f;ob/y L-
;oekoh gokfJwoh ;e{b ihsrVQ (wkB;k) d/ u'Eh iwks d/ pZfunk ftZu dhtko xVh dh wdd Bkb ;wk ns/ ;w/ dhnK fJekJhnk f;ZyD d/ gZXo ftZu ;[Xko eoBk .
fJZe
fefonkswe y'Ii (2011)
gqkgs eosk
oki y'ia f;fyZnk s/ f;ybkJh ;z;Ek gizkp uzVhrVQ
uzvhrVQ (gzikp)
rkfJv y'ikoEh
vk H p{Nk f;zx ;/y' ;hwk ;aowk JhNhNh nfXnkge
vkfJN p[Ybkvk (wkB;k) ;gq; ihs rVQ .
fibQk f;fyZnk s/ f;ybkJh ;z;Ek p[Ybkvk (wkB;k)
sseok
· ikD gfjukD 1 s' 5
· ;pzXs ;kfjs dk w{bKeD 06
· ;wZf;nk dh T[sZgsh 07-08
· ;wZf;nk dk eEB 09
· T[d/;a 09
· ;hwktK 10
· Bw{Bk 10
· ;kXB 10
· :'iBk ns/ ekoia ftXh 11-13
· nzefVnk dk ft;ab/;aD 14-15
· Bshia/ 16
· nrb/oh y'i bJh ;{Mkn 17
·
· ;konz;a 18
· gq;aBktbh 19
· T[sZowkbk 20
d' ;apd
n?e;aB oh;ou n;b ftZu ehs/ ik oj/ ezw ftZu ;[Xko fbnkT[D dk ;cb :sB j? fi; okjh nfXnkge nkgDhnk gVQkT[D ftfXnk ;pzXh ns/ ftfdnkoEhnK dh f;yZD ;pzXh ;wZf;nktk dk nfXnZD ns/ T[jDk ;wZf;nktK dk jZb ftfrnkBe sohe/ Bkb eo ;edk j? . ftfdnkoEh d/ f;yZDg gqfeqnk ftZu dog/;a n'eVk dk jZb ns/ T[jBk dk w{bkeD T[; t/b/ ;EkBe s'o s/ bZG e/ eodk j? T[; d/ T[dZw ;dek ftfdnkoEh f;yZD gqhfeqnk ftZu wBukjhnk ;[Xko gqsZy o{g ftZu fdykJh d/D brdk j? nfijk eoB Bkb T[j ekor[ikoh d/ wkgdzvK s/ yok T[sZo ;edk j? fJjBk ekor[ikoh d/ wkgdzvk d/ wBw[Zy ftfdnkoEh B{z fJ; edo :'r pDk ;edk j? fe T[j iwks nzdo fe;/ th ft;a/ B{z f;ZyD bJh dog/;a n'eVk dk itkp d/ ;e/ ns/ f;yZD gqhfeqnk Bkb i[V/ T[skn uVQkn dk wB' ftfrnkB s'o s/ ;kwDk eo ;e/ .
w? XzBtkdh jK vkfJN b?euoko dh fijQBK B/ n?e;B oh;ou d[nkok ftfdnkoEh dhnK f;yZD f;ykT[D ;pzXh ;wZf;nktK dk jZb f;ykfJnk ns/ T[jBk d/ f;ZyD f;ykT[D d/ gZXo ftZu ;[Xko fbnkT[D ;kekokswe sohe/ f;ykJ/ . fJ; s' fJbktk w? ngD/ ;e{b d/ ;w{j ;Nkc dh XzBtkdh jK fiBQk B/ w?B{z n?e;aB fo;ou okjh pZfunk dhnK ;wZf;nktK jZb eoB d/ e[M ;koEe ;[Xko fdZs/ ns/ nkgD/ gohtko tZb' th w?B{z pj[Zs ;kE fwfbnk j? .
nk; eodh jK fe w/oh fJj n?e;B fo;ou okjh ftfdnkoEh d/ f;yZD ns/ w/o/ f;ykT[D d/ gXZo ftZu ;[Xk j't/rk ns/ fJj oh;ou nfXnkge ns/ ftfdnkoEhnK d'tk tork bJh bkj/ tzd f;ZX j't/rh .
