Pulling it all together
The distribution of your mistake types is going to be a good indicator of what topics you need to work on, and how hard you’ll need to work going forward; meanwhile, your diagram will help indicate what foundational concepts you need to tackle first.
Take a look at where most of your conceptual and logical mistakes are centered. Within these topics, you’ll want to go in order of most basic to most applied by tracing back which concepts depend on which others. If you have a basic concept (probably from early in the course) that you have a good number of mistakes in, this will be the topic you want to focus your attention on. What kind of attention, you might ask? Well, it depends on the types of mistakes you’ve made here.
Having mostly silly mistakes means you’ll probably be alright, given you pay extra attention to checking your work. Having some logical mistakes means you should redo some practice problems to make sure all the technical pieces of your problem-solving are in good shape. In general, practicing will help make both the mechanical steps of problem-solving and the concepts clearer. Since you’ve already listed out which previous problems correspond to every topic, you’ve set yourself up with a list of practice problems to redo, no matter what concept you start with!
If you find you’re having mostly conceptual problems, it may be time to seek outside help — this type of mistake is hard to resolve alone! To combat conceptual misunderstandings, you will have to re-learn the material before you practice. This is when rewatching lectures or reading the textbook before you try to redo any problems will come in handy.
Hopefully having a roadmap like this can help you streamline your studying procedure. The biggest takeaway is to use your time wisely if you’re under some pressure. It will always be worthwhile to learn something you’re struggling with concretely rather than to sweep it under the rug. Good luck!