"The List"

To make sure that you are retaining the material you learn in this course, many tests/quizzes will contain material from earlier in the course. To help you achieve well on these tests, and to eliminate classtime spent reviewing old topics, you will be required to do the following. Think of The List as your own personal Cliffs Notes for the course. This idea is not new. Noted physicist Kip Thorne [LA Times Article] used this technique during his studies.

"[As an undergraduate] ... I started identifying the important ideas that were being taught and writing my own analyses of where they came from and how they related to each other. So instead of having textbooks with some underlining as my major source of information, I had my own summaries. I think this process enabled me to understand things more deeply than other people and allowed me to make connections that they didn't see."

The Daily Requirement

Each evening, in addition to your assigned homework, your implied homework is to maintain a running list of ideas that were taught during the day. This list must include (but should NOT be segregated into these categories; see Grading below):

Connections (how was a topic introduced; any memory gimmicks or cute stuff the teacher does; how does it relate to other math you know, why is something true; making your own new connections is most valuable of all)
Definitions (e.g., what is the slope of a line)
Theorems and Rules (e.g., Pythagorean theorem; x ^a x ^b = x ^a+b )
Problem strategies (e.g., to solve a quadratic equation, usually you want to "solve for 0" first)

Non-trivial examples of each item, e.g.,

how to compute a specific slope,
x ² x = x ³

how to use the Pythagorean theorem,
x ² + 2x = -1 might be solved by first writing it as x ² + 2x + 1 = 0

2 more sample problems with answers, but not the steps to arrive at the answer (that should be covered under examples above). These problems should not be easy ones, as they will be used for studying for tests.

Appendix to The List: The Top Ten. Keep track of the problems you found difficult in the homework, quizzes and tests. If the Top Ten needs to be longer than 10 problems, so be it. These should always be your highest priority in studying.

Studying for a Quiz or Test

When you study for a test, begin several days before the test.

First review your List and create a Summary List of theorems, definitions, rules and problem strategies that are not yet at your immediate recall. The emphasis should be on new material, but since you can be tested on anything covered in the course, it must include the important items from prior material as well.
Then, each day or 1/2 day, review your Summary List and create a Sublist of items not yet memorized. Also review the original List to ensure nothing has fallen out of immediate recall. Hopefully by the time the test arrives, you will have no items on your last sublist.
Studying for a test should also include doing homework problems again (some from your List, most from your homework papers, with emphasis on your "Top Ten"), and doing them for speed as much as accuracy.

Grading

For grading purposes, you should organize your List by section number of the chapter being studied. It will primarily be graded for completeness. To make sure you are creating this List, you will be asked to turn it in from time to time for grading purposes, with at least 1 day notice. The best media for the List is probably looseleaf paper; do NOT use a thick, multi-subject spiral-bound book for this List.

Most of all...

This is NOT an exercise in handwriting; THINK as you do it.
Don't view it as an assignment, think of it as a tool.
Do NOT split The List among friends to complete.

Make it meaningful to you.
Make it complete.
Make it visually interesting [sample] so your eyes can find ideas very quickly.