Leaving luck out of the equation | Cosmos

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Photo: Robyn Arianrhod

Robyn Arianrhod, senior adjunct research fellow at the School of Mathematical Sciences at Monash University. Her research fields are general relativity and the history of mathematical science inform, "Joseph Mazur introduces Fluke with two childhood stories about accidents: one that blighted the life of his uncle and another that left Joseph himself blind in one eye when he was only 12.

Photo: Cosmos

Young Mazur tormented himself with questions about chance, the most poignant being: “What if I hadn’t stopped to look around?” The answer is all too clear: the stone would not have hit his eye. This is a hallmark of Mazur’s writing: the human touch in a book about mathematics. In Fluke, he sets out to mathematically disentangle such coincidences from our all-too-human notions of fate and destiny. I say “too human” because we all love a happy coincidence story: as Mazur puts it, “in this enigmatic galaxy, [such stories] validate our longing for individuality”. This is another Mazur hallmark: discursive forays into psychology, physics, philosophy, and history.

Indeed, he is careful not to let the mathematics of chance rob us of any meaning we may ascribe to our own coincidence stories, and introduces Carl Jung’s famous “synchronicity” concept: that coincidental events can be “meaningfully related in significance, but not causally connected”. In other words, magic can happen for us on a psychological level, but we don’t have to suspend the laws of physics or probability. Many seemingly impossible coincidences turn out to be fairly likely: it is their timing that is key, and the fact that we happened to notice them. Meanwhile, myriad coincidences occur without us noticing: in the mathematics of chance, the number of “failures” must be counted, as well as the amazing “successes” (to use the language of the binomial distribution, a cornerstone of Mazur’s 70 pages of mathematical explanations for the general reader).

Mazur stresses that it is the numerical vastness of the world – 7 billion people, and “gazillions” more atoms – that makes probability theory work. It is astonishing that we can estimate the likelihood of seemingly random events whose chains of causality and multitudes of hidden variables we can never know. Yet mathematics enables us to skip straight to the big picture, thanks to the weak law of large numbers. Mazur explains that by choosing a large enough sample, the actual probability of an event will be approximately the same as its mathematical probability. In other words, “If there is any likelihood that something could happen, no matter how small, it’s bound to happen sometime.”

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Source: Cosmos

Top 10 philosophers' fictions | Books | The Guardian

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Photo: Esther Leslie

"Philosophy tends to be arid, more related to mathematics or dispatches from the courtroom than art, but some philosophy exhibits playfulness or poetic sensibility in relation to language or narrative form and some has even been speculative in a literary or imaginative sense." according to Esther Leslie, lecturer in English and humanities at Birkbeck College, London. She is the author of Walter Benjamin: Overpowering Conformism and sits on the editorial boards of Historical Materialism, Radical Philosophy andRevolutionary History.

Jean Baudrillard, for one, coined the term “theory fiction” and speculated on scenarios for future real worlds that were more wild and improbable than science fiction. In his case, it was part of a quest to exacerbate the groundlessness of signs and meaning.

‘Humouristic’ ... the tomb of Karl Marx in Highgate Cemetery, London. 
Photograph: Paul Grover / Rex Features

But postmodern suspicion is not the only way in which philosophers have used the strategies of fiction to further their projects. Hegel’s great work Phenomenology of Spirit can be read as a vast novel in which the characters, avatars of the spirit, move progressively through the world and through history. Its French translator, Jean Hippolyte, called it a “philosophical novel”: in one section the characters of Lord and Bondsman struggle dramatically over questions of recognition. Nietzsche was a stylist and his Thus Spoke Zarathustra often appears in lists of top philosophers’ novels. It has a protagonist and a plot that resembles something like a bildungsroman, as the tragic teacher hero learns lessons in life through his failures.

As industrial capitalism, with its wars and its factories, shook Europe up, literary form loomed as a crucial issue for disaffected philosophers – especially those in war-broken Germany, who were schooled in the Hegelian tradition, with its sense of universal history and dialectical method. Some understood the epic poetry of a seemingly harmonious and integrated ancient world to be unobtainable in the modern epoch that had birthed the novel, a form that is individually composed and consumed. Georg Lukács’s Theory of the Novel, written as the first world war raged, described the fallen personages of modern life as transcendentally homeless and barred from greater meanings. 

