REN CHO SINH VIEN SUPHAM CHUYfiN NGANH TOAN Kil O ThS D6 V A N H O N G " Dqy hpc (DH) cde kiln lhi>e (KT) s l hpc d tllu hpc (TH) dupe thyc hi|n lidn tye, xuydn su^t t(>ldpl dlnldoS CdcKTsdhpcdTHtuy d[.]
REN CHO SINH VIEN SUPHAM CHUYfiN NGANH TOAN Kil O qy hpc (DH) cde kiln lhi>e (KT) s l hpc d tllu hpc (TH) dupe thyc hi|n lidn tye, xuydn su^t t(>ldpl dlnldoS-CdcKTsdhpcdTHtuy don gldn, d mOc dd oon ddu nhung Id nln ldng CO sd d l xdy dyng KT d cdc b^c hpc sou vd cd nhllu i>ng dyng ddi sd'ng Myc tidu DH cdc KT ndy khdng phdl ehl di>ng Ipl d eh£ gido vidn (GV) eung edp, truyin thy dung KT todn hpc, rdn kr ndng (ICN) thyc hl|n phdp tfnh cho hqc sinh (HS) Id dO; quon trpng hem, GV phdl nhdn thd'y, dy dodn dupe nhOng khd khdn, sal ldm nhdn thi>c cua HS vd nguydn nhdn d l ttm cdch hudng dfin, hfi trp thfch hqp; ddng thdi, glup HS bill v$n dyng KT dd hpc m$l cdcn llnh hoqt aud trinh hoqt ddng (HD) kiln tqo KJ mdi vd dp dyng vdo thye tlln D l dqt duqc myc Hdu DH, GV khdng nhOng phdl am hiiu ndi dung DH, ndm v&ng KT todn hpe, phuemg phdp dpy hqc (PPDH) bd mdn md cdn phdl ed ndng lye chdn dodn (NLCD) D ThS D6 V A N HONG" mfil bdl hpc (Hit hpc), mfil kSp vd chuong trtnh lodn cip hpe; 3) Xdc dinh dOng, dO ede KT, KN md HS dd cd vd cdn chutfn bj cho vl|c nh^n thi}c cdc ndl dung DM mdl; 4) Nhdn bilt dOng v l ddc dllm tu duy, nhdn lhi>c eOa HS DH cdc KT s^ hpc; 5) Nhdn bill, hllu dupe nhOng bilu hl|n Idm ll, nhdn thue cOa HS qua cdc HD hpe tdp; d) Lidn tudng vd huy ddng ede Kl, KN, kinh nghi|m vdo xem xdt, phdn Hch cdc ndl dung DH; / J Nhdn bill, dy dodn dCng nhOng thudn Ipl vd khd khdn cOa HS nh^tn thi>c cdc KT s^ hpc; 8) Phdn Kch, dy dodn dung nhOng sai Idm vd nguydn nhdn dfin din sai ldm Irong nhdn thue cdc KT sd hpc CI}G HS; 9) Phdt hl|n, dy bdo chfnh xdc, kjp thdi xu thl phdt h-lln (ed phdt triin Kch eye vd hqn ehl) Irong nhdn thi>c cdc KT sd hpc cua HS; 10) Dy dodn dung nhu edu nhdn thue, Idid ndng, mi>c d$ tTrih h$l cdc KT sd hpc ci3a HS m^t cdch Uioa hpc, khdch quon; M/Duaracdch DH thfch hqp vdi tOng trudng hpp, khd ndng xdy ra, glOp HS Hip nhdn KT, phdt trlln khd ndng nhdn thue vd dqt dupe myc ttdu DH NLCD vd kr ndng chdn dodn (KNCD) DH cdc KT sd hpc Cde nhd Tdm If hqc dd chung minh, ndng lye NLCD Irong DH duge cdu thdnh mdt phdn tit (NL) Clio mfil cd nhdn duqc htnn thdnh vd phdt yiu td bd'm sinh dl truyin, edn chO yiu dupe hinh trlln ehu yiu qud trinh HD vd giao luu thdnh, phdl trlln qua HD