;hwk ;aowk
JhNhNh nfXnkge ;gq; ihsrVQ (wkB;k)
ikD gfjukD
f;fyZnk T[wo Go uZbD tkbh bzGh gqhfeqnk j? fJj w[Zedh Bjh ns/ jo ftnkesh d/ iBw s' ;a[o{ j' ikdh j? . ns/ nkyoh ;w/ sZe ubdh ofjzdh j? .f;fyZnk jo ftnkesh B[z ;jh noEk ftZu fJB;kB pDkT[dh j? . fJj fJZe io{oh wB[Zyh B?fsesk j? . nkdwh f;fyZnk d[nkok ;fGn nkdwh pDdk j? . nkdwh jo gb jo ;w/ jo fdB e[M Bk e[M f;yZdk ofjzdk j? . f;fyZnk jh jo ftnkesh B{z ;wkfie , B?fse , ;ZfGnkuoe ns/ nfXnkswe gZy s' g{oD eodh j? . ns/ T[; B{z nrKjtX{ ;fGnZe ns/ sfjihp tkbk pDkT[dh j? . f;fyZnk ;pzXh gh ;h p?Boiah B/ nkfynk j? ,
“‘fJj jw/;ak pdbd/ ;wkfie wkj'b B{z rqfjD eoB dh ;esh dk jh ftek; j? .”
T[j fdB rJ/ id' f;fyZnk gqkgs eoB s/ e[M ft;a/;a b'ek dk jh jZe ;h . j[D f;fyZnk b?D bJh ;ZG d/ jZe ;KM/ jB .feT[fe f;fyZnk j[D ;fGnZsk dk io{oh nzr j? .
f;fyZnk fJZe ftnkge XkoBk j? fJ; ;pzXh tZy tZy ftdtkBk , dko;afBek , wB'ftfrnkfBnk , nfXnkgeK , BhshtkBk ns/ f;fyZnk ;ak;asohnK B/ nkgD/ fdq;aNhe'D nB{;ko tZy tZy ftuko gqrN ehs/ jB .
wjkswk rKXh nB{;ko f;fyZnk okjh pZu/ ;w[Zu/ s'o s/ nfw eoe/ wB[Zyh ;oho , fdwkrh ns/ iip/ ftZu ft;a/;a eoe/ fByko fbnkT[dk j?
Gkosh f;fyZnk ewh;aB (1964-1966) dh fog'N nB{;ko f;Zfynk fizdrh Bkb ;pzXs b'ek dhnK b'Vk ns/ fJSktK nB{;ko j'Dh ukjhdh j? . fJj ;wkfie , nkofEe ns/ ;fGnkukoe ekfJnk gbNZD tk;s/ gqpb pDkT[Dh ukjhdh j? .
f;fyZnk fJZe ftXh j[zdh j? fi; d[nkok S'N/ pZfunk d/ frnkB, nkuoB ns/ ftjko B{z w'V e/ yk; ;aeb gqdkB ehsh ikdh j? .
f;fyZnk ftZu feqnkswe y'i dk ftuko jkb BtK j? e[ZM toQ/ gfjbk fJj nB{Gt ehsk frnk fe w'fbe y'i okjh gqkgs f;ZfNnk okjh fttjkoe y/so ftZu ezw eoB tkb/ eowukoh bkG gqkgs Bjh eo ;ed/ , f;ZN/ tZi' fJZe Bth y'I gqhfeqnk dk iBw j'fJnk fi; dk T[d/;a f;fyZnk , ;wki ;[Xko , feZsk ns/ T[d:'fre y/so d/ eowukohnK okjh y[Zd nkgDhnK ;wZf;nktk dk nfXnZD ns/ ftfrnkBe ftXh Bkb T[jBk dk fBtkoB eoBk j? fJ; fefonk okjh gqkgs f;fNnK d/ nXko s/ toswkB fefonk ftZu ;[Xko ehsk iKdk j? ns/ GftZy w[yh :'iBktk pDkJhnK ikdhnk jB . go f;fyZnk d/ y/so ftZu feqnkswe y'I dh XkoBk ;B 1926 s' gq’:'r ehsh ik ojh j? .