The novel developed its forms in a world in which the inner life of individuals, revolution and disenchantment clash and combine. By the early 20th century the novel was frayed and had absorbed the chaos, clatter and clutter of modern life. As a communist, Lukács turned to recommending that novelists invent rational and functioning worlds, like those once embodied in the work of a Walter Scott or a Balzac. In short, for Lukács, the choice was Thomas Mann over Franz Kafka. Others, those philosopher-poets who montaged Hegel, Marx and Nietzsche and invented critical theory, added up literary form, politics and philosophy differently. They drew on the exaggerations and emotional resonances of expressionism, the playfulness of Dada or the fairytale, the enigmas of allegory and the sharp wit of New Objectivity. One such was Walter Benjamin, with whom this top 10 begins.
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Source: The Guardian

What's Keeping Women Out of Science, Math Careers? Calculus and Confidence | Education Week's blog - Curriculum Matters

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Photo: Liana Heitin

Liana Heitin, assistant editor for Education Week, and co-author of the blog Curriculum Matters notes, "It's well-known there's a gender gap within science, technology, engineering, and math majors and careers, and a new study traces the moment many women give up on STEM to a single college class: calculus."

Photo: Getty

The study, published in PLOS One last month, found that women are 1.5 times more likely to drop out of the STEM pipeline after Calculus I than men are. And that's likely because women, when compared to men of similar capabilities, tend to start and end the course with lower confidence in their math skills. (During the course itself, men and women lose math confidence at about the same rate.)

"This work points to female students' mathematical confidence entering college as a major contributing factor to women's participation in the STEM workforce," write the researchers, who are from Colorado State University and San Diego State University, "and thus more work is needed to understand the factors (such as classroom environment, home environment, extra curricular involvement, etc.,) that help to shape students' perceptions of their own success before they enter college."

Previous studies have pointed to gender gaps in confidence starting at a young age. Boys were more likely than girls to say they could learn computer science, according to a Google study. And results from the 2012 Program for International Student Assessment, or PISA, show that girls are more likely to report feeling math anxiety than boys.

A Different STEM Workforce  
The recent study looked at survey results from about 5,000 college students. The researchers asked students who switched out of STEM after Calculus I why they made that decision. Thirty-five percent of women who previously had intended to pursue STEM fields said they did not understand the Calculus I material well enough to take Calculus II. Just 14 percent of men who switched out said the same.

But according to their grades, those men and women performed similarly: 16 percent of those men and 19 percent of those women reported having gotten grades that weren't good enough to allow them to move on to Calculus II.
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Source: Education Week's blog - Curriculum Matters   

Ask a Scientist: What's the Best Type of Math to Teach in Kindergarten? | Education Week's blog - Early Years

Photo: Lillian Mongeau

Lillian Mongeau, covers news, trends, and policy in early education summarizes, "New research shows that learning more advanced content in kindergarten, such as simple addition and subtraction, not just counting, makes for bigger gains in mathematics later on."

Photo: GraphicStock.com

Photo: Mimi Engel

The math children learn in kindergarten can set the stage for later success in school. Mimi Engel, an assistant professor of public policy and education at Vanderbilt University, was on the team that first showed that conclusively. Today, Engel is taking that research to the next logical place and asking: If math is so important, does it matter exactly what kind of math is taught? 

The answer is "yes." Engel's research found that children who learn things like simple addition and subtraction do better in math later than children who learn things like counting to 10. Many children, Engel points out, can already count to 10 when they reach kindergarten, which eliminates the need to teach it. Most kindergartners, she posits, are developmentally ready to get beyond counting and dive into the next level of mathematics learning.

"We shouldn't underestimate their capacity to learn mathematics content," Engle said. "We shouldn't assume that a kindergartener isn't ready to learn some basic addition and subtraction or assume that that might not be an exciting and intriguing task for those children."

Our conversation, edited for length and clarity, appears below.

