2,000yr-old calculator that just didn't add up
BY DANIEL BATES
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
Now, after painstaking reconstuction, physicists say it could track astronomical
movements with remarkable precision. It was also able to follow the movements
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
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
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.
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 .
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?
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