fJ; gqhfeqnk dh ;jkfJsk Bkb f;fyZnk gqhfeqnk ftZu nkT[D tkbhnk w[;afebk ns/ ;wZf;nktK dk ftfrnkBe Yzx Bkb nfXnZB ns/ fBtkoB ehsk ikdk j? . feqnkswe y'i okjh nfXnkgD d/ Yzx ftZu spdhbh fbnkT[dh ;Gzt j? . f;fyZnk Bkb ;pzXs jo fJZe ;wZf;nk dk ftfrnkBe ftXh Bkb nfXn?D eoe/ nkgDh ekor[ikoh ftZu ;[Xko fbnkT[Dk jh feqnkswe y'i j? ns/ fJj fJ;dk T[d/;a th j? .
f;fyZnk d/ y/so ftZu fJ; soK dh y'i ;e{b dh ekoigqDkbh d/ tX/o/ B/V/ j? . feT[fe fJ; ftZu y'i eoB tkbk e'Jh pkjobk ftnkesh Bk j' e/ ;e{b dk jh nfXnkge j[zdk j?. feqnkswe
y'i fBZs dhnK feqnktk ftZu ftek; dk T[gokbk eodk j? . feqnswe y'i ;wZf;nk d/ fBtkoB bJh f;bf;b/ tko ftXh j? fJ; fJZe tko ftZu j'D tkbk ezw Bjh ;r' eJh gVQktk ftZu j'D tkbk nfGnk;swe ezw j? . nfXnkge ftfdnkoEhnK dk w{bkeD eodk j? . w{bkeD d/ nXko s/ T[; tko/ ;G e[ZM ikfDnk iKdk j?ns/ T[; Bkb ;ztkd oukTdk j? . i/eo T[;dh gqkgsh gZXo xZN j? sK T[;d/ ekoDk dh gSkD eo e/ T[gukoswe f;fyZnk dk phVk u[Zedk j? f;ZN/ tZi' ftfdnkoEh B{z T[; dhnK n'eVK w[skfpe nfXnkge tZb' ;jh ;/X fwbdh j? .
fJ; soK dh ;/X T[jh nfXnkge gqdkB eo ;edk j? i' jo/e pZu/ dhnK ftnkeshrs fGzBsktk fit/ fe f;yZD rsh , f;fyZD io{osK nkfd B{z w[Zy oZyd/ j'J/ f;yZD f;ykT[D gqfeqnk d'okD T[jBk dh Gkrhdkoh :ehBh pDkT[dk j?, i/eo pZuk e'f;a;ak d/ pkti{d th f;fyZnk gqkgsh dh e;'Nh s/ g{ok g{ok Bjh T[soZdk sK T[j nfXnkge g{oh sok y[Zd B{z i{w/tko mfjokT[dk j'fJnk feqnkswe y'i eodk j?, pZu/ dhnk ewhnk dk gsk bkT[dk j? , T[jBk ewhnK B{z d{o eoB dk :sB eodk j? . :sB s' pkd Bshihnk dk w{bkeD eodk j? , ofj rJhnk B{z d{o eoB bJh w[V :sB eodk j? . fJt/ T[j T[d' sZe e'f;a;a ikoh oyZdk j? id' sZe pZuk T[; dh nk; w[skfpe f;y Bjh b?dk fJ;/ okj s[odk T[j nfXnkge fwZE/ rJ/ ekor[ikoh d/ wkgdzvk s/ g{ok T[sodk j? .
‘;dhnK s' f;fyZnk wB[Zy dk ftek; eodh nkJh j? go rfDs B{z wB{Zyh wkBf;e feqnktk dk e/do fpzd{ wzfBnk frnk j? . w[Y ;fdnk s' jh rfDs fJZe nZr/ tZXD tkbh fJZe wkBf;e feqnk ojh j?. fJ; dhnK iVQk ;kv/ o'ikBk ezw eko ftZu bZGdhnK jB ns/ ;kvh nfs nkX{fBe seBkb'ih nXkfos fizdrh dk w[Zy X{ok j? fJj ;kB{z fdwkr dhnK fyVehnk y'QbD ns/ Bt/ f;oikDswe ftukok B{z ngDkT[D d/ w'e/ gqdkB eodk j? . rfDs dh wB[Zy d[nkok pDkJhnk rJhnk pkeh t;s{n tKr wB[Zy dhnK b'VK , io{osK dh g{osh bJh j? .
