Foundation of math education presentation.pptx

Foundation of math

1. M.Ed. First Semester(2080/081), ul0ft lzIff (Math Education) ; d"xsf ] ul0ft lzIffsf cfwf /x? (Foundation of Mathematics Education),Math. Ed. 515 sf] cf+lzs cfjZostf k"0f{ ug]{ k|of ] hgsf nflu tof / kfl / Psf ] kl/of] hgf sfo { Instructional Media and Technology for Mathematics Teaching -ul0ft lzIf0fsf z}Ifl0fs ; fwg tyf k|ljlwx ?_ Submitted by Tek Prasad Lingden M.Ed., 1 st Semester Roll No.: 42 TU Registration no.: 9-2-214-111-2011 Campus Name: Sukuna Multiple Campus, Sundarharaincha , Morang Submitted to Faculty of Education, Master Level, Sukuna Multiple Campus,Sundarharaincha , Morang

2. z}Ifl0fs ; fdu|Lsf ] kl/ ro Pp6f lrlgofF pvfg 5 s'g } klg ljifosf ] lzIf0f k|efjsf /L, /f] rs / Jojxf / d"ns agfO { ;sf/ fTds ¿ kdf lzIffsf ] u'0f:t/ j[l4 ug{] dxTjk"0f{ ; fwg g} z}Ifl0fs ; fdu|L x'g \ . z} lIfs lqmofsnfkdf k|of ]u ul/g] ; fdu|L g} z}Ifl0fs ; fdu|L x'g \ . lzIf0f eg ]sf] ljifoj:t ', z}Ifl0fs ; fdu|L , z} lIfs jftfj /0fsf ; fy ljleGg lcd"t { ¿ kdf /x]sf ljifoj:t'nO { d"t { ¿k lbg z}Ifl0fs ; fdu|Ln ] ; xhtf k|bfg ub {5 . ljBfy {L{sf] ; lqmotfdf j[l4 ug{], sl7g kf7nfO{ ;/n agfpg ], l;sfOnfO { d"t { ¿k lbO { ljBfy {L{df 7f]; wf /0ff a;fn \g], lzIf0f l;sfO k|lqmofnfO { /f] rs / ?lrk"0f{ agfpg ] sfo {df z}Ifl0fs ; fdu|Lsf ] dxTjk"0f{ e"ldsf /xG5 . d}n] ;'g]+, d}n] la;{]+ (I hear, I forget) d}n] b]v]+, d}n] ;Dem+] (I see, I remember) d}n] u/]F, d}n a'em ]+ (I do, I understand)

3. Ufl0ft lzIf0fdf z}Ifl0fs ; fduL|sf ] cfjZstf / dxTjM l ;sf?df ul0ftk|lt pT;fx hufO { l;Sgk|lt clek |]l/t ug{, l;sf?nfO { ; lqmo agfpgsf nflu , ljifoj:t'sf cfwf / e"t s'/ fx¿nfO { ;/n agfO { k|: t't ug{, cd"t { s'/ fx¿nfO { d"t {¿ kdf k|of ]u u/L cy{k"0f{ lzIf0f ug{, cWoog ul//x]sf] ljifo j:t'nfO{ : yfgfGt / / : yfoL :d[ ltsf nflu tof / u/ fpg , ljifo j:t'k|lt ;s/ fTds wf /0ffsf] ljsf ; ug{, l;sfOaf6 ljBfy { LnfO { pQd ;Gt'li6 k|bfg ug{ .

