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JOURNAL 01 SCII ;NCI; O P HNUE Educational Sei 2012, Vol 57, No 9 pp 20 30 VAN DUNC; I V THUYET KIKN IAO VAO VIEC DAY HOC KHAI NIEM DAY SO CO G l 6 l HAN H O U HAN CHO HS L 6 1 '''' 11 THPT CHUYEN, Pham[.]
JOURNAL 01- SCII-;NCI; O P HNUE Educational Sei 2012, Vol 57, No pp 20-30 VAN DUNC; I.V THUYET KIKN IAO VAO VIEC DAY H O C KHAI NIEM DAY SO C O G l l HAN H O U HAN C H O HS L ' 11 T H P T CHUYEN, Pham Sy Natn Truimg THPT chuyen Phan Boi Chdu, Nghe An E-mail; phamsynampbe@gmail.com Tom tat, Mol Irong nhiing kho khan ldn nhal viec giang day va hpc tap cac khiii nicin gii^i han khdng chi nam Irong sU phong phu va phiic lap cua no, ma pham vi ma cac khia canh nhan IhiJc khdng cd the dupc lao hoan toiin lit dinh nghia loan hoc Trong bai bao nay, chiing loi ihill ke cac nhiem vu loan hiic CO ban de ho Irp hpc sinh kidn lao kien Ihiic vc gidi han cua day so Kel qua nghien Cliu cho thay vice thuc nghiem bSng each sU dung cac thao tac dpng, cho phep hpc sinh de dang hon viec hinh cac gia thuyel, kiem nghiem, bac bd nhitng cai sai va xay dung kien Ihiic ve gidi han cua day sd TUkhda: Ly thuyet kiSn tao, gidi han day so, mo hinh dpng Md dau Ly thuyet kien tao cd anh hudng manh me giao due bdi viec van dung Ly thuyel kien tao day hpc dap Ung dupc cac yeu cau dd'i mdi phUdng phap day hoc Trong bai viel chiing tdi trinh bay mpl so quan diem cua Ly thuyet kien tao va viec vta dung vao viec day hpc kbai niem day so cd gidi ban hOu han cho HS Idp 11 TFiPT chuyen 2.1 Noi d u n g n g h i e n ciiu Mot s8 quan iliem cua Ly thuyet kien tao day hoc Ly thuyet kien tao khang dinh "tri thilc dUdc tao nen mot each tfch cue bdi chu tha nhan thilc, chil khdng phai dUdc tilp nhSn mpt each thu ddng tit moi trudng ben ngoai" [3;208] Va rang, "nhan thilc la qua trinh thich nghi va tfi chile lai thi gidi quan ciia chinh mdi ngudi [3;208] Trong mpt moi trudng hpc tap kiln tao, hoc sinh (HS) that sU bi cu6n hut vao viec hpc, thay vi chi la nhung ngudi iSng nghe thu dpng Ly thuyit kiln tao cung cho ring, giao viSn (GV) nSn tim kiim va coi nhiing quan diem, nhiing ly giai ciia hoc sinh bdi Vl chung la canh ciia md den nhiing wi thiic 20 Van dting ly thuyit kiin tgo vdo viec dgy hgc khdi niim ddy sd cd gidi hgn him hgn Qua trinh day hpc c4n phai dUdc thuc hien cho HS kidn tao dudc kien thdc ehU khdng phai de HS ghi nhd kien thiic De HS cd the kiSn tao dUdc kien thdc ihi viec id chUc qua trinh day hpc cSn phai tao dieu kien dc kicn thdc mdi dUdc ket ndi vdi kien thUc cu, khiSn HS tai hien mpt each tich cue cac y tudng da cd, tren cP sd dd phal trien nhan thiic Clia ban than "Qua trinh day hoc can dUa ngUdi hpc di tU sU bao quat bd mat ve mot chii dl tdi chd hieu can kc hdn ki^n thUc ciia chii de dd, bao gom vice soat khao cUu va td chiic cac thdng tin y tUdng ve chii de ti( rat nhieu gdc nhin hoac quan dicm khac nhau, phu hdp vdi giai doan phat trien cua ngudi hpc" [4;30] De thUc hicn dUdc dieu ddi hdi GV phai suy nghi ve each thUc hinh cac kien thUc mdi bang vice gan ket vdi cac kien thiic cu, ddng thdi xem xel nhiing mdi lien he gida cac kien Ihiic 2.2 