Success in mathematics—however you wish to define it—comes from a strong sense of self-confidence: the confidence to acknowledge one's emotions and to calm them down, the confidence to pause over ideas and come to educated guesses or conclusions, the confidence to rely on one's wits to navigate through unfamiliar terrain, the confidence to choose understanding over impulsive rote doing, and the confidence to persevere.

Success and joy in science, business, and in life doesn't come from programmed responses to pre-set situations. It comes from agile and adaptive thinking coupled with reflection, assessment, and further adaptation.

Students—and adults too—are often under the impression that one should simply be able to leap into a mathematics challenge and make instant progress of some kind. This not how mathematics works! It is okay to fumble, and flail, and to try out ideas that turn out not help in the end. In fact, this is the problem-solving process and making multiple false starts should not at all be dismissed! (Think of how we solve problems in everyday life.)

It is also a natural part of the problem-solving process to react to a problem.

“This looks scary.”

“This looks fun.”

“I don't have a clue what the question is even asking!”

“Wow. Weird! Could that really be true?”

“Who cares?”

“I don't get it.”

“Is this too easy? I am suspicious.”

We are each human, and the first step to solving a problem is to come to terms with our emotional reaction to it—especially if that reaction is one of being overwhelmed. Step 1 to problem-solving mentioned in the previous section in vital.

Once we have nerves in check, at least to some degree, there are a number of techniques one could try in order to make some progress with the problem.

The ten strategies we briefly outline in the appendix are discussed in full detail on the MAA's CURRICULUM INSPIRATIONS webpage, www.maa.org/ci. There you will find essays and videos explaining each technique in full, with worked examples and slews of further practice examples and their solutions.