hpc ldp vd DH, ndn, nlu cuo ngudi, khdng chi Id bdm sinh (1), (2) khdng duqc td' ehue cdc HD rdn luy|n ihfch hqp, Nhu vdy, d mil sinh vidn su phgm (SVSP) diu cOng vdl nfi lye cOo SV th) NLCD DH ed thl tlim ndng mit NLCD Irong DH d mdc di nhd't bj thul chdt hodc ch^m phdt triin VI v ^ , d l ndng djnh, nhldn, dqt muc dd cao hay thdp, nhilu cao NLCD DH sd hpc cho SV, ngodt vl|c hay ft cdn phy thudc vdo mdl td hpp cdc NL bj cdc KT, KN stf hpc, PPDH bd mdn, glup khdc (do cdc dllu kl^n bdn vd bdn ngodi SV nghldn cuu, gldl quylt ede Hnh hu^ng xudt too ra) hl|n qud Irlnh DH mdt cdch bl|n dnOng, ' NLCD DH cdc KTsd hpc dTH cuo SVSP edn edn thudng xuydn rdn cde KNCD dupe thl hl$n qua Idid ndng CD dung, nhanh vd Mdt sd bl$n phdp r«n KNCD DH diy cdcHD qud trtnh DH (h> chudn bj k l cdc KT sfi: hqc d TH cho SV hoqch din td chuc, trlln khoi thyc hl#n vd ddnh U Rin KNCD cho SV qua DH mdn PPDH gid kit qud DH) D l dqt dupe dllu dd, SV cdn ed Todn TH DH mdn PPDH Todn TH phdl lufin gdn mdt sd KNCD CO bdn: JJTlm kllm, thu thdp thdng kit vd khoi thdc nrtdl quan h | vdi ndl dung DH cdc tin Ilin quon din ndl dung DH cdc KT sd hqc KT s^ hpc d TH, tu dd, glup SV cd cdl nhin dOng v l mfil bdi hpc, mSl tdp vd lodn cdp hqc; 2} Xdc djnh dOng, ey thl myc Kdu DH cde KT sd hpc Tap Ghl Glao due s6 (fci a - io/aoia) quon dllm, tu hidng, phuong phdp cija todn hqc hl$n dqi Irong xdy dyng, htnh thdnh cdc KT sd hpc Ding thdi, td chuc cde hinh thiic DH phCi hqp (gloo nhi|m vy cho SV ly hpe, ty nghldn cuu, ldm bdl ldp, Kiu ludn, thdo ludn nhdm ) d l rdn cho SV mdt sd KNCD Irong DH nhu: o^ Tim klim, thu thip thdng tin lidn quan d i n DH ede KT sd hqc h>ng bdl, tChig Idp vd todn bde hqc qua nghldn ci>u ndi dung chuong Irinh DH, sdch gido khoa, sdch gido vidn, ldl li$u PPDH Todn TH, Tdm If hqc lua lull TH b)Xdc djnh cy thim^c tidu DHcOa tOng bdl, li>ng kSrp vd todn bde hqc (vl KT, KN, thdi dd) c) Quan sdt, nhin blil nhOng b l l u h l | n qud trtnh hpc t$p d l dy dodn khd ndng nhdn tniic cOa SV Ti> dd, tOng bude giup SV cd duqc KNCD nhOng bllu hi|n tdm If cOo HS h-ong qud trtnh DH cdc KTse: hpc d T H dj Thd/ quon Hm ldl, suy nghT phdl hlin nhCtng mil quan h | glCto mdn PPDH Todn TH vdi cde KT s l hpc dTH Vf dy: - Cho SV nhdn thdy v l eo bdn oSc KT sd hpc TH (htnh thdnh khdi ni|m sd vd cdc phdp tfnh v l sd hf nhldn) duqc h-lnh bdy vdi tu tudng cOa todn hpc cao cdp, todn hpc hl|n dpi, thdng qua tn/c quan bilu tupng ldp hpp cde dd vdt (vdt thdt, md hinh, htnh vd, ) Ndn, vdl nhung KT ndy chi su dyng dd dung DH d muc dd phCi hpp (khdng Iqm dyng) d l htnh thdnh bllu tupng vl s l lupng vd |:^dp Knh; - T$p hpp sd' h/ nhldn (N) ddng kfn ddl vdi phdp cdng vd phdp nhdn, cdn vdl phdp tru vd phdp chlo tht mdng, hon nCta (N,+) vd (N,x) cd cdu hiJc Id nhOng vj nhdm Cho ndn, vdl phdp edng vd phdp nhdn hdn tdp hpp N ludn thyc nl|n dupe, cdn vdi phdp hv vd phep ehla hdn tdp N thl khdng phdl luc ndo cung thyc hlfn dupe VI v ^ , DH ede phdp lodn trfin tdp hpp N vd hdn cdc sd khde (pndn sd, sd thdp pnfin) cho HS d TH phdl luu y dilm khdc bill ndy f) Blil xdc djnh mdc di, khd ndng vdn dyng KT, KN tht/c hdnh cOa HS DH cdc KT sd hpc quo v i ^ kllm Vf dy, dqy v l thyc hl^n phdp Knh edng (triy, nhdn, ehio) ede sd cd nhilu chu sd eho HS ldp 3, Idp 4, GV cd t h l ydu cdu HS h/ thyc hi#n phep tfnh theo cdc KN thyc hdnh Clio HS: KN d^t phdp Knh, KN thye hi§n Hnh nhdm khdng nhd vd ed nhd, KN nhdn bill, phdn bl^t glOa «3d''vd «chOsi', khdl ni|m «hdng' g) Blit dg dodn nhOng khd khdn v i ^ trnh hdl, v$n dyng cde KT sd hpc cDa HS Chdng hqn: hil hinh Hidnh cdc si din JO(hdngdon vj) thl ldp hpp su dyng d l hinh thdnh bldu hjpng thudng td que Knh (d vudng) vd HS d i m sd lupng, ti> dd GV gldi thl|u cdch dpc si vd vllt sd bdng cho sd tuong ung Nhung htnh thdnh ede sd hdn chye (hdng cnye) tht bllu hiqng Id nhung bd 10 que Hnh (cdt 10 d vudng); htnh thdnh cde si hdn hdm (hdng trdm) thi bleu h/png Id nhihig bd 100 que tfnh (bdng 100 vudng) vd htnh thdnh ede sd cd nhllu cTiu sd (h> cha sd hd ldn) tht bilu tugng gdm nhung «hdng" VI vdy, DH nhung ndi aung KT ndy, SV phdl dy dodn dupe nhiJng khd khdn Id HS khd phdn bl|t gliJa «sd'' vd «cnu si", mil e^uan hd glua cde «hdng" vdi nhou; khd nhqn thdy «trong mgt sied nhleu chu si, cde ehu sd'gid'ng ndm d ede vj trf khdc thl cd gid trj khdc nhau", ndn HS khdng gldl dupe bdi lodn ed lien quan v l cdc chct so cOo sd' cd nhilu chu sd d cdc Idp sou; v.v h) Biil dg dodn nhi/ng sai lam vd phdt hlin nguydn nhdn dan den sal ldm hong trnn hdl, vdn dyng ede KT sd hqc eua HS Chdng hpn dy dodn: - Khi hge cdc sied nhleu chu si, HS cd t h l mdc sal Idm «trong mgtsoed nhiiu chu si, cdc chd si gling thl cd gid trj nhu nhau" Id HS khdng hllu v l khdl nl|m vd cdch vilt mdt sd cd n h l l u chu sd'; - Kfi/ sSp xip m^t ddy cdc sidd cho (9, 5, 12, 8, 10) theo thu h/ h> bd din kSn e; Nhdn blil nhung KT, /CN md HS dd cd hodc (hodc ngupc