Math-a-manics

She is also frustrated by the predictable nature of many of the “dirty dozen,” the teachers’ nickname for the basic lab exercises now recommended by the College Board. In one that her class did last fall, the students looked at pre-stained slides of onion root tips to identify the stages of cell division and calculate the duration of the phases. She and her students, who historically score 4’s and 5’s on the exam, were one of several schools asked by the College Board to road test one of the proposed new labs to see if it brought back the “Oh, wow!” factor. The basic question: What factors affect the rate of photosynthesis in living plants? The new twist: Instead of being guided through the process, groups of two or three students had to dream up their own hypotheses and figure out how to test them. Caroline Brown, a senior who stages the school’s plays, connected the lab to her passion for theater. She borrowed green, sky blue and “Broadway pink” filters from the playhouse to test how different shades of light affected photosynthesis in sunken spinach leaves.

He studied math and physics at Yale, got a masters in physics and was working on his Ph.D. at UC Berkeley. Then he realized his real love was music, and his Ph.D. turned into the study of music perception and cognition.

Nor is it clear that the math we learn in the classroom has any relation to the quantitative reasoning we need on the job. John P. Smith III, an educational psychologist at Michigan State University who has studied math education, has found that “mathematical reasoning in workplaces differs markedly from the algorithms taught in school.”

It’s not hard to understand why Caltech and M.I.T. want everyone to be proficient in mathematics. But it’s not easy to see why potential poets and philosophers face a lofty mathematics bar. Demanding algebra across the board actually skews a student body, not necessarily for the better.

Instead of investing so much of our academic energy in a subject that blocks further attainment for much of our population, I propose that we start thinking about alternatives. Thus mathematics teachers at every level could create exciting courses in what I call “citizen statistics.”

Dr. Atkinson, an expert at applying mathematical methods to linguistics, has found a simple but striking pattern in some 500 languages spoken throughout the world: A language area uses fewer phonemes the farther that early humans had to travel from Africa to reach it.

Dr. Atkinson is one of several biologists who have started applying to historical linguistics the sophisticated statistical methods developed for constructing genetic trees based on DNA sequences.

11 Mathematics Resources to Try in 2011

Taking a test is not just a passive mechanism for assessing how much people know, according to new research. It actually helps people learn, and it works better than a number of other studying techniques.

Then, in November, she posted on YouTube a video about doodling in math class, which married a distaste for the way math is taught in school with an exuberant exploration of math as art .

At first glance, Ms. Hart’s fascination with mathematics might seem odd and unexpected. She graduated with a degree in music, and she never took a math course in college.

The ensuing attention has come with job offers and an income. In one week in December, she earned $300 off the advertising revenue that YouTube shares with video creators. She is also happy that, unlike in her early efforts, which drew an audience typical of mathematics research — older and male, mostly — the biggest demographic for her new videos, at least among registered users, are teenage girls.

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.

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.

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

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.

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.

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.

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

“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,”

The impact of data abundance extends well beyond business. Justin Grimmer, for example, is one of the new breed of political scientists. A 28-year-old assistant professor at Stanford, he combined math with political science in his undergraduate and graduate studies, seeing “an opportunity because the discipline is becoming increasingly data-intensive.” His research involves the computer-automated analysis of blog postings, Congressional speeches and press releases, and news articles, looking for insights into how political ideas spread.

But the computer tools for gleaning knowledge and insights from the Internet era’s vast trove of unstructured data are fast gaining ground. At the forefront are the rapidly advancing techniques of artificial intelligence like natural-language processing, pattern recognition and machine learning.

“We’re trying to take kids who haven’t been engaged in school and hook them to an expanded vision of what their future might be,” he said. When they return to their own schools, the hope is that they’ll be more interested in history, math and English — and have a sense of environmental stewardship as well.

“The most important thing really is teaching kids through hands on, experiential learning,” said Rees. “Our kids do this because they’re inspired to be there every week, to work with adults and do hands on things.”

Like many children with autism spectrum disorders, Ravi is fascinated by trains and buses, entranced by their motion and predictability.

Now, the museum, and others like it, are moving beyond accommodating the enthusiasm for trains and buses among children with autism and trying to use it to teach them how to connect with other people — and the world.

The link between trains and autism is well documented. Autism refers to a spectrum of disorders that typically includes impairment in social interaction and sometimes includes stereotyped interests, like trains. People with autism have difficulty processing and making sense of the world, so they are drawn to predictable patterns, which, of course, trains run by.