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Peter Kronfeld

The Singular Mind of Terry Tao - The New York Times - 0 views

  • his view of mathematics has utterly changed since childhood.
  • But it turned out that the work of real mathematicians bears little resemblance to the manipulations and memorization of the math student.
  • he ancient art of mathematics, Tao has discovered, does not reward speed so much as patience, cunning and, perhaps most surprising of all, the sort of gift for collaboration and improvisation that characterizes the best jazz musicians.
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  • n class, he conveys a sense that mathematics is fun.
  • at 8 years old, Tao scored a 760 on the math portion of the SAT — but Stanley urged the couple to keep taking things slow and give their son’s emotional and social skills time to develop.
  • Tao became notorious for his nights haunting the graduate computer room to play the historical-­simulation game Civilization. (He now avoids computer games, he told me, because of what he calls a ‘‘completist streak’’ that makes it hard to stop playing.) At a local comic-book store, Tao met a circle of friends who played ‘‘Magic: The Gathering,’’ the intricate fantasy card game. This was Tao’s first real experience hanging out with people his age, but there was also an element, he admitted, of escaping the pressures of Princeton
  • Gifted children often avoid challenges at which they might not excel.
  • At Princeton, crisis came in the form of the ‘‘generals,’’ a wide-­ranging, arduous oral examination administered by three professors. While other students spent months working through problem sets and giving one another mock exams, Tao settled on his usual test-prep strategy: last-­minute cramming. ‘‘I went in and very quickly got out of my depth,’’ he said. ‘‘They were asking questions which I had no ability to answer.’’
  • The true work of the mathematician is not experienced until the later parts of graduate school, when the student is challenged to create knowledge in the form of a novel proof.
  • As a group, the people drawn to mathematics tend to value certainty and logic and a neatness of outcome, so this game becomes a special kind of torture. And yet this is what any ­would-be mathematician must summon the courage to face down: weeks, months, years on a problem that may or may not even be possible to unlock.
  • Ask mathematicians about their experience of the craft, and most will talk about an intense feeling of intellectual camaraderie. ‘‘A very central part of any mathematician’s life is this sense of connection to other minds, alive today and going back to Pythagoras,’
  • ‘Terry is what a great 21st-­century mathematician looks like,’’ Jordan Ellenberg, a mathematician at the University of Wisconsin, Madison, who has collaborated with Tao, told me. He is ‘‘part of a network, always communicating, always connecting what he is doing with what other people are doing.’’
  • Early encounters with math can be misleading. The subject seems to be about learning rules — how and when to apply ancient tricks to arrive at an answer. Four cookies remain in the cookie jar; the ball moves at 12.5 feet per second. Really, though, to be a mathematician is to experiment. Mathematical research is a fundamentally creative act.
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    Great insight into how math is learned, and how it should be taught
Peter Kronfeld

Will Africa Produce the 'Next Einstein'? | WIRED - 0 views

  • There are three formal AIMS undertakings: a master’s degree program in Mathematical Sciences, research, and teacher training. The master’s program offers free tuition to accepted students and trains them in both general principles – problem formulation, the scientific method, communication – and cutting-edge math in subjects including computer science, biomathematics, and financial mathematics. Research will allow for international collaborations and advanced student training.
    • Peter Kronfeld
       
      Brilliant: applied math (CompSci, bio, financial) and 3 keys: problem formulation, the scientific method, and communication
  • Traditionally, classrooms were led by an authoritative teacher who disseminated information to silent students, but Zomahoun hopes to turn that paradigm on its head. “We train people who can challenge the status quo,” he explains, “not just people who learn from books, listen to lectures, and just repeat it.” Rather, he hopes to instill qualities like “critical thinking, independent thinking, and problem solving” in order to prepare students for real-world problems.
Peter Kronfeld

How Tests Make Us Smarter - NYTimes.com - 0 views

  • used properly, testing as part of an educational routine provides an important tool not just to measure learning, but to promote it.
  • Various kinds of testing, though, when used appropriately, encourage students to practice the valuable skill of retrieving and using knowledge.
  • 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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  • researchers have also found that the most common study strategies — like underlining, highlighting and rereading — create illusions of mastery but are largely wasted effort
  • Just as it is with the multiplication tables, so it is with complex concepts and skills: effortful, varied practice builds mastery.
Peter Kronfeld

Big Bang to Little Swoosh - NYTimes.com - 0 views

  • 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.
Peter Kronfeld

5-Year-Olds Can Learn Calculus - Luba Vangelova - The Atlantic - 0 views

  • But this progression actually “has nothing to do with how people think, how children grow and learn, or how mathematics is built,” says pioneering math educator and curriculum designer Maria Droujkova.
  • The current sequence is merely an entrenched historical accident that strips much of the fun out of what she describes as the “playful universe” of mathematics
  • “Calculations kids are forced to do are often so developmentally inappropriate, the experience amounts to torture,” she says. They also miss the essential point—that mathematics is fundamentally about patterns and structures, rather than “little manipulations of numbers,” as she puts it.
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  • Studies [e.g.,  this one, and many others referenced in this symposium] have shown that games or free play are efficient ways for children to learn, and they enjoy them.
  • start by creating rich and social mathematical experiences that are complex (allowing them to be taken in many different directions) yet easy (making them conducive to immediate play). Activities that fall into this quadrant: building a house with LEGO blocks, doing origami or snowflake cut-outs, or using a pretend “function box” that transforms objects (and can also be used in combination with a second machine to compose functions, or backwards to invert a function, and so on).
  • What is learned without play is qualitatively different. It helps with test taking and mundane exercises, but it does nothing for logical thinking and problem solving.
Peter Kronfeld

Who Says Math Has to Be Boring? - NYTimes.com - 0 views

  • That’s because the American system of teaching these subjects is broken. For all the reform campaigns over the years, most schools continue to teach math and science in an off-putting way that appeals only to the most fervent students.
  • The system is alienating and is leaving behind millions of other students, almost all of whom could benefit from real-world problem solving rather than traditional drills.
  • the most important factor that predicted math success in middle school and upward was an understanding of what numbers are before entering the first grade. Having “number system knowledge” in kindergarten or earlier — grasping that a numeral represents a quantity, and understanding the relationships among numbers — was a more important factor in math success by seventh grade than intelligence, race or income.
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  • A growing number of schools are helping students embrace STEM courses by linking them to potential employers and careers, taking math and science out of textbooks and into their lives.
Peter Kronfeld

Kids Like to Learn Algebra, if It Comes in the Right App - Wired Science - 0 views

  • non-­scientist gamers developed more-­complex proteins than biochemists did
  • As harder concepts are introduced, students who need more time on a level get additional problems; those who understand it move on.
  • 93 percent of K–12 students successfully mastered concepts after only 90 minutes of gameplay, and they didn’t want to stop
Peter Kronfeld

How a Radical New Teaching Method Could Unleash a Generation of Geniuses | Wired Busine... - 0 views

  • As she headed into fifth grade, she assumed she was in for more of the same—lectures, memorization, and busy work. Sergio Juárez Correa was used to teaching that kind of class. For five years, he had stood in front of students and worked his way through the government-mandated curriculum. It was mind-numbingly boring for him and the students, and he’d come to the conclusion that it was a waste of time. Test scores were poor, and even the students who did well weren’t truly engaged.
  • Juárez Correa didn’t know it yet, but he had happened on an emerging educational philosophy, one that applies the logic of the digital age to the classroom. That logic is inexorable: Access to a world of infinite information has changed how we communicate, process information, and think. Decentralized systems have proven to be more productive and agile than rigid, top-down ones. Innovation, creativity, and independent thinking are increasingly crucial to the global economy. And yet the dominant model of public education is still fundamentally rooted in the industrial revolution that spawned it, when workplaces valued punctuality, regularity, attention, and silence above all else.
  • knowledge isn’t a commodity that’s delivered from teacher to student but something that emerges from the students’ own curiosity-fueled exploration. Teachers provide prompts, not answers, and then they step aside so students can teach themselves and one another. They are creating ways for children to discover their passion—and uncovering a generation of geniuses in the process.
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  • “So,” Juárez Correa said, “what do you want to learn?”
  • His defining principle: “The children are completely in charge.”
  • if you’re not the one who’s controlling your learning, you’re not going to learn as well,”
  • Peter Gray, a research professor at Boston College who studies children’s natural ways of learning, argues that human cognitive machinery is fundamentally incompatible with conventional schooling. Gray points out that young children, motivated by curiosity and playfulness, teach themselves a tremendous amount about the world. And yet when they reach school age, we supplant that innate drive to learn with an imposed curriculum. “We’re teaching the child that his questions don’t matter, that what matters are the questions of the curriculum. That’s just not the way natural selection designed us to learn. It designed us to solve problems and figure things out that are part of our real lives.”
  • He squatted next to her and asked why she hadn’t expressed much interest in math in the past, since she was clearly good at it. “Because no one made it this interesting,” she said.
Peter Kronfeld