rfDs fJZe nfijh uhia j? wB[Zy B{z nkgD/ ;w/ dhnk ;ZfGnkuoe b'Vk dh g{osh bJh nkg jh Jhiakd ehsh j? . ;kvh ni'eh nfs nX{fBe fizdrh rfDs dh wdd s' pr?o fe;/ sohe/ th uZb ;eDh n;zGt j? i/eo n;h fJZe fdB fe;/ th nze iK frDsh s' fpBK fpskT[D dh ;'u e/ t/fyJ/ sK ;kB{z gsk uZb/rk fe rfDs fe; soK ;kvh fizdrh ftZu o'brs j? . T[dkjoD tZi' ;w/ dh ikDekoh s' fpBk fdB bzxkT[Dk ;kv/ bJh pj[s efmB j? .
rfDs fJZe nfijk Gzvko j? fijVk fe wkgD , s'bD , frDsh eoB nzek BzpoK B{z ;wMD ns/ gqkfeqsh d/ r[Dk B{z ;wMD ns/ o'ikBk ihtB dhnK r[zMbdko ;wZf;nktk B[z sZEk ns/ nzefVnk d/ nkXko d/ ;wMD ns/ jZb eoB ftZu ;jkfJsk eodk j? .
Accordint to locke “ Mathematics is a way to settle in the mind a habit of reasoning math is the mother of all sciences”
rfDs ;wM ns/ ;wZf;nk B{z fB;akBk ns/ fuzBQk dh Gk;ak ftZu pdb e/ ;'y/ Yzr Bkb f;ZyD ns/ ;eMD dk ftfrnkB j? . rfDs dh nkgDh Gk;ak jz[dh j? . fi; ftZu nze , fB;kaB fuzBQ, nkfd ;akfwb j[zd/ jB .
rfDs dh f;fZynk ftZu pj[s wjZssk j? . rfDs wB[Zy dhnK fdwkrh ;wM ;aeshnK Bz ftef;s eoB tkbk ns/ fdwkrh e;os gqdkB eoB tkbk ftfrnkB j? . rfDs tZy tZy fynkbk ns/ ftukoK d/ noE eZYD ns/ soe , dbhb d/ nXko s/ fBoD/ eZYD ftZu :'rdkB gkT[dk j? .
wB[Zy jo tes ikD/ ns/ nDikD/ o{g ftZu rfDs dh tos' eodk j? . ;t/o t/b/ T[mZD d/ ;w/ s' b? e/ oks ;'D ;w/ sZe fit/ fe mhe ;w/ T[mZDk o'ikDk ns/ bzp/ ;w/ d/ ezwk dh :'iBk , xo d/ ezw dh soshp xo' pkjo o;s/ iKd/ ;w/ Gkt fe jo tes rfDs dh tos' eodk j? .
fe;/ th ft;a/ B{z gVQkT[D s' gfjbk T[; ft;a/ B{z gVQkT[D d/ wzst ikBDk io{oh j? . id' sZe fe;/ ft;a/ B{z gVQkT[D d/ wzst ;g;aN Bjh j'Dr/ T[d' sZe T[; ft;a/ B{z gVQkT[d dk ;wk ns/ ;aesh popkd j't/rh . n;ah fi; wzst ns/ fi; wzib s/ ftfdnkoEh B[z gj[zukT[Dk j? , T[; s/ gj[zuD bJh fejVk okj j? . fejV/ gVkn j'Dr/ . o;sk eh j't/rk nkfd pko/ i/eo nfXnkge ;g;aN Bjh sK T[j wzib gqkgs eoBh n"yh j't/rh . fJ; bJh j' ftf;ank dh soK rfDs B{z gVkT[Dk ;'yk Bjh j? Gkt fe f;om rfDs fjZe nfijk ft;ak j? fijVk ftfdnkoEhnK B{z io{oh s/ r?o io{oh uhiK ftZu coe gfjukDB d/ :'r pDkT[dk j? .