Iql) ed thl HS ehf so sdnh cdc sd d cdn chudn bj cho vide trnh hdl cdc KT mdl vd cd cpnh (9, 5) vd (12, 8) md khdng quon tdm thivqn dyng chung DH cdc KT sd hpc qua d i n ede sd d vj trf khdc, nen dua ro kit qud (5, 9, vl$c kllm Vf dy, htnh thdnh khdl nl|m sd 8, 12, 10), nguydn nhdn HS mdc sai lam Id thdp phdn, cde phdp Knh v l sd thdp phdn eho HS hpc chi chu y d i n vide bill so sdnh hai sd; v.v ldp 5, edn kllm bilt chdc chdn HS dd ndm 1} Xdc djnh nhung KT md HS ed thi tg hgc, tg duqc mdt sd KT, KN CO bdn v l sd h/ nhldn (khdl nghlSn cOu, Idiol ihdc phd^ trl^ md ring ni$m cdc «hdng', gid hi eOa chO sdd mfil «hdng", mfil ndi dung DH ede ^ sd hpc Chdng hpn, mil quan hi giOa cde ffhdng" ], ede khdl ni^m DH cdc KT sd hqc (ldp 3, kSp 4) vdi cdc bdl lidn phdn sd, phdn sd thdp phdn, phdn mudl cda dan quon din sded nhieu diu* sd, ngodl v l ^ xdc (^nh vj, phdn trdm cOa don vj sou dd GV mdl Hin ydu edu HS ndm dupe khdi nl&n sd', khdl ni|m hdnh thyc hidn «hdng", bill phdn h'c^ mdl sd cd nhilu chu sd theo jgPtChi 61^0 duc s6 lut a • lo/aeia) Kcd'u tqo thip phdn", phdn bl^t glOo «sa'" vd «chi> d l thyc hl^n ede nhl$m vy theo yfiu edu dijt ro si' c6n hifdng dfin HS hpe li;c khd, gldl tim hl^u (trong dd cd DH mdn Todn): - Tim hllu v l nhl^m cdch bllu diSn s6 cd nhldu cho s6 dudi dqng tfing, vy, edng vl^c ey t h l ci5o G V phdl thyc hl$n tich cuo cde ehO sd' de chudn b| KT, KN cho HS DH Todn trvdng TH; - Tim hllu, xdc djnh myc gldl bdl tdp, bdl todn llSn quon d^n khdl nlfm sd tifiu, nhl^m vy cua mdn hqc d tung Idp vd cd vd chu sd d phdn sou vd cdc Idp trSn bde hqc (vl ede mdl KT, KN vd thdi d?); - Tim k} C6 Y thvc, thdi quen liSn tudng vd huy ding hllu ddc dllm sy phdt trlln tv todn hqc cOo KT, KN, kinh nghlim vdo xem xit, phdn tich cdc HS d trqng thyc t l ; • Tdp cho SV Hm hllu v l nil dung DH VI dg, eho HS cd hpe li/e khd, gldl nhiJng khd khdn, sal Idm, nguyfin nhdn ddn din gldl bdl todn iTrong sd' ti/ nhiSn, niu td'ng sal ldm, khd ndng iTnh hdl KT ciio HS thyc cua si bd't ki ludn ldn han ting cOa si cdn Iql t l , tu dd d l bl$n phdp gldl quylt thlch hqp vd 2012 Ihl tiled cdc sd'diu Idn hon 2012' Di gdp phdn ndng coo khd ndng tinh h^l cdc KT gldl bdl todn ndy cd thl llSn ludng Mn v l ^ s^p DH cde KT sdf hqc d TH; • Tdp eho SV flm x6'p cdc sd' dd cho ihdnh mdt day s i cd thd ty hllu vd vdn dyng m^t sd PPDH, hinh thiic tdehi/c (old su o < b < c < d < e) vd chi chung td s6 DH Todn TH thyc t l nhd nhd't a > 