4. Different types of materials required for equipping the mathematics classroom ul0ft sIffnfO { ;'; lHht ug{ cfjZos ljleGg k|sf /sf ; fdu|Lx ¿ / ltgsf ] Joj:yfkgsf ] af /]df oxfF rr {f ul/ Psf ] 5M s_ kf7\ok': tsx ¿ / ;Gbe{ k': tsx¿M k|fylds tx b]lv pRr :t/sf kf7\ok': tsx¿M sIffsf ] :t/ cg';f / ul0ftsf ljleGg ljifoj:t'x ¿ ; dfj ]z ePsf k': tsx ¿ . ;Gbe{ k': tsx¿M yk hfgsf /L / ulx /f] cWoogsf nflu . v_ b[Zo ; fdu|Lx¿M u|flkms rf6{x¿: ljleGg u|fkmx ¿, tflnsfx ¿, / kmfd {' nfx ¿ ; dfj ]z ePsf rf6{x¿ . u_ lzIf0f pks/0fx¿M ;] tf ] af ]8{, / ltgsf nflu cfjZos dfs {/ / 8:6/x¿ . k|f ]h]S6/M l8lh6n ; fdu|Lx ¿ k|bz {g ug{ . 3_ cGtlqm { ofTds pks/0fx¿M sDKo'6/ / 6\ ofAn ]6x¿M z} lIfs ;km\6j]o/ / cgnfOg ;|f] tx ¿ kx'Fr ug{ / :df6{ af ]8{M cGt / lqmofTds lzIf0fsf] nflu . ª_ ul0ftLo pks/0fx¿M HofldtLo ;]6M sDkf ;, k|f ]6]S6/ h:tf pks/0fx¿ / Sofn \ s'n ]6/M ljBfy { Lx¿sf ] u0fgf ; xfotf ug{ . r_ ;km\6j]o/ / cgnfOg ;|f] tx¿M u|flkmË ;km\6j]o/M GeoGebra, Desmos h:tf / l;d'n ] zg ;km\6j]o/M MATLAB, Mathematica 5_ xftdf k|of ]u x'g ] ; fdu|Lx¿M Ansx ¿ / df]8nx¿M 7f]; Ansx ¿, y|L8L df]8nx¿, / cGo ef } lts ; fdfu|Lx ¿ .

5. The use of software packages in math teaching ul0ft lzIf0fdf ;km\6j]o/ Kofs ] hx¿sf ] k|of ]u ul0ft lzIf0fdf ;km\6j]o/ Kofs ] hx¿sf ] k|of ]un] lzIf0f / l;sfO k|lqmofnfO { k|efjsf /L, cfsif {s, / cGtlqm { ofTds agfpF5 . oxfF ul0ft lzIf0fdf ;km\6j]o/ Kofs ] hx¿sf ] k|d'v k|of ]u / ltgsf ] dxTjsf ] rr {f ul/ Psf ] 5g\M != b[ ZofÍg (Visualization): u|flkm+u ;km\6j]o/: ljBfy { Lx¿n ] hl6n ul0ftLo sfo {x¿ / u|fkmx ¿ ; lhn } a'em \g ;S5G. pbfx /0fsf nflu , GeoGebra , Desmos h:tf ;km\6j]o/ x¿n ] ul0ftLo u|fkmx¿nfO { b[ Zodfg / cGtlqm { ofTds agfpF5G. y|L8L df]8nM y|L8L df]8n ;km\6j]o/n] HofldtLo cfs [ ltx¿sf ] lqMcfofdLs b[Zo k|bfg ub {5, h;n ] j:t'sf] jf:tljs hLjgdf kl/df0f / cfsf / a'em \g d2t ub {5 . @= cg's/0f (Simulation): ul0ftLo l;d'n ] zg : ;km\6j]o/n] ljleGg ul0ftLo l;¢ fGtx¿sf ] cg's/0f u/]/ ljBfy { Lx¿nfO { hl6n ; d:of ; dfwfg k|lqmofsf ] cg'ej k|bfg ug{ ;S5. pbfx /0fsf nflu , MATLAB, Mathematica h:tf ;km\6j]o/ x¿df ljleGg ul0ftLo df]8] nx ¿ lgd {f0f ug{ ;lsG5. #= cGtlqm { ofTds cEof;M ;'¿ jftL / pGgt :t/sf cEof;x¿M ;km\6j]o/ Kofs ] hx¿n ] ljleGg :t/sf cGtlqm { ofTds cEof;x ¿ k|bfg u5{G. of] cEof;n ] ljBfy {L{ x¿nfO { pgLx¿sf ] cfkm \gf] ult / Ifdtfcg ';f/ cEof ; ug{ ;' ljwf lbG5. $= lSjh / v] nx¿M ;km\6j]o/n] lSjh / v] nx ¿ k|bfg u/]/ ul0ft l;sfOnfO { dgf ]/~ hgfTds agfpF5. lzIfsx¿sf nflu ; xfotfM kf7 of] hgf / Joj:yfkg : ;km\6j]o/ Kofs ] hx¿n ] lzIfsx¿nfO { kf7 of] hgf agfpg ], ljBfy { Lx¿sf ] k|ult 6\o{fs ug{], / JolQmut lzIf0f of] hgf lgd {f0f ug{ ; xof ]u k'o {fpF5. %= d"Nof ª\ sgM ;km\6j]o/n] : jrflnt d"n \ ofÍg / ljZn ]if0f ug{] ;' ljwf lbG5, h;n ] ub {f lzIfsx¿n ] l56f] / k|efjsf /L ¿ kdf ljBfy { Lx¿sf ] k|bz {g d"n \ ofÍg ug{ ;S5g\ . ^= ; xof ] ufTds l;sfOM cgnfOg Kn ]6kmd{x¿: ;km\6j]o/ Kofs ]hx¿ h:t}M Google Classroom , Microsoft Teams n] ljBfy { Lx¿nfO { ; d"xdf sfd ug{ / hfgsf /L cfbfgk|bfg ug{ ; lhnf ] agfpF5G. &= ; d"x k|f ]h]S6x¿M ;km\6j]o/n] ; d"x k|f ]h]S6x¿ ; lhn } Joj:yfkg ug{ / ;fem]bf/L ug{ ;' ljwf lbG5 .

