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"The Middle School Stream aims to motivate and engage middle school students (grades 5 through 8) in STEM learning, 21st Century Literacy Skills and Systems Thinking by challenging them to design original video games. The High School Stream aims to motivate and engage high school students (grades 9 through 12) in STEM learning, 21st Century Literacy Skills and Systems Thinking by challenging them to design original video games. The Collegiate Stream challenges emerging game developers at the graduate and undergraduate levels to design video games for children (grades pre-K through 8) that teach key STEM concepts and foster an interest in STEM subject areas. The Educator Stream challenges educators to design video games for children (grades pre-K through 12) that teach key STEM concepts and foster an interest in STEM subject areas."

"Developing a 21st Century Global Library for Mathematics Research discusses how information about what the mathematical literature contains can be formalized and made easier to express, encode, and explore. Many of the tools necessary to make this information system a reality will require much more than indexing and will instead depend on community input paired with machine learning, where mathematicians' expertise can fill the gaps of automatization. This report proposes the establishment of an organization; the development of a set of platforms, tools, and services; the deployment of an ongoing applied research program to complement the development work; and the mobilization and coordination of the mathematical community to take the first steps toward these capabilities. The report recommends building on the extensive work done by many dedicated individuals under the rubric of the World Digital Mathematical Library, as well as many other community initiatives. Developing a 21st Century Global Library for Mathematics envisions a combination of machine learning methods and community-based editorial effort that makes a significantly greater portion of the information and knowledge in the global mathematical corpus available to researchers as linked open data through a central organizational entity-referred to in the report as the Digital Mathematics Library. This report describes how such a library might operate - discussing development and research needs, role in facilitating discover and interaction, and establishing partnerships with publishers."

"This site represents a collective effort to explore teaching and learning in the 21st century and beyond. The list of teachers and student knowledge, skills, and dispositions was initially generated by teachers and administrators from Rockland County BOCES who explored a number of resources and references on 21st learning. The lists are a work in progress and will benefit greatly from the continued exploration and addition of outcomes by those who visit this site."

Published 2012. "Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation for its elegant proofs and often surprising conclusions. Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries."

"Fascinating Mathematical People is a collection of informal interviews and memoirs of sixteen prominent members of the mathematical community of the twentieth century, many still active. The candid portraits collected here demonstrate that while these men and women vary widely in terms of their backgrounds, life stories, and worldviews, they all share a deep and abiding sense of wonder about mathematics."

"Mathematician Shinichi Mochizuki of Kyoto University in Japan has released a 500-page proof of the abc conjecture, which proposes a relationship between whole numbers - a 'Diophantine' problem. The abc conjecture, proposed independently by David Masser and Joseph Oesterle in 1985, might not be as familiar to the wider world as Fermat's Last Theorem, but in some ways it is more significant. "The abc conjecture, if proved true, at one stroke solves many famous Diophantine problems, including Fermat's Last Theorem," says Dorian Goldfeld, a mathematician at Columbia University in New York. "If Mochizuki's proof is correct, it will be one of the most astounding achievements of mathematics of the twenty-first century." See additional commentary at: http://bit-player.org/2012/the-abc-game?utm_src=HN2

"Contrary to what you've probably read, you don't have to be engaging to be a great teacher-at least not in any charismatic and charming sense of the word. You can be relatively "boring" and lead students to outstanding academic progress, mainly by staying organized, being reflective, flexible, and in constant contact with an active and ambitious professional learning networking. Teaching differently requires work."

"Ah, listening, the neglected literacy skill. I know when I was a high school English teacher this was not necessarily a primary focus; I was too busy honing the more measurable literacy skills -- reading, writing, and speaking. But when we think about career and college readiness, listening skills are just as important. This is evidenced by the listening standards found in the Common Core and also the integral role listening plays in collaboration and communication, two of the four Cs of 21st century learning. "

This resource is your online partner for teaching the core curriculum: English, history, science, mathematics, Spanish Learner-centered tools, lessons, and resources with measurable outcomes Interactive components that foster higher-order thinking skills Twenty-first century skills integrated into content

Students talk about good mathematics teachers « 21st Century Learning

"This book is designed to provide mathematics undergraduates with some historical background to the material that is now taught universally to students in their final years at school and the first years at college or university: the core subjects of calculus, analysis, and abstract algebra, along with others such as mechanics, probability, and number theory. All of these evolved into their present form in a relatively limited area of western Europe from the mid sixteenth century onwards, and it is there that we find the major writings that relate in a recognizable way to contemporary mathematics."