Tell me a little bit about how you got interested in researching early math.
My interest in early math actually came from work I was involved about a decade ago [with Greg Duncan of the University of California, Irvine, and others], that showed that the correlation between math learning across the kindergarten year and students' later school-related outcomes was very high. So early math is very predictive of not just how you do in math later on in schooling, but how you do in reading and other important outcomes. 

Tell me more about your most recent work looking at what kids actually learn in kindergarten math.
The National Center for Education Statistics compiles these wonderful longitudinal datasets that are available for researchers, for policymakers, for people in general to use to answer questions about education. Building on this interest that I and my coauthors had developed in early math, we used those data about kids who were in kindergarten in 1998-99—that school year—to look at what mathematics content children are exposed to in kindergarten, and what their across-kindergarten learning gains were.

What we saw is kids were getting a lot of exposure to very basic mathematics content that evidence suggested in the very same dataset that they already knew when they started kindergarten.

They were getting less exposure to advanced content, and what we mean by that for kindergarten is content such single-digit addition and subtraction. And we show that time teachers report spending on the very basic content such as numbers one through 10 or basic shapes is negatively associated with learning in kindergarten, whereas time on more advanced content is positively associated with learning across kindergarten.

This most recent publication replicates the original study and shows that this pattern is again true using data from kids who were more recently in kindergarten, in 2010-11. Teachers are reporting that they're spending some more time on more advanced math content [than they were in 1998-99]. But the majority of time is still spent on the more basic mathematic content. And we can again show that time on basic content is associated with less learning in mathematics in kindergarten.
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Source: Education Week's blog - Early Years

Philosopher of the month: René Descartes | OUPblog (blog)

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"This August, the OUP Philosophy team honors René Descartes (1596–1650) as their Philosopher of the Month. Called “The Father of Modern Philosophy” by Hegel, Descartes led the seventeenth-century European intellectual revolution which laid down the philosophical foundations for the modern scientific age" inform John Priest, Marketing Assistant at Oxford University Press.

Frans Hals - Portret van René Descartes.jpg

His philosophical masterpiece, the Meditations on First Philosophy, appeared in Latin in 1641, and his Principles of Philosophy, a comprehensive statement of his philosophical and scientific theories, also in Latin, in 1644.

Born in La Haye, France, Descartes was educated at the Jesuit College of La Flèche and at the University of Poitiers. Much of Descartes’s early work as a “philosopher’ was what we now call scientific. The World, composed in the early 1630s, explored physics and cosmology, but Descartes cautiously withdrew it from publication in 1633 after the condemnation of Galileo by the Roman 
Inquisition for his heliocentric hypothesis (which Descartes too supported).In the Discourse on Method, a popular introduction to his philosophy, Descartes developed his celebrated method of doubt. By doubting all his ideas, he reached one unquestionable proposition: “I am thinking”, and from this that he existed: cogito ergo sum (“I think, therefore I am”).

Developing the theory later known as Cartesian dualism, Descartes maintains that there are two different kinds of substance: physical, or that which has length, breadth, and depth and can therefore be measured and divided—and thinking substance, which is indivisible. Mental phenomena, for Descartes, have no place in the quantifiable world of physics, but have an autonomous, separate status. Fascinated by the problems of ascertaining natural knowledge, Descartes’s metaphysics can be seen as an attempt to make a mathematical physics possible while paying tribute to traditional metaphysical and theological concerns like the existence of God and the immateriality of the soul.
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Source: OUPblog (blog)

If You Think Training Should Make Learning Easy, You Are Doing It Wrong | Learning Solutions Magazine

Certain “desirably difficult” conditions of learning that more actively and effortfully engage learners lead to better long-term learning. In other words, training that makes learning difficult is more effective, according to Veronica Yan, University of California, Los Angeles) postdoctoral researcher at the University of Southern California in the Department of Psychology and Morris Davis, associate professor of history at Drew University. 

Photo: Learning Solutions Magazine

Does that seem shocking to you? Read this article to find out why the common wisdom that says you should make eLearning easy is wrong, and to learn what “desirably difficult” entails.

Have you noticed that while using GPS for directions is an effective way of getting to your destination, it hasn’t significantly improved your knowledge of geography? If you are like most users of maps and satellite data, you probably have found that even if you followed the directions from your GPS device precisely on your first trip to an address, repeating the same trip without the aid of GPS is less successful.

