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Q&A #6013

Teachers' Lounge Discussion: How Pi fits into the K-12 curriculum

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From: PRASAN WILFRED <dpwilfred@hotmail.com>
To: Teacher2Teacher Public Discussion
Date: 2002051903:40:08
Subject: THE CONCEPT OF Pi CAN BE CLEAR TO 9 YEAR-OLDS

	I advise my teachers to start from scratch with nine and
ten-year-olds.  Do not use any principles even if they know them
already.

The idea of circumference can be understood by the little ones when
you tell them to imagine walking around a circular lake.  The distance
that one walks to go once around the lake would be called the
'circumference'.  A similar explanation can be given for the diameter.
I have seen a teacher even explain the origin of the word ('dia' means
'through' or 'across') and meter is a word indicating measurement. 
[This explanation re-inforces the language truths that they learn with
another teacher - about Greek and French roots of English words!]

Now draw a circle using a protractor and measure the circumference
using a string.  Measure the diameter by putting a ruler across the
circle ensuring that its edge touches the centre.  Divide the
circumference by the diameter.  Indian children learn the concept of
operations with decimal fractions only from Class Five.  However in
Class three and four we can use approximations.  If the teacher
chooses a diameter carefully while drawing the circle in the first
place it helps.

When we divide even with approximations the answer would always be a
little over 3.  Demonstrate to the class with circles of different
sizes.  Everytime the diameter would be found to be go into the
circumference approx. 3 times.  Then give them the correct figure for
the constant as 3.14 or 3 1/7 - and tell them that they should draw
more circles of varying sizes and divide the circumferences by the
diameters.

The little ones will discover for themselves the amazing truth that
this constant is indeed universal.  (I imagine Archimedes would have
used a similar method to discover this truth for himself!).

At this point we can show them that if we knew the circumference of a
circle we can determine the diameter or the radius without actual
physical measurement and vice versa.

I have used the method of discovery to teach mathematical as well
scientific truths.  Do not hesitate to start from basic facts and work
up like an ignoramus and help children to discover the truths for
themselves.  In fact a teacher should put on an act of surprise at
each such discovery and exclaim how wonderful some of these truths
which were hidden from them all till then until they discovered them!
They will simply love you for teaching them to love Mathematics.

Happy teaching!

- - - Prasan Wilfred, "THE GENIUS" (an institution devoted to IQ
enhancement of children), INDIA

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