At our university, as at many universities around the world, students are now very suddenly studying remotely, separated from others. Studying remotely is a new challenge, but the habits you learn to overcome this challenge will be helpful in all your future courses, because it teaches independence and dedication.
THE GOLDEN TIP: Do a little every day. Schedule regular worktime every day, either to work through the most recent daily post, to review material, or to attend Zoom or watch videos. This way you’ll stay on top of deadlines, and you won’t wear out your brain. Learning math is like learning a language or training for a marathon: you need to do it regularly, in moderate doses. (This is so much less stressful than cramming, too.)
- Learn to recognize your mental state: Where are you on the scale from Sharp-Witted-and-Energetic to Tired-and-Distracted? Save math for when you are at the top of your game (maybe that’s first thing in the morning, or maybe it’s late evening, or something else). If you find yourself reading the same sentence over and over, quit and come back to it later. You can use that time to eat, drink water, go for a walk, exercise or otherwise take care of yourself to regain your good mental state. I speak from long experience.
- Make all your work active. That means give yourself mental exercises while you read, break from reading to work out your own invented examples, ask yourself questions and write them down explicitly and carefully for later to ask me or your study mates, do exercises, close your eyes and re-explain what you just learned, etc. Math is a performance art. Passing your eyes over the page simply doesn’t count. Read more about active reading here.
- Communicate mathematics: find study-mates or other support. You’re disconnected now, so make it a habit to come to office hour or to meet with study mates on Zoom. You need a place to bounce ideas around, and explaining something to a classmate working on the same things is a great way to test if you understand things. Math is a community effort and it is about communication, so find ways to engage in active communication. Talking about something is a great way to process it analytically, and it will help you learn and rout out hidden misunderstandings.
- Keep a list of questions. Write down (very carefully and precisely) the questions that come up while you are studying, so you have them ready when you get a chance to meet with myself or other students on Zoom. Even if you never ask it, the act of writing a question out in all its detail will often shed light on things. You can also help keep these questions floating in your consciousness by paying them their due in this way, and then your brain may work on them in the shower or while you sleep.
- Set bite-sized tasks. Don’t approach your work as a giant mountain. Set yourself small goals for your hour of work, for example, for my Math 2001 class, that means working through the daily post, preparing one badge, doing a really good job on one proof.
- Revisit things. When you have a few minutes on a walk or similar, think about the big picture and what you’ve learned, or ponder questions about where to go from here. Or just go over and remind yourself of key definitions and strategies from memory. This helps put things in context and keep them current in your mind.
- Take care of yourself. Get enough sleep, in particular. Getting enough sleep improves academic performance significantly in scientific studies, and perhaps more importantly, it boosts your immune system and makes you live longer too. Here’s a TED talk about that. We’re all in a stressful situation now, and your health and safety comes first. Let your professor know if you need help.