Maths
ONE CLASS RUINED MY PROSPECTS IN MATHS
James Clarke
May 18 2009 at 06:04AM www.iol.co.za
James Clarke's Tour de Farce
Anton Oberholzer of Fairland, Joburg, experienced a painful but retrospectively amusing flashback when he read my recent column on Pi Day - the day when mathematicians annually let their hair down to celebrate Pi and the elegant formula "Pi r squared".
He writes, "My singular lack of distinction in the field of mathematics has through the years (as can be attested to by school reports and the like) been blamed on everything from a lack of application to base stupidity.
"Personally, I believe the doodskoot came shortly after I arrived at St Stithians College in the late 1960s fresh from Lichtenburg Afrikaans Medium Laerskool without any sort of command of the English language. You should bear in mind that, in those days in the Western Transvaal, English was not a second language but rather a foreign one.
"My mathematics teacher at Saints was a Soutie who developed an instant and intense dislike for me.
"Then came the day when he had to explain to us the beauty of the mathematical constant Pi. After a lengthy and convoluted explanation he ended, grandly, with the formula: 'The area of a circle equals Pi r squared'.
"Bear in mind that I was still grappling with the fundamentals of English - but I could take no more. I immediately corrected him. 'No Sir', said I, 'Bread are square, but pie are round'.
"Maths has been an uphill battle since then."
Anton's story reminds me (as we old columnists like to say) of an incident in the late 1970s when a press photographer asked President John Vorster if he would smile for the camera.
Vorster growled, "I ARE smiling!"
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USING INDIGENOUS CULTURE TO TEACH MATHS Impti Du Toit 11 January 2006 at 11h00 IOL News
The scope of career choices is often unnecessarily narrowed down simply because a learner has not had the opportunity to study Grade 12 maths and science, or obtained pass marks in these subjects, which are regarded as "difficult".
Without maths or science, the student is often unable to unlock the doors to a challenging career to which he might otherwise have been extremely well suited.
Vuyiseka January of the Shuttleworth Foundation says most learners in South Africa find mathematics hard to understand because traditionally it has been taught as an abstract subject.
As maths is often divorced from a real world context when taught at school, most pupils are unable to understand how it is used in business and everyday activities.
An additional challenge facing black learners is that education in this country is often eurocentric which removes learners mentally and spiritually from their roots.
Lessons are often conducted in English, which may be the pupil's second, third, fourth or even sixth language, she says.
To help educators overcome these learning problems and introduce a more realistic understanding of maths, the Shuttleworth Foundation has piloted a project called Africa meets Africa, which aims to incorporate indigenous cultural knowledge into education.
The aim is to use African arts and crafts, with which learners are familiar, to demonstrate that maths is part of their daily lives and therefore neither abstract nor that difficult to understand, says January, who has an arts and social science background, and manages the project.
For example, in traditional Zulu culture women make pots, weave baskets and produce complex pieces of beadwork. the project aims to use the understanding of shapes and counting skills inherent in producing these crafts to introduce learners to mathematical concepts.
In this way, educators will build on a framework of understanding already familiar to the learner.
At an elementary level, pupils are introduced to natural numbers by counting the beads in one triangle within the design of a crafted object.
Learners in higher grades are taught to understand maths pictorially by looking at the patterns in these objects, as they learn to apply arithmetic formulae and geometry concepts.
As a first step in the project, which is aimed at Grade 4 to 9 learners, the Shuttleworth Foundation has produced an illustrated book and video for educators to use in developing lesson plans for maths or arts and culture classes.
The organisation is funding the testing of these resources in classrooms to see whether they address the educational issues.
January says that during the project, material will be prepared and introduced to department of education officials, and training workshops will be conducted for 800 educators and trainee educators.
Classroom visits and interviews with educators will also be held to ascertain the usefulness of the material in the classroom. A website will be developed and maintained to enable educators to share material and access new material as it is developed.
In 2006 the project will be introduced to schools in KwaZulu-Natal. later it will be rolled out to Gauteng, where it is already in demand, as well as to other parts of the country.
The launch of the project has not been without its own challenges.
January says that in KwaZulu-Natal some parents actually viewed it as a step backwards to have their culture incorporated into education, and cultural overtones in the syllabi were shunned as "proper" education is seen as eurocentric.
But she points out that by incorporating indigenous knowledge into education, learners come to value their culture and the contribution it makes to their general knowledge.
