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JOURNAL OF SCIENCE OF HNUE Educational Sci , 2014 Vol, 59 No 8 pp, 76 83 This paper is available online al htlp //stdb hnue edu vn TANG CUCJNG KHA NANG CHIEM L I N H N H L T N G DANG TRI THLfC CHO HOC[.]
JOURNAL OF SCIENCE OF HNUE Educational Sci., 2014 Vol, 59 No pp, 76-83 This paper is available online al htlp://stdb.hnue.edu.vn TANG CUCJNG KHA NANG C H I E M L I N H N H L T N G DANG TRI THLfC CHO H O C SINH TRONG QUA TRINH DAY H O C DAI SO VA GIAI TICK T R U N G TRUNG H O C P H O T H O N G Nguygn Hiiu Hau Khoa Khoa hpc Tu nhien Tnfdng Dgi hpc Hdng Dvte Tom tat Trong bai vilt tac gia trinh biiy trinh biiy vl mot so phUdng thflc mil giao vien cd the sfl dung gop phan giflp hoc sinh chuyen hda cae dang Ui thflc vdi nhau, dd c6 dl cap din cac tri thflc ihuoc pham tru Trilt hpc vat bien chflng qua trinh day hpc Todn Vdi cac phUdng thflc se gop phan thUc hien viec luyen tap cac tn thflc de thiic day, dilu chinh hoat dgng tiing cUdng khii nang chilm ITnh tri thflc cho hoc sinh qua trinh day hoc Dai so - Giai tich Tif khda: Hoat dpng, tri thflc phUdng phap day hpc Dai sd •• Giai tich Mot dau Day Toiin la day hoat dpng Toan hgc Luan diem cd the hieu nhU sau: Mudn day Toan cd hieu qua thi nhat thilt phai cho hgc sinh hoat ddng, chi bang dUdng dd mdi cd the liim cho hpc sinh nam bat tri thflc mot ciich vflng vang Tiim ly hgc va Lf luan day hoc hien dai da khang dinh rang, dudng cd hieu qua nhat de lam cho hoc sinh nam vflng kien thflc va phat trie'n nang lUc sang tao lii phai dUa hgc sinh vao vj trf cua chu the boat ddng nhan thflc Thdng qua boat dgng tu life, tu giac, tfch cUc cua ban thSn mil chilm linh kien thflc, phat trie'n nang life sang tao Dinh hudng phat trien nang lUc ngUdi hpc hien cung idy cac luan diem dd lam nen tang Hdn nfla, tri thflc khong phai la ciii dl dang cd the cho khong De day mdt tri thflc nao do, giao vien thudng khdng the trao cho hpc sinh dieu thay mudn day, each lam tdt nhat thudng la ciii dat tri thflc dd vao nhflng tinh hudng thich hpp de hgc sinh chilm linh nd thdng qua hoat dgng tu giac, tich cUc va sang tao cua btin than Thuc tiln su pham da khdng dinh tfnh dung dan cua nhan dinh Chang phai nhflng mong mudn cfla thay ve sfl tiep thu cua hpc sinh deu trd thiinh hien thuc Dilu cho thay rang, Eruyin thu tri thflc cho hpe sinh la viec lam khdng de neu khdng cd each thflc va dudng dung dan Mudn hgc sinh chilm ITnh tri thflc Toan hpc mgt each vflng chSc, thi dudng hdp li nhat la tao nhflng tinh hudng day hoc, cho hpc smh dUde phat huy tdi da sU chii dgng chflng mflc cd the Khdng the nao cd mdt sU chiem ITnh tdt thdng qua dudng thu dpng Tuy nhien, vi nhflng If khac nhau, nen khong phiii giao vien nao cung hil'u ro va vdn dung Iuan diem Vi vay da va dang tdn tai each day hgc Eheo ldi truyin thu mgt chieu Trong Ngay nhan bai' 25/02/2014 Ngiiy nhan dang' I l/l 1/2014 Lien he: Nguyen HCdi Hau, e-mail: hauncslhanhhoa@gmail.coin Tdng cudng khd ndng chiem lmh nhdng dang In thifc cho hgc sinh quan niem cfla nhieu giao vien, giang giai cac kien thflc Toan hoc mdt each chi