








Comeback for Mental
Arithmetic

All pupils will get new maths tests at 11 and 14.
By BENEDICT BROGAN Political Reporter
MENTAL arithmetic is to be made part of national tests
for 11 and 14yearolds.
They will face a quickfire string of questions to test their grasp of basic
maths principles.
The move is intended to reverse a decline in standards and stop Britain slipping
further behind its economic competitors.
The students who can't do simple sums

AT least four out of 10 college students need extra help
with reading, writing and arithmetic, a survey claimed today.
One in 20 students needed "very considerable" help with reading and writing,
and one in seven had "serious difficulties" with basic maths As many as a
third needed remedial help to achieve a pass mark, the survey by the Adult
Literacy and Basic Skills Unit showed.
Compiled
The survey was compiled from the results of a 20minute test sat by more
than 10,000 students in 12 colleges in England and Wales. Numeracy test questions
included:

Using the 24hour clock, what time do you set your video to
start at 6.15pm and end at 7.30pm?

If 12 people drink three cans of coke each, how many cans do
they drink altogether? The students included people studying business,
management, building and engineering.

It will be welcomed by parents groups who have been dismayed
at the erosion of mental agility by decades of trendy teaching methods.
The change,from next year, will have farreaching effects in the classroom.
Teachers will have to devote more time to the fundamentals of education and
return to traditional learning by rote,including
memorising multiplication tables. In a parallel move on
standards in English, the assessment of 14yearolds
will take greater account of grammar, spelling
and punctuation.
The changes come with alarming evidence emerging that our youngsters plunging
down the world education leagues.
A survey of 13yearolds in 41 countries, to be released later
this year, shows that British pupils came last of all the industrialised
nations for algebra and number work, raising further questions about the
way maths is taught. Another study found,astonishingly, that we are almost
3% below the world average in English. That represents a sharp fall since
1990, when our pupils were above average by the same amount.
The results reinforce concern among Ministers that the existing
tests do not do enough to ram home the importance of the three Rs which the
Government is pledged to defend An education department source said: "The
system is not delivering what we want. We are a bit concerned that people
are not concentrating on the basics."
The new mental arithmetic exam is likely to consist of about
50 questions, read out in quick succession by the teacher, with pupils given
only seconds  without the help of a calculator  to write down an answer.
Some questions will demand a thorough knowledge of multiplication tables.
Under the reform package, schools will also be ordered to publish
standardised scores for test results at the ages of 7 and 11 parents more
precise information on how their children are performing compared to the
average for their age group. Until now they have been told only whether their
child has reached a vaguely defined 'level of achievement'.
Announcing the changes, Education Minister Lord Henley said:
"This will bring extra focus to basic literacy and numeracy , increase rigour
and provide more help for schools. These reforms are good news for teachers
and parents. They will further refine and improve the assessment regime."
Labour accused the Government of "catching up with Labour
policy". A spokesman said: "Ministers still have to tell us when they intend
to introduce another Labour idea  baseline assessment at the start of
school so schools can bring in yearonyear targets for improvement
for children."
But Doug McAvoy, general secretary of the National Union of
Teachers, welcomed the package, saying it kept teachers at the centre of
student assessment.
The announcement came as Government advisers warned that progress towards
improving the qualifications of the country's workforce is slowing.
The National Advisory Council for Education Training and Targets
said it would need 'concerted action' if Britain is to reach the target levels
set for the year 2000  levels which other countries have already achieved.
Chairman Peter Davis warned: " Failure would inevitably affect our economic
performance and prosperity."
11yearolds
will be asked questions like : 
Q. 5 x 5 
A.25 
Q.16 + 39 
A.55 
Q. 9 x 9 
A.81 
Q.19 + 7 
A.26 
Questions
for 14yearolds would be more difficult : 
Q. 85 + 95 
A.180 
Q. 350  75 
A.275 
Q. 39 x 9 
A.351 
Q. 105  85 
A.20 
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Maths mastermind takes on her father!
WHEN Rakhshinda Ayub stepped into the 'times table challenge'
hot seat she was taking on an opponent she knew well her dad. The 11yearold
had chosen to pit her wits against her old man in a competition devised by
one of her teachers, John Burns. The times table challenge aims to test and
improve pupils maths ability, those beating their parents taking on an even
more formidable foe, Mr Burns himself. 
Rakhshinda, who beat her father, Akthar, lost
out to Mr Burns 73 right answers to 57 in the Mastermindstyle final at Aldwyn
County Primary School in Audenshaw [My old junior school LB]. Both had to
answer correctly, in turn, as many times tables questions as possible in
two minutes. For Rakhshinda it's now back to the drawing board. Not only
does she have to get full marks in a preliminary test again, but she has
to beat another adult before she can take on the reigning champion, Mr Burns,
again. "He is very good at maths," she reluctantly conceded. But the modest
victor responded: "The pupils are getting better. We have got one of two
who will beat Mr Burns eventually." Young maths mastermind Rakhshinda is
pictured left with her father Akthar and teacher John Burns.
The Advertiser
23/11/2000 
The Mathematical Experience

