How to Take Notes

You make be accustomed to a model of learning in which you were expected to sit quietly, copy down what the instructor wrote on the board or overhead, then go and "review" your notes at home.

Decades of research in teaching and learning have shown that this is one of the least effective methods of learning. In particular, very little learning takes place in the "lectures".

As you have experienced, we are using a model of learning which involves much more active participation in the classroom. The primary activity during class is NOT copying down information - it is transforming, working with, making sense of, and personalizing information that you already have (from prior learning, and from reading through material in the textbook and other sources). This happens through individual and team problem solving and discussion.

Taking notes

There is still a place for note-taking - both in the classroom and at home.

First, because you will need to start with some information, you will be assigned reading almost every day. See here for reading assignments. This reading should be a very active process. See How To Read Mathematics. By its very nature, it is impossible to read mathematics in this way without writing some mathematics, and this writing should form part of your notes.

One very important thing that these notes should contain is questions - things that you are confused about, not certain of, don't understand, don't see the point of, can't explain in your own words. Keep a list of these handy, and refer to them often. Ask these questions of people in your team, ask them in class, in the discussion forums, via e-mailing your instructor; ask your TAs, or talk to your instructor after class or during office hours. It's OK to keep asking the same question (try rephrasing it!) until you feel your understanding shift.

Don't be surprised if the answer to your question is another question, or an attempt to have you work through an example or problem

Make summaries

You should also make summaries - lots of summaries. Things to summarize:

Your reading - key points, relationships, examples (and of course, questions)

class "lectures" and activities. An excellent way to do this is via a Wiki page, in collaboration with your team.

each section and chapter

For section and chapter summaries - start with a blank page and write the key concepts, definitions, theorems, examples without looking at the text or other notes. Then go back to the text, online lecture notes, and other materials, and check if you have missed anything important. If so, put this on your list of things to read in more detail.

You'll probably find that you want to re-work your summaries as your understanding of a topic deepens and gathers more connections.

Learning objectives

Have a look at the learning objectives for the course. The main learning objectives are presented in each day's "lecture" notes, and will be collected on the course wiki. The learning objectives describe what you will be able to do to show that you have learned something. When reviewing these, actually "do" what you are supposed to be able to do. Write the definitions, write a short explanation, give an example function or two...

In doing this, you will be writing notes - essentially your own personalized version of the textbook. Since it came from your experience, you will find you remember it much more vividly than something you 'heard' in a lecture or skimmed over in a book.

Here's a little hint. Most mathematicians haven't memorized (learned by rote, the way you would memorize a verse of Shakespeare) most of the definitions, theorems, formulas, and other things they 'know'. They understand these things as concepts, and will construct appropriate versions of these if and when they are needed.