o'ikBk ihtB ftZu jo wB[Zy S'N/ s' b? e/ tZv/ sZe rohp s' nwho sZe , rfDs dh f;ZX/ iK nf;ZX/ o{g ftZu tos' eodk j? . ;kB{z ;t/o/ T[mZD d/ ;w/ s' b? e/ gVQB ikD ns/ ezw s/ ikD ns/ fdB Go d/ eJh ezw eoB ftZu ;w/ dh pjj[s io{os g?dh j? . ;w /d/ frnkB s' fpBk ;kB{z ;kB{z nkgD/ o'ikBk d/ ezw eoB ftrZu pj[s w[;afeb j[zdh j? .
;w/ tko/ ikDBk ;kv/ bJh pj[zs io{oh j? . ;w/ d/ frnkB s' fpBk ;kvhnK eJhnK :'iBktk n;cb j' ikDrhnk ns/ ;w/ s/ g{ohnK Bjh j'DrhnK .xo d/ ;ko/ ezwK ns/ pkjo d/ ;ko/ ezw B{z mhe t/b/ f;o ns/ ;jh fBp/VB bJh ;w/ ns/ ;w/ dhnK fJekJhnK dk frnkB j'Dk pj[s io{oh j? .
dhtko xVh L-
;w/ dh fJekJhnK B{z dhtko xVh dh wdd Bkb tXhnk sohe/ Bkb ;wfMnk ns/ ;wMkJhnk ik ;edk j? . fJ; s/ pZfunK B{z tZvh ;{Jh , S'Nh ;{Jh , ;zfeN tkbh ;{Jh pko/ pV/ jh tXhnk sohe/ Bkb ;wMkfJnk ik ;edk j? . fJ; B{z ;wMkjTpD bJh n;ah Eow'e'b s/ fe;/ yokp dhtko XVhnK dh tos' eoe/ th f;yk ;ed/ jK . ;w/ pko/ ikDekoh f;ykT-D bJh n;ah tZy tZy tZvh S'Nh xVh dh tos' eo e/ dZ; ;ed/ jK fe ;kohNk ;{Jhnk ukj/ dhtko xVh dhnK ;{Jhnk jB iK jZE xVh dhnK ;{JhnK jB . T[jBk B{z 60 fwzN ns/ 60 ;zfeN s/ jh ;?N ehshnK j[zdhnk jB .
pb?e p'ov L-
;w/ dhnK fJekJhnk B{z pb?e p'ov T[go uke dh wdd Bkb ty -2 xVhnK pDk e/ , T[jBK ftZu tZy -2 ;w/ pDk e/ pV/ jh tXhnk sohe/ Bkbn ;wMkfJnk ik ;edk j? . pb?e p'ov ns/ uke nfXnkge bJh tXhnk ;;sk ns/ n;kBh Bkb T[gbZGX j'D tkbh f;fyZD ;wZroh j? .
;pzXs ;kfjs dk w{bKeD $ foft>
v ;'wk ;pb'e L- y'I nfGnkB ( Action Research ) ;jkfJZe ;N/N gq'i?eN vkfjo?eNo , ;ot f;Zfynk nfGnkB nEkoNh n?;H;hHT 104-106 d{iah wzib 34 J/ uzvhrVQ , gzikp .
v n?wHn?; ;Zud/tk f;fyZnk d/ dko;afBe ns/ ;wkfie nXko (Twenty first century publications Patiala)
v vkH e/He/ ftf;a;aN ;ot f;fyZnk nfGnkB nEkoNh gzikp uzvhrVQ 2005 ;t? f;yZD ;wZroh -4
v Teaching of Mathematics i;aB gpbhe/;aB cohee'N .
