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gps]; ^ ,aw;gpay; nghJj; NjHT - gFjp 2
,aw;gpay; Nju;T vOJk;NghJ...

Nrh.rk;ge;jd;> 

KJfiy ,aw;gpay; Mrpupau;> 

n[aNfhghy; fNuhbah Njrpa Nky;epiyg;gs;sp> 

jhk;guk;> nrd;id-59.

gFjp-2

 

FW tpdhf;fs; ,lk;ngWk; ,g;gFjpapy; nfhLf;fg;gLk; 20 tpdhf;fspy; 15 tpdhf;fSf;F kl;Lk; tpilaspf;f Ntz;Lk;. tiuaiw> jj;Jtk;> tpjp> vLNfhs;> R+j;jpuk;> rpy mwptpay; epfo;TfSf;fhd fhuzq;fs; Nghd;wit tpdhf;fshff; Nfl;fg;glyhk;. ,t;thW tiuaiw my;yJ tpjpiaf; $Wk;NghJ nghJg;gilahf mika Ntz;LNk md;wp> VNjh xU jdp epfo;Tf;F kl;Lk; cupajhf (in general terms, not in specific terms) ,Uf;ff; $lhJ.

 

Nfl;fg;gltpy;iynadpy;> Njitapy;yhky; vLj;Jf;fhl;Lfisj; je;Njh> NkYk; tpsf;fj;ijf; nfhLj;Njh fhyj;ij tPzhf;ff; $lhJ. Nfl;fg;gLk; tpdhit ,UKiwNaDk; gbj;jhy;> vd;d tpil vjpu;ghu;f;fg;gLfpwJ vd;gJ mwpag;gLk;> mij kl;Lk; vOJtNj rhyr;rpwe;jJ.

 

R+j;jpuq;fs;> fzpjr; rkd;ghLfs; Nghd;wit Nfl;fg;gl;lhy;> rkd;ghl;il vOjpaTld; mjpy; tUk; FwpaPLfis tpupthf;fk; nra;a Ntz;Lk;. tpupitj; juhky; R+j;jpuj;ij kl;LNk vOjpdhy;> xU kjpg;ngz;iz ,of;f NeupLk;.

 

,g;gFjpapy; MW tpdhf;fs; fzf;Ffshf mikAk;. fzf;fpy; jug;gLk; tptuq;fis tupirg;gLj;jp vOjptpl;L> Njitahd tptuj;ij mtw;NwhL njhlu;GgLj;jp epidT $u;e;jhy;> cupa R+j;jpuNkh my;yJ rkd;ghNlh vspjpy; epidTf;F te;J tpLk;.

 

rpW gpiofisj; jtpu;f;f ve;jnthU RUf;FjiyAk; (simplification) kdf;fzf;fhfr; nra;ahky; rough work nra;J tpilia miltJ ey;yJ.

 

tpjpfis vOJk;NghJ> ghlg;Gj;jfj;jpy; cs;sthNw vOj Ntz;Lk;. Vnddpy;> vOjg;gLk; tpjpapy; VNjDk; epge;jid tpLgl;lhy;> mt;tpil KOik ngwhky; mike;J tpLk;. kjpg;ngz;Zk; KOikahff; fpilf;fhJ.

 

,uz;L kjpg;ngz; nfhz;l ,t;tif tpdhf;fspy; gad;ghLfs;> gz;Gfs; Nghd;wit Nfl;fg;gl;lhy; ,uz;L my;yJ %d;W Fwpg;Gfs; vOjpdhNy NghJkhdJ. Gj;jfj;jpy; cs;s midj;J Fwpg;GfisAk; KOg;gf;f mstpy; vOj Ntz;ba Njitapy;iy.

