Trigonometry: A Clever Study Guide
The Mathematical Association of America’s American Mathematics Competitions’ website, www.maa.org/math-competitions, announces loud and clear:
Teachers and schools can benefit from the chance to challenge students with interesting mathematical questions that are aligned with curriculum standards at all levels of difficulty.
For over six decades dedicated and clever folk of theMAAhave been creating and collating marvelous, stand-alone mathematical tidbits and sharing them with the world of students and teachers through mathematics competitions.
Each question devised serves as a portal for deep mathematical mulling and exploration. Each is an invitation to revel in the mathematical experience.
And more! In bringing together all the questions that link to one topic a coherent mathematical landscape, ripe for a guided journey of study, emerges. The goal of this series is to showcase the landscapes that lie within the MAA’s competition resources and to invite students, teachers, and all life-long learners, to engage in the mathematical explorations they invite.
Learners will not only deepen their understanding of curriculum topics, but also gain the confidence to play with ideas and work to become agile intellectual thinkers.
I was recently asked by some fellow mathematics educators what my greatest wish is for our next generation of students. I responded: . . . a personal sense of curiosity coupled with the confidence towonder, explore, try, get it wrong, flail, go on tangents, make connections, be flummoxed, try some more, wait for epiphanies, lay groundwork for epiphanies, go down false leads, find moments of success nonetheless, savor the “ahas,” revel in success, and yearn for more.
Our complex society demands of our next generation not only mastery of quantitative skills, but also the confidence to ask new questions, to innovate, and to succeed. Innovation comes only from bending and pushing ideas and being willing to flail. One must rely on one’s wits and on one’s common sense. And one must persevere. Relying on memorized answers to previously asked—and answered —questions does not push the frontiers of business research and science research.
The MAA competition resources provide today’s mathematics thinkers, teachers, and doers:
- the opportunity to learn and to teach problem-solving, and
- the opportunity to review the curriculum from the perspective of understanding and clever thinking, letting go of memorization and rote doing.
Each of these study guides
- runs through the entire standard curriculum content of a particular mathematics topic from a sophisticated and mathematically honest point of view,
- illustrates in concrete ways howto implement problem-solving strategies for problems related to the particular mathematics topic, and
- provides a slew of practice problems from the MAA competition resources along with their solutions.
As such, these guides invite you to
- review and deeply understand mathematics topics,
- practice problem-solving,
- gain incredible intellectual confidence,
and, above all,
- to enjoy mathematics!
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