In this talk, an look inside the problem development process will be presented from one of the current Co-Editor's-in-Chief of the MAA AMC 10/12 Contest. What makes a problem interesting for a broad audience of students participating in the contest will be discussed, and a few favorite problems will be shared.
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Drawing from my experience in crafting problems for various mathematical competitions, including the AMC, I will share examples of some of the most beautiful and elegant problems I've encountered. These examples will illustrate the blend of creativity and rigor that goes into problem creation. We will explore the art behind writing competition questions, discussing the key elements that make a problem both challenging and engaging. Additionally, we'll address the broader process of designing contest tests, ensuring a balanced and comprehensive assessment of participants' skills.
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A lack of personal insight regarding a problem from the 2019 College of Charleston Math Meet Level III Written Test (#25: about the area illuminated by a spotlight) led to an encounter with the spheres of the 19th century French mathematician Germinal Dandelin. In this talk, we learn about Dandelin spheres and how they could be used to solve the CofC problem (and maybe also see a sketch of a sphere-less solution).
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In this talk we will share some specific problems from MAA competitions (pitched at middle- and high-school students), and we will show how these problems can be deconstructed and adapted to create engaging content for undergraduate students that promote active learning by intentionally addressing communication and problem-solving standards. Topics will include elementary number theory, combinatorics and probability in the context of an introductory course in discrete mathematics.
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