A lecture can feel perfectly clear while you watch it and still leave you stuck on the first problem an hour later. Following someone else’s argument and producing one yourself are different skills. The habits below are about closing that gap.
Watch with paper and a pencil
Have paper ready before you press play. Write down each definition, the statement of each theorem and every worked example as it happens. Copying by hand is slow, and that is the point. It makes you notice each step instead of letting it slide past.
Keep the matching reference sheet open as well. The calculus reference sheet and the multivariate statistics reference collect the results that come up most, along with the conditions they need. If a lecture leans on matrix facts you have forgotten, the linear algebra refresher goes over them.
Pause before the answer
Whenever a step is set up, pause and try it yourself first. Guess the next line of a derivation. Finish the example before you see how it is done. You will often be wrong, and that is fine. A wrong guess you then correct tends to stay with you longer than a right answer you only watched.
When an example is done, rewrite it with different numbers and solve it without the video. If you can’t, you have found the exact part worth watching again.
The interactive tools work the same way. Before you compute a derivative, predict where the slope is zero or negative and then check with the tangent line explorer. Before you read a covariance matrix, guess what the cloud of points should look like and test it in the covariance explorer.
When you get stuck
Rewind to the last point you are sure you understood, not to the start of the video. Watch forward from there until you lose the thread, then write down as precisely as you can what you don’t follow. “I don’t see why the second term goes to zero as ” is something you can work on. “I don’t get this” is not.
Often the real gap is further back, in an algebra step or a definition you skimmed the first time. Look that up, then return to the lecture.
After each video
Close the video and write a three line summary from memory. Cover the main idea, the key formula or method, and one example that uses it. Only then check your notes. Whatever you left out is what to look at again.
Then do some problems on your own. Watching someone solve a problem is not practice at solving it. Start with problems close to the worked examples and move on to ones that look a little different, since those are the ones that tell you if you understood the idea or only memorized the pattern.
Come back to it later
Quiz yourself a day later and again about a week later. Keep it short. Write the main result from memory, or redo one example on a blank page without looking. Pulling something out of memory, even when it takes effort, makes it stick better than rereading your notes does. Spreading those attempts over several days also works better than packing them into one long evening. Both effects are well supported by research on learning.
Keep a running list of the mistakes you tend to make. Dropped minus signs, a forgotten chain rule factor, dividing by something that might be zero, writing when you meant . Most people repeat the same handful of errors, and once they are written down they are much easier to catch. Read the list before you start a problem set or a test.
Playback speed
Speeding up is fine when you are reviewing something you already understand. For new material, normal speed or even slower usually works better, however slow the speaker seems. The time you save by rushing tends to disappear the first time you have to rewind. If a stretch of the lecture covers things you already know well, skip ahead rather than playing everything fast.