CERTIFICATEPROGRAMME IN
TEACHING OF PRIMARY SCHOOL
MATHEMATTCS (CTPlrO
Term-End Examination
June,2005
LMT-O1 LEARNING
: MATHEMATICS
MaximumMorks: 700
Note t Ansuer any ten questions,
r. (a) What is the differencebehreen a 'scheme' and a
'schema'
? Give an exampleeach to bring out the
difference.
{b) List two charactedstics informailearning.Also give
of
an exampleof informal learning of mathematics by
childrenoutsidethe classroom.
(c) One child thowht ihat 0 3 was smallerthan 0.300
while anotherchild thoughtthat 0.3 was biggerthan
0 300. What do you think are the reasonsbehind
these responses How would you help the children
?
realisetheir error ?
LMT-O1 P.T.O.
)
2, (a) What is the difference bet\r/em conceptual and
proceduralknowledge Explainthis using'division'as
?
an example.Also descdbehow you wouldexplainthe
concept of divislon by adoptlng a 'conshuctlvist'
apprcacn.
(b) Describean activlty that can be usedto explaln the
concepts perimeterand area.Also explalnhow you
of
would use the activity to illustrate the difference
behlreentheset\ro concepts,
3. {a) What doesarea mean ? Gve hvo d,stlnct actMties
to help children Lmderctandwhy area is not
length x breadth.
(b) Explain the processoI'abstraction'. In what ways
does 'thinking mathematically'require dealncgwith
abstraction ? Your explanation should include
examples relatedto developingspatialabilities.
4. (a) Gving hro examplesfrom operationson fractions,
explainthe needtor dewlopingthe abilityto estimate.
Further, give two disiinci activitiesthat would h€lp
childrendeveloptheir eshmation skills.
{b) Do childrenleam by imitation? Give reasons your
Ior
LMT-O1
5. (a) What is meant bg 'egocentrism' ? D€scribe the
experiment don€ by Piaget to t€st whether
pre-schoolers take another person'sperspecti\re,
can
How did later researchers
modil!' the o.p€dment,and
what did they find ?
{b) Explainthe prccasses inolved in'handling data'.
Illustratethem ttnowh an example.
6. (a) Givean e l
LMT-OI 3 P.T.O.
8. (a) Supposeyou haveto teach childrenmultiplicationof
fractions.What would yout methodbe if you follow '
{i) the bankingmodel ?
model?
(ii) the constructivist
(b) Explain,with an exampl€from your o\r,'nlearningof
mathematrcs, how solving probl€ms helps in
understanding relatedconcepts
the
(c) Without finding &e L C.M. say which of the t'r'/o
hactions is bisger : 217/597 or 217/589 Gl.'"e
reasons your answef.
fof
9 . Gve the stageswe need to go through while solving a
problem,according Davisand Mayer Alsoillustratethem
to
in the context of solvingthe followingproblem '
ln a sports club there ore 30 people who ptoy footbot'
20 people L,hopta\ badmintonand 70 rDho plov both
games.Hol, mony club members play ot least one of
tu
lO. GIve one example €ach in support of the following
statements: 10
(i) Children tearn when they are active
{ii) There is a diflerence between guided learnlng and
simply imPartlng information.
(iii) We rped to adapt the cw{iculurn to elofue
child-sensitivePedagogies
(iv) t nguage aftects children's maihematical l€aming'
LMT.O1
ff. (a) My frtend beltevesthat South Indiansare ttetter at
mathernaticstlran North lndians. How would you
checkwh€therthis statement cotect or not ? What
is
data would you needto collectlot this ?
(b) I-lst tv,roconceptsthat a chlld neeJsto know befote
she ls inkoduced to decimal fractions. JustlfrJ!'o!r
cholce of conceFrts,
(c) 'asslmilation' and
Rplain the processes of
'accomrnodation'of a schema in the context of
leaming to inteQret data.
f 2. (a) Mrv is it lrnportant to let ch dren speak out their
for
i&as ? Give three reasons this.
(b) List five chamcteristics an activi9 that encourages
of
learning.
{c) l tlat is the dilference betreen irducti\€ and
. deducti\€logic ?
LMT-OI
qo.gr.d.-or
qrqFmfrsrfiq qfirro eqcc S
*
rrrm-rnrq,r{6q (fi.d.fr.qc.)
v*in qtsr
TT, 2OO5
rg.qr.*. -or , qfrn eqrr
€tg : 3 qvt etftrids si6 : 1oo
alz ffi
r. (6) 'Sc' sil{ 'dql' * d-q:r
St qs qti * fdq r+4 qt gs-q6 sqrc{ur
€fss t
(q) sr-iqflFq sq i fuc * A eeror {aFq r
qEit er'{r
Wd } qrtr erffi+ sq t lFn
ffi sr c4 csrE{"r dfus r
S
(rT) qd ffi t fr os,osoot +fr A Eeh
q6
qs+{d 6r qr++t t+ os, osoo q-fl t t
i
tnq+f{sn fr q.di + {4 str'i t ffi dq +
er qnort ? {d + 3-i-frq€fr 613r{snr
ffi t qrqc+d q{d *'+ qti ?
LMT.Ol P.T.O.
sidt
2. (6) erqsRqleis flq eil{ clfiqrdq nt{ t FIr
'qrq' qr sqE{or gq q+ Ec dfqq t
ia
i z
'rq-{qrd TiR( d 3rq{6{ qrq qn d {i6ff{r
d Bs {6R Mn, gsqr S qslq dFq I
(s) cd ES qldfrftr6r sslc dfqs + qf'tufid
'
d{
,j*" qi 3rqq@rrcii srgri q trq g*Iqt(
+r
*r qi vq-a i r qt ft ffi{q 16 5{ st'ii
eneqnsltaii 6-s qfr{ sc 6G + fdq efic
$
!q rfrfrRTqr cdr *l +ti I
'd-{rd tr ' !H
3. (q) td.Fd ff wt ed t ?