Forthcoming July 2011, available for pre-order. a biography of the 13th century Italian mathematician Leonardo of Pisa, better known as Fibonacci, who introduced the Hindu-Arabic system of numbers to the west. "Fibonacci's book Liber Abbaci (The Book of Calculation) was the first to recognize the power of the 10 numerals, and to aim them at the world of commerce."

"a century ago this week. Mathematician Andrey A. Markov delivered a lecture that day to the Imperial Academy of Sciences in St. Petersburg on a computational technique now called the Markov chain. Little noticed in its day, his idea for modeling probability is fundamental to all of present-day science, statistics, and scientific computing. Any attempt to simulate probable events based on vast amounts of data - the weather, a Google search, the behavior of liquids - relies on Markov's idea."

by David Berlinski, published January 2013. "In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements. Berlinski shows that, for centuries, scientists and thinkers from Copernicus to Newton to Einstein have relied on Euclid's axiomatic system, a method of proof still taught in classrooms around the world. Euclid's use of elemental logic-and the mathematical statements he and others built from it-have dramatically expanded the frontiers of human knowledge. The King of Infinite Space presents a rich, accessible treatment of Euclid and his beautifully simple geometric system, which continues to shape the way we see the world."

Abstract: "Together, brain science and learning design inform Adaptive Interaction Design (AID), a technique for curriculum planning and development. Mathematics is a particular case in which AID can help. The Way of the Game is vital to learning design. There are many definitions of "game." Here, we mean game to be the means by which spontaneous play becomes responsible learning. That innovative games figure as the centerpiece of many 21st century curricula is no accident. Games are a critical element in modern theories of learning design especially when related to insights from neuroscience and online learning/teaching methods. But beyond simple gamification, can games provide the disruptive transformation to mathematics education that is required to effect substantive and sustainable improvement? Can we game the educational system to ensure students' success in mathematics? To find out, we will look at the AID process and two sample products for the development of mathematical thinking and practice based on the Way of the Game."

Profile of a reissue of Elements of Euclid with colored designs and graphics by Oliver Byrne, 19th century engineer and mathematician

Published in 2014, tells the story of how, in the seventeenth century, Italian Jesuit authorities evidently tried to suppress the idea of infinitesimals in mathematics and how subsequently their flourishing led to the development of calculus and shifted the balance of world culture and the influence of nations.

"π has fascinated mathematicians, engineers and other people for centuries. It is a mathematical constant that is the ratio of a circle's circumference (C) to its diameter (d); This also explains why and how this number got its name: the lowercase π was first adopted in 1706 as an abbreviation for this number because it is the first letter of the Greek for "perimeter", specifically of a circle." Introduces a video by Numberphile explaining more about the determination of π

Summaries of presentations from a symposium at Florida International University in 2012

Prometheus Books The Glorious Golden Ratio [978-1-61614-423-4] - "For centuries, mathematicians, scientists, artists, and architects have been fascinated by a ratio that is ubiquitous in nature and is commonly found across many cultures. It has been called the "Golden Ratio" because of its prevalence as a design element and its seemingly universal esthetic appeal. From the ratio of certain proportions of the human body and the heliacal structure of DNA to the design of ancient Greek statues and temples as well as modern masterpieces, the Golden Ratio is a key pattern that has wide-ranging and perhaps endless applications and manifestations. What exactly is the Golden Ratio? How was it discovered? Where is it found? These questions and more are thoroughly explained in this engaging tour of one of mathematics' most interesting phenomena. With their talent for elucidating mathematical mysteries, veteran educators and prolific mathematics writers Alfred S. Posamentier and Ingmar Lehmann begin by tracing the appearance of the Golden Ratio throughout history. They demonstrate a variety of ingenious techniques used to construct it and illustrate the many surprising geometric figures in which the Golden Ratio is embedded. They also point out the intriguing relationship between the Golden Ratio and other famous numbers (such as the Fibonacci numbers, Pythagorean triples, and others). They then explore its prevalence in nature as well as in architecture, art, literature, and technology. "