On the other hand, you likely have also found that once you’ve worked to find a location on your own, following verbal directions or even simply driving around looking for an address, you have a much stronger knowledge of where the location is and how to get there.

In other words, even though GPS provides effective guidance to a location through clear and simple directions (i.e., it provides good performance support), it is less effective at teaching you how to get somewhere than if you were putting in more effort with less guidance (i.e., using GPS does not lead to effective learning).

Why does effort help learning? In this article, we explore this question and offer some ideas to help you increase the effectiveness of your eLearning products.
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Source: Learning Solutions Magazine

Sophos: Inside an Oxfordshire cybercrime facility | IDG Connect

Kathryn Cave, Editor at IDG Connect notes, "We visit Sophos’ Oxfordshire HQ, see a live hack and visit the labs." 

Photo: IDG Connect

Somewhere in the depths of the Oxfordshire countryside, in an inauspicious looking business park, sits Sophos’ global headquarters. This is a big glass ‘greenhouse’ with plenty of bright open spaces, wide staircases and lots of plants. From here it strives to fight the ever changing world of international cybercrime.
 
At 31, with a $125m IPO last year, Sophos, like Sage, is one of those great British companies. And now, with the increased emphasis on cybercrime everywhere, it is growing at a furious pace with a year-on-year increase of 20% and revenues of $478m [PDF of latest results].
 
This still puts it some way behind most of its main competitors though. These are Symantec ($6.5bn), McAfee ($2bn) and Trend Micro ($1.2bn) in the end-point security space and Fortinet ($1bn) and SonicWALL ($265 million) in the networking space. Yet it is the only company to straddle both areas – its business is divided almost 50/50 between each area. And as a business strategy Sophos has set its niche on mid-market companies who want a comprehensive, easy to implement solution for their limited security staff.
 
Unlike many walks of technology, cybersecurity is rather egalitarian. There is a right or a wrong answer – it’s harder to trump quality with marketing in this space – which means if you’re good you can prove yourself to be good. After all, there are “bad guys” to be fought and the threats are constantly evolving.
 
This is the reason behind Sophos’ recent high profile spat with Cylance, explains CEO Kris Hagerman who is keen to stress that Cylance is not a particular competitor. The problem is that this company is “consistently making bold claims but never makes its software available to test,” he says. This lets the whole industry down and “that’s why we ultimately made a point of it.”

Due to the nature of the business – competing against criminals – cybersecurity has a long pedigree of shared research, peer-reviewing and academic-style in-depth white papers. And Hagerman is generally happy about the collaboration between vendors. “I think the industry has got better because the bad guys have got better,” he says.
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Source: IDG Connect 

Does philosophy have a problem with women? | Opinion | | The Guardian

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Critical Reflections on Ownership (Edward Elgar) by Mary Warnock and Freedom Regained: The Possibility of Free Will (Granta) by Julian Baggini are both out now.

"Only 25% of philosophy posts in UK universities are occupied by women. So what, if anything, should be done to redress the balance?" insist Mary Warnock, crossbench life peer, moral philosopher and author of a number of books on philosophy and Julian Baggini, author of Freedom Regained: The Possibility of Free Will (Granta). He also runs the website Microphilosophy. 

Mary Warnock, philosopher and writer
This question has been debated by women and men in philosophy for years, and last week became the cover story in the Times Literary Supplement. Of all the humanities departments in British universities, only philosophy departments have a mere 25% women members. Why should this be? How can the balance be redressed? On the whole I am very much against intervention, by quotas or otherwise, to increase women’s chances of employment, whatever the field, and there is nothing intrinsically harmful about this imbalance. I certainly don’t believe it shows a conscious bias against women. Nor that it can be explained by the supposition that, philosophy being concerned above all with arguments, women are naturally less adept in the field...