Van d u n g Ly thuyet kien tao vao vice day hoc khai niem gidi han day s6 cho H S I6p 11 T H P T chuyen TU cac quan die'm neu tren, ta cd the thSy qua trinh day hpc khai niem toan hpc ndi chung va khai niem Giai tich ndi rieng theo Ly thuygt kiSn tao dien theo quy trinh sau: 2.2.1 Birdc 1: Lam sinh nhu cau nhan thu'c if HS thong qua hoat dong trufc quan Cach lam tot nhat de sinh nhu cau nhan thUc d HS la tao tinh hudng sU pham nhSm xu4t hien y thdc cua HS mdt tJnh hudng cd van de Dd la tinh huong (ly thuySt hay thuc tien) chiia dung mau thuin giua cai da bi^t va cai chua bill Mau thuin dUdc HS y thiic va cd nhu cau giai quyet Thdng qua viec giai quyet mau thuan HS gianh dupc mpt cai mdi (kiSn thUc, ky nang, ky xao ) Mat khac, ta thay rang hau het cac khai niem Giai tich cd ban chat "ddng" vdi nhiing thuat ngfl thudng dupc suf dung dinh nghia khai niem nhU "dan tdi", "nhd y" VI vay, cac md hinh ddng, de tac ddng true ti8p vao cac giac quan ciia ngUdi, la dieu kien thuan ldi de giup HS chiSm linh nhiing IhuSt ngii nhu vay Trong budc ngUdi giao vien can thUc hiSn hai cdng doan: - GV gidi thieu nhflng vln d6, hien tfldng thUc tidn hay nhung nghich ly xuil phat tfl khai niem mdi sap hpc nhSm tao dpng CO, thu hiit sU chu y va sU tich cue cija HS tham gia vao viec tim hieu va giai quyit cac van dd ma GV dat - GV gidi thieu, hudng din sii dung md hinh ddng va neu nhiem vu ma HS cin thUc hien thao tac vdi md hinh ddng do, kit qua cua viec thao tac, kham pha vdi md hinh chfla dung kien thflc mdi 2.2.2 Bu'dc 2: HS kham pha, khao sat nham dua cac phan doan va de xuat cac gia thuyit ve khai niem Hinh bieii tUdng ve khai niem Trong budc nay: - HS dupc thao tac trUc tiep vdi cac mo hinh dpng, HS huy dpng cac kiln thflc da cd, cung nhflng trai nghiem phat hien nhflng khd khan, chfldng ngai, cd the xuat hien nhiing Pham Sy Nam tinh hudng nidi niiy sinh ddi hiii ciic cm phai dat i a dUdc nhflng cau hdi, thu thap dUdc d i lieu vil ticn h.inh nghii;ii edu Nhting eau hdi trpng lam vao kicn thilc sc dupe hpc chi co the tni ldi hin eiie em tham gia lieh cue viio qua tiinh khiim pha vii bpc tap - IKS triii qua linh huong ei) van de, dude kham pha md hinh dd chUa dung nhflng npi dung kicn thtic, nhflng thao lac, ky nang dc liim sinh kiln thilc mdi Tifdd dfla ciic ph,in doan, dc xuat eiie gia Ihuyel vc khili niem RUdc niiy hinh thiinh d ngUdi hpc nhUng nen tiing kinh nghiem ban dau ve hi|n tflpng Ticn ed sd mol lien he ben iigoiii (chfl khiing phai moi lien he ben trong) ma call tail nen id hdp chfla rd net vii Ihieu siip xep cua doi Ifldng, ehu ylu dUa vao kha nang long hop Ciie quii tiinh tu giiie ciia IIS day dien hai Ihdi ki; Tbdi ki thii sai tUduy va hinh anh tdng hdp (edn chfla tiieh biich, quyen vdi nhau) ifldng dudng vdi khiii niem dfldc hinh thiinh tren mol cd sd phtic tiip hiln, diia viio kit qua ciic dai dien cua cac nhdm khac dupc dfla vc mdt nghia thong nhal tn giac Sau qua trinh tren, vice nhan thflc cda I IS ve khiii niem dfldc chuyen sang mpt giai doan mdi - tAng bae hinh thiinh tflng bd (nhdm) doi tudng; phUdng phiip tfl bay gia dan din c5u lao nen eae moi lien he, quan he gifla cac