Bills, L (Ed) Proceedings of the British Society for Research into Learning Mathematics 19(3) November 1999
PRACTICAL ACTIVITIES FOR POST- 16 MATHEMATICS.
Ruth Forrester
University of Edinburgh
The \rL\iLIC
~~t’practical wxjrk in learning mathematics has long kcn rwx>gniscd. The
Hwklow Conln~ittcc ( 1926) rcxxJ1mrnendd giving greater enlphasis to practical work
for “not only does it sLlpply a concrete and experimental basis from which the pLIpil
may proceed to abstract rcasonin:, but it vitalises the work for the pupil and
stimula{cs his (sic) interest in it”.
Practical activity is a key clcn~ent in the cleve]opnlent of understanding.
Icl
Bills, L (Ed) Proceedings of the British Society for Research into Learning Mathematics 19(3) November 1999
(Potari, D. & .I.W’.Sear], Teach. Math. Appl.& , 2,56-68, 1989)
y [hat sho~ving applications to real life will provide motivation.
Despite these bcnc!. its, practical activities arc rarely Llscd in secondary mathematics
classes.
Most tcachcry blumc l:lck of time. 1[does seem that some investigation of the
~31~ssi13i
litics/c!i fiicllllics of practical work (or upper secondary pupils may bc
iv(~rth~~hile,
At [he Edinburgh Ccnlrc for h4a[hcmatical Education wc have dclclopcd a number
(J!’practica] activities on the theme c~fparabolas. These aI-Cpractical in two
di ffcrcnt ways:
Lci
Bills, L (Ed) Proceedings of the British Society for Research into Learning Mathematics 19(3) November 1999
T]~eyin\{>]vct hcp L\pi]sin “doino~“, e.g. lego parabola activity.
and/or
. They relate the school nxi[hematics to real life. e.g. building a suspension
bridge.
●
Activities which cm be adapted for usc with pupils across the till range of abilities
haJTcbcwn dctcloped.
One ~ctivi[y, for examp]c, invo]vcs pLlpils in curve stitching [o envelope a par-abolzl
and then using their own cardboard parabola to make a parabolic mirror which will
l-OCLIS
light to a singlt line. This activity can involve working on equation of a
s[rai:ht iinc, ncga[ivc nUnIbCI-S, decimals, coordinates in ~ qLiadI”ants,a~gebrai~
work at dil[crenl levels (USCof variables, sLlbstitLltiorl,the discrimiriant...).
sprc:~dshccts iind s(}on, as appropriate to the stLldcnt. It also makes a connectiml
with real Iii’c (discLlssion of radar etc. ) dcmonstralirrg clearly a Lv+cfulapplication of
this mathematics.
WC ha~re carried OL[lsonic pi]ol studies, trying out ideas with pupi]s in secondary
school (S2 (age 13/14) a runge of different abilities), in primary school, special
school, M a workshop for- vcrjr able pupils and a workshop for all ages at
Edinburgh In[crnational Science Festival. We have also tried out our ideas with
Llndcrgraduatc t~li~tllet~l:~ticit~lls
and surveyed their responses to the material.
We ha~c now mude arrtingcnwnts to work with the Ccn(rc for- Mathematics
Teaching at Plyn~oL~thUniversity and have recrL~i[eda number of schools to take
part in the prc>jecl. WC plan to concentrate on S5 pupils (a:c 16/17) across [he fLlll
range of abi]itics.
The ethnographic / iil Llnlina[ivc c~alualion methodology will bc LISCCI.We hope to
look c]ose]y at tcachcr as WC1las pupil responses to the LISCof practicol tictivi(ics
and to make comparisons bctwwn male and female responses and city and rural as
;vcII as Scottish and English schools.
Bills, L (Ed) Proceedings of the British Society for Research into Learning Mathematics 19(3) November 1999