You are asked to turn in each class period a  3"x 5" index card with what you consider to be the most important mathematical fact or proof strategy stated during the previous class period. (Of course, nothing needs to be turned in the class period following an exam.) A record will be kept of whether or not you turn in a card, and after the first few cards are checked and returned, a few points (probably 2) will be assigned for each card. Please read the following guidelines on how to prepare these cards.

Purpose:

• So I can see what you got out of the class;
• So I can correct any misapprehensions that you may have received;
• So you have a summary of important facts to use in studying for exams.
• The index cards are also used as a way of keeping track of attendance, although this is not their primary purpose. (See the comments on attendance in the Course Policy and the comments below on the use of index cards for this purpose.)

What to say:

• What you write on your card should be a complete, grammatically correct English or mathematical sentence.

• Example of a  “mathematical fact”:  Suppose a portion of class period was seriously devoted to a discussion of the mathematical fact that  2 + 2 = 4.  Then at the beginning of the following class period, you could turn in an index card which contains this mathematical fact:

  2 + 2 = 4.

  You don't have to say  “We discussed the fact that ... ”  or  “I learned that ... ”;  just record the fact.

• Counterexample of a  “mathematical fact”:  Suppose a portion of a class period was seriously devoted to a discussion of the mathematical fact that  2 + 2 = 4.  You should not turn in a card saying:

  We discussed how to add 2 and 2.

  This is not a mathematical fact!

• Counterexample of a  “mathematical fact”:  Of course, the preceding was a fictitious example. You already know, and are assumed to know, that  2 + 2 = 4;.  this is not part of the content of Math 323. So suppose that during a class period we happen to mention, in the course of discussing something else, the mathematical fact that  2 + 2 = 4.  Then it would NOT be appropriate to turn in an index card which contains this mathematical fact:

  2 + 2 = 4.

  This is (we hope) NOT one of the most important mathematical facts, from the point of view of Math 323, stated during the class period.

• By a “proof strategy”, I am referring to any of the numerous suggestions which are made throughout the semester regarding how to present your work and how not to present your work -- in particular, how to do proofs and how not to do proofs. For example, I might discuss the fact that when you are writing a proof, you should be sure to distinguish for your reader between the statement that you are trying to prove and the proof itself. This “strategy” could be recorded on your index card. “Strategies” can also be negative: Do NOT do something in a proof.
  
  Again, you don't have to say  “We discussed ... ”  or  “I learned that ... ”;  just record the strategy.

Always keep in mind when writing facts on your index cards that one of the purposes is to give you a summary of important facts to use when studying for exams. This should be a guide in deciding what to write down on the index card. (You might even use more than one index card per class and then turn in just one!)

Use as attendance record:

A secondary use of the index cards is as an approximate attendance record. If you do NOT turn in an index card on a day when one should be turned in, that may be used as evidence that you were not in class on that day. On the other hand, since a student can give an index card to someone else to turn in, the fact that an index card has been turned in is not taken as evidence of attendance on that day.

Last modified Jan 12, 2008

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