iik rdi sau cho hgc sinh ap dung xem nhU la du Khi xem xet mdi lien he gifla boat ddng va tri thflc dUdc quy dinh chUdng trinh mdn Toan phd thdng, tac gia Nguyin Ba Kim da Iam sang td: Tri thflc, dac biet la tri thflc phUdng phap vfla la dieu kien vfla la muc dich cfla hoat ddng [1; 143] Tri thflc can phai dUdc tao nen mot each tich cue bdi chfl the nhan thflc chfl khong tilp thu mdt each thu ddng tfl ben ngoai Tfl quan niem do, day hpc phai coi trpng van de hinh cho hgc sinh each hpc, each tao nen tri Ehflc, each EU hpc chfl khdng chi ddn thudn la cung cdp kiln thflc Day hpc nhU vay khdng chi hinh cho hpc smh cac tri Ehflc sU vat, tri thflc chuan tri thflc gia tri; He thdng tri thflc phifdng phap; Cdn phai luyen tap cac tn thflc dd de nham tang cudng kha nang chiem ITnh Eri Ehflc toan hgc cho hoc sinh Noi dung nghien ciru Cac loai tri thflc dfldc xet Erong chUdng Erinh Toan phd thong bao gdm: Tri thflc sU vat; Tri Ehflc phUdng phap; Tri Ehflc chua'n; Tri Ehflc gia Eri, nhflng loai hinh tri thflc la cd sd cho hoat dpng tu duy, boat dpng nhan thflc loan hpc De nang cao viec luyen tap cac tri thflc thflc day, dilu chinh boat ddng tang cUdng khii niing chilm ITnh tri thflc cho hpc sinh chflng loi tap trung tap trung vao mgt sd vdn dl sau 2.1 Tri thiic phifOng phap Do tri thflc phUdng phap day hgc Toan da dang, phong phu nen kho cd the cd phan loai cho cac tn thflc Tuy nhien can thiet dl cap cac dang tri thflc phUdng phap cdn luyen tap cho hpc sinh va can phat hien Ehdng qua hoaE dgng giai loan sau day - Nhflng tri thflc phUdng phap dinh hifdng cho hoat dpng: Nhflng tri thflc phudng phap tiln hanh nhihig boat ddng toan hgc cu the; Nhflng tri thflc phUdng phap tien hanh nhflng hoaE ddng toan hpc phflc hdp; Nhflng tri thflc phifdng phap tien hanh boat dpng tri tue phd biln mdn Toan; Nhflng tri thflc phudng phap thifc hien nhflng hoat dpng trf tue chung; Nhflng tri thflc phUdng phap tien hanh hoat dpng ngdn ngfl logic - Xet ve npi dung cd ban tri thflc phUdng phap cd hai dang cbu yeu: Nhflng tri Ehflc phUdng phap cd Einh chat thuat loan; Nhflng tri thflc phUdng phap cd tfnh chdt tim doan [1,144] Khi ndi din vai trd cua Eri thflc phUdng phap tac gia Dao Tam cho rang "Tri Ehflc phUdng phap ddng vai trd la cd sd dinh hUdng trUc tilp cho boat ddng" [4,37], Yeu cau cua Li Iuan day hoc theo quan diem hien dai la khdng nhflng trang bj tri thflc sU vat cho hpc sinh ma cdn dac biet chu trpng trang bi nhflng in thflc ve each thflc boat ddng chiem ITnh tri thflc Dflng trudc mgt van dl cu the neu cd dupc he thdng u-i thflc phUdng phap day du thi hpc sinh de dang tiln hanh nhilu hoat dpng tim tdi kham pha cac tri thflc mdi, Chang han, de phat hien mpt quy luat; Mdt dinh li; Mdt quy tac cd the cho hpc sinh khao sat mdt trUdng hdp rieng lay tfl ngi bp loan hoac khao sat cac hien tifdng thUc tiln Tfl dd nhd boat ddng phan tfch so sanh, tong hdp, khai quat hoa de phat hien ket qua mdi * Tri thflc phUdng phap gdp phdn quylt dinh viec hinh bdi dUdng cac thao tac tfl cua hpc sinh, tren cd sd dd ren luyen cho hgc sinh kha nang sang tao Toan hpc: Cd nhflng bai