Group items tagged

"computerbasedmath.org is the project to perform this reset. We're building a completely new math curriculum with computer-based computation at its heart, while campaigning at all levels to redefine math education away from historical hand-calculating techniques and toward real-life problem-solving situations that drive high-concept math understanding and experience."

"The Millennium Mathematics Project (MMP) is a maths education and outreach initiative for ages 3 to 19 and the general public. The MMP is a collaboration between the Faculties of Mathematics and Education at the University of Cambridge, and is active nationally and internationally. Our focus is on increasing mathematical understanding, confidence and enjoyment, enriching everyone's experience of mathematics, and promoting creative and imaginative approaches to maths."

For centuries, some of the greatest names in math have tried to make sense of partition numbers, the basis for adding and counting. Many mathematicians added major pieces to the puzzle, but all of them fell short of a full theory to explain partitions. Instead, their work raised more questions about this fundamental area of math. Emory mathematician Ken Ono is unveiling new theories that answer these famous old questions.

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

"THE GRAPHING CALCULATOR FOR FUNCTIONS, GEOMETRY, ALGEBRA, CALCULUS, STATISTICS AND 3D MATH!"

"Based on data from a randomized sample of universities and online volunteers who completed a survey, men and women who pursue STEM degrees tend to become interested in science in elementary school. When asked which people and experiences helped to spark their interest, women were more likely than men to select a teacher, a class at school, solving math problems and spending time outdoors, whereas men were more influenced by tinkering, building and reading. As men and women enter college, passion for the field far outweighs all other influences as the main reason for their persistence"

"Den Forschern zufolge legt dieses Ergebnis nahe, dass der Grund für die Diskrepanz der Einschätzungen beim Selbstbild von Mädchen zu suchen ist. Schülerinnen werden vermutlich eher durch Geschlechterklischees und Stereotypen als aufgrund tatsächlicher Leistung dazu gebracht, ihre Fähigkeiten in Mathe schlechter einzuschätzen. Dies führt dazu, dass sie ihre Angst im Bereich Mathematik überbewerten. Mädchen denken demnach also nur, sie hätten mehr Angst, obwohl dies in der konkreten Unterrichts- und Prüfungssituation nicht zutrifft. Dies wiederum sei vermutlich ein wichtiger Grund dafür, dass Frauen weniger häufig als Männer mathematikintensive Berufsfelder wählen, meinen die Forscher. Originalarbeit der Forscher: Goetz, T et al. Psychological Science, 28. August 2013"

Interactive Science Simulations Fun, interactive, research-based simulations of physical phenomena from the PhET project at the University of Colorado.

WHAT do earthquakes, spinning stellar remnants, bright space objects and a host of other natural phenomena have in common? Some of their properties conform to a curious and little known mathematical law, which could now find new uses.

sounds like good value proprietary science + math software for schools

ETHEREAL quantum entanglement has been captured in solid crystals, showing that it is more robust than once assumed. These entanglement traps could make quantum computing and communication more practical.

COULD the structure of space and time be sketched out inside a cousin of plain old pencil lead? The atomic grid of graphene may mimic a lattice underlying reality, two physicists have claimed, an idea that could explain the curious spin of the electron. Graphene is an atom-thick layer of carbon in a hexagonal formation. Depending on its position in this grid, an electron can adopt either of two quantum states - a property called pseudospin which is mathematically akin to the intrinsic spin of an electron. Most physicists do not think it is true spin, but Chris Regan at the University of California, Los Angeles, disagrees. He cites work with carbon nanotubes (rolled up sheets of graphene) in the late 1990s, in which electrons were found to be reluctant to bounce back off these obstacles. Regan and his colleague Matthew Mecklenburg say this can be explained if a tricky change in spin is required to reverse direction. Their quantum model of graphene backs that up. The spin arises from the way electrons hop between atoms in graphene's lattice, says Regan. So how about the electron's intrinsic spin? It cannot be a rotation in the ordinary sense, as electrons are point particles with no radius and no innards. Instead, like pseudospin, it might come from a lattice pattern in space-time itself, says Regan. This echoes some attempts to unify quantum mechanics with gravity in which space-time is built out of tiny pieces or fundamental networks (Physical Review Letters, vol 106, p 116803). Sergei Sharapov of the National Academy of Sciences of Ukraine in Kiev says that the work provides an interesting angle on how electrons and other particles acquire spin, but he is doubtful how far the analogy can be pushed. Regan admits that moving from the flatland world of graphene to higher-dimensional space is tricky. "It will be interesting to see if there are other lattices that give emergent spin," he says.

It's not quite Cyclops, the sci-fi superhero from the X-Men franchise whose eyes produce destructive blasts of light, but for the first time a laser has been created using a biological cell. The human kidney cell that was used to make the laser survived the experience. In future such "living lasers" might be created inside live animals, which could potentially allow internal tissues to be imaged in unprecedented detail. It's not the first unconventional laser. Other attempts include lasers made of Jell-O and powered by nuclear reactors (see box below). But how do you go about giving a living cell this bizarre ability? Typically, a laser consists of two mirrors on either side of a gain medium - a material whose structural properties allow it to amplify light. A source of energy such as a flash tube or electrical discharge excites the atoms in the gain medium, releasing photons. Normally, these would shoot out in random directions, as in the broad beam of a flashlight, but a laser uses mirrors on either end of the gain medium to create a directed beam. As photons bounce back and forth between the mirrors, repeatedly passing through the gain medium, they stimulate other atoms to release photons of exactly the same wavelength, phase and direction. Eventually, a concentrated single-frequency beam of light erupts through one of the mirrors as laser light.

In 1967, Simon Kochen and Ernst Specker proved mathematically that even for a single quantum object, where entanglement is not possible, the values that you obtain when you measure its properties depend on the context. So the value of property A, say, depends on whether you chose to measure it with property B, or with property C. In other words, there is no reality independent of the choice of measurement. It wasn't until 2008, however, that Alexander Klyachko of Bilkent University in Ankara, Turkey, and colleagues devised a feasible test for this prediction. They calculated that if you repeatedly measured five different pairs of properties of a quantum particle that was in a superposition of three states, the results would differ for the quantum system compared with a classical system with hidden variables. That's because quantum properties are not fixed, but vary depending on the choice of measurements, which skews the statistics. "This was a very clever idea," says Anton Zeilinger of the Institute for Quantum Optics, Quantum Nanophysics and Quantum Information in Vienna, Austria. "The question was how to realise this in an experiment." Now he, Radek Lapkiewicz and colleagues have realised the idea experimentally. They used photons, each in a superposition in which they simultaneously took three paths. Then they repeated a sequence of five pairs of measurements on various properties of the photons, such as their polarisations, tens of thousands of times. A beautiful experiment They found that the resulting statistics could only be explained if the combination of properties that was tested was affecting the value of the property being measured. "There is no sense in assuming that what we do not measure about a system has [an independent] reality," Zeilinger concludes.