A man's world: a marble statue of Plato at the Academy in Athens. 
Photograph: Alamy

Julian Baggini, philosopher and writer I agree there is little or no conscious discrimination against women in philosophy. But that is not to say there isn’t a great deal of unconscious bias. The puzzle is why this should be stronger in philosophy than in other disciplines. The answer, I think, is to be found in philosophy’s self-image. Philosophers have tended to have an inflated sense of their ability to “follow the argument wherever it leads”, as Plato’s old saw has it. What matters is the argument, not the arguer, which means there is no need even to think about gender or ethnicity. Philosophers have thus felt immune to the distorting effects of gender bias. Logic is gender-neutral, philosophy is logical, ergo philosophy is gender-neutral. I suspect this has led to complacency, a blindness towards all the ways in which, in fact, gender bias does creep in. It is a well-established finding in psychology that believing you are an objective judge actually makes your judgments less objective, and I’m sure philosophy suffers from this. I admit that this explanation for at least part of the under-representation of women in philosophy is somewhat speculative, but I would be interested to hear what you make of it.
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Source: The Guardian  

Read this Free eBook - 183 Tips on Sparking Design Creativity | The eLearning Guild

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Take a closer peek at this complimentary eBook, 183 Tips on Sparking Design Creativity as below.

Creativity plays an essential role in the world of learning and performance.

Download the free eBook now

This complimentary eBook, 183 Tips on Sparking Design Creativity, includes insights on sparking creativity from members of the eLearning Guild community. This eBook can be consumed in a single sitting and looked back upon at times when you need a spark of inspiration to release your creativity. 

The enclosed tips fall into a number of categories and are sure to inspire the creative side of your design and development work. The topics include:

• Broadening your views and knowledge
• Challenging yourself to think differently
• Finding sources for inspiration
• Creating an environment of inspiration
• Capturing design inspiration
• Solving problems creatively
• Getting unstuck
• Making creativity a habit
• Pushing boundaries

David Kelly, Senior Vice President and Executive Director, The eLearning Guild writes in the introduction, "For this eBook, we’ve reached out to the eLearning Guild community and asked people to share insights on how they spark their creativity. There’s no one correct way to feed your creative side, as evidenced by the variety of suggestions your peers have shared in this eBook."

What follows is a collection of over 180 tips that are sure to inspire the creative side of your design and development work. 183 Tips on Sparking Design Creativity is the type of book that you can enjoy reading in a single sitting, and that you will also enjoy as a reference for those moments when you need a spark to ignite your creative fire.

I hope that you enjoy this eBook. Creativity applies in just about every field, so I expect you will find the tips in this eBook to be useful in your work.
Download the free eBook now

Source: The eLearning Guild

Math Teaching: What We've Learned From Research Over a Decade | Education Week's blog - Curriculum Matters

Photo: Liana Heitin

Liana Heitin, assistant editor for Education Week, and co-author of the blog Curriculum Matters inform, "A new paper lists 28 ways federally funded research has changed what we know about how to teach whole numbers, fractions, algebra, and other math topics." 

Photo: Getty

IES, part of the U.S. Department of Education, funded more than 200 studies about math instruction between 2002 and 2013. A synthesis of that research, published this month, lays out some of the contributions these studies have made to the field.
 
For example, IES-funded research found that:

• Switching up the formatting of arithmetic problems can help students better understand the equal sign. That is, instead of just presenting 9 + 4 = ___, teachers may also want to show  ___ = 9 + 4. 
• Students do better with fractions when they view them as numbers on a number line, rather than as parts of a whole. (This is a big change in many classrooms, and something the Common Core State Standards require.) 
• Students should confront and analyze common math misconceptions. For instance, many students believe that 0.25 is bigger than 0.5, since 25 is bigger than 5. The teacher should show examples in which a student gets this wrong. "This stands in contrast to concerns by teachers that presenting and discussing incorrect solutions will reinforce and increase their use," the report states. 
• Using gestures and physical movement can help students better understand math concepts. "For example, teachers [can use] gestures to simulate actions, such as placing their arm at different angles to simulate the action of altering the slope of a line," says the report.

There are two dozen more of these concrete findings in the report, as well as information on the research studies they were distilled from. 

The whole report is worth a look—particularly by teachers looking to incorporate more "research based" practices into their everyday instruction.

Source: Education Week's blog - Curriculum Matters