In preparation for their friendly match with Spain, Romanias players have swapped their normal squad numbers for problems in a bid to help their countrys children with their maths
In preparation for their friendly match with Spain on Sunday night, Romanias players have swapped their normal squad numbers for maths problems in a bid to help their countrys children with their education.
The idea for the new numbers, printed on the back of training tops, will be supported by a video at the Cluj Arena explaining the initiative, which is designed to combat Romanian children dropping out of school as of 2014 the rate is 18%, one of the worst records in the European Union.
Football and mathematics are not mutually exclusive, said the Romanian Football Federation president, Razvan Burleanu. We must look at sports and education as not only complementary but fundamental elements integrated in the training and perfection of children. We want to have healthy generation and smart students who achieve performance and tools through tailored passions. Through this project, children will learn the basics of football and have an opportunity for the first time in our country to discover mathematics through an attractive approach.
Romania host Spain off the back of a 1-0 win over Lithuania on Wednesday. Having finished second in their Euro 2016 qualifying group behind Northern Ireland, they will play France in the opening match of the tournament on 10 June before going on to face Switzerland and Albania in the group stage.
The results are in and yes, most of you got this one wrong. Heres why.
Earlier today I set you this puzzle:
Jack is looking at Anne, but Anne is looking at George. Jack is married, but George is not. Is a married person looking at an unmarried person?
C: Cannot be determined
The correct answer is A.
Before I get to the explanation, a few words on why I set the question. I wanted to test if it really was the case that more than 80 per cent of people choose C. Well, the results are in, and with more than 200,000 submissions, this is how you voted:
A 27.68 per cent
B 4.55 per cent
C 67.77 per cent
More than 72 per cent of you chose the wrong answer. Maybe its an exaggeration to say that almost everyone gets this question wrong but the vast majority of you did! (And thats not accounting for the fact that many of you who took part are seasoned readers of this puzzle column, and were warned that this question was not all it seemed.)
Why is this question so tricky? It is because it appears to give you insufficient information. Annes marital status is not known, nor can it be determined, and so you make the inference that the question posed cannot be determined.
In fact, Annes marital status is irrelevant to the answer. If she is married, then a married person is looking at an unmarried person (Anne is looking at George), and if she isnt, a married person is looking at an unmarried person (Jack is looking at Anne).
Written down it becomes more obvious. If > means looking at then:
Jack > Anne > George, or
Married > Unknown > Unmarried
Replace Unkown with Married or with Unmarried and either way there is clearly a married person looking at an unmarried one.
This image may be helpful:
The puzzle caused many hands to be slapped on many foreheads.
As I expected, some people blamed getting the answer wrong on the poor wording of the question. For those of you who thought that Anne was not a person, then yes, C is the correct answer. But, come on guys, we can assume that Anne is a human being.
Others said that married and unmarried are not binary states, since what about widowed, or divorced. The Wikipedia article on marital status clears that one up.
Todays puzzle really belongs more to psychology than it does to mathematics or logic, as it is about the lazy assumptions we make, rather than whether or not we have the ability to solve the question.
Yet the reasoning that is used – that in order to solve something we need to consider all possibilities without knowing which is true – is frequently used in maths. In this video, the brilliant James Grime gives an example using irrational numbers.
The Study of Mathematically Precocious Youth (SMPY) is one of the more colorfully named scientific studies. Now on its 45th year, it tracked the careers and accomplishments of up to 5,000 individuals, starting from when they were children or teenagers. As detailed by Nature, it would go on to transform the way gifted children are both identified and nurtured by the US education system.
More than anything other longitudinal study, it arguably is the best source in the world for understanding how to make children grow up with some impressive intellectual heft. It has produced hundreds of academic studies, and in particular, it appears to know how to spot talent ripe for development in the science, technology, engineering and mathematics (STEM) fields.
Unsurprisingly, many of those in SMPY which is coordinated by Vanderbilt University have gone on to become high-profile scientists. So whats the secret to turning your kids into potential geniuses?
Well, it appears that, contrary to many other studies, SMPYs data seems to suggest that a lot of it is born and bred in youth, and that inherent intelligence beats repeated practice when it comes to becoming an expert in something. In fact, early cognitive ability has a greater effect on achievement than either continued practice or other factors like the familys socio-economic status.