Scientific Data Has Become So Complex, We Have to Invent New Math to Deal With It - Wir... - 0 views

  • This approach can even be useful for applications that are not, strictly speaking, compressed sensing problems, such as the Netflix prize.
    • Peter Kronfeld
       
      Took 2006 - 2009 to accomplish, by an "international team of statisticians, machine learning experts and computer engineers"
  • Given the enormous popularity of Netflix, even an incremental improvement in the predictive algorithm results in a substantial boost to the company’s bottom line. Recht found that he could accurately predict which movies customers might be interested in purchasing, provided he saw enough products per person. Between 25 and 100 products were sufficient to complete the matrix.
  • It wasn’t the size of the data set that was daunting; by big data standards, the size was quite manageable. It was the sheer complexity and lack of formal structure that posed a problem.
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  • Across every discipline, data sets are getting bigger and more complex, whether one is dealing with medical records, genomic sequencing, neural networks in the brain, astrophysics, historical archives, or social networks. Alessandro Vespignani, a physicist at Northeastern University who specializes in harnessing the power of social networking to model disease outbreaks, stock market behavior, collective social dynamics, and election outcomes, has collected many terabytes of data from social networks such as Twitter, nearly all of it raw and unstructured. “We didn’t define the conditions of the experiments, so we don’t know what we are capturing,” he said.
  • calculus lets you take a lot of simple models and integrate them into one big picture.” Similarly, Coifman believes that modern mathematics — notably geometry — can help identify the underlying global structure of big datasets.
  • The key to the technique’s success is a concept known as sparsity, which usually denotes an image’s complexity, or lack thereof. It’s a mathematical version of Occam’s razor: While there may be millions of possible reconstructions for a fuzzy, ill-defined image, the simplest (sparsest) version is probably the best fit. Out of this serendipitous discovery, compressed sensing was born.
  • Using compressed sensing algorithms, it is possible to sample only 100,000 of, say, 1 million pixels in an image, and still be able to reconstruct it in full resolution — provided the key elements of sparsity and grouping (or “holistic measurements”) are present. It is useful any time one encounters a large dataset in which a significant fraction of the data is missing or incomplete.
Peter Kronfeld

