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Mathematics education in the United States is broken. Open any newspaper and stories of math failure shout from the pages: low international rankings, widespread innumeracy in the general population, declines in math majors. Here’s the most shocking statistic I have read in recent years: 60 percent of the 13 million two-year college students in the U.S. are currently placed into remedial math courses; 75 percent of them fail or drop the courses and leave college with no degree.

We need to change the way we teach math in the U.S., and it is for this reason that I support the move to Common Core mathematics.

One of the reasons for these results is that mathematical problems that need thought, connection making, and even creativity are more engaging for students of all levels and for students of different genders, races, and socio-economic groups. This is not only shown by my research but by decades of research in our field.

“Almost every kid — and I mean virtually every kid — can learn math at a very high level, to the point where they could do university level math courses,”

“If you ask why that’s not happening, it’s because very early in school many kids get the idea that they’re not in the smart group, especially in math. We kind of force a choice on them: to decide that either they’re dumb or math is dumb.”

In particular, math teachers often fail to make sufficient allowances for the limitations of working memory and the fact that we all need extensive practice to gain mastery in just about anything.

One can argue that the preeminence of each civilization was, in part, due to their sophisticated understanding and use of mathematics. This is particularly clear in the case of the West, which forged ahead in the 17th century with the discovery of calculus, one of the greatest scientific breakthroughs of all time.

The United States became the dominant force in the mathematical sciences in the wake of World War II, largely due to the disastrous genocidal policies of the Third Reich. The Nazis’ obsession with purging German science of what it viewed as nefarious Jewish influence led to a massive exodus of Jewish mathematicians and scientists to America

Indeed, academic institutions in the United States have thrived largely because of their ability to attract talented individuals from around the world.

James H. Simons likes to play against type. He is a billionaire star of mathematics and private investment who often wins praise for his financial gifts to scientific research and programs to get children hooked on math.But in his Manhattan office, high atop a Fifth Avenue building in the Flatiron district, he’s quick to tell of his career failings.He was forgetful. He was demoted. He found out the hard way that he was terrible at programming computers. “I’d keep forgetting the notation,” Dr. Simons said. “I couldn’t write programs to save my life.”After that, he was fired.His message is clearly aimed at young people: If I can do it, so can you.

Down one floor from his office complex is Math for America, a foundation he set up to promote math teaching in public schools. Nearby, on Madison Square Park, is the National Museum of Mathematics, or MoMath, an educational center he helped finance. It opened in 2012 and has had a quarter million visitors.

Dr. Simons received his doctorate at 23; advanced code breaking for the National Security Agency at 26; led a university math department at 30; won geometry’s top prize at 37; founded Renaissance Technologies, one of the world’s most successful hedge funds, at 44; and began setting up charitable foundations at 56.

reflecting on his career so far, Tao told me that his view of mathematics has utterly changed since childhood. ‘‘When I was growing up, I knew I wanted to be a mathematician, but I had no idea what that entailed,’’ he said in a lilting Australian accent. ‘‘I sort of imagined a committee would hand me problems to solve or something.’’

But it turned out that the work of real mathematicians bears little resemblance to the manipulations and memorization of the math student. Even those who experience great success through their college years may turn out not to have what it takes. The 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

Tao now believes that his younger self, the prodigy who wowed the math world, wasn’t truly doing math at all. ‘‘It’s as if your only experience with music were practicing scales or learning music theory,’’ he said, looking into light pouring from his window. ‘‘I didn’t learn the deeper meaning of the subject until much later.’’

EACH time I hear someone say, “Do the math,” I grit my teeth.

Imagine, if you will, using, “Do the lit” as an exhortation to spell correctly.

my field is really about ideas above anything else. Ideas that inform our existence, that permeate our universe and beyond, that can surprise and enthrall.

My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.

one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.

Algebra is an onerous stumbling block for all kinds of students: disadvantaged and affluent, black and white. In New Mexico, 43 percent of white students fell below “proficient,” along with 39 percent in Tennessee

How do you strengthen your mind as you age?

Physical exercise helps encourage neuron growth. Some forms of meditation improve creativity, while others sharpen focus. In one study, “reading a book for around 3½ hours a week was shown to extend the lifespan . . . by something like two to three years.” Learning a foreign language “gives a workout to the very centers of the brain that are most affected by the aging process, so it’s super healthy.”

“Action videogames are incredibly helpful in keeping you sharp,” Ms. Oakley says. “They’ve been shown by research—top-notch research—to make a big difference in your attentional centers.”

Last week the DeepMind researchers got out the gong again to celebrate what Alex Davies, a lead of Google DeepMind’s mathematics initiative, described as a “massive breakthrough” in mathematical reasoning by an A.I. system.

A pair of Google DeepMind models tried their luck with the problem set in the 2024 International Mathematical Olympiad, or I.M.O., held from July 11 to July 22 about 100 miles west of London at the University of Bath.