by Philip J Davis & Reuben Hersh

6.Confessions of a Prep School Math Teacher (p272)
TED WILLIAMS (pseudonym) is the Chairman of the Mathematics Department in
a fine private school in New England. He was interviewed in April, 1978.
Williams, who is in his early forties, teaches mathematics, physics, and
general science. He also coaches the boys' baseball team. He says that he
prefers to teach mathematics rather than physics because it is hard to keep
up with the new developments in physics. Williams has a master's degree
in mathematics from an Ivy League school and has had an introductory
college course in philosophy. As far as philosophy of science is concerned,
he informed the interviewer that some years ago he had
read Poincaré's
Science and Hypothesis, and recently he had read in Minsky's book
on perceptrons (but he says he didn't get the point). He also read
Bronowski's book that went with the TV series. He
has read a bit of the history of mathematics. He says that his school expects
him to do too much and he has very little time for reading.
Williams says that the history and philosophy of mathematics just don't
come up in his classroom.
In answer to the question of whether mathematics
is discovered or invented, he answered with a snap, "There's not much
difference between the two. Why waste time trying to figure it out? The
thing that is important is that doing math is fun. That's what I try to put
across to the kids."
When pressed harder on this question, he said, "Well, I think it's discovered."
Asked whether he'd ever thought about the consistency
of mathematics, he said, "I've heard about the Russell
paradox and all that, but I really don't understand it. I think
math is like a sandcastle. It's beautiful, but
it's made of sand."
"If it's made of sand, how do you justify its study to your students?"
"I tell them that figures don't lie. You know they don't. No one has come
up with any counterexamples to show that they do.
[This defeats the primary axiom of finding positive proof rather than
asking for disproof of an assumption,and is chronically naive in that you
can get two distinct answers from calculators,depending on whether they work
hierarchically or linearly LB]
But the whole question is irrelevant to me.
In answer to the question as to whether there is a difference between pure
and applied mathematics, Williams answered, "Pure math is a game. It's fun
to play. We play it for its own sake. It's more fun than applying it. Most
of the math that I teach is never used by anyone. Ever. There's no math in
fine arts. There's no math in English. There's no math to speak of in
banking. But I like pure math. The world of math is nice and clean. Its
beautiful clarity is striking. There are no ambiguities."
"But there are applications of math?"
"Of course."
"Why is math applicable?"
"Because nature observes beautiful laws. Physicists
didn't get far before math was around."
"Does the number p exist apart from people? Would
the little green man from Galaxy X9 know about
p?"
"As one gets older, one is less and less inclined to trouble oneself about
this kind of question." "Is there beauty in
mathematics?"
"Oh yes. For example, if you start with a few axioms for a field, you get
a whole powerful theory. It's nice to watch a theory grow out of nothing."
Mr. Williams alluded to the fact that his school now had a computer and he
was teaching programming.
"What's the purpose of computing?"
"No one in high school asks 'why.' It's there. It's fun."
"Is programming a form of mathematics?" "No. Programming is thinking. It's
not math."
"Is there such a thing as mathematical
intuition?"
"Oh, yes. You see it in students. Some are faster than others. Some have
more. Some have less. It can be developed but that takes sweat. Mathematics
is patterns. If a person has no visual sense, he is handicapped. If one is
'tuned in,' then one learns fast and the subject is fascinating. Otherwise