- ' '
i-€? qEit s} qE4( €q{l i {qE 6r} *
t',
fds 3rq A wn-*ldr lldFftzi {fqq I
(s) 3T{fiq-{ul si*qr d qq{Fq r trFrrfrq
+1 Fc
n iEi t ffis fo-c6{Eq 3T1ii6{ur $r-dr
sir
6 gsrt tfr i ? 3rc+ Rtror"r ii rqrq-qqifi
Mffiq{fiE.as
:rjqrc
4. (q) Fr=ii {BqFii n 5B i sqr6{ur gq qsfd
sit it
fl'ni d qTqtr ffid 6d d
e€Fq r {s+ efi, i '?arr-erd'IqftfrFr'il
*ls + *di i :qrn e'nt + +k!ii A
s$ ii qo++ difi t
ffid
(q)Fr qA qrq o$ ffi t ? 3rG st-{ +
. 6Rur {drgq I
LMT-O1
5. (6) 3rq*qt{dr' sr qr 3trfi z qq-S {d Ed
qtu + i-sfts n fu vne t qr r-fi, rS
dq+ + tds firqr$ tqq q ml'r er auf+
em
d f r Sr f f i * e K * d q - r d f w n + q t
FrTccdF{ oT\a 6s 6rw{ cr cd+ ?
drs
'e@ *r qeqTd fi+' n {[kd frwii +1
tel
sTtlES I la se6ol dRI qqIfESr
6. (4) qe ai wa3-gwdr Rs sd qr$ ffi t+
ii
fta qr r+*q qfus n Fffi sBqrd qTlfdr
€r I ts fuii $r tcor 6o qEii $i +
qfss
r-rd$-dFFi Frtr B, rt* i s-
d
fld i ffi gq rmdsdfr q{e) q'e * fds
erc qdi d {<<*-t qli ?
(€) 6i EEii +i g+ qa6 * qa t snr rd d6i
+ fdq IMd-d 6'{r qrfrq r tqr q'+ + fdC
srqwr s* Edi q)'{iEr+qr'tsft t M
+ tci t Rr 4ti ? 3nq+1 ffiFsftT
cqnrrd € tg+r {-si++e*q+i qti ?
7. (6) T+{rc+n qqqqEii si n ffi dffi t s"i
t d-cffii {dr{q r 3
(@) 'irfi'Tdtq
3cqfr flr e ? 2
(T) rrftrii|q xrrrqqfaqqqr Ei'Td 6G lsa siFsq
72+22+32+...+n2
n-
= . 3 * n_ + v n : r
2 a
LMT.O1 P.T.O.
q-ii
s. (s) cri dfqq rd 3{rqs d ffd * yn oc+
fuor+ rqReTrc
t
( dG-'rqisd
tiit r++rqr0{ise
qccri t A i{rr* fqqrt d RFrqr dfi ?
fc) 'rft|{ d€i + 3rqi 31-{.!+iirt+ csrd{"T
t t6.t
{qgrss f6 {srcii d-E-d fi} t s-{+ g-$
d {c-s}n rrec ffi
€rqqnun3ii ++ t I
t'rl k{r q{fic cqrq{diucr\at fr6rd ffirss fd a-n
n t ++?e1 nrr q-de I zti/ss7qr 277/s8s.
sTc+ * qnsrffTEs I
rfl
g. tfuq 3il{ nq{ e rgvn, vqre d re s,A n r6c
a*"ii t l-gr+ qw t I sM Fl FIqfrfun {aE d
6d *'{+ } gq{ ii F€ qtn{s :
('a ei{d ffid I so qfu vean 6-; P, 2s af6
dsrqe+ rc qfa ffi
rr\ eilT -r
$zaia
d r a-argq wq * Qd'R-ai
fr d qi srd
6q A 6s c6' +d.q6T ffi d t 10
10.tTlqfrfuq ssrS + qq ii rS+ w S-W **
dlss :
(i) {r+ Fq ffi t qs a str-c €t I
(i ripHc t ffi 3TtI cr+rfr ii + frs
fr,i
eirri r
r"') d qr
d
Rigurfrftiqi ffid a nii r
{tq {€i fr qFrn ffi d cFfiqIct qTqr 3fiR
61
*'i +drA ?
LMT-OI
'10
I
rr. (s) R q6 fFdsr qr{qrA ft str{ qFdiii 61(tr{I
q <&qqr.frq i +rdrit t r qr oq-a
ffi'm
s-€l€ qr € eFS qi? 3rNi* 6$ ? IF+
fdq qrc-dfuq F6R* efisi csFd *'d An ?
(q) Evrqtr{ Frn i qfifudq'{ri $ c-6d
s,'r q-€i a}
fqq efrqqmniq1qF-srt+4r .q6frd, c{ri n
d er+qnuneit {S {fiq r .qqi s}
d
3r-qutroTq t -{dr ge S dfrq r
Tfr
('T) 3?isiiin firq{ f{6rd-+€@i + {i
d 'Ffu-d{ *{ '€qr+s{' d ltrqrcil +
{llgrgq I
12.(6) EEird 3{qq-xqc ffit q} 4s +.{r t{ +dt
q€FWft ? ss* d-q*Rq ffss r 3
(€) W qfrBlq d lis friqtn( ffqs + ffi *1
frq s} iFsfer qt r s
(rr) srrri n+ S{ t{rrq4T* + sl-qwr eftr t ? z
LMT.O1 11 7,OOO