6. The various ways of using computers in teaching and mathematics -ul0ft lzIf0fdf ljleGg tl /sfx ¿ af6 sDKo'6/sf] k|of ]u+_ !_ ul0ftLo ;km\6j]o/ / PlKns ]; gx ¿ Geometry software M h:t} GeoGebra , h;n ] ljBfy {L{ x¿nfO { HofldtLo cfsf /x¿ lgdf {0f ug{, cGj ]if0f ug{, / ljZn ]if0f ug{ d2t ub {5. Calculus tools M mathematica jf Wolfram Alpha h:tf ;km\6j]o/n] hl6n u0fgfx ¿ ug{ / Calculus sf ; d:ofx ¿ ; dfwfg ug{ d2t ub {5. @_ cgnfOg z} lIfs Kn ]6kmd{x¿ ljBfy {L{ x¿n ] ljleGg ul0ftLo ljifox¿sf ] lel8of] tutorial x]g{ / cEof ; ; d:ofx ¿ ug{ ;S5g\ . ljBfy {L{ x ¿ n ] : jMcWoog ug{ / cgnfOg cEof;x ¿ dfkm {t cfkm \gf] ; Lkx ¿ ;' wf / ug{ ;S5g\ . #_ Virtual manipulative ; fdu|Lx ¿ cgnfOg sfpG6/x ¿ , u|fkm Knf ]6;{, / gDa / nfOg h:tf er { ‘ cn pks/0fx ¿ k|of ]u u/L ljBfy { Lx ¿ n ] ul0ftLo cjwf /0ffx¿ a'em \g ;S5g\ . Interactive games: ul0ft l;sfpg ] v] nx ¿ h;n ] ul0ftLo ; d:ofx ¿ ; dfwfg ug{] Ifdtfsf ] ljsf ; ub {5 . $_ cgnfOg sf];{x¿ / j] lagf /x¿ MOOCs: Massive Open Online Courses h:t} Coursera , edX , / Udacity dfkm {t ljBfy {L{ x¿n ] pRr:t /Lo ul0ft sf];{x¿ lng ;S5g\ . Live webinars: ljBfy {L{ x¿n ] nfOe j] lagf / x¿df efu lnP / ljz ]if1x¿af6 k|ToIf ¿ kdf l;Sg ;S5g\ . %_ ul0ft l;sfpg ] Apps :df6{ kmf ]g / 6\ ofAn ]6 Apps h:t} Photomath , h;n ] ljBfy {L{ x¿n ] ul0ftLo ; d:ofx¿nfO { scan u/L ; dfwfg k|lqmof x]g{ ;S5g\ . Z} lIfs v]n Pkx ¿: ul0ftLo cjwf /0ffx¿ v]n dfkm {t l;sfpg d2t ug{] Pkx ¿.