This finding also runs against the grain of most Western educational ethoses, which prioritize improving the abilities of children who struggle in this regard rather than those who have potential to reach great heights. Essentially, SMPY finds that if youre smart, and you are identified as such and nurtured, you will make it.
As such, standardized testing was a common method used by the initiative to find intellectually potent kids. Along with the partnered program at Johns Hopkins Universitys (JHU) Center for Talented Youth, the program tended to admit those who scored in the top 1percent in their university entrance exams.
Alumni included Mark Zuckerberg, Lady Gaga, and Google co-founder Sergey Brin, along with pioneering mathematicians Terence Tao and Lenhard Ng. Whether we like it or not, these people really do control our society, says Jonathan Wai, a psychologist at the Duke University Talent Identification Program in Durham, North Carolina, and a collaborator with JHU, told Nature.
Standardized testing is used to find those with high potential. bibiphoto/Shutterstock
Initiatives like the SMPY have also been criticized for how it may be putting too much emphasis on the smartest kids. Some worry that those with slightly more limited potential may be ignored by such initiatives. Additionally, labelling kids as smart from an early age could undermine their willingness to learn.
Importantly, it has not been conclusively shown that theres just one single factor that will guarantee your child will grow up to be the next Richard Feynman or Rosalind Franklin. Many different studies trying to pick apart the varying influences of nature versus nurture seem to settle on the idea that its a bit of both genetics and their upbringing.
One suggests that parental love, in terms of being very supportive and cooperative with your child around the pre-school age, significantly boosts their brain growth rate. Another study strongly hints that complex tasks that get increasingly difficult over time are huge boons to neural connectivity and mental flexibility.
Interestingly, computer games of varying kinds are structured in this way, and an increasing body of evidence suggests that the occasional spurt of virtual roaming, puzzle solving, or competitive combat in video games may contribute towards improving cognitive functions in later life. Learning how to play a musical instrument and regularly reading booksis just as neurologically beneficial for adults as it is for children.
SMPY suggests it’s clear early on if children will rise to the top of their fields. Pressmaster/Shutterstock
Want to feel like a genius? These mind-expanding podcasts will give you everything you need to do just that
As the cold rustle of conkers start to hit the pavements and a new generation of pencil cases bulge under the weight of novelty felt-tips, it must be the start of a new term. Sadly, we cant all be going back to school. But that doesnt mean we need to let our brains fester like an opened tub of yoghurt on a hot day. The audio wonderland of modern podcasts is ripe with all the insight, analysis, facts, statistics and research you need to at least blag a GCSE. Here is a rundown of some of the best podcasts to make you feel (if not actually sound) like a genius:
The weekly stories from This American Life often spread beyond traditional state borders their recent episodes from Greeces refugee camps were brilliant, with reports on romance, wild pigs, women doing their laundry in a baseball stadium locker room and what its like to live in a former psychiatric hospital. You can also trawl the archive for stories from Haiti, the lie that saved Brazils economy and even the odd look at Europe (yes, they too covered Brexit).
A weekly listen to From Our Own Correspondent will do more for your understanding of global news than my curriculum ever managed, while The Documentary podcast from BBC World Service can cover anything from protest in Putins Russia to Syrias secret library and incubator babies on display in Coney Island.
The New Yorker Fiction Podcast is like the greatest book group, English seminar and public lecture you never joined. Each month the magazines fiction editor, Deborah Treisman, invites a different New Yorker author to choose and read aloud a story from the magazines archive then discuss it. I started with AM Homes reading Shirley Jacksons short story The Lottery, set in a sinister village, and it haunts me still.
Is English language your bag? Then Helen Zaltzmans The Allusionist is the etymology party youve been waiting for. After all, who knew a simple word like please could have such completely different meanings and uses on either side of the Atlantic?
If you like your journalism lengthy, perhaps the Longform interviews with journalists such as Malcolm Gladwell and Kathryn Schulz, speechwriters like Jon Favreau who worked with President Obama and editors like David Remnick will tickle your pickle, or the Guardians own excellent Long Reads audio series. After all, readings for squares, I heard.
