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"A research team led by Carnegie Mellon University's Robert Siegler has identified a major source of the gap -- U. S. students' inadequate knowledge of fractions and division. Although fractions and division are taught in elementary school, even many college students have poor knowledge of them. The research team found that fifth graders' understanding of fractions and division predicted high school students' knowledge of algebra and overall math achievement, even after statistically controlling for parents' education and income and for the children's own age, gender, I.Q., reading comprehension, working memory, and knowledge of whole number addition, subtraction and multiplication. Published in Psychological Science, the findings demonstrate an immediate need to improve teaching and learning of fractions and division."

Math teacher and researcher Tom O'Brien offers resources and activities through this site, with planned updates each month to add more materials. These include books published by the UK's Association of Teachers of Mathematics--some out of print --now downloadable and available for purchase. Excerpts from the e-books are available free, as well as three articles by O'Brien and colleagues. O'Brien recommends software as well, some of which is available free of charge.

"Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving" by Sanjoy Mahajan, published in 2010. "Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool-the general principle-from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest." Available as a free download (Creative Commons License), .pdf): http://mitpress.mit.edu/books/full_pdfs/Street-Fighting_Mathematics.pdf

"mathematics in everyday life" (published in 2010), highlights mathematical solutions to everyday problems and points to unsolved questions

Book to be published in November 2011

Published in 2011, "reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician. ... Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today's mathematical knowledge. For example, the Gilbreath Principle--a fantastic effect where the cards remain in control despite being shuffled--is found to share an intimate connection with the Mandelbrot set. Other card tricks link to the mathematical secrets of combinatorics, graph theory, number theory, topology, the Riemann hypothesis, and even Fermat's last theorem." Read more about one of the authors here: http://chronicle.com/article/The-Magical-Mind-of-Persi/129404/

A random addition question worksheet generator with lots of options and levels. Publish your worksheets online and give the link to your student to complete. Worksheets are self marking. You can also print your worksheets. http://ictmagic.wikispaces.com/Maths

See real-time data on a host of topics important to daily life around the world!! * world population (e.g., births this year, deaths today, net population growth for today) * government and economics (daily government spending by category; computers sold) * society and media (new book titles published, money spent on video games, Google searches) * environment (forest loss, carbon dioxide emissions, current average temperature) * food (tons of food produced; people who died of hunger) * water (water consumed, people with no access to safe drinking water) * energy (solar energy striking Earth; oil pumped; oil, gas, and coal left) * health (deaths caused by alcohol, suicides, road traffic accident fatalities) Worldometers' algorithm takes the latest statistical data available from the United Nations (UN), the World Health Organization (WHO), the Food and Agriculture Organization (FAO), and other institutions, and then processes them together with its estimated progression to compute figures current up to the millisecond. Available in dozens of languages, this site is part of the Real Time Statistics Project. Read more about that here: http://www.realtimestatistics.org/

review of "THE CALCULUS OF FRIENDSHIP: What a Teacher and a Student Learned about Life While Corresponding about Math" published in 2010 and now in paperback. Transverses thirty years of correspondence between Strogatz and his teacher, insights into student-teacher relationship and lifelong learning

"For the first time, scientists have identified the brain pathway that links a positive attitude toward maths to achievement in the subject. In a study of elementary school students, researchers at the Stanford University School of Medicine found that having a positive attitude about maths was connected to the better function of the hippocampus, an important memory centre in the brain, during the performance of arithmetic problems. The findings will be published online Jan. 24 in Psychological Science."

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."

Published March 2013. "The Golden Ticket provides a nontechnical introduction to P-NP, its rich history, and its algorithmic implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives. The Golden Ticket explores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of this compelling problem."

Published 2012

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."

"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."

Published 2013 by CRC Press. A collection of essays and stories on mathematics for the general reader, including such topics as mathematicians, mathematical discoveries, prime numbers, puzzles, equations, proofs and the value of mathematics.

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.

"A physicist faced with a fine for running a stop sign has proved his innocence by publishing a mathematical paper, and has even won a prize for his efforts. Dmitri Krioukov is a physicist based at the University of California in San Diego."

Published 2012 "Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier--"Don't disturb my circles"--words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction."

"The Real Time LaTeX Collaborative Editor in Your Browser"

Regarding researchers' boycotting Elsevier journals, a mathematician comments on the publisher's high priced mathematics titles as well as apparent lack of peer review.