an IUdng cu thi;' khac nhau, lap hpp lai, khai quat len, sap xIp he thong loan bp kinh nghiem 2,2.3, Budc 3: Kiem nghiem - giai thich, khai quat hda de riit cac dSu hieu ban chat cua khai niem Trong budc nay; - HS liln hanh qua trinh phan lich nhflng kit qua khao sat dupc NhSng hieu biet ciia cac em dupc lam sang td va chinh xae hda nhd ed nhflng boat ddng phan hoi cua cac HS khac hoac ctia GV - HS kit noi cae y tudng dfla cac gia thuyit va cac ke-t qua quan sat, kham phii dudc thdng qua, HS bat dau hinh nhflng hieu bill khai quat thong qua nhiing gi ma cac em thu nhan dupc sau qua trinh uao doi va tranh luan thdng tin Qua trinh tim tdi kham pha ciia HS la dinh hudng cho GV dfla cac chi dan sudt qua trinh hpc GV cd the cung cap md hinh mdi va yeu c§u HS tilp tuc khao sat neu nhu d4u hieu ma HS dua chua phai la dau hieu ban chat, hoac HS cd nhiing dU doan sai (trong trudng hdp md hinh se ddng vai trd nhu la phan vi du) Cac boat dpng tren cd the thuc hien vdi Idp, hoac nhdm nho, ca nhan, cap ddi HS Ngon ngii la cong cu dS' giao tilp, nd giiip ngudi hpc phat trien cac y tudng, lap luan cac gia dinh, xac lap gia thuyit, tii dd Uinh bay y kiln ban than Thdng qua dd, GV djnh hudng va dieu chinh cau tra Idi ciia HS Trong giai doan HS cd tfl td'ng hdp vdi hai dac diem; sap xIp bieu tfldng vao cac nhom, bp va cd khai quat d6ng thdi cd them phan tich (tach bach cac bieu tudng) trflu tudng, d6' rieng re cac ylu to ra, co ky nang xem xet cac to S ngoai moi lien he cu the, co thuc Giai doan cd hai pha: pha diu la pha khai quat cac doi tUdng cu 22 Van dung ly thuyel kiin tgo vdo viec dgy hgc khdi niim ddy so cd gidi hgn hifu hgn the khac theo nhung chd rat giong nhau; pha thfl hai la pha cd khai niem tiem nang, dUa xIp vao mdt nhdm doi tUpng theo mdt tinh chat 2.2.4 Budc 4: Nhan bict thuat ngii', ki hieu va phat bieu khai niem Khi tu phat trien thi keo theo kha nang ngdn ngfl cua HS cung phal trien Ngdn ngfl ben ngoai va ben da phiit trien, nhien viec didn dat cac suy nghi ciia HS nhilu chua dupc ranh mach, rd rang Cac hoat ddng ciia HS bUdc la: - Thdng qua nhflng dau hieu ciia cac khai niem ma HS linh hdi, GV can to chflc cho HS quan sat, hudng din HS nhan xet su khac gifla nhung thudc tinh ban chat va khdng ban chat cua cac doi tUdng va sfl dung cac ihuat ngfl de kel ndi lien he nhflng dau hieu da dUdc tach nhUng chung cho ca mot ldp cac doi tfldng GV phan tich va dua thuat ngfl, ki hieu cho khai niem mdi HS sfl dung cac thuat ngfl, hudng dan ma GV cung cap de phat bieu khai niem - GV khuyin khich HS phat bieu khai niem dUdi nhieu hinh thflc khac theo each hieu cac em GV dilu chnih phat bieu ciia HS nlu cd sai sdt hoac diing tfl chfla chinh xac „ Den day, viec nhan thflc ve khai niem dUpc chuyen sang mpt giai doan mdi - tang bac cd khai niem thuc stt: khai niem xuit hien ca mdt loat dau hieu trflu tUdng mdt lan nfla dfldc tdng hdp lai d mdt trinh dp cao hdn, tong hdp trflu ifldng trd phUdng thflc chii ylu ciia tU ma tre dung de tiep can va suy nghi vl thUc tai xung quanh day tfl gifl vai trd quyit dinh Vygotsky viet: "Chinh nhd vao tfl tre chii dinh hudng chu y cua minh vao mdt sd