7. ^_ ; xof ] ufTds cgnfOg pks/0fx¿ Google Classroom / Microsoft Team M lzIfsx ¿ n ] ljBfy {L{x ¿ ;Fu c;fOgd ]G6x ¿ ; femf ug{, k[i7kf]if0f lbg , / ; xof ] ufTds k|f ]h]S6x ¿ ug{ k|of ]u ug{ ;S5g\ . cgnfOg / kmf ]/d ; d"xx¿M ljBfy {L{ x¿n ] cgnfOg kmf ]/ dx¿df k|Zgx ¿ ;f] Wg / 5nkmndf efu lng ;S5g\ . &_ Data analytics l;sfO pknlAw dfkg lzIfsx¿n ] ljBfy {L{ x¿sf ] k|ult dfkg ug{ / ljZn ]if0f ug{ sDKo'6/ pks/0fx ¿ k|of ]u ug{ ;S5g\ . h;n ] pgLx ¿ sf ] sdhf ]/Lx ¿ klxrfg ug{ / ;' wf /sf] nflu of] hgf agfpg d2t ub {5 . (_ Multiledia package lel8of] / Plgd ]; gx¿M ul0ftLo cjwf /0ffx¿ a'emfpg / ljBfy {L{ x ¿ sf ] Wofgfslif {t ug{ dlN6ldl8of ; fdu|Lx ¿ k|of ]u ug{ ;lsG5 . !)_ Powerpoint Presentation M cfsif {s / hfgsf / Ld"ns k|h ]G6] zgx ¿ dfkm {t lzIfsx ¿ n ] ul0ftsf] kf7x ¿ a'emfpg ;S5g\ . sDKo'6/ x ¿ sf ] k|of ]un] ul0ft lzIf0fnfO{ cfw'lgs , cGt / lqmofTds , / k|efjsf /L agfpF5 . o;n ] ljBfy {L{ x ¿ nfO { hl6n cjwf /0ffx ¿ ;/n / / dfOnf ] tl / sfdf a'em \g d2t ub {5 .