January is also working on the Paarl Local Science Expo, which aims to get learners and educators in townships involved in science.
For details call the Shuttleworth Foundation on 021 970 1200.
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BLACK ACTUARIES ARE ON THEIR WAY, SAYS ASSA January 22, 2006 by Lloyd Coutts
Johannesburg - Hillary Murashiki points out that it is in fact not true that there are only three black actuaries in the country and that none of them is South African.
The statement would have been true as recently as two years ago, he says, but thanks to a R20 million series of initiatives by the Actuarial Society of SA (Assa) and its sponsors, there are today four black South African actuaries and many more to come.
He says there are more than 20 candidates "within striking distance" of joining the ranks of actuaries and about 60 percent of the 800 students who apply to study actuarial science at university are now black.
Murashiki is the chairman of the diversity committee of Assa, set up in 2000 to address the shortage of black actuaries in the country.
At the time research pointed to four factors that were responsible for the shortage:
The high standard of mathematical achievement required for admission into a university actuarial science programme was not generally prevalent in schools in previously disadvantaged communities.
The number of black high school students who took higher grade mathematics to the senior certificate was very small, with even smaller numbers passing, and the number of A symbols was negligible;
There was a very high dropout and failure rate in university and post-university actuarial science programmes, aggravated by the long and strenuous course of study and examinations required by the Institute and Faculty of Actuaries for qualification as an actuary; and
The profession was virtually unknown in previously disadvantaged communities. Potential actuaries from these communities were aware of the medical, accounting, engineering and auditing professions and therefore pursued qualifications in these professions.
"The real reason there were no black actuaries was because black people didn't know about it. It wasn't really so much that there'd never been bright enough black people; that certainly wasn't the problem.
"The problem was that guys would finish three, four, five degrees, have a PhD, and never have heard about it," Murashiki says.
Assa then launched a series of interventions to address the problem.
Its flagship project is called Actuaries on the Move and is aimed at high school pupils.
Project manager Sitshengisiwe Mthembu says the programme was launched as a pilot project in Gauteng in 2002, and 40 pupils from Soweto schools underwent an intensive two-year period of extra tuition in mathematics, physical science, English, study skills, life skills and computer skills.
Thirty-seven students sat for their matric exams and all passed, with three attaining an A aggregate and four achieving 90 percent or more for higher grade mathematics.
Today six of those pupils are studying actuarial science. Of a second group, 12 began studying actuarial science.
The 2005 class obtained 18 distinctions in mathematics, out of a pool of 44 candidates.
There are currently 440 students in the programme, following its extension to Pretoria, Durban, Bloemfontein and Cape Town.
The second initiative, according to Murashiki, is aimed at students at tertiary level "to try and level the playing field for them because they're coming in with a bit of a disadvantage. We wanted those guys who made it to university to try and optimise their performance."
The diversity committee approached government political risk insurer, the SA Special Risks Insurance Association (Sasria), which was refunding to government an accumulated surplus and was interested in spending some of it on social development projects .
A section 21 company called the SA Actuaries Development Programme, with representatives from the universities, the department of education, Assa and Sasria, was formed to assist students with extra tuition, social support bursaries and scholarships.
The high standard of maths required is still a barrier to entry, and there is still a high dropout rate at university.
"It's a substantial problem," says Murashiki. "One doesn't want to get too political, but it's a problem with the school system because what we're finding is that the universities don't have enough guys with a high enough calibre of mathematical skills coming into the system with a reasonable chance of making it through the university programme, let alone the industry's professional qualifications, because it's maths all the way."
What made the two interventions special was that they were financed and supported by the industry.
"We've set them up in such a manner that they're institutional. They have a life of their own.
"There are certain other projects we run under the auspices of the Actuarial Society, for instance we do the Mathematics Olympiad with the Maths Society," adds Murashiki.
"That's supposed to sift out the best maths brains in the country and harvest them for our vocation. We have other interventions which provide in certain schools maths tutoring kits in order to uplift the standards of maths training in specific areas."
According to Murashiki: "What we're looking at now is mentorship programmes for the guys who finish the graduate programme but now get into the workplace, to assist guys to make it through their professional qualification. A long-term goal of ours is to try and sanitise the workplace environment so that it is a bit more supportive of the guys."
