Basic Tips for Studying

Make sure to have read all of the material before discussing it in class.
While reading, make use of some of the Prelude strategies below to help better understand the material.
The Prelude strategies should also be used to determine what portions of the material you do not understand.
Bring an "outline" of the material to class with at least 3 questions about issues that seem unclear to you.
Never leave class without making sure your "3 questions" are answered.
Take notes intelligently: use pictures, symbols, personal shorthand. You cannot write as fast as the professor can talk and the professor cannot speak as rapidly as you can think.
As soon as possible after class, rewrite your notes in as great of detail as possible.
Review the meta-strategies from your Prelude classes (see below) and use any that are appropriate for your learning style.

It is worth your time to occasionally look through the following list of specific techniques and strategies used in the Prelude exercises. for analyzing readings.

Gathering Information

Finding illustrative quotations (LeGuin, Lorde, Snyder, Wright/West)

Identifying images (Dove, LeGuin, Lorde, Snyder): Has the author provided any physical interpretation or other image to illustrate the concepts?

Identifying types of statements: authoritative, persuasive, etc. (Bristow,ed., Gelernter): Which statements of the author are based more on opinion than on logical deduction?

Listening carefully and recording details (Block, Lecture): This is the basic advice of all note-taking.

Making lists (LeGuin, Dove, Gelernter): If you can list the facts supporting it you are most of the way to understanding a mathematical argument.

Marking, and then defining, unfamiliar words/phrases (Block, ed., Bristow,ed., Camus, Class preparation exercise, Claus-McGahan, Cohen/Hogan, Gelernter, Hofrichter, Lecture, Wright/West): Authors of mathematical texts go out of their way to specifically define all pertinent words and phrases. If you don't know these definitions you will never understand the concepts.
Observation, identifying significant elements (Claus-McGahan, Hofrichter, Pennies, Poverty and Income, Smith): Look carefully at all of the figures and pictures as well as the exposition.

Paraphrasing a reading (Bristow, ed., Camus, Class preparation exercise, Gelernter, Hofrichter, Smith, VanEnkevort, ed.): If you can paraphrase the general argument in a discussion with a study group, then you will really understand the material.
Reading aloud (Bristow, ed., Camus, Cohen/Hogan, Dove, Gelernter, LeGuin, Lorde, short stories, Snyder) Rereading (Camus, Cohen/Hogan, Dove, Gelernter, LeGuin, Lorde, short stories, Snyder): Technical material requires at least three readings. Two of them should be slow and careful rather than skimming.
Comparing and contrasting (Block, ed., Claus-McGahan, Hofrichter): Find another source and see how they develop the ideas.

Analyzing visual material (Claus-McGahan, Cohen/Hogan, Smith)
Sketching from observation (Claus-McGahan): Drawing pictures to illustrate mathematical concepts and problems is always a good idea.

Reasoning

Analyzing an argument (Bristow, ed., Camus, Cohen/Hogan, Gelernter, Smith, Wright/West): It is not enough to just be able to "follow the argument". You need to spend some time determining how the individual logical steps fit together.

Constructing an assertion or thesis (Dove, Gelernter, Hanson, ed., LeGuin, Revision, short stories)
Constructing evidence (Block, ed., short stories, Smith, VanEnkevort) Developing hypotheses (Claus-McGahan, Hanson, ed., Smith, Snyder, VanEnkevort, Wright/West: These three are appropriate for problem solving since they point to methods for "Understanding the Problem" (see Polya's 4 Steps.)


Drawing (Claus-McGahan, Cohen/Hogan, Smith)
Looking for patterns (Dove, LeGuin, Lorde, Revision, Smith, Snyder, VanEnkevort, Wright/West)
Reasoning deductively (Claus-McGahan, Smith, VanEnkevort)
Sorting images (Dove, LeGuin, Lorde, Smith, ,Snyder)
Relating the specific to the general (Claus-McGahan, Hanson, ed., Revision): These are all standard techniques in mathematical reading and problem solving.

Small group discussion of questions (Bristow, ed.): Always a good idea -- provided everyone has already done their preparation. Otherwise it is a waste of time for those who are prepared.

Writing a paragraph about authors' assumptions (Bristow, ed., Gelernter, Hofrichter)
Evaluating questions for pertinence (Camus, Cohen/Hogan)
Differentiating evidence and interpretation (Bristow, ed., Poverty and Income, Wright/West)
Distinguishing between types of statements (Bristow, ed., Gelernter, short stories, Poverty and Income, Wright/West)

Generating/Creative thinking

Brainstorming (Bristow, Ed., Camus, Gelernter, Smith, Snyder, Wright/West)
Discussion/speculation of answers to questions (Bristow, ed., Poverty and Income)
Free Association (Dove)
Generating assertions (Dove, Hanson, ed., short stories)
Generating questions (Camus, Cohen/Hogan)
Interpreting (Bristow, ed., LeGuin, Smith, Poverty and Income, VanEnkevort)
Writing as a way of learning (Camus, Cohen/Hogan, Dove, Greene, Lorde, Gelernter, Share): These are useful methods for coming up with the techniques for solving difficult problems. After you have generated some approaches be sure to carefully WRITE your solution. If you can honestly convince yourself in writing then it is probably correct.

List parts of an argument that would be strengthened by additional authoritative testimony (Gelernter)
Taking different points of view (Gelernter, Poverty and Income)

Revising/Responding

Group discussion (Bristow, ed., Camus, Class preparation exercise, Claus-McGahan, Greene, Hanson, ed., Hofrichter, Lecture, LeGuin, Lorde, Gelernter, Poverty and Income, Revision, Share, short stories)
Presenting to a group (Hofrichter, Lorde)
Reconsidering one's responses (Block, ed., Claus-McGahan, Poverty and Income, short stories, Smith, Wright/West)
Revising writing (LeGuin, Revision, short stories, Wright/West): First drafts are not good enough. You should always revise your presentation.

Writing emotional and intellectual responses (Block, ed., Greene, Lorde, Gelernter, Share, Wright/West)