8. Differences between manipulative and virtual manipulative materials and discuss their use in mathematics teaching Manipulative materials / virtual manipulative materials aLrsf ] km/s s_ k|of ] ufTds ; fdu|Lx ¿ ( Manipulative Materials): k|of ] ufTds ; fdu|Lx ¿ jf:tljs , ef } lts j:t'x ¿ x'g \ h'g ljBfy {L{ x ¿ n ] xftn ] ; dfpg / rnfpg ;S5g\ . oL ; fdu|Lx¿n ] ljBfy {L{ x¿nfO { ul0ftLo cjwf /0ffx¿sf] 7f]; cg'e"lt lbG5, h;n ] cjwf /0ffx ¿ nfO{ / fd|f ];Fu a'em \g / ; Demgdf d2t k'of {pF5 . Ufl0ft lzIf0fdf, k|of ] ufTds ; fdu|Lx ¿ k|f / lDes afnljsf ; / k|fylds txsf ljBfy {L{ x ¿ nfO { ;+ VofTds cjwf /0ffx ¿ , hf]8, 36fp, u'0ff, efu , HofldtLo cfsf /x¿, / dfkg h:tf ljifoj:t'x ¿ l;sfpg Jofks ¿ kdf k|of ]u ul/G5 . v_ er {' cn k|of ] ufTds ; fdu|Lx ¿ (Virtual Manipulative Materials) er {' cn k|of ] ufTds ; fdu|Lx ¿ l8lh6n ¿ kn ] l;h {gf ul/ Psf j:t'x ¿ x'g \ h'g sDKo'6/, 6\ ofAn ]6, jf :df6{ kmf ] gdf OG6/km]; dfkm {t x]l/g] / rnfpg ldN5 . oL ; fdu|Lx¿df online tools interactional tools / l8lh6n u]dx ¿ ; dfj ]z 5g\ h;n ] ljBfy {L{ x ¿ nfO { ul0ftLo cEof;x ¿ u/fpF5 . er {' cn k|of ] ufTds ; fdu|Lx ¿ n ] ljBfy {L{ x ¿ nfO { cfsif {s / OG6]/]lS6e jftfj /0fdf ul0ft l;Sg d2t k'of {pF5, h;n ] ub {f l;sfO k|lqmofnfO { / dfOnf ] / k|]/0ffbfoL agfpF5 . oL ; fdu|Lx ¿ ljleGg txsf ljBfyL { x ¿nfO { k|of ]u ug{ ;lsG5, / lzIfsx¿n ] cfkm \gf kf7\ oqmdcg ';f/ er {' cn cEof;x ¿ ug{ ;S5g .

9. Implications of manipulative and virtual manipulative materials Doflgk'n ]l6e ; fdu|Lx ¿ k|of ]u ubf {, lzIfsx ¿ n ] ljBfy {L{ x ¿ nfO { j:t'x ¿ ;Fu k|ToIf cGt / lqmof u/ fO { ul0ftLo cjwf /0ffx¿ a'em \g / cg'; Gwfg ug{ ; xof ]u ug{ ;S5g\ . pbfx /0fsf nflu , ljBfy {L{ x ¿ n ] uGtL l;Sg Ansx ¿ k|of ]u ug{ ;S5g\ / cfsf / / kl/df0fsf] cjwf /0ffx ¿ a'em \g HofldtLo cfsf /x ¿ k|of ]u ug{ ;S5g\ . er {' cn k|of ] ufTds ; fdu|Lx ¿ k|of ]u ub {f, lzIfsx¿n ] Digital tools sf] k|of ] udfkm {t ljBfy {L{ x ¿ nfO { ; d:of ; dfwfg ug{, ul0ftLo cjwf /0ffx ¿ sf] cEof ; ug{, / cfkm'nfO { d'Nof ª\sg ug{ d2t k'o { fpg ;S5g\ . pbfx /0fsf nflu , Ps ljBfy {L{n] cgnfOg Kn ]6kmd{df ul0ftLo v]n v]Ng ;S5, h;n ] ul0ftLo ; d:of ; dfwfg ug{sf] nflu ljleGg pkfox¿sf ] vf ] hL ug{ k|]l/t ug{ ;S5 . b'j } k|sf /sf ; fdu|Lx ¿ , ul0ft lzIf0fdf dxTjk'0f{ 5g\ . b'j }sf] ldl >t k|of ]un] ljBfy {L{ x ¿ sf ] l;sfO cg'ejnfO { dha't agfpg ;S5, pgLx ¿ sf ] ljleGg l;sfO z} nLx ¿ nfO { ; Daf ] wg ub {} hfg ' cfhsf ] cfjZostf xf ] .