The event is said to be the premier math competition for the world’s “brightest mathletes,” according to a promotional post on social media.

“When you cover too many topics,” Coleman said, “the assessments designed to measure those standards are inevitably superficial.” He pointed to research showing that more students entering college weren’t prepared and were forced into “remediation programs from which they never escape.” In math, for example, if you examined data from top-performing countries, you found an approach that emphasized “far fewer topics, far deeper,” the opposite of the curriculums he found in the United States, which he described as “a mile wide and an inch deep.”

The lessons he brought with him from thinking about the Common Core were evident — that American education needed to be more focused and less superficial, and that it should be possible to test the success of the newly defined standards through an exam that reflected the material being taught in the classroom.

she and her team had extensive conversations with students, teachers, parents, counselors, admissions officers and college instructors, asking each group to tell them in detail what they wanted from the test. What they arrived at above all was that a test should reflect the most important skills that were imparted by the best teachers

The American philosopher Wilfrid Sellars was challenging this assumption when he spoke of “material inferences.” Sellars was interested in inferences that we can only recognize as valid if we possess certain bits of factual knowledge.

That the use of standard algorithms isn’t merely mechanical is not by itself a reason to teach them. It is important to teach them because, as we already noted, they are also the most elegant and powerful methods for specific operations. This means that they are our best representations of connections among mathematical concepts. Math instruction that does not teach both that these algorithms work and why they do is denying students insight into the very discipline it is supposed to be about.

according to Wittgenstein, is why it is wrong to understand algorithm-based calculations as expressions of nothing more than “mental mechanisms.” Far from being genuinely mechanical, such calculations involve a distinctive kind of thought.

Most of us take it for granted that math works—that scientists can devise formulas to describe subatomic events or that engineers can calculate paths for space­craft.

As a working theoretical astrophysicist, I encounter the seemingly “unreasonable effectiveness of math­ematics,” as Nobel laureate physicist Eugene Wigner called it in 1960, in every step of my job.

by Larry Bartels on April 9, 2013

“When something new is encountered, the follow-up steps usually require mathematical and statistical methods to move the analysis forward.” At that point, he suggests finding a collaborator

But technical expertise in itself is of little avail: ”The annals of theoretical biology are clogged with mathematical models that either can be safely ignored or, when tested, fail. Possibly no more than 10% have any lasting value. Only those linked solidly to knowledge of real living systems have much chance of being used.”

Research shows that the more skills children bring with them to kindergarten -- in basic math, reading, even friendship and cooperation -- the more likely they will succeed in those same areas in school.

Now it's time to add language to that mix of skills, says a new University of Washington-led study. Not only does a child's use of vocabulary and grammar predict future proficiency with the spoken and written word, but it also affects performance in other subject areas.

The team analyzed academic and behavioral assessments, assigned standardized scores and looked at how scores correlated in grades 1, 3, and 5. Growth curve modeling allowed the team to look at children's levels of performance across time and investigate rates of change at specific times in elementary school.

The imaging analysis found four stages in all: encoding (downloading), planning (strategizing), solving (performing the math), and responding (typing out an answer).

The analysis found four separate stages that, depending on the problem, varied in length by a second or more. For instance, planning took up more time than the other stages when a clever workaround was required. The same stages are likely applicable to solving many creative problems, not just in math. But knowing how they play out in the brain should help in designing curriculums, especially in mathematics, the paper suggests.

According to a new psychology paper, our political passions can even undermine our very basic reasoning skills. More specifically, the study finds that people who are otherwise very good at math may totally flunk a problem that they would otherwise probably be able to solve, simply because giving the right answer goes against their political beliefs.

Survey respondents performed wildly differently on what was in essence the same basic problem, simply depending upon whether they had been told that it involved guns or whether they had been told that it involved a new skin cream.

What's more, it turns out that highly numerate liberals and conservatives were even more—not less—susceptible to letting politics skew their reasoning than were those with less mathematical ability.

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at the force behind all that exists actually intervened in the consciousness of humankind in the form of a man so saturated in godliness that merely being near him healed people of the weight of the world's sins.

He almost failed his first calculus course. But he trained himself to break down complicated tasks and practice them until things that initially confused him became second nature. He went on to do a Ph.D in mathematics.

This path is more common than we imagine. Research on experts – whether in chess, cello or computer programming – indicates that natural ability is less a predictor of success than effort and deliberate practice. A big part of what we call “giftedness” is “task commitment” – and that can be encouraged.

Jump’s approach follows in the Socratic tradition. “Socrates was a master of introducing concepts incrementally through a series of questions,” he says. “To do Socratic inquiry the questions have to be very well designed. People don’t recognize in math how difficult it is to design those questions so that the whole class can answer them.”