You can go a long way at a dinner party with a couple of the BBCs Inside Science episodes under your belt, and first dates will whizz by with the science anecdotes afforded by the last season of Invisibilia. Not to mention the unending popularity of Prof Brian Cox and Robin Inces Infinite Monkey Cage.
If Melvyn Bragg had been my history teacher, rather than a woman who decorated her classroom with warnings about the dangers of ragwort, I may have ended up with quite a different degree. In Our Time will teach you more about world history than most museums and you dont even need to pack a lunch. Im particularly enjoying the latest series on the history of The North.
Elsewhere, Stuff You Missed in History Class will give you a good grounding in everything from Chinas Great Leap Forward to the Matchgirls Strike and the Anglo-Cherokee war.
For those who prefer their history a little more specific, Im a huge fan of Great Lives, in which a notable modern figure looks at a person from the past who has inspired or excited them try Sara Pascoe on Virginia Woolf or Anthony Horowitz on Alfred Hitchcock.
If The Essay from BBC Radio 3 was a country, Id move there. There are amazing features on everything from British film comedians to Dadaism, great sonnets, and the artistic impact of the fall of the Berlin Wall. Adventures in Design is a topical (if now behind-paywall) look at modern graphic design, while Song Exploder invites musicians and songwriters to pick apart their compositions in forensic detail. And if you want to delve into the world buildings-first, then 99% Invisible is far more than just an architecture podcast.
What I know about sport could fill the sweaty confines of a Slazenger Classic Abdo Guard, but even I have been known to laugh at the ArseBlog podcast. Particularly when Irish writer and presenter, Andrew Mangan, described striker Olivier Giroud as a big fucking ride.
The murky subjects of toxic debt, trading in oil, the economy of housing, Brexit and how to count your bitcoins are made more comprehensible thanks to NPRs Planet Money. It wont teach you how to do long division, but it will give you some prime number chat. Also worth a listen is the BBCs mathematics show More or Less, hosted by the Undercover Economist Tim Harford, which takes a look at the real stories behind the statistics found in the news.
Whether youre dating, starting a new job, or just want something new to say to your pets, you can learn a lot from the The Inquiry, which has programmes on everything from coral reefs to putting solar panels in the Sahara desert. The Middle East Week podcast will give you a great grounding on some of the worlds most controversial issues, More Perfect is a fascinating look at the American justice system and you can get to grips with some serious international relations via Global Dispatches. Little Atoms, from Resonance FM, will help you scrub up on politics, literature, science, art and comedy, and I have learned pretty much everything I know about farming, food, technology, growing vegetables and the rural economy thanks to The Archers (not to mention the rigours of baking ginger scones).
Jeremy Shuler, who was home-schooled by his aerospace engineer parents, is settling in at Cornell University and finding classes kind of easy so far
When he was two, Jeremy Shuler was reading books in English and Korean. At six, he was studying calculus. Now, at an age when most children are attending middle school, the exuberant 12-year-old is a freshman at Cornell University, the youngest the Ivy League school has on record.
Its risky to extrapolate, but if you look at his trajectory and he stays on course, one day hell solve some problem we havent even conceived of, said Cornell engineering dean Lance Collins. Thats pretty exciting.
Jeremy is the home-schooled child of two aerospace engineers who were living in Grand Prairie, Texas, when he applied to Cornell. While Jeremys elite-level SAT and advanced placement test scores in math and science at age 10 showed he was intellectually ready for college, Collins said what sealed the deal was his parents willingness to move to Ithaca. Jeremys father, Andy Shuler, transferred from Lockheed Martin in Texas to its location in upstate New York.
I wanted to make sure he had a nice, safe environment in terms of growing up, Collins said.
With his bowl-cut hair and frequent happy laughter, Jeremy is clearly still a child despite his advanced intelligence. He swung in his chair while his parents, who he calls Mommy and Daddy, recounted his early years during an interview at the engineering school where his grandfather is a professor, his father got his doctorate and Jeremy is now an undergraduate.