10. The Importance of Multimedia packages in teaching and learning math ul0ft lzIf0f ug]{ / l;Sg ] k|lqmofdf multimedia Kofs ] hx¿sf ] dxTjk"0f{ : yfg /x]sf] x'G5 . multimedia packages n] lzIf0fnfO{ clws cfsif {s / k|efjsf /L agfpF5 . oxfF Multimedia packages sf] dxTj o; k|sf / 5g\ M != b[Zo / >j0f ; fdu|Lsf ] k|of ] uM dlN6ldl8of Kofs ] hn ] tl:a /, lel8of], Plgd ] zg , / cl8of] ; fdu|LnfO { ; dfj ]z u5{, h;n ] ljBfy {L{ x¿nfO { hl6n ul0ftLo cjwf /0ffx¿nfO{ ; lhn } a'em \g d2t u5{ . @= cGt / lqmofTdstfM dlN6ldl8of Kofs ] hn ] cGtlqm { ofTds ; fwgx ¿ h:t} lSjh , v]n, / l;d'n ] zgsf ] k|of ]u u5{ . o;n ] ljBfy {L{ x¿nfO { ; lqmo l;sfO {df ;+ nUg u/fpF5 / pgLx¿sf ] rf;f ] a9fpF5 . #= JolQmut ultM ljBfy {L{ x¿n ] dlN6ldl8of ; fdu|LnfO { cfkm \g} ultdf cWoog ug{ ;S5G. o;n ] pgLx¿nfO { sl7gfO ef ] lu /x]sf ljifox¿df Wofg lbg / bf] xf ]o{ fP / cWoog ug{ ;' ljwf lbG5 . $= ljljw lzIf0f z} nLsf ] ; dy { gM dlN6ldl8of Kofs ] hx¿n ] ljleGg lzIf0f z} nLx¿nfO { ; dy {g u5{g\. h:t} b[Zo, >j0f, / cGtlqm { ofTds l;sfO . o;n ] ljleGg k|sf /sf ljBfy { Lx¿sf ] cfjZostf k"lt { u5{ . %= ; d:of ; dfwfgsf ] ; LkM dlN6ldl8of ; fdu|Lx¿n ] ljBfy {L{ x¿nfO { jf:tljs hLjgsf ; d:ofx ¿ ; dfwfg ug{ cEof ; u/fpF5, h;n ] pgLx¿sf ] ; d:of ; dfwfg ug{] Ifdtfdf ;' wf / n\ofpF5 . ^= pTk |]/0ff / ; xeflutfM dlN6ldl8of Kofs ]hx¿ k|of ]u ub {f ljBfyL { x¿nfO { ul0ft l;Sg k|]l/t ug{ ;lsG5 . cfsif {s ; fdu|L / cGt / lqmofTds cEof;x¿n ] pgLx¿nfO { ;+ nUg / pTk |]l/t agfpF5 . o;/L, Multimedia packages n] ul0ft l;sfO { k|lqmofnfO { cToflws cfsif {s, cGtlqm { ofTds , / k|efjsf /L agfpF5 . o;n ] ljBfy {L{ x¿sf ] a'emfO ;' wf / ug{ / pgLx¿sf ] l;sfO cg'ejnfO { ;d[4 agfpg dxTjk"0f{ e"ldsf v]N5 .

11. z} lIfs v] nx ¿ / kf /f8S;x¿sf] z} lIfs p2] Zox ¿ w]/} dxQ \jk"0f{ 5G. oL ljlwx¿n ] lzIf0f / l;sfO k|lqmofnfO { cfsif {s / k|efjsf /L agfpg d2t u5{G. oxfF z} lIfs v] nx ¿ / kf /f8S;x¿sf] k|d'v p2] Zox ¿ 5g\M s_ cg's/0fLo l;sfOM v] nx¿df cGtlqm { ofTdstf / k|lt:kw { fTdstf x'G5, h;n ] ljBfy {L{ x¿nfO { ; lqmo / ;+ nUg agfpF5 . v_ ; d:of ; dfwfg ug{] Ifdtf ljsf;M v] nx¿df ljleGg ; d:of ; dfwfg ug{] r'gf } tLx ¿ x'G5G, h;n ] ljBfy { Lx¿sf ] tfls {s / cfnf ] rgfTds ;f] rnfO { k|f ] T;flxt u5{ . u_ ; d"xsfo { / ; xsfo {M s] xL v] nx¿n ] ; d"xdf sfd ug{ cfjZos k5{, h;n ] ljBfy { Lx¿nfO { ; xsfo { / ;+rf/ sf} znsf ] ljsf ; ug{ d2t u5{ . 3_ pTk |]/0ffM v] nx¿sf ] k|lt:kw { fTds : jefjn ] ljBfy {L{ x¿nfO { a9L l;Sg / d] xgt ug{ k|]l/t u5{ . ª_ dgf ]an / cfTdljZjf ; j[l4M v] nx¿df ; kmntf kfpFbf ljBfy { Lx¿sf ] cfTdljZjf ; a9\5 / c;kmntfaf6 l;Sg klg k|]l/t x'G5g\ . . The Educational objectives of Games and Paradoxes in teaching maths

12. s_ tfls {s / cfnf ] rgfTds ;f] rsf ] k|f ] T;fxgM kf /f8S;x¿n] ljBfy {L{ x¿nfO { cfkm \gf] a'emfOsf ] k'glj {rf/ ug{ / ulx /f] ;f] Rg afWo kf5{ . v_ 1fgsf] ; Ldf k/LIf0fM kf /f8S;x¿n] k|foM ; fdfGo 1fg jf ; xh ljZjf;x¿nfO { r'gf } tL lbG5g\, h;n ] ljBfy {L{ x¿nfO { cfkm \gf] 1fgsf] ; Ldf klxrfg ug{ / lj:tfl /t ug{ d2t u5{ . u_ / rgfTds ;f] rsf ] ljsf;M kf /f8S;x¿sf] ljZn ]if0fn] ljBfy {L{ x¿nfO { c;fdfGo / / rgfTds tl / sfn ] ;f] Rg k|]l/t u5{ . 3_ bz { gLotf / lh1f;f pTkGgM kf /f8S;x¿ k|foM rlst kfg {] / lh1f;f hufpg ] vfnsf x'G5g\, h;n ] ljBfy {L{ x¿nfO { ljifoj:t'k|lt a9L pT ;'s / ;+ nUg agfpF5 . ª_ l;4fGtsf] ulx /f] a'emfOM kf /f8S;x¿sf] cWoogn ] ljBfy { Lx¿nfO { ul0ftLo / j}1flgs l;4fGtx¿sf] ulx /f] / lj:t [t a'emfO k|fKt ug{ d2t u5{ . o;/L, z} lIfs v] nx ¿ / kf /f8S;x¿n] lzIf0f / l;sfO k|lqmofdf ljleGg dxTjk"0f{ p2] Zox ¿ k"/f u5{G. oL ljlwx¿n ] ljBfy { Lx¿sf ] tfls {s, cfnf ] rgfTds , / / rgfTds ;f] rsf ] ljsf ; ug{ d2t u5{ / l;sfOnfO { yk /f] rs / k|efjsf /L agfpF5 . Paradoxes x¿sf ] p2] Zox ¿

13. Games in Mathematics ul0ft ‌ nfO{ cy{k"0f{ t/ Lsfn ] lzIf0f ug{ v] nx ? k|efjsf /L / pkof ] uL dfWodx ? x'g \ . ulzt lzIf0fdf v]n / Puzzles x? k|of ] udf Nofpg ] ul0ft1 8fOg] x'g \ . pgsf cg';f / ul0ft lzIf0f l;sfOsf $ j6f v] nM 1. Preliminary games.. 2. structural games 3.‌ practice games 4. mental games s_ cfwf / e't wf /0ff lzIf0fsf nflu v]n (Games for Teaching Basic Concepts) ul0ft lzIf0fdf ljBfy { Lx?nfO { gofF wf /0ff lzIf0f ug{ ljleGg v] nx?sf ] k|of ]u ug{ ;lsG5 . hfb'ju { (Magic Square) hfb'ju {sf] k|of ]uaf6 afnaflnsfdf hf]8 ; DaGwL ul0ftLo wf /0ff ljsf ; u/ fpg ;lsG5 . oxf lbOPsf ] hfb'ju { ;g\ !%!$ df Durer n] ljsf ; u/]sf x ’ g . o;nfO { Melancholia elgG5 . oxfF ! b]lv !^ ; Ddsf ;+ Vofx?nfO { ju { fsf / sf]7fx?df lgDgff ';f/ n] lvPsf ] 5M oxfF lbOPsf ] hfb'ju {df h'g;'s } nx / / k+lQmnfO { tyf 58s] nfO { hf]8\bf hf]8kmn #$ x'G5 . o;sf /0f of] hfb'ju { xf ] . 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1

