For all those little papers scattered across your desk

I study effective study habits and present some advice. How meta.

Effective students

- Study regularly
- Find the study techniques that work for them
- Know their toolboxes and their material
- Know the steps they need to solve their problems

I spent the summer tutoring a student (we’ll call him Pierre) in a Linear Algebra course. I hadn’t done any formal tutoring in some time, so I needed to refresh myself on the mechanics of teaching, encouragement, and studying.

Encouragement is easy: be realistic, set goals, and work towards them. Teaching is only slightly harder with the E.D.G.E. method (explain, demonstrate, guide, enable). The hardest is always the mechanics of studying.

Things started bumpily at first, but Pierre and I developed a routine and finished with a few simple, memorable mantras that guided his study efforts. We’ll know if it paid off when he gets his final grade, but the improvement from exam to exam tells me we did something right.

Not everybody is a STEM major like Pierre and me. In light of that, I will make use of two examples near-and-dear to me: a French literature course, and an advanced Math course. In this way I will be sure to keep my techniques focused and relevant to students.

Alright, let’s dig in: this is your opportunity to learn how to study!

Yes, yes, yes, I know you got through high school by memorizing the material the day before and forgetting it as soon as you walked out the door.

Newsflash, folks: you’re not in Kansas anymore. College isn’t about memorizing material. You need to master it. Most of what you study for your major may not be relevant for your career—learning how to learn will be relevant for your life. For now, though, let’s assume you will need to know the content of these courses.

You are not expected to master an entire semester in a few days. That’s why midterm exams are given. That’s why material is spread across a semester. If you don’t expect to master it in a few days, why try to cram before the final? You’re setting up for failure.

Pierre and I focused on studying regularly (this was aided tremendously by the summer schedule). The goal here is to study just a little bit each week. Every day is too much to ask, in my experience: you have class half the week anyways.

So, tip: every day you don’t have a given class, look at two concepts from that class’s notes. First, pick a concept you’re confident in. Review it and give yourself a high-five—you know that stuff.

Now that your brain is warmed up, go over the second concept—one you don’t know very well. This is the perfect opportunity to identify questions to ask in office hours, problems to research, and areas you need to study.

Pro tip: make a cheatsheet of all the core concepts you need to know before each exam or paper. Even if you can’t actually use it, these sheets will help you prepare for the final as well as the actual exam.

Throughout the semester, I’m expected to read sections of various works for my French literature class. So that’s half the battle right there: the material is constantly in front of me.

But I can still be going over notes, jotting down paper ideas and questions, taking a look at the themes we’ve been discussing, and showing up to class prepared.

In general, reading-heavy classes put the burden on you to keep up with the studying. Just don’t forget that even reading-heavy classes require you to know what you’re reading.

Math courses tend to encourage review via problem sets. This is not enough, just like in the literature case.

Pierre and I were able to make progress because he could identify areas where he was confident (and I would spot check) alongside areas he struggled (and I would tutor).

This may sound unorthodox, but I’m not going to recommend any specific study techniques. I’m here for habits, the meta-side of studying.

In other words, how you study is and should be up to you. Now that you’ve
decided to do a little bit frequently rather than a lot at once, you need to
decide what you’re going to do. Get organized with flash cards, or don’t. Do
*not* copy your friends: what works for them may not work for you. Experiment
and find out how you study. Then improve that process.

As an example, the cheatsheet-per-exam method works incredibly well for STEM and exam-based classes. It helps organize concepts and gets down what you need. Pierre, though, preferred to iterate on that by re-doing lots of example problems. Also a good technique.

In literature courses, I would tend to stick to outline-style studying, where I could outline papers and major themes.

These are personal techniques. Discover yours.

This is a habit that comes from craft and art: in order to succeed, you’ve got to know the tools you’re working with.

What I bring to bear on a problem depends heavily on the problem, and may involve research to find the right tools, but ultimately I can be far more effective at, say, completing an exam question, if I know what tools are relevant. The only way to do that is to know the tools and how to apply them.

This section benefits heavily from example.

Obviously, I’ve got to know French. So that’s my first tool.

The next one is the literature umbrella: I need to know genres, motifs, themes, their applications and intended usages, their common messages.

Then I need to know about the authors, their lives, and how that affected their work. More broadly, I need to understand the period the literature appeared in.

These are my tools (alongside some rhetorical devices). With them in hand, I can craft an analytical essay.

I’ll cut straight to the chase: the tools of math are essentially the following three things:

- First-order logic
- Proof strategies
- The theorems, definitions, lemmas, and techniques of the course

To work in math, you’ve got to understand first-order logic:

- implications,
- conjunctions and disjunctions,
- and universal and existential quantifiers

These are the building blocks of proofs, theorems, and pretty much every other mathematical statement you’ll make. You have to be comfortable manipulating them. Once Pierre refreshed these, the structure of his problem solving became far cleaner.

For proofs, you need these and some strategies. Typically, you’ll use

- direct proofs (use of definitions and theorems)
- proofs by contradiction or contrapositive (there’s that first order logic again)
- proofs by induction

Master these, and you’ll have a better understanding of the shape of a problem.

The rest is simply knowing what tools you have to write a given proof or compute a given property. For that, you need the relevant domain knowledge.

Bonus: get comfortable with set notation. Most of math is essentially sets. Wikipedia has decent a primer.

I talked about what you need to solve problems in the last section. This is the how.

Effectively, you want to know the shape of a problem: many courses’ problems fit into regular patterns for which you can identify a series of goals to accomplish.

These are your steps, should you choose to accept them.

Every paper you write, every paragraph, every sentence, has to accomplish a specific goal. Identify it, and accomplish it.

For most papers, this amounts to outlining. An outline is a blueprint, and with it in hand I find that I can write fluidly without worrying about the organization. It’s been pre-designed. I’m just following the steps.

As I told Pierre, the less thinking I have to do when solving a problem, the better.

We return to proofs: the basic set of steps is

- Identify the assumptions of the statement to prove
- Identify what you would like to conclude
- Use the available bits of knowledge to make progress

The knowledge comes from the theorems, definitions, and assumptions. The rest comes from the problem.

Often, exam proofs are intended to be relatively simple, *if you just stick to
the tools*. You don’t generally have more than one or two pieces of knowledge to
lean on, so use them.

To recap, effective students

- Study regularly
- Find the study techniques that work for them
- Know their toolboxes and their material
- Know the steps they need to solve their problems

Let me know in the comments if you’re interested in the story of how *I* learned
how to study!

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