diu hieu, nhd vao tfl tre tdng hdp cac diu hieu ay, nhd vao tfl tre bieu trflng hda khai niem trflu tupng va sfl dung khai niem nhu la mdt diu hieu cao nhit tat ca cac dau hieu tU cua ngudi tao " [5;201] 2.2.5 Budc 5: Cung co va van dung khai niem Mdt khai niem dUdc linh hpi va chi HS cd the van dung dupc khai niem dd Ci budc nay, HS tien hanh cac hoat ddng de luyen tap, cting cd va van dung khai niem vfla hpc Viec thuc hien budc thdng qua giai quyet h£ thong bai tap ma GV dua Day la giai doan ren luyen cho HS cac thao tac tu duy, kha nang suy luan va diln dat ngdn ngii Viec cung cd va van dung khai niem bao g6m cac boat ddng: - Nheln dang va the hien khai niSm, hoat dpng ngdn ngfl - Van dung khai niem, y tfldng dfldc hinh qua trinh xay dUng khai niem de giai thich vln de thUc tidn cupc sdng, vao giai quyet cac bai tap Cac bai tap can dUdc thilt kl cho giai, HS cd th^ bi mac phai nhflng ldi sai hieu chfla diing ve khai niem, cac bai tap can da dang vl the loai va cd mflc dp khd dfldc nang din 2.2.6 Bu6c 6: Md rong va he thong hda khai niem Trong bfldc nay: 23 Phiim Sy Nam - GV yeu cSu IIS tim moi lien he gifla khiii niem vfla hoc vdi nhflng kbiii niem da cii, dat khiii niem vao he thong khiii niem - Khai thiic, phiit trien khiii niem dii eii dc md rpng sang khai niem mdi, cd pham vi long hdn 2.3, Vl tiu ap dung: Day hoc khai niem day so co gidi han hfi'u han cho HS 16p 11 THPT chuyen Budc 1: Urn iinh nhu ciu nhgn thtic d HS thdng qua hoal dpng trtfc quan Gidi thieu van di Nham Ihu hut HS tbam gia vao boat dpng hoc uip GV gidi thieu nghich li Zenon sau day; "D'Elec Zcnon (496 - 429) mpl trill gia ngUdi Hi lap cd' dai van the ky thfl V trfldc Cdng nguyen, da dfla bai toiin A-sin (Aebilis) dudi riia va lap luan nhu sau; A-sin lii mpl lUc si than thoai Hi lap, ngUdi dUdc menh danh la "co doi ehan nhanh nhfl gid "dufii theo mdt rua tren mpl dfldng Ihang Gia sfl A-sin xuat phat lai vj tri Ol va rua xuat phat tiji vj tri (, (nhfl Hinh I) Khi A-sin din diem ri^ =- /] thi riia chay len phia trfldc lai vi tri 1.2 Khi A-sin den vj tri (13 = /,, thi riia din vi tri (3 Qua trinh tiep tuc vd han va dflpc minh hpa bang Hinh 1" Hinh J A-sin duoi rita GV: Bdng lap lugn nhu tren, theo em A-sin co duoi kip riia khong ? GV: Theo em, kit lugn co diing khiing? Vi sua? CV dgt vdn di vdo hdi hpc: Nh vay, ehung ta nhan dfldc la lap luan tren khong diing, nhUng cd the van dung kiln thilc Toan hpc nao de chflng to lap luan tren la sai? Bai hpc hdm se giiip chiing ta se di tim hieu kiln thflc nhu vay Gidi thieu mo hinh dong va neu nhiem vu: GV gidi thieu mo hinh dpng cho HS g6m ba phan; Gidi thieu, hudng din thao tac vdi mo hinh hoac khao sat tu hoac cau hdi Gidi thieu, hudng dan HS each thao tac vdi mo hinh: HS dUdc biet mo hinh bao gom cai gi, tat ca cac ylu to va d6i tUdng dUdc mo ta chi tilt va GV hudng dan each lara thi nao de tUdng tac vdi chiing Cho day so u„ = Tren thi Hinh 2, mdi chSm dd the hien hai thong so n • (n; u„), chang han chim dd thil hai (ke tfl u-ai sang phai) la ilng vdi n = va u„ = - Cac cham dd cd the dUdc xda bang each nhan phim Esc u-en ban phim nhilu lan Chim co Van dung