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GREATEST MATHS PROBLEM 'SOLVED' : A mathematician at Perdue University in America claims to have proved the Riemann Hypothesis - called the greatest unsolved problem in maths. The hypothesis concerns prime numbers and has stumped the world's mathematicians for more than 150 years. Now, Professor Louis De Branges de Bourcia has posted a 23-page paper on the internet detailing his attempt at a proof. There is a $1 million (GBP555,000) prize for whoever solves the hypothesis. "I invite other mathematicians to examine my efforts," says de Branges. "While I will eventually submit my proof for formal publication, due to the circumstances I felt it necessary to post the work on the internet immediately." The Riemann Hypothesis is a highly complex theory about the nature of prime numbers - those numbers divisible only by 1 and themselves. It has defeated mathematicians since 1859 when Bernhard Riemann published a conjecture about how prime numbers were distributed amongst other numbers. Since then the problem has attracted a cult following among mathematicians, but after nearly 150 years no one has ever definitively proven Riemann's theory to be either true or false. (from Edufax)
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THIRTY-THREE in all directions!
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I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.
-Isaac Newton, philosopher and mathematician (1642-1727)
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This site provides math tricks and tips for students and teachers.
(Courtesy of About.com Anti-virus software)
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Any number squared is equal to one more than the multiple of the numbers on either side of it: 4 x 6 is 24, 5 x 5 is 25.
(Edufax)
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MATHS NOT AN ISSUE FOR QUIET BRAZILIAN TRIBE
(from IOL News August 20 2004 at 07:07 am)
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Washington - Some people have a great excuse for being bad at maths - their language lacks the words for most numbers, United States-based researchers reported on Thursday.
Members of a tiny, isolated Brazilian tribe have no words for numbers other than "one or a few" or "many" and seem to have trouble counting, the researchers reported.
The Piraha tribespeople are clearly intelligent, so the finding opens questions into how language may affect thinking, the researchers say in this week's issue of the journal Science.
Peter Gordon of Columbia University in New York and colleagues studied the Piraha because there had been reports about their unique use of numbers.
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They live along the banks of the Maici River in the Lowland Amazonia region of Brazil
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"I was able to take three field trips ranging from one week to two months living with the Piraha along with Dr Daniel Everett and Keren Everett, two linguists who have lived and worked with the tribe for over 20 years and are completely familiar with their language and cultural practices," Gordon writes in his report.
"They live along the banks of the Maici River in the Lowland Amazonia region of Brazil. They maintain very much of a hunter-gatherer existence and reject assimilation into mainstream Brazilian culture," he added.
There are only about 200 Piraha and they live in groups of 10 to 20. Their words for numbers appear limited to "one", "two" and "many", and the word for "one" sometimes means a small quantity.
"There is no word for 'number', pronouns do not encode number (eg: 'he' and 'they' are the same word), and most of the standard quantifiers like 'more', 'several', 'all' and 'each' do not exist," Gordon wrote.
Gordon got the tribespeople to take part in some number-matching tests.
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'One can safely rule out that the Piraha are mentally retarded'
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"In all of these matching experiments, participants responded with relatively good accuracy with up to two or three items, but performance deteriorated considerably beyond that up to eight to 10 items," he wrote.
"Piraha participants were actually trying very hard to get the answers correct, and they clearly understood the tasks," Gordon said in a statement.
While Piraha adults had difficulty learning larger numbers, Piraha children did not.
"One can safely rule out that the Piraha are mentally retarded. Their hunting, spatial, categorisation and linguistic skills are remarkable and they show no clinical signs of retardation," Gordon added.
They also show some other unexpected differences from many world cultures.
"Not only do the Piraha not count, but they also do not draw," Gordon wrote. "Producing simple straight lines was accomplished only with great effort and concentration, accompanied by heavy sighs and groans."
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Jackie Scheiber of Radmaste and Mary Stuart of The Teacher Network at a recent Maths seminar.
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The Association for Mathematics Education of South Africa - AMESA - is the professional association of Mathematics educators in South Africa. AMESA is the voice of Mathematics Education in South Africa, representing the interests of the discipline and its members at provincial and national level. See the AMESA website if you are interested in the teaching and learning of Mathematics.
