Programme of Study for Mathematics at Key Stage 2

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2Page 1 KEY STAGE M AT H EM AT IC S P ro gr am m e o f S tu d y Introduction Key Stage 1 and Key Stage 2 should be seen as a continuum. Pupils will come to Key Stage 2 with a spread of mathematical ability and attainment and should be allowed to continue to learn at their own individual pace. Time should be allowed for pupils to develop and consolidate their mathematical ideas using practical materials before moving on to more formal recording.

• wider range of metric units
• further lines of development
• need for appropriate accuracy
• temperature through practical activities
• mathematical shapes
• perimeter of the playground to the nearest metre
• 2 pupils
• pupils
• numbers
• use
• data

Sujets

• Exposé
• Pupil
• Mathematics
• Development
• Near
• Numbers

Informations

• Publié par: orzi
• Nombre de lectures: 13
• Langue: English

Extrait

HOW THINGS ARE

Edited by John Brockman, Katinka Matson



Introduction


How Things Are is a gathering together of some of the most sophisticated and distinguished scientists and thinkers in
the world, each contributing an original piece-an elementary idea, a basic concept, a tool for thought-relevant to his or her

field of science.


The appeal of the essays is their focus and their brevity: a single theme; a surprising point of view; an explanation
shout why a theory is acceptable or not.


How Things Are gives us a chance to see the minds of distinguished scientists and thinkers at work: the questions they
ask, the methods they use; the thought processes they follow in trying to arrive at an understanding of the world around

us, and of ourselves.


Imagine that you found yourself in a roomful of distinguished scientists, and that you were able to pose just a single
question to each one. These essays can be read as their responses to your questions--written in a language that you can

understand. What a rich resource, this gathering of important thinkers.


Some of the questions whose answers we find in the book are: What's natural? Why are there differences in skin
colour? What are the biological bases of racial differences? How do we understand the current world population, through
history and into the future? What is the difference between mind and brain? What's good about making mistakes? What
are the differences between living and nonliving matter? What is evolution? Why incest? How is human communication

possible? How do computers change the way we think? When did time begin?


Reading the essays is like overhearing a conversation among scientists dining at a nearby table. You will discover not
only what topics get their attention, but also how they formulate the questions they seek to answer. Most important, you

will come away from the book with a deep sense of how scientists inquire and how they discover How Things Are.

In "Part One: Thinking About Science," we find zoologist Marian Stamp Dawkins on scientific explanation;
anthropologist Mary Catherine Bateson on the concept of "natural"; and evolutionary biologist Richard Dawkins on

believing.


"Part Two: Origins," features theoretical physicist Paul Davies on the "big bang"; chemist Peter Atkins on water;
chemist Robert Shapiro on the origins of life; biologist Jack Cohen on DNA; biologist Lewis Wolpert on the miracle of

cells; biologist Lynn Margulis on what a drink called kefir can teach us about death.


In "Part Three: Evolution," zoologist Stephen Jay Gould writes on the idea of evolution; anthropologist Milford
Wolpoff on the relationship between humans and apes; anthropologist Patrick Bateson on the development of the incest
taboo; biologist Steve Jones on why people have different skin colors; paleontologist Peter Ward on the role chance plays
in evolution; and evolutionary biologist Anne Fausto-Sterling on the normal and the natural versus the abnormal and the

unnatural.


In "Part Four: Mind," philosopher Daniel Dennett reports on the importance of making mistakes; logician Hao Wang
on the mind versus the brain; neurophysiologist William Calvin on ways to think about thinking; neurobiologist Michael
Gazzaniga on the unique patterns of each brain; an- thropologist Pascal Boyer on thinking tools; psychologist Nicholas
Humphrey on illusion; psychologist and artificial- intelligence researcher Roger Schank on learning by doing;
anthropologist Dan Sperber on human communication; neuroscientist Steven Rose on the mind /brain dichotomy;
computer scientist David Gelernter on learning how to read; and psychologist Sherry Turkle on how computers change

the way we think.