ty thuyit kiin tgo vdo viic dgy hge khdi niim ddy w ed gidi hgn hifu hgn II = h = O SOOIJt/cm I "n = - = '0000 Hinh Cach the hien sUphu thudc cda v.,, vdo n tren man hinh vdng den bao quanh la gia tri hien tai cua /) Gia tri ciia n thay ddi dUdc bang each keo re dau mflt cua trUdt tham sd Khdo sdt tu do: Gpi y mdt sd thao tac ma HS nen lam, sau HS se thao tac vdi md hinh va cd gidi han thdi gian • Thay ddi gia tri cua n bang each keo re trUdt tham sd Hay quan sat nhflng thay doi cua cac ddi tudng khac • Nhln phim ESC de xda vet • Thay doi dp dai ddn vi bang each keo diem tren true hoanh xa hoac tdi gdc tpa dp Vdi mdi lln thay ddi, hay nhan ESC de xda vet cu Cdu hoi cho HS Day la phin chinh cua nhiem vu, HS can phai khao sat vdi md hinh de tra ldi cac cau hdi Mflc dp khd khan cua cau hdi dUdc tang din tfl true quan din trflu tupng, tfl cu the den khai quat Phan yeu cau HS tra ldi cac cau hdi sau thao tac vdi md hinh HS se khao sat cac gia tri cua day sd jz„ n thay doi, thdng qua cac kit qua vdi cac gia tri cu the cua n, de tii dd cd nhflng dfl doan tong quat va di din xay dung dinh nghia day so cd gidi han Cdu hoi 1: Em hay thay doi gia tri cua tham so n tfl dd dUa nhan xet vl su thay doi cac gia tri u„ n cang ldn? Cdu hoi 2: Em hay chi it nhat gia tn cua n de khoang each gifla Un va sd nhd hdn ? 100 Em cd the chi so tfl nhien n nhd nhat thda man dieu kien tren khdng? Em hay lly mpt so tU nhien M ldn hdn 100 va hay chi sd tu nhiSn n nhd nhit de khoang each gifla u^ va so nhd hdn — ? 25 Pham Sy Nam Cau luii 3: Neu thay — bdi mdl s6 dfl(Jng e be uiy y, lieu ta ludn cd the tim dfldc sd tu nhicn //„ dc vdi mpi // > /in thi khoang each giUa //,„ va sd nhd hdn £ hay khong? Till s;io? liifdc HS khdm phd, khdo sdt nhdm dUa cdc phdn dodn vd di xudt cdc gid thuyet ve khdi niem Hinh thdnh bieu tiii/ng ve khdi niem froiig cac hoat ddng, cac ihao lac cu the can lam rd dUdc: Phai tach nhflng dau hicu niio ciia ddi lfldng va theo liinh tU nau? Phai thUc hien nhflng hanh ddng nao cd nhflng dau hieu hay nhflng dau hieu khac? Nhflng hanh dpng cd the mang lai nhflng kcl quii niio? Vdi yeu cau ihU nhal "thay ddi gia iri cua tham sd n" HS thflc hien iiiinh ddng "dich chuyen dau mut dd ciia n sang phai (.sang trai)" nham lang (giam) giii tri Clia n dd HS co dfldc hinh anh sau (Hinh 3) h = 0.Ol3S9cm 'I'i'lIiVlVlViVriViViViViVV.v.'iV.-.-.-, Hinh Khi n cdnh tdng khodng each giiia u„ vd cdng nho ifinh anh thu dflpc giup HS nhan dfldc diiu bieu "khi n cang tang thi khoang each giua «„ va eang nhd" Day la mpl diu hieu cin thill ma chung ta mong muon HS nhan Tuy nhien dd chua phai la dau hieu ban chit Trong kit qua nay sinh vln de chUa rd rang la "khoang each dd nhd di nhfl Ihl nao?" De Ua Idi dfldc cau hdi, ddi hoi HS phai cd hanh dpng tilp dd la; Keo ?i xa hdn nua nham tang gia trj n, tang ddn vi tren true tung de cd them dfl lieu cho cac phan doan ve dau hieu Cac yeu clu cau hdi 2) nham giup HS thiy dUdc ton tai gia trj n thda man dieu kien tren va cd the cd nhilu gia tri nhu vay va bang viec thao tac vdi md hinh dpng cd the giup HS xac djnh dfldc so n ldn nhal va tap hpp cac gia trj n thda man dieu