;wZf;nk dh T[sgsh
y'ikoEh ;kb 2010 s' u'Eh iwks d/ ftfdnkoEhnK B{z fj;kp dk ft;ak gVQk ojh ;h . T[; B/ ;ko/ nfGnk; pV/ jh ;ob sohe/ Bkb , f;yZD ;wZroh dh tos' eoe/ ftfdnkoEhnk B{z ;wMkJ/ . go id' T[j nkgD/ f;yD – f;ykT[D d/ ekoi ftZu fJ; nfGnk; s/ nke nNe rJh id' T[j ftfdnkoEhnK B{z ;w/ dhnK fJekJhnk dk nfGnk; eotk ojh ;h feT[ fe jo nfXnkge dh fJj fJZSk j[dh j? fe T[; dk f;y;aD pVk gqGkt;akbh j't/ .T[j ukj[zdk j? fe T[j i' gVQkJ/ T[j ftfdnkoehnK B{z uzrh soK ;wM nk ikt/ . nkgD/ wB'oEk B{z g{ok eoB bJh T[j eJh gqeko d/ f;y;aD ;jkfJe tosdk j? fit/ ukoN wkvb Be;a/ ekria w'VBk cb?;a ekov, pb?e p'ov i[w?Noh p'e; fj;kp dh feskp nkd dh tos' eodk j? . feT[ fe rfDs dh jo/e ;wf;nk B[z jb eoB bJh fJZe nfXnkge ns/ fJZe ftfdnkoEh B{z ;'uD ftuoB d/ tZy-tZy ftebgK ftu' ;jh ftebg u[DBk ns/ fco Bshi/ d nkBd wkBDk nkfd dh gqfeqnk ftu' bzxDk g?dk j? .
id' y'ikoEh ;w/ s/ ;w/ dhnK fJekJhnK pko/ pZfunk B{z ;wMk fojk ;h sK y'ikoEh B/ fJ; wfj;{; ehsk fe pZfunK B/ T[Bk frnkB rqfjD Bjh ehsk fiBk T[; B/ pZfunk B{z dZf;nk j? ns/ T[; B/ wfj;{; ehsk fe ftfdnkoEh B{z ;w/ dhnK fJekJhnk d/ f;yZd d/ gZXo ftZu ;[Xko dh io{os j? .
y'ikoEh B/ nkgDh f;yZD f;ykT[D dh w'i{dk jkbks Bkb n;zs[;aNsk wfj;{; ehsh s/ T[; B/ fJj ;'uDk ;a[o{ eo fdZsk fe fJ; jkbks Bz[ p/jso fet/ pdkjfJnk ikt/ < fJ; eoB Bjh T[; d/ fdwkr ftZu eJh soQk d/ gq;aB T[m/ s/ T[; B/ fJjBK gq;aBk s/ fXnkB e/dos eo fdZsk . y'ikoEh B{z wfj;{; j'fJnk fe fJ; ;wZf;nk B[z fefonkswe y'I d[nkok jZb ehsk ik ;edkj? .
y'ikoEh B/ fJ; fefonkswe y' d/ ezw bJh ;'uDk ;[o{ eo fdZsk ns/ :'iBk pDkT[Dh ;a[o{ ehsh . y'ikoEh wB ftZu eJh soQk d/ ;tkb T[m/ ns/ T[; B/ ;wZf;nk d/ jZb bJh ftfrnkBe Yzr ngDkT[D dk wB pDkfJnk fit/ fe fefonkswe y'ia fJZe' tkoh ftZu j'D tkbk ezw Bjh j? ;r' fJ; bJh eJh gVQktK ftu' bzXDk g?dk j? .
id' y'ikoEh gVQk fojk ;h sK T[; B/ nuBu/s fJZe ftfdnkoEh B{z dcso ftZu bZrh dhtko xVh s' ;wK d/y e/ nkT[D bJh G/fink go ftfdnkoEh t[; B[z ;w/ pko/ ;jh ikDekoh Bk j'D eoe/ ;wk Bjh dZ; ;fenk sK y'ikoEh d/ wB ftZu nkgDh nkgDh f;y;aD B{z b? e/ eJh soK d/ ;tkb T[sgzB j'J/ , T[; B/ fJe dw fJj c?;bk fbnk fe T[; B{z fJ; ftZu ;[Xko eoBk ukjhdk j? sK i' T[; d/ f;e;aD gZXo ftZu ns/ ftfdnkoEh d/ rqfjD gZXo ftZu ;[Xko j't/ . T[; B/ feqnkswe y'I okjh fJ; ;wZf;nk dk jZb bZGHD pko/ ;'funk s/ fJ; y'Ii s/ ezw eoBk ;a[o{ eo fdZsk .