Go Ahead, Mess With Texas Instruments - Phil Nichols - The Atlantic - 0 views

  • If you had asked them, most of my high school teachers would have called me an unmotivated student or said that I lacked discipline and didn't take learning seriously. And yet, that abandoned storage bin told another story: with the aid of my calculator, I'd crafted narratives, drawn storyboards, visualized foreign and familiar environments and coded them into existence. I'd learned two programming languages and developed an online network of support from experienced programmers. I'd honed heuristics for research and discovered workarounds when I ran into obstacles. I'd found outlets to share my creations and used feedback from others to revise and refine my work. The TI-83 Plus had helped me cultivate many of the overt and discrete habits of mind necessary for autonomous, self-directed learning. And even more, it did this without resorting to grades, rewards, or other extrinsic motivators that schools often use to coerce student engagement.
  • I've now begun to see Texas Instruments graphing calculators as unique among educational technologies in that they enable learning that is couched in discovery more than formal teaching.
  • take the notion of "correctness." School typically assumes that answers fall neatly into categories of "right" and "wrong." As a conventional tool for computing "right" answers, calculators often legitimize this idea; the calculator solves problems, gives answers. But once an endorsed, conventional calculator becomes a subversive, programmable computer it destabilizes this polarity. Programming undermines the distinction between "right" and "wrong" by emphasizing the fluidity between the two. In programming, there is no "right" answer. Sure, a program might not compile or run, but making it offers multiple pathways to success, many of which are only discovered through a series of generative failures. Programming does not reify "rightness;" instead, it orients the programmer toward intentional reading, debugging, and refining of language to ensure clarity. This is a form of learning that privileges the process of discovery over the interventions of formal teaching. It can fuel an intrinsic desire to pursue similar learning experiences, but even more, it gradually transforms the outlook of the student
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  • Subversion encourages students to take an imaginative stance toward learning, to embrace failure as an integral part of success, to see the world for what it is and consider what it might look like under a different set of conditions.
  • The iPad is among the recent panaceas being peddled to schools, but like those that came before, its ostensibly subversive shell houses a fairly conventional approach to learning. Where Texas Instruments graphing calculators include a programming framework accessible even to amateurs, writing code for an iPad is restricted to those who purchase an Apple developer account, create programs that align with Apple standards, and submit their finished products for Apple's approval prior to distribution. As such, for the average student, imaginative activities on an iPad are always mediated by pre-existing apps and therefore, are limited to virtual worlds created by others, not by students themselves. Pair this with the fact that most teachers and administrators only allow classroom use of a few endorsed apps and it becomes clear that these devices are doing more to centralize the school's authority over the learning process than to encourage self-directed creative activity.
  • learning to program taught habits of mind that persist to this day in small yet vital ways. In my work as a teacher, I often hear colleagues lamenting the widespread use of calculator games among students. They consider such forms of "play" an abuse of educational technology and a threat to student learning. But this assumption ignores the tacit learning that arises from repurposing conventional learning apparatuses. My TI-83 Plus awoke a curiosity that exerted a subtle but powerful push toward autonomy and self-direction.
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    Learning to program a graphing calculator gave the author a deeper education. Results: intrinsic motivation and an ability to "embrace failure as an integral part of success", as well as developing creativity, problem-solving skills, and persistence. Interesting critique of the iPad as a more conventional tool of learning vs. subversive.
Peter Kronfeld

The Ugly, Corrupted, Brilliant Games of Michael Brough | Game|Life | Wired.com - 0 views

  • Corrypt, upon proper exploration, revealed itself to be a brilliantly designed puzzle game, unforgiving and unwilling to accommodate players who refuse to give it their full attention. Peel back one layer, and it reveals another more surprising one.
  • After completing a degree in math and computer science at the University of Auckland, Brough moved to London and began working towards a Ph.D. He landed a decent-paying programming job while continuing his scholastic work, but continued making games, including the beautiful, abstract strategy game Vertex Dispenser, which even Brough admits may have been too esoteric. It combined elements of shooters and real-time strategy games with a complex puzzle system, and many players felt overwhelmed. “I just could not get my head around those concepts at the same time,” said one.
  • Well-designed games, he believes, can teach people how to do some things better. By simulating challenging situations, games can teach us about “managing unexpected situations… making good decisions, thinking about the costs of our actions and dealing with the consequences,” he says.
Peter Kronfeld

Haresh Lalvani's SEED54 - A Sculpture With a Twist - NYTimes.com - 0 views

  • “I’m interested in seeing what design principles nature uses,” Dr. Lalvani said. “Math, perhaps; maybe physics, whatever. The whole D’Arcy Thompson-type stuff.” The biologist D’Arcy Wentworth Thompson’s book “On Growth and Form,” published in the early 20th century, was a seminal work on the subject of patterns in nature. Thompson, a Scotsman, argued that growth and the structures that resulted were governed by physical principles and could often be described in mathematical terms. He saw examples throughout nature — in the spiral shell of a nautilus, the branching veins on an insect wing and the scales of a pine cone, to name just a few.
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