14. v_ pTk |]/0ff hufpg ] v] nx ? (Motivational Games) i ) Preserving Product (PP) Games: ljBfno txdf lgd {f0fafbsf] :ki6 wf /0ff a;fn \g of] v]n pkof ] uL x'G5 . o; v] nsf ] lgod o;k|sf / 5 : a × b = (a × c) x (b × 1/c) where a and b must be non- zerowhole numbers and c a real number, again but a x c and b x is C non zero whole number. Such a numbers a and b called product preserving pair. For example, in this games the teacher would have to write two pair of PP numbers. Preserving product e. g. 10×40= 20×20 And ask student to find the rule and find the others pair. ii) Preserving Product and Altering the Place Value (PPAP) Games ljBfno txdf lgd {f0fjfbL ljlwjf6 ul0ft l;sfpg pkof ] uL x'G5 . o;sf ] v] nsf ] lgod o;k|sf / 5 . e. g. 12 x 84 = 21 × 48 And ask student to find the rule and find the other pairs. The rule is: (10a + b) x (10 c + d) = (10b + a )x (10d + c) where a, b, c, d are non-zero one digit whole numbers and c is obtained by multiplying b by some real number and d is obtained by multiplying the same real number.

15. u_ ;+ Vof 9fFrfx? (Number Patterns) ;+ Vof 9fFrfx?sf] k|of ]u u/]/ w]/} u0fLtLo v] nx ? v]Ng ;lsG5 . o:tf a] nx ? k|of ]u u/L ul0ft lzIf0f ub {f ljBfy {L{x? k|ToIf ? kdf ; xefuL x'G5g\ . ltgLx?sf ] lg0f{o Ifdtfdf j[l4 x'G5 / lzIf0f k|efjsf /L x'G5 . ;+ Vof 9fFrf;DaGwL s] xL pbfx /0fx? tn k|: t't ul/ Psf 5g\ . 1. Number pattern in symmetrical form 11 x 1= 1 11 x 11 = 121 ...…......……... 2. Number pattern in one digit in the product   (3 × 1) × 37 = 111 (3 × 2) × 37 = 222 ....…..….. 3. Square number pattern whivh ends in digit 5 (115) 2 =11×12 = 132 (115) 2 =13225 5 2 =25 (125) 2 =12×13 = 156 (125) 2 =15625 5 2 =25 3_ ul0ftLo uNtL (Mathematical Fallacy ) ul0ftLo v]n 1=2 lgsfNg ] dfgf }+ a = b b'a } tkm { a n] u'0fg u'0fg ubf { ab = b 2 b'a } tkm { b 36fpFbf ab - a 2 = b 2 - a 2 or, a(b - a) = (b - a)(b + a) or. a = a + b since a = b ,then, a = 2a or, 1=2 (Find the mistake of this game) oxfF ; fwf /0f tl / sfn ] x]of}{+ eg ] k|To ]s r/0f Psbd l7s 5g\ t/ cln ulxl /P/ ljrf / ubf { of] k|i6 x'G5 ls b 2 - a 2 ; dLs /0f sf] vl08s/0f ug{' ;/f;/ unt x'G5 lsgsL b - a = 0 x'G5 sf] vl08s/0f ug{' k"0f{? kdf unt x'G5 .

16. Thank You for watching my presentation