Book contents
- Frontmatter
- Contents
- About these Study Guides
- This Guide and Mathematics Competitions
- This Guide and the Craft of Solving Problems
- This Guide and Mathematics Content: Trigonometry
- For Educators: This Guide and the Common Core State Standards
- Part I: Trigonometry
- Part II: Solutions
- Solutions
- Appendix: Ten Problem-Solving Strategies
Appendix: Ten Problem-Solving Strategies
- Frontmatter
- Contents
- About these Study Guides
- This Guide and Mathematics Competitions
- This Guide and the Craft of Solving Problems
- This Guide and Mathematics Content: Trigonometry
- For Educators: This Guide and the Common Core State Standards
- Part I: Trigonometry
- Part II: Solutions
- Solutions
- Appendix: Ten Problem-Solving Strategies
Summary
Here, in brief, are the ten problem solving strategies that apply particularly well to solving competition mathematics problems. Please go to www.maa.org/ci for full explanations of these strategies and further practice problems.
Remember that these strategies come after conducting the first, and most important, step in problem solving:
STEP 1 : Read the question, have an emotional reaction to it, take a deep breath, and then reread the question.
The strategies:
STRATEGY 1: Engage in Successful Flailing
Often one can often identify to which topic a challenge belongs—this question is about right triangles, or this question is about repeating decimals—but still have no clue as to how to start on the challenge. The thing to do then is to engage in direct flailing.
To do this, think about everything you know about right triangles or about repeating decimals. Read the question out loud and then describe it again in different words. Draw a picture. Try an example with actual numbers. Mark something on the diagram. And so on. Do everything you can think of that is relevant to the content at hand. In doing so, a step forward with the problem often emerges.
See the FEATURED PROBLEMS of sections 1 and 13 of this guide to see this strategy in action (as well as www.maa.org/ci).
STRATEGY 2: Do Something!
Innovation in research and business is not easy. Many times one is stymied and not even able to conceive of any next step to take. This can happen in mathematics problem solving too.
Perhaps the most powerful of problem solving techniques, in mathematics and in life, is to simply DO SOMETHING, no matter how irrelevant or unhelpful it may seem. Unblock the emotional or intellectual impasse by writing something—most anything—on the page. Turn the diagram upsidedown and shade in a feature that now stands out to you. Underline some words in the question statement. Just do something!
See the FEATURED PROBLEMS of sections 10 and 17 of this guide to see this strategy in action (as well as www.maa.org/ci).
STRATEGY 3: Engage inWishful Thinking
As I tell my students, if there is something in life you want, make it happen.
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- Information
- TrigonometryA Clever Study Guide, pp. 207 - 211Publisher: Mathematical Association of AmericaPrint publication year: 2015