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From the Introduction of Exeter Math 2

You should approach each problem as an exploration. Reading each question carefully is essential, especially since definitions, highlighted in italics, are routinely inserted into the problem texts. It is important to make accurate diagrams whenever appropriate. Useful strategies to keep in mind are: create an easier problem, guess and check, work backwards, and recall a similar problem. It is important that you work on each problem when assigned, since the questions you may have about a problem will likely motivate class discussion the next day.

Problem-solving requires persistence as much as it requires ingenuity. When you get stuck, or solve a problem incorrectly, back up and start over. Keep in mind that you’re probably not the only one who is stuck, and that may even include your teacher. If you have taken the time to think about a problem, you should bring to class a written record of your efforts, not just a blank space in your notebook. The methods that you use to solve a problem, the corrections that you make in your approach, the means by which you test the validity of your solutions, and your ability to communicate ideas are just as important as getting the correct answer.

Getting help is an integral part of staying on top of the math. It can be rather frustrating to be lost and feel you have nowhere to turn. There are a few tricks of the trade however, which ensure your “safety.” The very first place to turn for help should be your teacher. Getting help from your teacher before school, after school, during common time, or during study hall, is the first and most reliable source to turn to, for extra help.

Remember! Teachers have their own style of teaching, fitted to their philosophy of the subject they teach. Teachers vary at all levels: they grade differently, assess your knowledge differently, teach differently, and go over homework differently. They offer help differently, too. This simply means that it is essential that you be prepared to adapt to a particular teaching style. You must learn to be flexible to teaching styles and even your teacher’s personality.

How to Read Mathematics

I think this goes along nicely with the 15 Minute Rule and the Threshold Principle. If you just read over all my solutions and play with the applets without being engaged in what you are doing, you will get very little out of this wiki.

Mathematics says a lot with a little. The reader must participate. At every stage, he/she must decide whether or not the idea being presented is clear. Ask yourself these questions:

  • Why is this idea true?
  • Do I really believe it?
  • Could I convince someone else that it is true?
  • Why didn't the author use a different argument?
  • Do I have a better argument or method of explaining the idea?
  • Why didn't the author explain it the way that I understand it?
  • Is my way wrong?
  • Do I really get the idea?
  • Am I missing some subtlety?
  • Did this author miss a subtlety?
  • If I can't understand the point, perhaps I can understand a similar but simpler idea?
  • Which simpler idea?
  • Is it really necessary to understand this idea?
  • Can I accept this point without understanding the details of why it is true?
  • Will my understanding of the whole story suffer from not understanding why the point is true?

Putting too little effort into this participation is like reading a novel without concentrating. After half an hour, you wake up to realize the pages have turned, but you have been daydreaming and don’t remember a thing you read.

The 15 Minute Rule

If you get stuck on something promise to give yourself another fifteen minutes of complete focus. If you can’t solve your problem by that point, take a short break. Giving yourself less than fifteen minutes means you lack the persistence necessary to learn. But creating space between yourself and a problem can renew your creative energies towards solving it.