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Educational researchers at the Technical University of Munich (TUM) have found that schoolchildren can independently develop strategies for solving complex mathematical tasks, with weaker students proving just as capable as their stronger classmates. Researchers in mathematics education worked with approximately 1600 8th grade high-school students in various German states. Following an introduction to the general topic by their teachers, the school children were given a workbook of geometric tasks that they had to solve on paper and using a computer over four school periods. Calculating the surface area of Gran Canaria was one of the real-world, free-form assignments the students had to tackle. The workbook material included explanations and examples of various problem-solving approaches. The teachers took a back seat during the session but were on hand to answer questions from the children, who worked in pairs. After testing the students' skills before and after the session, the researchers recorded a significant improvement in their capabilities. The students learned to apply mathematics more effectively, the researchers said. The students were also able to call on these skills in a further test three months later. "We expected students who were weaker at math to benefit more from a greater degree of guidance through the module," said professor Kristina Reiss.  "But we didn't see a significant difference between these and stronger students." The researchers also found that there were also no differences between boys and girls. "We now know that students - also those who are weaker in math - have the skills to master even very complex subject matters at their own pace," said Reiss. Topics: Cognitive Science/Neuroscience

Economics writer Tim Harford studies complex systems -- and finds a surprising link among the successful ones: they were built through trial and error. In this sparkling talk from TEDGlobal 2011, he asks us to embrace our randomness and start making better mistakes.

The strange simplicity of economic relationships An odd feature of economics is that economies constitute an apparently complex system, but analysts are often willing to give confident answers about aggregate outcomes, based on simple relationships that always hold.

In the spring of 2000, I began a three-year stint on Citigroup's corporate-derivatives team. I was just months past my twentieth birthday, with no work experience to speak of, in a world beyond my imagination. As my boss summed me up after a day of interviews, I was "fucking unpolished." The credit-derivatives group, then just three or four people I sat next to, soon spawned an ever-expanding team managing ever-more complex creations: credit-default swaps, collateralized debt obligations, and the myriad other structures built with black boxes and shrouded by acronyms. Meanwhile, my group continued to peddle mostly the forbears of these recent menaces, the more mundane interest-rate swaps and Treasury-rate locks. The newer derivatives, though hardly identical to their predecessors, nonetheless evolved in similar environments, were likewise designed to manipulate risk, and were also customized on a trade-by-trade basis. Our clients were non-financial corporations, the Deltas and Verizons of the world, which relied on us for advice and education. Our directive was "to help companies decrease and manage their risks." Often we did just that. And often we advised clients to execute trades solely because they presented opportunities for us to profit. In either case, whenever possible we used our superior knowledge to manipulate the pricing of the trade in our favor.

The failure of social scientists to seriously question their own ideological and methodological assumptions contributes to the complex interrelationship between global ecological and individual psychological problems. Much of the literature on the tragedy of the commons focuses on saving the global commons through increased centralization and regulation, at the expense of the individual's autonomy and psychological sense of community. "Utopian" speculation in general and anarchist political analysis in particular are necessary correctives to misplaced attempts to merely rearrange the elements of the status quo rather than to radically alter it in a direction more in keeping with both survival and human dignity.

Civilizations rise, decay and die. Time, as the ancient Greeks argued, for individuals and for states is cyclical. As societies become more complex they become inevitably more precarious. They become increasingly vulnerable. And as they begin to break down there is a strange retreat by a terrified and confused population from reality, an inability to acknowledge the self-evident fragility and impending collapse. The elites at the end speak in phrases and jargon that do not correlate to reality. They retreat into isolated compounds, whether at the court at Versailles, the Forbidden City or modern palatial estates. The elites indulge in unchecked hedonism, the accumulation of vaster wealth and extravagant consumption. They are deaf to the suffering of the masses who are repressed with greater and greater ferocity. Resources are more ruthlessly depleted until they are exhausted. And then the hollowed-out edifice collapses. The Roman and Sumerian empires fell this way. The Mayan elites, after clearing their forests and polluting their streams with silt and acids, retreated backward into primitivism. As food and water shortages expand across the globe, as mounting poverty and misery trigger street protests in the Middle East, Africa and Europe, the elites do what all elites do. They launch more wars, build grander monuments to themselves, plunge their nations deeper into debt, and as it all unravels they take it out on the backs of workers and the poor. The collapse of the global economy, which wiped out a staggering $40 trillion in wealth, was caused when our elites, after destroying our manufacturing base, sold massive quantities of fraudulent mortgage-backed securities to pension funds, small investors, banks, universities, state and foreign governments and shareholders. The elites, to cover the losses, then looted the public treasury to begin the speculation over again. They also, in the name of austerity, began dismantling basic social services, set out to break th

As the New York Times has detailed, "Some of the nation's largest corporations have amassed vast profits outside the country and are pressing Congress and the Obama administration for a tax break to bring the money home." Yet, across America, thousands of teachers are being laid off, programs to help feed needy children have been eliminated, and Medicare is under attack. It's time for us to fight back and tell Congress that corporations need to pay their fair share. The first step? Understanding the complex accounting tricks and loopholes giant corporations use to evade taxes. Here's the video that explains it all: