2,000yr-old calculator that just didn't add up

BY DANIEL BATES

Ahead of its time: These 3D images show how the dials and gears of the device would have looked [Pictures: Dragon]

IT WAS sunk with a wrecked ship in 80BC, found by divers in 1900 and until now has baffled scientists. But the secrets of the Antikythera mechanism have finally been unlocked - and scientists claim it is  more valuable than the Mona Lisa. The device is a complex arrangement of more than 30 bronze gears, wheels and dials, and is at least 1,000 years ahead of its time. Remnants of a case containing the pieces (one is pictured below) were found in a shipwreck off the Greek island of Antikythera in 1900. In June this year, physicists used X-rays to read inscriptions and identified it as a clock-like astronomical calendar. But the precise function remained an enigma. Now, after painstaking reconstuction, physicists say it could track astronomical movements with remarkable precision. It was also able to follow the movements of the Moon and the Sun, predict eclipses even recreate the irregular orbit of the Moon.
It may have predicted the positions of some of the planets. Lead researcher Prof Mike Edmunds, from Cardiff University, said: 'The design is beautiful, the astronomy is exactly right. The way the mechanics are designed makes your jaw drop. Whoever has done this has done it extremely well.' The findings. published in Nature, suggest Greek technology' was far more advanced than previously thought. No other civilisation created anything as complicated for another 1 ,000years.

Other marvels from the past.

  • The Pyramids: In the 3rd millennium BC, there were no cranes or diggers. But the Egyptians managed to create 110 structures reaching 146m high.
  • The Incas: The South American empire lasted just 110 years from 1438AD, but built 22,530km of road.
  • Aztecs: They lived in Central America in the 14th to 16th centuries with education and religion.
  • Stonehenge: The Druids moved huge rocks 320km from Wales to Salisbury, Wiltshire, in the Neolithic and Bronze Age - and put them on top of each other.
  • A 14 cm clay battery was found near the Iraqi capital Baghdad. It appears to be 2,000 years old.


Y earlier algebra = results

Amid concerns children are not numerate enough,Ian Benson looks at a new teaching method

Never too young: Influential research is encouraging the introduction of algebra to children at an early age

An end to one of America's most bitter 'education wars is in sight - and it may have significant implications for Britain's schools. Algebra is set to he taught in primary schools across the US, following recommendations from the National Council of Teachers of Mathematics (NCTM) in September. This report represented a U-turn by the teaching council. In 1989, it sparked off the 'maths wars' with a set of guidelines for teachers that emphasised 'open-ended' solutions to problems, encouraging children to develop their own techniques. The result was a generation of underachieving schoolchildren and angry parents, many of whom petitioned their schools to drop what they called 'fuzzy maths'.

Turning the tables
Universities became increasingly concerned by undergraduates' poor numeracy; a fifth of first- year students now require remedial maths teaching. The final straw came in 2003 when the Trends in International Mathematics and Science Study (Timss) ranked 13 to 14-year-old American students 15th in a table measuring the mathematical abilities of schoolchildren around the world. The list was topped by Singapore, ahead of South Korea, Hong Kong, Taiwan and Japan. England and Scotland were 18th and 19th respectively. The strong showing of Asian countries in the study influenced the latest NCTM report. Council president Francis Fennell has said that the new guidelines will move US mathematics teaching closer to the Singapore model. Now, pre-algebraic concepts will be introduced as early as the first year of school. The Singapore model of teaching derives from the post-war Russian curriculum, devised by working mathematicians who emphasised teaching algebra in primary school. American maths teaching, along with that of most of Western Europe, is based on the work of the Swiss developmental psychologist Jean Piaget.

Elementary approach
Piaget argued that children develop by passing through a senes of tour cognitive stages, not until the last stage were they able to reason about permutations and combinations of figures. Educationalists who follow Piaget, therefore, ensure that children are not introduced to algebra before early adolescence. The Timss results, on the other hand, indicate that children can cope quite readily with abstract concepts before early adolescence. Denying young children algebraic concepts and notation, as Piaget and his disciples do, causes irreparable damage: the curriculum is reduced to a shopping list of loosely connected topics - fractions, long multiplication, division. In the US, the currlculum is set state by state but, given the backlash against 'fuzzy maths', there is every reason to believe the new recommendations will be followed on a national scale. Some of the strongest proponents for the change come from California, where highly numerate immigrant engineers and technicians from Asia are unwilling to let the system fail their children.
What about Britain? For the past three years, I have been providing booster mathematical lessons at ten British schools, state and private, to put into place the ideas of educationalist Caleb Gattegno, the major figure in mathematics teaching innovation in the 20th century. Along with Belgian teacher Georges Cuisenaire, Gattegno revolutionised the teaching of maths. Using rods to teach algebra, Cuisenaire and Gattegno found that children were able to grasp difficult ideas earlier  than Piaget predicted. When this approach was first introduced to British schools in the 1950s, 100,000 textbooks and sets of rods were sold to parents, schools and teacher training colleges. Nevertheless the innovation failed to cross the chasm from early adoption to general use and was almost lost .

School Britannia
A project known as the Stanford Tizard aims to reintroduce early algebra to British maths teaching. It has been able to reproduce a systematic gain in performance by children oyer their peers by teaching algebra before numbers. Now, with politicians ceaselessly talking up the 'knowledge economy' and warning us about the competitive threat we face from Asia, what better move could there be than to replace an outdated model of mathematical learning that holds back our children? America has come to its senses. How long before our own mandarins wake up? Work needed:Britain has underperformed on numeracy skills [Metro Jan 2007]

  • More information can be found at http://parents.sociality.tv/ BETT07/SW65
  • This is an extract from an article first published in the January 2007 issue of Prospect magaine (www.prospect-magazine.co.uk)

Edited by BEL JACOBS focus@ukmetro.co.uk


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