 

xU tpdhTf;F ,uz;L epkplq;fs; vd vLj;Jf; nfhz;lhy;> 15 tpdhf;fSf;F Rkhu; 30 epkplq;fspy; tpilaspf;fg; gof Ntz;Lk;. tPl;by; mku;e;J gbf;Fk;NghJ> rkd;ghLfisAk; tiuaiwfisAk; tha;tpl;Lg; gbj;jhy;> mit midj;Jk; kdjpy; Nt&d;wp MokhfTk; KOikahfTk; gjptilAk;. Nju;tiwapy; epidT $u;tJk; vspjhfptpLk;.

 

gFjp-3

 

gFjp-jp-3-y; gj;jp mstpyhd tpilfis vjpu;nfhs;Sk; rpW tpdhf;fs; Nfl;fg;gLk;. nfhLf;fg;gLk; 10 tpdhf;fspy; nkhj;jkhf 6 tpdhf;fSf;F tpilaspf;f Ntz;Lk;. ,tw;wpy; VNjDk; xU Fwpg;gpl;l tpdh (fzf;F mbg;gilapyhd tpdh) fz;bg;ghf tpilaspf;fg;gl Ntz;Lk;.

 

,t;tpdh ngUk;ghYk; mf tpUg;gj; Nju;T (internal choice) mbg;gilapy; ,U fzf;Ffs; xNu tupir vz;zpy; jug;gl;L> mtw;wpy; xU Nfs;tpf;F tpilaspf;Fk; tz;zk; mikayhk;. 

tpdhit ,uz;L my;yJ %d;W Kiw jpUk;gj; jpUk;g Cd;wpg; gbj;Jtpl;L> vd;d tpil vjpu;ghu;f;fg;gLfpwNjh me;j mstpy; kl;Lk; tpilahf vOJtJ fhy tpuaj;ijj; jLf;Fk;. Njitapy;yhj Fog;gj;ijAk; ,jd; %yk; jtpu;f;fyhk;. tpilAk; mjpf Jy;ypaj; jd;ikiag; ngWk;.

 

gFjp 3-y; 3 fzf;Ffs; Nfl;fg;gLk;. fzf;Ffisj; jPu;T nra;Ak;NghJ> klf;if ml;ltiziag; gad;gLj;j Ntz;Lk; my;yJ vz; fzf;fhfNt $l jPu;itf; fz;L gpbf;fyhk;. Nju;tiwapy; fzpdpiag; (calculator) gad;gLj;j KbahJ. fzpj topKiwfisr; nra;J jhd; ,Wjp tpilia mila Ntz;Lk;. fzf;FfSf;fhd ,Wjp tpilia vOJk;NghJ> mtw;wpw;Fupa myFfis eI Kiwapy; juNtz;Lk;.

 

NkYk; vz; kjpg;GfSk; mstpay; FwpaPl;by; mika Ntz;Lk;. tpiliar; rpW rpW gj;jpfshff; $lg; gpupj;J vOjyhk;. tpilapy; tuf;$ba rpy Fwpg;G thu;j;ijfis mbf;NfhbLtjd; %yk; (highlighting) Nju;thsupd; ftdj;ij <Hj;J ed;kjpg;igg; ngwTk; tha;g;G cz;L.

 

xt;nthU tpdhitAk; 5 epkplq;fSf;Fs; vOjp Kbf;Fk; mstpy; tPl;by; gapw;rp nra;a Ntz;Lk;. Mf ,g;gFjpapy; vjpu;ghu;f;fg;gLk; 6 tpdhf;fisAk; 30 epkplq;fspy; tpilaspf;Fk; tz;zk;> gs;spapy; ePq;fs; vOjg;NghFk; jpUg;Gj; Nju;Tfspy; gof Ntz;Lk;.

 

gFjp 4

 

vl;L Nfs;tpfs; nfhLf;fg;gl;L mtw;wpy; VNjDk; ehd;F Nfs;tpfisj; Nju;e;njLj;J vOJk; ,g;gpuptpy;> xt;nthU tpilAk; tpsf;fkhfj; Njitahd glq;fSld; ,Ug;gJ mtrpak;.

