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Many talented young problem solvers can find their first math circle visits challenging because they simply haven’t been exposed to some of the concepts and tools of discrete mathematics.  In the US many of these concepts are reserved for “university level” mathematics but it has been proven that these ideas can be well understood and applied by very young students.  The students who add these concepts to their toolbox will have much more success in math circles and math contests as well as a great advantage going on to university.

To help fill this void, the good people at IMACS, creators of the popular eIMACS courses, have launched a series of short and focused online courses under the title of Elements of Mathematics: Foundations.  The first course in this series, Operational Systems, focuses on the very important concept of modular arithmetic and is free for students who register before January 1, 2013.

This course covers modular arithmetic using secret codes and online games. Learn about operational systems and their properties (commutativity, associativity, neutral elements, invertibility) by building interactive machines and evaluating non-numeric operations. Get a solid introduction to the concepts of least common multiple and greatest common divisor, as well as to the geometric notions of midpoint and reflection.

IMACS has provided the following description of the origins of this series and curriculum.

The Elements of Mathematics: Foundations online courses are based on Book 0: Intuitive Background of the Elements of Mathematics (EM) series of textbooks. EM is the result of a collaborative effort of an international team of eminent mathematicians and mathematics educators.

Through more than a decade of research and development, these scholars created an original curriculum that is fun and engaging for talented middle and high school students while maintaining a level of mathematical rigor found only at the university level. Aimed solely at talented students and unconstrained by the need to follow a standards-based curriculum, EM focused on providing precocious students with a deep understanding of mathematical structure.

Along the way, Book 0: Intuitive Background covered all of middle and high school mathematics except calculus before the end of middle school. After completing the Intuitive Background series, students would begin the EM formal logic series which covered a significant portion of a college undergraduate mathematics degree by the end of high school. The formal logic segment of the EM curriculum is already available online at www.eimacs.com as part of the Advanced Mathematical Logic track.

Don’t allow yourself to forget over the holidays, sign up for the first course in the series today.

 

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Does our approach to teaching math fail even the smartest kids?” is the title of a great article published on the Great Schools website which liberally quotes our good friend Richard Rusczyk.  Following are a few key points made, but please go and read the whole article for yourself (and pass it along to other families who don’t yet enjoy the benefits of a math circle).

Rusczyk recalls, formerly accomplished students were faced with a new idea: that math required more than rote learning — it required creativity, grit, and strenuous mental gymnastics. “They had been taught that math was a set of destinations and they were taught to follow a set of rules to get to those places,” he recalls. “They were never taught how to read a map, or even that there is a map.”

When Rusczyk looked around him, he noticed a pattern. His classmates who had experienced this kind of difficult problem solving — usually in after-school math clubs — could survive the transition to college math. The ones who had only been exposed to traditional math curriculum, the ones who, as Rusczyk puts it, have experienced the “tyranny of 100%” — gave up too easily because they thought if they weren’t getting top scores, they weren’t meant to do math. “Suddenly, a solid B was a 40%, the top grade [was] an 82%, the next 68%, and no one is getting a 100%,” he recalls. “But they didn’t know this.” Rusczyk realized that these kids had been dealt a bad hand: “They were taught [math] is a set of facts, not a process.”

Rusczyk cautions that kids who love math and science often end up filling up their time with AP classes that aren’t central to their aspirations but more focused on GPA calculations (like AP Art History), and shortchange themselves when it comes to exploring math and science learning outside the classroom.

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Richard Rusczyk has created a number of excellent videos for MATHCOUNTS.  These would be excellent primers for our younger problem solvers.

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A very interesting discussion of the three stages of mathematical education by the amazing Terence Tao:

There’s more to mathematics than rigour and proofs.

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Radu Sorici’s talk on the “The Mathematics of Computer Science” that kicked off our 2011 fall semester was very popular and we had many requests for copies of his  slides.

 

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A Museum of Mathematics is scheduled to open next year in New York City.  They already have hosted speakers and their presentations are remarkably similar to what one finds in a typical math circle, a brilliant and passionate speaker talking about their favorite subject and their career in mathematics and problem solving.

Here is Erik Demaine talking about the mathematics of folding and his passion for origami.

Part 1 of 4

Part 2 of 4

Part 3 of 4

Part 4 of 4

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This coming Saturday we will have two lectures in one.  Students who are not yet proficient in LaTeX will learn this critical skill while parents and other students are encouraged to come hear about the resources that will help build on their love of problem solving while opening up new academic and professional opportunities.

LaTeX is the typesetting markup language used by mathematicians and scientists to format mathematical and scientific expressions. Learning LaTeX is easy and fun for even elementary school students and it allows older students to write up science fair presentations and mathematical proofs like the pros.

While the students work on problems to develop their LaTeX skills, parents and students who have already mastered LaTeX are encouraged to attend to learn about resources that build upon what is being taught in Metroplex Math Circle. Competitions, online resources and advice on preparing for college admissions will all be discussed.

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