2012 Tu dd, HS huy d^ng cde KT, KN vd kinh nghldm vi so sdnh cdc s6 Iv nhl«n, hal sd' tv nhlftn khdc nhou thl ludn hon (hodc k6m) nhou m^tstf don vj, sddd cho td'ng cua sd' bd't kl nhd nhdt niu 2s6\d nhd nhd't, Khi dd HS cd M gldl bdl todn: a + b + c>d + e + 2012; a > Id • bl + (e • c) + 2012: a > 20IZ 2) Rin KNCD qua vlic ti chuc rin luyin nghlip VI, su phqm thudng xuyin Td' choc DH vd rfen luy^n nghlip vy su pham ihvdng xuydn eho SV d tn/dng sv phqm gdm nhldu HD, nhlen, thvc hl§n cdn rdn cho SV m^t si KNCD DH cde KT sd hqc d TH: - Cd thdi quen, y thvc, thdi dq dung v l vide thudng xuySn thu thdp tu lieu vd tfch luy kinh nghldm thvc tiSn phyc vy cho vlec DH cdc KT sd hqc tu ban bd, gidng vlfin; - Tim hllu v l nhl§m vy gido dye todn hqc ndl chung vd ndi dung, myc tifiu y§u cdu cy t h l v l KT, KN vd thdi dd eua vide DH cdc KT sdhqc d TH (qua thdo lu$n v l chuong trinh, sdch gido khoo, sdch gido vlfin, tdl ll^u PPDH Todn TH); • Ddt minh vdo v| tri cuo HS d l xem xfit, khol thdc phdt hl§n, dv dodn nhvng khd khdn, sol Idm vd nquyfin nhdn ddn din sol tdm, dy dodn khd ndng llnh hdl KT s^ hqc cuo HS; • Tdp eho SV (nhdm SV) d l ro bifin phdp thlch hqp M glup HS khdc phyc nhOng khd khdn, trdnh sol Idm vd ndng coo khd ndng trnh h^l KT cuo HS ; Rin KNCD qua ti chuc cho SV klin tip vd thi/c tip su phqm Vl§c glup SV cd dtlu klfin sdm tISp c^n vdl thye tlln DH d TH d l tim hliu, thu thdp cdc thdng tin thyc t l vd rdn KNCD DH Id cdn thilt Vi vdy, cdc trudng sv phqm phdl yeu cdu vd gloo nhi^m vy cho SV chd ddng ldp k l hoqch d i n cdc trvdng TH kiln tdp SP (ti> hqc ki ndm thv nhd't) vd thyc top SP (ndm cu6l) Trong DH cde KT sd hqc dTH, v l ^ CO dCing s« glup GV nhdn bilt duqc nhu cdu nhdn thvc cuo HS, dy dodn dvqc cdc khd ndng cd thl xdy qud trinh DH, d l d l ro dvqc b i ^ phdp gidl quylt phu hqp, chu d^ng v l ^ td chvc, dllu hdnh HD hqc ldp ciio HS VI vdy, phdl r*n KNCD DH cdc KT sd hqc cho SV ngoy tu dong hqc d Irudng su phqm Mdl sd bifin phdp rin KNCD DH cde KT sd hqc trfin ddy Id tlln d l glOp SV ndng coo NLCD DH d l ddp ung yfiu cau v l chdt luqng, hl^u qud DH h l ^ tql vd ddl mdl v l ndl dung, PPDH Todn dTH a (1) Trudng DHSP H& NOi - Dy i n ph&t aiia gi&o vi£n udu I1QC "Nflng cao cti^t luyng d^o t^o giio vien ti^u hdc" ICi yiu tiOi thSo khoa hoc, H 11/2003 (2) V A Ko-ni-tec-xky TAm It nfing lye toin I19C cda hye sinh NXB Gido iJKcH 1973 T i l ll(a tham Ithio v n Qufic Chung (chil bien) Phumig ph