 

,it fl;Liu tbtpyhd tpdh vd;gjhy;> cupa njhlf;fj;JlDk;> tpilapd; ,Wjpapy; Ma;tpd; mbg;gilapy; fpilj;j kjpg;Gfs;> mwpe;Jnfhz;lit (inferenfe)> rpwg;Gj; Nju;Tfs; Nghd;w KbTfSld; tpilfs; mikag; ngWjy; mtrpak;.

 

tpsf;f tif (descriptive type) tpilfSf;Fg; gjpyhf> fzf;fPLfs;> fzpj ep&gzq;fs;> tiugl kw;Wk; gl mbg;gilapyhd tpsf;fj;Jld; $ba tpilfisj; Nju;e;njLj;jhy; KO kjpg;ngz;fs; ngw tha;g;Gs;sJ.

 

xt;nthU tpdhTf;Fk; mjpfgl;rk; 15 epkplq;fspy; tpilaspf;Fk; jpwikia tsu;j;Jf; nfhs;s Ntz;Lk;. Neu xJf;fPl;ilr; rupahd Kiwapy; filg;gpbj;J Nju;T vOjpdhy; epiwthd kdepiyapy;> gjw;wkilahky; tpdhf;fis vjpu;nfhs;s KbAk;. gpupT xd;W-50 epkplq;fs;> gpupT ,uz;L-30 epkplq;fs;> gpupT %d;W-30 epkplq;fs;> gpupT ehd;F-60 epkplq;fs;> kPs; ghu;itf;nfd 10 epkplq;fs; vd xJf;fpf; nfhs;tNj rpwe;jnjhU Neu epu;thfkhFk;.

 

Nju;tpy; glq;fspd; gq;F:

 

Njitahd glq;fis vg;NghJk; tpilapd; njhlf;fj;jpNyNa tiua Ntz;Lk;. mg;NghJ jhd; Nju;thsupd; ed;kjpg;igg; (good impression) ngw KbAk;.

 

glq;fis Kbe;j tiu Jizf;fUtpfs; ,y;yhky; (free hand drawing) ifapdhy; tiujy; Neuj;ijr; Nrkpf;f toptFf;Fk;. jtWfSk; jtpu;f;fg;gLk;.

 

,jw;Nfw;whw;Nghy; tPl;by; glg;gapw;rp (diagram practice) nra;jy; mtrpak;. glk; tiuAk; NghJ ek; kdjpy; mg;glj;ijnahl;ba jj;Jtk;> nray;ghL> gad;ghL Nghd;wtw;iw epidtpy; epWj;jpf; nfhz;Nl (visualization) tiujy; mtrpak;.

 

,g;gof;fj;ij tsu;j;Jf; nfhz;lhy;> Nju;Tf;F Kd;jpdk; rpy kzp Neuq;fspy;> mjpf ghlq;fis ntWk; glk; tiue;Nj kPs; ghu;it nra;Jtpl KbAk;. 

Nju;tpd;NghJk; tpilapd; njhlf;fj;jpy; glk; tiuAk;NghJk;> vOjg;NghFk; tpilia Ntfkhf xUKiw epidj;Jg; ghu;f;f tha;g;G fpilg;gjhy;> glk; tiue;J Kbe;j mLj;j fzk;> kpf Ntfkhf kdj;jilapd;wp tpilia vOjp Kbf;f KbAk;.

 

,jdhy; khztu;fSf;F jp-matthematical brain vd;w ey;ynjhU jpwik tsUk;. ,jw;Fg; nghUs;> ehk; xU tpilia vOJk;NghJ ek; vz;zj;ij ,jw;fLj;j gbapy; my;yJ tpilapd; ,Wjpg;gbapy; epWj;jp tpil vOJk; jpwikahFk;.

 

(Mathematical Brain: Thinking a few ahead of what you are writing now)

 

khztu;fNs! ,Jtiu $wpa El;gq;fisg; gpd;gw;wp> gyKiw gapw;rp nra;jhy;> ,Wjpg; nghJj;Nju;tpy; cau; kjpg;ngz;fs; ngWtJ cWjp!

ed;wp : jpdkzp mf;NlhgH 03 2005
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