The Long Read: Employers are turning to mathematically modelled ways of sifting through job applications. Even when wrong, their verdicts seem beyond dispute and they tend to punish the poor
A few years ago, a young man named Kyle Behm took a leave from his studies at Vanderbilt University in Nashville, Tennessee. He was suffering from bipolar disorder and needed time to get treatment. A year and a half later, Kyle was healthy enough to return to his studies at a different university. Around that time, he learned from a friend about a part-time job. It was just a minimum-wage job at a Kroger supermarket, but it seemed like a sure thing. His friend, who was leaving the job, could vouch for him. For a high-achieving student like Kyle, the application looked like a formality.
But Kyle didnt get called in for an interview. When he inquired, his friend explained to him that he had been red-lighted by the personality test hed taken when he applied for the job. The test was part of an employee selection program developed by Kronos, a workforce management company based outside Boston. When Kyle told his father, Roland, an attorney, what had happened, his father asked him what kind of questions had appeared on the test. Kyle said that they were very much like the five factor model test, which hed been given at the hospital. That test grades people for extraversion, agreeableness, conscientiousness, neuroticism, and openness to ideas.
At first, losing one minimum-wage job because of a questionable test didnt seem like such a big deal. Roland Behm urged his son to apply elsewhere. But Kyle came back each time with the same news. The companies he was applying to were all using the same test, and he wasnt getting offers.
Roland Behm was bewildered. Questions about mental health appeared to be blackballing his son from the job market. He decided to look into it and soon learned that the use of personality tests for hiring was indeed widespread among large corporations. And yet he found very few legal challenges to this practice. As he explained to me, people who apply for a job and are red-lighted rarely learn that they were rejected because of their test results. Even when they do, theyre not likely to contact a lawyer.
Behm went on to send notices to seven companies, including Home Depot and Walgreens, informing them of his intent to file a class-action suit alleging that the use of the exam during the job application process was unlawful. The suit, as I write this, is still pending. Arguments are likely to focus on whether the Kronos test can be considered a medical exam, the use of which in hiring is illegal under the Americans with Disabilities Act of 1990. If this turns out to be the case, the court will have to determine whether the hiring companies themselves are responsible for running afoul of the ADA, or if Kronos is.
But the questions raised by this case go far beyond which particular company may or may not be responsible. Automatic systems based on complicated mathematical formulas, such as the one used to sift through Behms job application, are becoming more common across the developed world. And given their scale and importance, combined with their secrecy, these algorithms have the potential to create an underclass of people who will find themselves increasingly and inexplicably shut out from normal life.
It didnt have to be this way. After the financial crash, it became clear that the housing crisis and the collapse of major financial institutions had been aided and abetted by mathematicians wielding magic formulas. If we had been clear-headed, we would have taken a step back at this point to figure out how we could prevent a similar catastrophe in the future. But instead, in the wake of the crisis, new mathematical techniques were hotter than ever, and expanding into still more domains. They churned 24/7 through petabytes of information, much of it scraped from social media or e-commerce websites. And increasingly they focused not on the movements of global financial markets but on human beings, on us. Mathematicians and statisticians were studying our desires, movements, and spending patterns. They were predicting our trustworthiness and calculating our potential as students, workers, lovers, criminals.
This was the big data economy, and it promised spectacular gains. A computer program could speed through thousands of rsums or loan applications in a second or two and sort them into neat lists, with the most promising candidates on top. This not only saved time but also was marketed as fair and objective. After all, it didnt involve prejudiced humans digging through reams of paper, just machines processing cold numbers. By 2010 or so, mathematics was asserting itself as never before in human affairs, and the public largely welcomed it.
Most of these algorithmic applications were created with good intentions. The goal was to replace subjective judgments with objective measurements in any number of fields whether it was a way to locate the worst-performing teachers in a school or to estimate the chances that a prisoner would return to jail.
These algorithmic solutions are targeted at genuine problems. School principals cannot be relied upon to consistently flag problematic teachers, because those teachers are also often their friends. And judges are only human, and being human they have prejudices that prevent them from being entirely fair their rulings have been shown to be harsher right before lunch, when theyre hungry, for example so its a worthy goal to increase consistency, especially if you can rest assured that the newer system is also scientifically sound.
