Embed Size (px)
Citation preview
What Was ...Author(s): Isobel CoxSource: Mathematics in School, Vol. 21, No. 3 (May, 1992), pp. 44-45Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30214887 .
Accessed: 09/04/2014 15:32
Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp
.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].
.
The Mathematical Association is collaborating with JSTOR to digitize, preserve and extend access toMathematics in School.
http://www.jstor.org
This content downloaded from 173.73.163.236 on Wed, 9 Apr 2014 15:32:41 PMAll use subject to JSTOR Terms and Conditions
WHAT WA..
by Isobel Cox, PGCE Student, Institute of Education
Following your plea for responses to the "What if" articles I thought I would write about stacker numbers (November 1991).
Investigations at the school, a mixed London compre- hensive, are very much a bolt-on extra. Many pupils seem to resent interruption to their steadfast passage through the SMP booklets. Their ears pricked up when I said we were going to look at some ntimbers which, so far as I knew, had only just been invented by a Mr Jim Smith. ! didn't know or have the answers having only just begun to doodle with the problem myself. They were told to work in pairs to discover which were stacker numbers and which were not.
As I walked round the class (Year 8) I was surprised at the range of comments.
"You can go on to infinity." "What do you do if the number can be stacked in two different ways?" "You can't do it with prime numbers."
Towards the end of the 45-minute lesson I asked these pupils to stand up and explain to the class their obser- vations or theories. They were to go away and develop and write up these ideas for homework. Samples of which are shown.
I was amazed at the range of mathematics thrown up in the homework and follow-up classroom discussion: infinity, prime numbers, factors, generation of stacker numbers using function machines and a computer pro- gram, labelling dots using ordered pairs, describing the problem algebraically and ideas concerning proof.
The lessons were alive. Part of this was my surprise at their discoveries and strategies. I enjoyed doing the maths myself.
This buzz would be lost I feel if, as suggested, you provide extension notes and examples of pupils work alongside the investigations. We may even feel let down by the comparative response of our own pupils.
:5o please continue as you do with interesting, open, classroom-tested starting points and leave the rest to the pupils!
Aftrtis
rs
wil
reehos twoshorter
tha by Jim Smith,
you feelike
stopr PoyMathecnematics Education Centre,
Sheffie/dAfethsrefnro Polyt ehos nico Thisinvstiatin cn b inrodued y, he eacer sin
explore the situatioi counti~ers
iaon can OHP jtor
ue by
sk e
, ece
, ig ,OnStacker Num~bers n nStack v
hweern ansber patnterns of the followin type.etching
on the board, pupils will also have1
Patte12 of th * 'esprne
th fr
Those who find it
*freedom to explore mi
b~rlrlr~rspecial about the Sta
Some ofthe things h
( s no a
tt-c-chir
++4- ++=C
44 Mathematics in School, May 1992
This content downloaded from 173.73.163.236 on Wed, 9 Apr 2014 15:32:41 PMAll use subject to JSTOR Terms and Conditions
iC~ b ound One the coCcel cSFe
bhe construction
of aStacker
Number bl ocome up with a reasonable
Ilves. Perhaps
something on theasone emerge; n te es
of Cunters,
then add a row which
ing, or it's impo be
03 Puicud be
allowedto
which are notb You might call the Surprise Numbers, but perhaps
leir own name for them.
'ht be drected to
consider wha
" .ker
Numbers made
witc- a result they COUld
move on
to/,
would be reluctant
to
do this too Ihj:eP.sy
to allo pupailsato Ithe
W zo OET =II 2
t a framework,
ate more ideas thinking ve were to
change
this we could change
include the de numbers, and perhaps we could
=(or more). What if we asked
Mathematics in School, May 1992 45
This content downloaded from 173.73.163.236 on Wed, 9 Apr 2014 15:32:41 PMAll use subject to JSTOR Terms and Conditions