In "Part Five: Cosmos," we find physicist Lee Smolin on the question of time; physicist Alan Guth on the importance
in science of thinking the impossible; mathematician Ian Stewart on the symmetric patterns of nature; and computer

scientist Daniel Hillis on why we can't travel faster than light.


In "Part Six: The Future," Freeman Dyson writes on the problem of scientific predictions; population mathematician
Joel Cohen on why Earth's present population growth is unique; palaeontologist Niles Eldredge on why the world is not

going to hell in a hand basket; and cosmologist Martin Rees on understanding the stars.


JOHN BROCKMAN and KATINKA MATSON

Bethlehem, Connecticut


Nothing But or Anything But?


Marian Stamp Dawkins


Are you one of those people who dislike science because of what you think it does to the "mystery" of the world? Do
you think that it somehow diminishes people to try to "explain" their behaviour or that it "takes away the beauty of the

rainbow" to talk about light rays passing through water drop lets?


If you are, can I ask you to pause just for a moment and very briefly allow your mind to entertain the opposite view,
perhaps one that will strike you as utterly preposterous and even repugnant? You can, if you like, think of yourself as
being like the captured prince in C. S. Lewis's story The Silver Chair - the one who had to be tied down every evening at
six o'clock because, for an unpleasant few minutes, he had hallucinations and then recovered and was perfectly normal
for the next twenty-four hours. The hallucinations will not last long, in other words. You are quite safe. Just five minutes

of raging lunacy is all you are in for.


The utterly preposterous idea is this: Explaining some- thing in a scientific way does not diminish it. It enhances it. Let
me tell you why. Understanding how things work, even your own brain, has grandeur and a glory that no non-scientific

explanation can come anywhere near.


I do not, of course, expect you to accept this without question. But I do ask that you start by thinking of something
reasonable and not scientific at all--like, say, Abraham Lin- coin. Ask yourself whether it enhances or diminishes your
view of his achievement when you remember that he was "nothing but" a country-born, self-taught lawyer. Then ask
yourself which you admire most: someone who starts from an unpromising background and achieves great things by his
own efforts and personality, or someone who comes from a wealthy and powerful family and achieves high office
because he has an influential father. I would be surprised if Abraham Lincoln didn't come out of that comparison very

well. Saying he is "nothing but" a backwoodsman doesn't get rid of him that easily.


Next, try the pyramids. Does it diminish the achievements of the ancient Egyptians to say that they built them with
"nothing but" the crudest of tools and measuring instruments? My own sense of awe and admiration for them only went
up when I realized that they moved gigantic blocks of stone with no wheeled vehicles and that they built the pyramids
with perfectly square bases using "nothing but" lengths of knotted cord and stakes in the ground. Even the slightest error would have led to the whole structure being hopelessly out of shape, and yet there they remain to this day--phenomenal
feats of engineering and nearly perfect shapes. "Nothing but" simple equipment becomes "anything but" a mean

achievement.


Perhaps by now you can see what I am getting at. If you look at a rainbow and then someone cells you how it comes
about, why should you say that "they have ruined it" by turning it into "nothing but" a trick of light and water? Why not
say the opposite? Out of the utterly unpromising raw material of drops of water and the laws of refraction has come

something so beautiful that it spans the sky and in- spires poets to write about it.


And if you look at animals and plants and all the extraordinary structures and behaviour they have, why reject a
scientific explanation of how they got here on the grounds that it makes them "nothing but" the products of a blind
evolutionary process? You could instead turn and face the full grandeur of the implications of what that process implies.
The bird that builds a nest and brings food to its young may be "nothing but" the result of evolution by natural selection.
But what a result! Birds, just like us, owe their existence to instructions carried on DNA molecules. The scientists in
Jurassic Park who grew dinosaurs out of DNA molecules that were found in preserved blood were on the right track,
even though nobody has yet done this in practice. DNA molecules do indeed carry-the instructions for building all kinds

of bodies-dinosaurs, birds, giant sequoias, and even human beings.


And the molecules do not stop there. Every breath you take, every extra second you remain alive depends on hundreds
of chemical reactions all taking place sc the right time. Life would be