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YOUR AGE IN CHOCOLATES
1. Pick the number of times per week you would like to have chocolate - (more than 1 but less than 10).
2. Multiply the number by 2 (two) - just to be bold.
3. Add 5 (for Sunday).
4. Multiply it by 50.
5. If you have already had a birthday this year, add 1760. If not, add 1759.
6. Now subtract the year of your birth. (This should leave you with three digits.)
7. The first digit was your original decision (the number of times you wanted to eat chocolate).
8. The next two digits are your age!!!
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A beautiful mind is not always a sane one (James Clarke)
This article was originally published on page 12 of The Star on October 20, 2003
The enigmatic Don, a reader who sends me many ideas, tells me that when Paul Lynde was asked, "Do female frogs croak?" He answered, "If you hold their little heads under water long enough."
I have never been one for swift repartee like this. Just once in my life have I come out with a good rejoinder and that was when I was about 12 and our maths master, Samuel Hope, exasperated by our dumbness, wrote on the board "0,222222222222".
He went on and on and on with the twos.
Then, breathlessly, for he was a tubby man, he said: "You can write one million more twos after that decimal point - you can write them across every wall in town, but you'll never, never, never get a whole!"
I said, "Except in your shoe."
I don't know what possessed me to say it, but the scene that followed was not a happy one, and maybe that's why I have never been driven to making wisecracks.
I was the dumbest kid in the class when it came to mathematics. I was therefore relieved, but not surprised, to read in New Scientist that Nobel laureate, John Nash - once described as "the world's most promising young mathematician" - told a press conference in London that there was a conspicuous link between mathematical genius and madness.
Nash admitted that he himself went mad, seriously mad - a couple of times.
I had always known that people who are brilliant at maths are bonkers. The evidence is so great that you would have to be mad to deny it.
It is probably quite significant that I was very bad at mathematics. I recalled some time ago in this very column, that only once at school did I achieve an ascertainable mark in mathematics. It was seven percent, whatever seven percent means.
I remember at the time receiving spontaneous applause from my classmates. Even Samuel Hope congratulated me.
Hope was unquestionably mad and unquestionably a genius. I strongly suspect that he turned into a werewolf every full moon, which, aesthetically, would have been an enormous improvement.
But, as I was saying, John Nash admits that for 16 years he suffered madness ranging from schizophrenia to paranoia. At one time he felt all the staff at the Massachusetts Institute of Technology were "behaving strangely" towards him.
This observation of his made me throw my mind back to the time I attained that seven percent mark, and I realised that I too went a little mad.
I was no doubt going through a brief but intense period of blinding mathematical insight because I had a burst of serious paranoia.
I was soon over it though, and I slid back to zero marks.
But it was strange how, from then on, brighter pupils and indeed Samuel Hope himself, seemed to be avoiding me. Obviously jealous because I had succeeded in shaking off my paranoia where they had failed.
The reason I am not surprised by this madness-goes-with-maths theory, is because I am fully aware of how the brain functions.
The cerebral cortex is divided down the centre - the right side being the pattern-recognising side. It recognises beauty for instance, while the left side analyses the situation.
While the right side appreciates a lovely pair of legs, the left side counts them for you.
The left side is the side we use to work out sums such as, "What is 567,9 divided by 7,8?"
I don't know the answer, of course. I am merely being hypothetical or something.
A person who used only the left side of his or her brain would be an ultra-logical thinker, cold and merciless and certifiably mad, like the Receiver's computer - incapable of enjoying beautiful things like duckling bigarade arranged on a plate.
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AUSSIE MATHS PRODIGY HAS HER EYE ON A DEGREE
from IOL News September 18 2003 at 08:48AM
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Sydney - Shona Yu's mathematical ability was evident at an early age. As a two-year-old she was adding up the numbers on letter boxes as the family drove down their street in Palmerston North, New Zealand.
"There is absolute truth in maths," Yu, 16, told Australia's "Sun-Herald" newspaper when it reported that next year she was likely to become the country's youngest PhD.
"There is always a right answer. It is good to have a definite answer at the end of your work rather than just saying the evidence suggests something is right," she said.
Yu, studying algebra at Sydney University, expects to get her doctorate next year. She hopes to stay on and become a professor of mathematics at Australia's oldest university.
Yu, at 14, was New Zealand's youngest ever honours graduate. She finished her first degree at Palmerston North's Massey University at 13.
She is happy at university. "I am surrounded by brilliant, smart people and I don't think of myself as special," she said. "Most of my friends do maths or science but the age difference isn't a factor for me." - Sapa-DPA
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