toan, neu dua vao logic binh thudng, f.n thflc phfldng phap thdng dung thi khdng the giai dfldc Chflng ta phai sfl dung tu linh hoat, phai cd kha nang quan sat, danh gia, nhan xeE de Elm cac moi lien he bai loan Nguyen Hflu Hau 2.2 Sir chuyen hoa gifia cac dang tri thfic mon Toan qua trinh day hoc Gifla cac dang tri thflc mdn Toan ludn cd stf chuyen boa anh hudng iSn qua trinh nhan Ehflc Tfl tri thflc sU vat hpc sinh hinh tri thflc phudng phap mdi, tri thflc phUdng phap, lai cd vai tro giflp hoc sinh hinh dung dflpc sif hinh va phat trien ciia tri thflc sU vat va hieu rd hdn ban chdt cfla tri thflc sif vat, Trong phan chflng tdi dl cap din sU chuyen hoa gifla cac dang tri thflc mdn Toan qua trinh day hgc Day la mdt vdn dl phflc tap vii da dang, chiu sit anh hudng cua nhieu yeu td 2.2.1 Sir chuyen hoa tuf tri thiic siT vat tri thii'c phtfdng phap Tfl tri thflc sif vat hpc sinh hinh tri thflc phUdng phiip mdi, tri thflc phUdng phap lai c6 vai trd giup hoc sinh hinh dung dUdc sif hinh va phat trien cfla tri thflc su viit va hieu rd hdn biin chdt ciia tri thflc sU vat Mdl tn thflc sfl vat mdi hinh tif no khdng trd tri thflc phifdng phap Si( chuyen hda dUdc thifc hien qua trinh quan sat, van dung tri thflc sif vat nhflng tinh hudng khac Chinh qua trinh lap lai nhieu lan sU van dung tri thflc sU vat la nhan to quyet djnh hinh nSn tri thflc phudng phap, Mpt tri thflc sU val dUdc van dung vao nhieu tinh huong da dang thi se lam su chuyen hda tri thflc phudng phap nhanh chdng hdn Trong trudng hdp hieu lUc cua phUdng phap cung vi thi mil dupc danh gia cao hdn Cflng cd trudng hdp sU phdi hdp nhieu tri thflc su vat cung lam sinh mpt phUdng phap, Theo 12] de nang cao hieu qua cua siJ chuyen hda tfl tri thflc nii vat thiinh tri thflc phudng phap cdn quan tam tdi mdt sd phifdng thflc sau: - Sfl dung nhflng vf du cflng loai de khac sau quy trinh thao tac van dung tri thflc sU vat Day lii mdt each phd biln va hflu hieu giflp cho hpc sinh nam difdc cac ylu td then chdt quy trinh van dung mdt tri thflc sif vat vao giai quylt mot loai tinh hudng Trong qua Erinh hudng ddn hgc sinh van dung tri thflc su vat, giao vien can nhan sfl hien dien cua tri Ehflc da bilt tinh hudng cu the, chi rd quy trinh thifc hien cac thao tac qua trinh van dung - Sfl dung cac linh hudng da dang cung ap dung mpt kien Ehflc va hifdng ddn hpc sinh quan sat, nhan xet de thdy ro tri thflc dUdc sfl dung lam cdng cu Iam phUdng tien giai quylt vdn de dat mdi tinh hudng Day la each giup hgc smh nhan sif gidng vii sif khac cac Einh hudng van dung kien thflc Chinh viec nhan su gidng da lam cho hgc sinh thdy dUdc gia tri y nghTa cua tri thflc sU vaE Vdi each niiy mdi giai quylt mot van de tinh hudng tUdng tu hgc sinh bilt each lien EUdng va huy ddng kiln thflc da hgc viio giai quylt vdn dl Khi mpt tri thflc sfl vat dupc chuyg'n hda cdng cu, phifdng tien, thao tac cfla hpc sinh thi nd da U-d tri thflc phUdng phap De cung co tri thflc phUdng phap can thflc hien sfl luyen tap nh^c lai qua trinh day hpc ve sau Vl du Dgy hpc chu de "Bdi ddng thdc" trong^ Sdch Gido khoa Dgi sd 10 De'hpc sinh hinh thimh nen mpt w phuong phdp ehdng minh bdt ddng thiic gido vien ed the kit hop vdi tri Ihdc vi phep bien doi ddng nhdt thong qua yiu cdu hoc sinh chiing minh nipt sd hdt dang thdc sau: Chiing minh rdng: a} a' + y^ -ab>0,\/a,be U; b) a'^ -I 6^ -i- e^ > oh -\- be: + ca, Va b c £ M.- d) {a + b){ - -\- - \ > vdi a, b duong \a bJ Chung minh rang vdi Va,ft,c e M : jo, - c\ 77m gid tri nho nhdt cua bieu thife f{-.r) ^ r -\ - Tfl dd giup hgc sinh hinh thiinh tri thflc phUdng phap mdi de chflng minh bat dang thflc: -i- Chflng minh bat dang thflc bang phUdng phap bien doi tUdng dUdng; + Chflng minh bdt dang thflc bang phfldng phap sfl dung bat dang thflc Cauchy Trong td chflc cho hpe sinh hoat dgng giai quyet cac nhiem vu nhan thflc can iam rd sfl phdi hdp gifla suy luan cd li, du doan va qua irinh huy dgng van dung tflng nhdm kiln thifc Viec lam cd lac dung hinh cho hgc sinh tri thflc phifdng phap mang tfnh chdt tim doan Nhflng Eri thflc cd vai tro dmh hudng hoat ddng giai quyet vdn de va kham pha sang tao tn thflc mdi, sang tao phUdng phap mdi giai loan 2.2.2 Sit chuyen hoa giii'a tri thiic sti vat va tri thiic chuan qua trinh day hpc Trong qua trinh day hgc, ngudi giao vien trang bi cho hpc sinh nhflng tri Ehflc sU vat nhU mdt dinh li, mgt khai niem mgt bai loan va dinh hudng cho hpc sinh cdn chu ddng suy nghT qua trinh tiep can cac tri thflc Qua dd hpe sinh nam bat va hieu rd cac tri thflc chuan de khai thac, sfl dung chflng mdt each hpp If nhat, diln dat cac tu tudng mdt each dung ddn nhdt, ddng thdi tiep can mdt tri thflc mdi mdt each hop If va hieu qua nhat Vi du Quy tae tinh dao hdm theo dinh ngliTu Mudn ttnh dgo hdm ciia hdm so f Igi diem XQ theo dinh nghia ta thifc hien hai hif(')c sau: Budc 1: Tinh Ay theo cong thdc A-ij = f{xQ -F Ax) — /(xo) dd A,r Id so gia cua biin so tai XQ; Ay J A.r' Ddy Id mpt tri thifc stf vdt Tri thifc ndy dehpc sinh van dtjng vdo hid todn linh dgo hdm cdo ham so theo dinh nghia Nd ciing chinh Id co sd de gido vien dinh tnfdng cho hoc sinh xdy difng edc quy tae tinh dgo ham Chdng hgn cho cde hdm sd y ~ xr vd y = siux, Tinh ilgo hdm cua hdm sP-y = x^ -\- sill X 2.2.3 SiJ chuyen hoa giiia tri thiic sti vat va tri thiic gia tri qua trinh day hpc tri thflc sU vat difdc sfl dung nhieu qua trinh tiep thu va chilm ITnh tri thifc, cd pham vi flng dung rpng rai Bdi vay, giao vien khdng chi trang bi tri thflc cho hpc sinh mil can phai tao hflng thu hgc tap, giup hoc sinh phat huy nang life sang tao va nang life tu hoc, tU danh gia kit qua hpc tap cua ban than, giao vien cdn nghien cflu din sU chuyen hoa gifla in thflc sif vat vii tri Ehflc gia tri Chang ban tfl tri thflc sU vat "Bdt dang thflc Cauchy" can cho hoc sinh thay bat dang thflc la mdt bat dang thflc quan trpng, cd nhieu flng dung mdn Toan Vi du Cho hai diein phdn biet A, B ed dinh vd so thife k khong ddi Tun tap lulp edc diem M cho MA^ - MB"^ = k Day la mgt bai toan khdng dl neu ta sfl dung each giai bang phUdng phap hinh hoc tdng hdp hoac phUdng phap vec td Cach giai bang phifdng phap toa se cho ta lbi giai ddn gian nhat Dat AB = a, a > Chpn he true toa dd Oxy co gdc O trung A Ox chfla B Khi dd ^(0;0) vaB(fi;0),GgiM(x;y), tacd: MX^ - MB^ = k -^{x^ + y^] - [{x - af-h y'^] = k k •t^x = \ 2a 2a Nguyen Hflu Hau Vay tap hdp cac diem M la difdng thang cd phifdng trinh ; ^ — + — he toa dp da chpn (dudng thang vuong gdc vdi AB) Tfl ldi giai bai toan Ea thay, nhung biu loan hinh hpc chfla cac ylu Ed khoang each, gdc, cung phUdng, vudng gdc nlu giai bdng phifdng phap loa dd se hfla hen cho klia nang tim 161 giai^Tfl giao vien yeu cdu hoc sinh neu cac budc de giai mdt bai toan hinh hgc bang phUdng phap toa 2.2.4 Su chuyen hoa giira tri thu'c chuan va tri thiic gia tri qua trinh day hoc Tn thflc chuan la thudc do, la chud'n mifc de danh gia qua trinh nhan thflc cua hpc sinh nhdm phan tich cho hoc sinh thay chd manh va chd ylu cfla minh, chd nao da nam vflng, chd nao cdn 16 hdng hoac sai sdt va nlu cd the thi vach rd nguyen nhan sai ldm de giao vien can cfl vao dd ma, cd nhflng phifdng hudng, bien phap giup hoc sinh khac phuc hay danh gia vai trd tdm quan trpng, pham vi flng dung cfla mot tri thflc Qua dd hinh phUdng phap mdi de giai quylt vdn dl Vi du Tim gid tri nhd nhdt eiia hdm sd Tri thflc chua'n d day difdc the hien chfnh lii yeu cdu cua biii toan, hoc sinh cdn phai nam.' vflng dinh nghia gia trj nhd nhat cua hiim sd Giao vien cho hoc sinh giai bai loan tren hoac yeu cdu cac em tim chd sai ciia !di giai sau day: Dat t = X -\- - thi T- -4- - ^ X /^ - nen bai Eoan trd tun q{i) X- vdi cj{t) -^ t^ - 2t + ?> = {t-\f + > 2, \/f t R Dang thflc xay t = Doddinin/(:f} = min/(.r} dat dUdc bang = Sai ldm d cho la chuyen biii toan khdng tUdng dUdng Gia Eri nhd nhdt cua f{x) khong trflng vdi gia trj nhd nhat cua y{t) vdi Vf G M Cd the thay vdi f = thi khdng tdn tai x de f{x) =^ Ldi giai tren khdng dflng la hpc sinh khong nam vflng djnh nghTa cua gia tri nho nhdt cua ham sd Qua dd giao vien dieu chinh lai nhan thflc cua hpc sinh thong qua ldi giai dung 2.3 Tri thfic thuoc pham tru Triet hoc vat bien chfing Thuc lien sU pham cho thdy, mpt sd giao vien chUa bilt each cai dat, ldng ghep mdt each thfch hdp nhflng kien thflc thudc ve phep vat bien chflng Erong qua trinh day hgc Toan Tfl dan den viec hpc sinh nhin cac ddi tUpng Toan hpc mpt each rdi rac, trang thai Einh ma chifa thay mdi lien he phu thugc, sif van ddng bien doi qua trinh phiit sinh vii phat trien, chfla thay dfldc sfl thdng nhdt va mau thudn gifla cac mat ddi lap nen chua hil'u rd ban chdt Toan hgc Vi vay nhieu hpc sinh gap khd khan giai cac biu toan, nhat la cac bai loan ddi hdi phai cd sfl sang Eao Xet vl phudng dien phUdng phap luan day hgc Toan, cd nhflng tri thflc thupc pham Eru Erilt hgc vat bien chflng ddng vai trd djnh hudng boat ddng tim doan mil ngudi giao vien can quan tam de trang bj cho hgc sinh De trang hi cho hgc sinh nhflng tri thflc thudc pham Eru Erilt hgc vat bien chflng can luu y nhflng van de sau: * Can id chdc cdi ddt, ldng ghep mot so kiin thdc ve phep bien chdng vgt mot cdch kheo leo thdng qua nhifng bdi todn de ddn dim trang bi cho hpe sinh ve the gidi quan val bien chdng Ddi vdi hpc sinh thdng viec van dung cac quy luat vii cac cap pham trfl cfla phep biSn chflng vat vao hpc loan cdn xa la vdi cac em NhUng neu giao vien bilt kheo leo cai dat cung Tdng cudng khd ndng chiim ITnh nhimg dgng tri thdc cho hpc sinh vdi nhflng dung y sU pham thi se giflp hpc sinh bilt hpc Toan dUa vao cac quy luat va cac cap pham trfl cua phep bien chflng vat Chang han, tri Ehflc Ehupc pham trii mdi hen he gifla hinh thflc va npi dung Hinh thflc cd the che ldp ndi dung, thay doi hinh thflc cac bai toan de thay rd npi dung thuan tien cho viec huy dpng kien thflc da cd cua hpc sinh la mdt viec lam hit sflc can thiet Do do, giao vien cdn djnh hudng cho hgc sinh lien tudng va huy ddng kiln thflc bang each ludn ludn dong vien nhac nhd hgc sinh xem xet bien ddi cac bai loan, vdn de dudi nhilu hinh thflc khac nhau, thich hpp cho viec tim mgt hinh thflc nghien cflu phiJ hdp nhdt Tri thflc cd the dude dien dat dUdi dang quy lg vi quen nhd bien ddi hinh thflc cua bai toan Vidu Cho clip (£} : ^ + ^ = Vfl dudng thdng (A) : Ax-\- By-^ C = Chdng minh a^ b^ rdng (A) liip xue vdi (E) vd chi a'^A'^ -\- b'^B'^ = C^ Cd hpc sinh giai bai toan nhu sau: Dudng thang (A) tiep xuc vdi (E) va chi h6 phUdng trinh: a^ ^ 62 Ax + By-\-C = CO nghiem nhat • Tim dilu kien de he phUdng trinh cd nghiem nhdt bang phifdng phap ihl la each giai kha phflc tap Hdn nfla chifdng trinh hien hanh khdng dung khai ni6m nghiem kep de giiii quylt cac bai toan ve tiep tuyen, tilp xuc Vay giao vien cdn phai djnh hudng nhu thi nao de hpc sinh cd the giai dfldc bai tdan Eren giao vien cd the neu cau hdi: Tfl viec tim dieu kien tiep xflc cfla mdt dudng thang va dudng (E) ed the dfla bai Eoan ve tim dieu kien de mot dudng cong quen thupc tiep xflc vdi mgt dudng thang khdng? Vdi cau hdi nhu vay hgc sinh cd the lien tudng din viec dUa phUdng trinh {E) ve phUdng trinh dudng trdn thdng qua phep daE X = - ; y ^ - se dUdc X'^ -\-Y- = I a b Khi dd, ta cung bien dd'i Ax + By->rC = Q aAX + hBY + C = Bai toan trd tim dilu kien de dUdng trdn X"^ -\-Y'^ = I tiep xuc vdi dudng thang aAX + bBY -h C = Bai toan da dUdc dUa ve dang quen thugc, dilu kien can tim d day la dudng thing (A') : aAX -H bBY -i- C = tiep xuc vdi dUdng trdn (T) : X"^ + Y"^ ^ I, va chi khoang each tfl Earn 0(0; 0) cua (T) din (A') bang I '•^1 = l ^ a U + 62B2 = C'' VaM2 + (,252 * Tochifc nhifng hogt dpng Todn hpe ihich hpp (phdt hien, md rpng, ddo sdu, nimg cao ), van dung linh hogt cdc thao tde tu (khdi qudt hod, dgc biet hod, luong tif) qud trinh dgy hpc Todn nham giiip hpc sinh tu day theo cdc quy lugt cua phep bien cluing vdt Trong qua trinh day hpc giao vien cdn td chflc nhflng hoat ddng Toan hpc thfch hdp giup hpc sinh biet phat hien nhflng van dl mdi, nhflng bai loan mdi, hoac giflp hgc sinh nhin thay dfldc su lien he gifla nhilu vSn de vdi Nhd hgc sinh cd the biet suy nghT tim tdi de cd the md rpng, dao sau them kien thflc, bang each neu len va giai quyet nhung van de tdng quat hdn, 81 Nguyen Hflu Hau nhflng van dl tUdng tu, hoac di sau vjio nhflng trUdng hdp dac biet, cd y nghTa vl mat nao dd (ket qua li diu, cd flng dung thuc tl, v.v ) Chang ban, van dung cap pham trfl cai chung - cai rieng de giup hgc sinh chiem linh tri thflc Eoan hpc Theo quan diem cua phep bien chflng vat vl mdi quan he gifla cai rieng va cai chung cd mdi quan he bien chflng vdi Cai chung tdn tai Erong cai rieng, bieu hien Ehdng qua cai rieng; NgUdc lai, cai rieng tdn tai moi lien he vdi cai chung, bao ham cai chung; Cai neng la cai toan bd, phong phu hdn cai chung, cai chung la cai bp phan nhung sau sdc hdn cai rieng, Tac gia Dao Tam cho rang cd the quan triet phep bien chflng vl mdi quan he gifla cai chung va cai rieng vao viec phat tnen nhan thflc cho hpc sinh day hoc Toan qua cac phUdng thflc sau day: Phfldng thflc 1: Luyen tap cho hoc sinh boat ddng khao sat,-tudng tac qua cac trudng hpp rieng thdng qua hoat dpng phat hien de tim cai chung - tri thflc mdi long quat hdn Cd the van dung phUdng thflc viio cac hoat dgng phat hien cai mdi nhU: Khai niem mdi, djnh li mdi; Quy tac mdi Phfldng Ehflc neu Eren cd the van dung vao cac li thuylt va cac phfldng phap day hpc Eich cue nhu: Day hpc theo quan diem hoat dpng; Day hoc phat bien va giai quyet vdn de; Day hpc kien Eao; Day hgc theo Li thuyet tinh hudng; Day hgc hgp tac Dieu ndi tren se hien hflu cu the thdng., qua to chflc cac tinh hudng day hpc nham viio viec khai thac phat hien va giai quylt cac mau thuan, vUdt qua cac chudng ngai, PhUdng thflc 2: Xudt phat tfl yeu cdu giai dap mdt vdn dl cu the (mdt trUdng hdp rieng), thdng qua boat dpng khai quat hoa, bien doi ddi tupng, de xuat vii giai dap van de tong quat (cai chung); tfl dd giai quyet trUdng hdp rieng ban dau va cu the boa nhieu trudng hdp rieng khac lien quan [4,49-50] Giao vien cdn lUu y cho hpc sinh bilt tim cai rieng cai chung, biet nhan thflc sau sac mdi quan he gifla cai rieng va cai chung De di den mpt cai chung ta co the phai khao sat mgt s6 trfldng hdp rieng, lay ket qua cua cai rieng de djnh hudng giai quyet cai chung Vi du Cho cdc so thuc phdn biel a, b, c Rut gpn tdng sau: (a -h){a- , I? [x - c) {x a.) c^ {x - a) [x - b) TT"^ -c){b-a) 777 \ c) - H {b (c - a) {c - b) Vdi bai toan neu Ehuc hien quy ddng mSu Ehflc sau phan tfch cac bieu thflc Ehanh cac Ehfla so de rut gpn bai toan la dieu khdng de Khi giai bai toan khong Ehe bd qua xiec xem xet cac trudng hdp rieng de dinh hUdng each giai Ta xet mgt sd gia tri dac biet cua x : vdi X = a ^ S = o?;v&i X = b =^ S = b^;\6\ X = c ^^ S = I? Qua mpE sd trudng hdp dd cd the du doan la = x^ vdi x bat kl DU doan dinh hudng cho each giai xem S nhu la mpt ham so S{x) va dat P{x) = S{x) - x'^ Ta cd P{x) la da thflc bac khdng qua 2, co ba nghiem phan biet a, 6, c ^ P(x) = vdi mpi x hay cd nghTa \kS = x"^ vdi mpi x Cd nhilu trudng hdp bai loan dang xet lai la trudng hpp neng cfla mdt biii toan tong quat nao dd Ta se giai quyet bai toan tdng quat rdi suy ldi giai bai toan ban ddu vi bai toan tdng qual cd the chfla dung nhieu thdng tin hdn va dac biet hoa ngUdi ta da ddu di nhflng thong tin * Den mdt chflng mflc nao dd, hpc sinh da cd mot sd kien thflc vl vat biSn chflng (fl dang an tang), tap cho hpc sinh bilt each van dung chflng vao viec hgc cac khai niem, cac dinh li va giai cac bai tap toan 82 Tdng cudng khd nang chiim ITnh nhifng dgng Iri thiic cho hex- sinh Khi dflng tnfdc mdt bai loan, de djnh hudng va Eim toi ldi giai phai biet nhin nhan nd difdi nhieu gdc dp, phai xem xet nd cd moi hen he nhu thi nao vdi cae bai loan da tflng giai, phai nhin nhan mdi lien he gifla cac ylu td gia thiet bai loan, gifla gia thilt va kit luan cua bai loan; tflc la hpc sinh dupc hieu dupc quan diem toan dien nhan thflc Hoac cd nhflng ldp bai loan ma dudng ldi giai cua chflng cd ngudn gdc la nhflng suy luan mang tinh chdt cd quy luat Chang ban, giai cac biii toan chfla nhieu dai lUdng thay doi (nhilu a'n) thi thdng thudng ta tim each chuyen vl bai toan chfla it dai lUdng biln dd'i hdn NgUdc lai, cd nhflng bai toan chfla it an nhUng khd giai vi tinh chat phflc tap cfla cac bieu thflc cd mat bai toan dd ta lai phai tim each chuyen ve biii loan nhieu an nhilu phUdng trinh hdn NhU vay cd nghia la da phan nao hieu dupc mdi quan he bien chflng gifla npi dung va hinh thflc hoac quy Iuat "lUdng ddi - chdt ddi", tflc la "chju thiet vl "mat Ifldng" nhung dUdc vl "mat chdt", Ket luan Tren day chung tdi da dl cap den mpt each ma giao vien cd the sfl dung de gdp phdn cai dat luyen tap cac tri thflc de thflc day, dieu chinh boat ddng tang cfldng kha nang chiem ITnh tri Ehflc loan hgc cho hgc sinh, Ngi dung, each thflc cai dat va luyen tap cac tn thflc cho hgc sinh can phai dfldc cu the hda muc Eieu day hpc, phUdng phap day hpc va kiem tra danh gia Tuy nhien, mudn dat dUdc dilu can phai lua chgn ngi dung vii phUdng phap day hpc mdt each thich hdp, TAI LIEU THAM KHAO [1] Nguyen Ba Kim, 2009 Phuong phdp dgy hpe mdn Todn Nxb Dai hoc Su pham Ha Ndi [2] Ki yeu Hpi thdo Quoc gia ve Gido due Todn hpc a trudng tlumg (2011) Nxb Giao due Viet Nam [3] Bui Van Nghj, 2009 Van dung li lugn vdo Ihuc tiin dgy hpc mon Todn a trudng thong Nxb Dai ligc Sfl pham Ha Ndi, Ha Npi [4] Dao Tam (Chii bien), Trdn Trung 2010, To chifc hogt dpng nhgn thtfc dgy hpe mdn Todn d trudng Trung hpc phd thong Nxb Dai hgc Sfl pham Ha Npi Improving the ahiUty of students to learn algebra and calculus in high school In this paper, the author proposed methods that teachers could apply in order to help students to change the forms of knowledge into each others These methods mention some knowledge belong to the categories of dialectical materialism Philosophy in the process of teaching mathematics These methods will improve students' ability to learn Algebra and Calculus ... tap cac tri thflc thflc day, dilu chinh boat ddng tang cUdng khii niing chilm ITnh tri thflc cho hpc sinh chflng loi tap trung tap trung vao mgt sd vdn dl sau 2.1 Tri thiic phifOng phap Do tri thflc... loan 2.2.2 Sit chuyen hoa giii''a tri thiic sti vat va tri thiic chuan qua trinh day hpc Trong qua trinh day hgc, ngudi giao vien trang bi cho hpc sinh nhflng tri Ehflc sU vat nhU mdt dinh li,... gifia cac dang tri thfic mon Toan qua trinh day hoc Gifla cac dang tri thflc mdn Toan ludn cd stf chuyen boa anh hudng iSn qua trinh nhan Ehflc Tfl tri thflc sU vat hpc sinh hinh tri thflc phudng