it is boring.There are many parts of math that bore me. Of course I don't
understand them."
"Is there a mystic aspect to math?"
"Math is full of arcane symbols and this is an
attraction. If one talks to a 'real' mathematician, one sees he is
bright. And he is prying open secrets. And because of this, people know
a little more. One is cowed by this larger knowledge."
"Where is mathematical research going?"
"I don't have the foggiest idea."
"How would you sum it all up?"
"As a teacher I am constantly confronted by problem after problem that has
nothing to do with math. What I try to do is to sell math to kids on the
basis that it's fun. In this way I get through the week."
[With these kinds of teacher teaching the subject it's no wonder people
hate mathematics. For those who think that having qualifications means you
understand something,then Mr Williams is a lesson in how dumb someone can
be whilst being academically trained.For those who
feel that they can't deal with mathematics,they can do no worse than
Mr Williams by seeing that mathematics is all around them,and in those areas
where he says it is not. No one should feel cowed either by mathematics or
such people as Mr Williams,having a certificate proves nothing about one's
understanding of the subject in hand,much less one's ability to apply it
and make use of it LB]
Scholastic Rotetation
Fear and intimidation rule
From the textbooks of the school
Don't be asking for more gruel
It's not as if it's sacred
Teachers hold the virtue and sanctity
Of algorithmic rote insanity
Professing knowledgeable banality
It's not their truth that's naked
A psychopathic freak show
Participants will never know
Blind lead blind,and off they go
It's all just Greek to me
Whatever can one learn
When the masters torture and burn
The minds of those who long to yearn
The chimps can have their tea
Playing follow the leader,step in time
Don't ask yourself questions,it's a crime
You'll never get to reach your prime
Accepting what you're told
Trying to teach basic precepts
Set in place unerring concepts
It's hard to stop the inevitable onset
Of a trail that will turn cold
There's no zest in this creation
To light the fire of imagination
And always to receive condemnation
From those who turn away,
Criticism met with indignation
Nonprogressive regressed stagnation
Neurones never feel elation
Sublimation order of the day
No wonder there's no inclination
To drive attempts at innovation
Because there is no implementation
Of logic mixed with art
No way to make an indentation
Of superficial instant gratification
The train is stuck in this one station
Cannot upset the applecart
Why does experience we postulate
Cause the King to instigate
His temper to become irate
At no comprehension from the Knave?
What implemented circumstance
Can clear this turgid arrogance
And haughty naive nonchalance
Of the master o'er the slave?
Advocate some curiosity?
Get rid of animosity?
Show the relevance of viscosity
To those who cannot see?
Simple dogmatic principles
Maintained by simple infidels
To indoctrinate its child pupils
With personal philosophy
What a shame they'll never gain
Insight never fraught with pain
Forever stultified;inane
Never be profound
Spend your life on drugs and driving
Lying,thieving and conniving
Never seem to be deriving
Something above the ground
Useless to maintain imploring
Told to deaf ears as boring
Continue to go on ignoring
Information with no appeal
No way to show the real connection
Or why the need for the selection
The choice of intellectual confection
Regardless of the zeal
To never know of something grander
Always verbalising slander
Always to the LCD* to pander
There's always someone to blame
Systematic robot teaching
Holier than thou pulpit preaching
"We know best",fruitless beseeching
It's time to change the game.
(*LCD  Lowest Common Denominator)
Lee