The difficulty is that last part. Few of the algorithms and scoring systems have been vetted with scientific rigour, and there are good reasons to suspect they wouldnt pass such tests. For instance, automated teacher assessments can vary widely from year to year, putting their accuracy in question. Tim Clifford, a New York City middle school English teacher of 26 years, got a 6 out of 100 in one year and a 96 the next, without changing his teaching style. Of course, if the scores didnt matter, that would be one thing, but sometimes the consequences are dire, leading to teachers being fired.
There are also reasons to worry about scoring criminal defendants rather than relying on a judges discretion. Consider the data pouring into the algorithms. In part, it comes from police interactions with the populace, which is known to be uneven, often race-based. The other kind of input, usually a questionnaire, is also troublesome. Some of them even ask defendants if their families have a history of being in trouble with the law, which would be unconstitutional if asked in open court but gets embedded in the defendants score and labelled objective.
It doesnt stop there. Algorithms are being used to determine how much we pay for insurance (more if your credit score is low, even if your driving record is clean), or what the terms of our loans will be, or what kind of political messaging well receive. There are algorithms that find out the weather forecast and only then decide on the work schedule of thousands of people, laying waste to their ability to plan for childcare and schooling, never mind a second job.
Their popularity relies on the notion they are objective, but the algorithms that power the data economy are based on choices made by fallible human beings. And, while some of them were made with good intentions, the algorithms encode human prejudice, misunderstanding, and bias into automatic systems that increasingly manage our lives. Like gods, these mathematical models are opaque, their workings invisible to all but the highest priests in their domain: mathematicians and computer scientists. Their verdicts, even when wrong or harmful, are beyond dispute or appeal. And they tend to punish the poor and the oppressed in our society, while making the rich richer. Thats what Kyle Behm learned the hard way.
Finding work used to be largely a question of whom you knew. In fact, Kyle Behm was following the traditional route when he applied for work at Kroger. His friend had alerted him to the opening and put in a good word. For decades, that was how people got a foot in the door, whether at grocers, banks, or law firms. Candidates then usually faced an interview, where a manager would try to get a feel for them. All too often this translated into a single basic judgment: is this person like me (or others I get along with)? The result was a lack of opportunity for job seekers without a friend inside, especially if they came from a different race, ethnic group, or religion. Women also found themselves excluded by this insider game.
Companies like Kronos brought science into corporate human resources in part to make the process fairer. Founded in the 1970s by MIT graduates, Kronoss first product was a new kind of punch clock, one equipped with a microprocessor, which added up employees hours and reported them automatically. This may sound banal, but it was the beginning of the electronic push now blazing along at warp speed to track and optimise a workforce.
As Kronos grew, it developed a broad range of software tools for workforce management, including a software program, Workforce Ready HR, that promised to eliminate the guesswork in hiring. According to its web page, Kronos can help you screen, hire, and onboard candidates most likely to be productive the best-fit employees who will perform better and stay on the job longer.
Kronos is part of a growing industry. The hiring business is becoming automated, and many of the new programs include personality tests like the one Kyle Behm took. It is now a $500 million annual business and is growing by 10 to 15% a year, according to Hogan Assessment Systems Inc, a company that develops online personality tests. Such tests now are used on 60 to 70% of prospective workers in the US, and in the UK, according to the Association of Graduate Recruiters, 71% of employers use some form of psychometric test for recruitment.
Even putting aside the issues of fairness and legality, research suggests that personality tests are poor predictors of job performance. Frank Schmidt, a business professor at the University of Iowa, analysed a century of workplace productivity data to measure the predictive value of various selection processes. Personality tests ranked low on the scale they were only one-third as predictive as cognitive exams, and also far below reference checks. The primary purpose of the test, said Roland Behm, is not to find the best employee. Its to exclude as many people as possible as cheaply as possible.
You might think that personality tests would be easy to game. If you go online to take a five factor personality test, it looks like a cinch. One question asks: Have frequent mood swings? It would probably be smart to answer very inaccurate. Another asks: Get mad easily? Again, check no.
In fact, companies can get in trouble for screening out applicants on the basis of such questions. Regulators in Rhode Island found that CVS Pharmacy was illegally screening out applicants with mental illnesses when a personality test required respondents to agree or disagree with such statements as People do a lot of things that make you angry and Theres no use having close friends; they always let you down.