World's Subways Converging on Ideal Form | Wired Science | Wired.com - 0 views
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After decades of urban evolution, the world’s major subway systems appear to be converging on an ideal form. On the surface, these core-and-branch systems — evident in New York City, Tokyo, London or most any large metropolitan subway — may seem intuitively optimal. But in the absence of top-down central planning, their movement over decades toward a common mathematical space may hint at universal principles of human self-organization. Understand those principles, and one might “make urbanism a quantitative science, and understand with data and numbers the construction of a city,” said statistical physicist Marc Barthelemy of France’s National Center for Scientific Research.
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On the surface, these core-and-branch systems — evident in New York City, Tokyo, London or most any large metropolitan subway — may seem intuitively optimal. But in the absence of top-down central planning, their movement over decades toward a common mathematical space may hint at universal principles of human self-organization.
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With equations used to study two-dimensional spatial networks, the class of network to which subways belong, the researchers turned stations and lines to a mathematics of nodes and branches. They repeated their analyses with data from each decade of a subway system’s history, and looked for underlying trends. Patterns emerged: The core-and-branch topology, of course, and patterns more fine-grained. Roughly half the stations in any subway will be found on its outer branches rather than the core. The distance from a city’s center to its farthest terminus station is twice the diameter of the subway system’s core. This happens again and again.
Rubik's Cube Enjoys Another Turn in the Spotlight - NYTimes.com - 0 views
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In the 38 years since the Hungarian architecture professor Erno Rubik invented his cube, it has alternately been regarded as an object of fun, art, mathematics, nostalgia and frustration
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“You can use Rubik’s Cube to teach engineering, you can use it to teach mathematics, and you can use it to talk about the interplay between design and engineering and mathematics and creativity,”
Kids Like to Learn Algebra, if It Comes in the Right App - Wired Science - 0 views
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non-scientist gamers developed more-complex proteins than biochemists did
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As harder concepts are introduced, students who need more time on a level get additional problems; those who understand it move on.
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93 percent of K–12 students successfully mastered concepts after only 90 minutes of gameplay, and they didn’t want to stop
Big Bang to Little Swoosh - NYTimes.com - 0 views
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By discovering hidden mathematical patterns and regularities in nature that we call equations of physics, we have gotten progressively better at predicting things — from tomorrow’s weather to tomorrow’s technology. The planet Neptune, the radio wave and the Higgs boson were all predicted mathematically before they were observed.
How Tests Make Us Smarter - NYTimes.com - 0 views
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used properly, testing as part of an educational routine provides an important tool not just to measure learning, but to promote it.
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Various kinds of testing, though, when used appropriately, encourage students to practice the valuable skill of retrieving and using knowledge.
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tests serve students best when they’re integrated into the regular business of learning and the stakes are not make-or-break, as in standardized testing.
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Shooting for the Sun - Magazine - The Atlantic - 0 views
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JTEC was only a set of mathematical equations and the beginnings of a prototype, but Johnson had made the tantalizing claim that his device would be able to turn solar heat into electricity with twice the efficiency of a photovoltaic cell
Researchers Use MRI to Predict Your Gaming Prowess | GameLife | Wired.com - 0 views
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Powerful statistical algorithms allow us to connect these patterns to individual learning success.
Free Technology for Teachers: 11 Mathematics Resources to Try in 2011 - 0 views
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11 Mathematics Resources to Try in 2011
Brain Calisthenics Help Break Down Abstract Ideas, Researchers Say - NYTimes.com - 0 views
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Yet recent research has found that true experts have something at least as valuable as a mastery of the rules: gut instinct, an instantaneous grasp of the type of problem they’re up against.
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Now, a small group of cognitive scientists is arguing that schools and students could take far more advantage of this same bottom-up ability, called perceptual learning. The brain is a pattern-recognition machine, after all, and when focused properly, it can quickly deepen a person’s grasp of a principle, new studies suggest.
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Yet there is growing evidence that a certain kind of training — visual, fast-paced, often focused on classifying problems rather then solving them — can build intuition quickly
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