kien dd Yeu cau thd ba nhim giiip HS nhan dupc rang nlu chung ta muon khoang each gifla u„ va sd nhd hdn mpt so nhd hdn Yjj5 thi cung ludn tim dupc gia trj n thoa man, dieu tao cd sd cho cau tra ldi cSu hdi tilp tbeo Vdi cau hoi 3) cd the cd hai hudng ma din tdi cau tra ldi dung ciia HS Thfl nhit, tfl cac hanh ddng va kit qua cac trudng hdp cu the' tao niim tin d l HS co thi khang 26 Van dung ly thuyet kiin lao vdo viic dgy hgc khdi niim ddy id ed gidi hgn hifu hgn djnh la ludn tim dUdc n,,, cung cd the HS se khao sat them vai gia tri cu the de tao sir tfl tin cho cau tra ldi cua minh Thfl hai, HS cd the sfl dung cac kien ihflc de chflng minh chat che Kll qua giiip cac em cd dfldc su khai quat hda dau hicu biin chat de ticn ldi hinh dinh nghia gidi han day so Budc Kiem nghiem - gidi thich, khdi qudt hda derut cdc dau hieu bdn chdt cua khdi niem Trong bfldc nay, GV yeu clu HS giai ihich cac kcl qua khao sal dUpc Neu HS chfla neu dupc nhflng diu hieu ban chat thi GV sfl dung cac cau hdi (neu can thiet) dfla ihem yeu clu nham trd giup HS Chang ban nham giiip HS nhan dUdc "kbi n cimg ddn idi dUffng vd cue thi khodng edch giiia v„ vd edng nbd vd nhd bcu> nhieu eung ducfc" GV yeu cau: "Chung ta thif keo ii va lufn nif a xem sif thay ddi se nhU thi ndo?" Tuy nhien hanh ddng "keo ddu mut trugt xa" cd the gay khd khan chu HS, bdi trUpl di het man hinh, khd khan cd the giai quyet bang vice giam ddn vi tren true hoiinh bang each di chuyen chim dd tren true hoanh sang trai, dd cd the thu dUdc hinh anh diem "(n, u.,^) ndm tren true hodnh" Hinh anh cd the gay quan niem sai "khodng cdeh giUa u.„ vd cdng nhd ddn vd din mgi liic ndn dd nd se hdng 0" Van de la lam the nao de HS cd the tranh hoac nhan quan niem tren la sai? Cd the thiy rang, nguyen nhan dan den quan niem sai la sfl han che cua viec bieu dien cac diem tren dd thi, sd eac diem vd han dd phan hinh anh mat phang cd ban Nham giup HS giai quyet dUdc sai lim nay, GV cd the trp giup bang cac each sau Cach thfl nhit GV cd the trd giup bang each gdi y them cac hoat ddng Chang ban: "Cbung ta thu tdng ddi don vi tren true tung U'fn lufn xem hinh dnh se nhu ihi ndo?" Hanh ddng "tdng dcfn vi tren true tung" se giup HS nhan dUpc rang chung ta cang tang ddn vi thi "die'm (TI, a„) edng cdeh xa true hodnh" hanh dpng tang ddn vi nhU la mdt each phdng to hinh anh tren, tUdng tU nhu viec nhin bang mat thudng va nhin bang kinh lup Tuy nhien, nlu HS vln cdn quan niem sai lim tren thi cd the yeu cau HS thflc hien viec "tdng don vi tren true lung" liep va cudi cung HS cd the nhan dupc diu hieu "khodng cdeh giifa Un vd cdng nhd ddn vd khdng bao gid bdng 0", "khodng edch gida Un vd nhd bao nhieu cUng duge mien n du ldn" Cach thfl hai, GV yeu clu HS van dung suy luan de kiem tra tinh dung dan cua quan niem tren de tfl khang dinh "(n, u^) khong the"ndm tren true hodnh", va khoang each cang nhd n cang ldn, bdi | ^^^ [ = ^ > va f{n) = ^ la ham nghich bien Nhfl vay, qua trinh thao tac, khdng phai mdt luc cd the "lach" dfldc cac diu hieu ban chit, ma de di din dfldc dau hieu ban chat HS phai trai qua mdt qua trinh va tren qua trinh cac dau hieu thu dUdc cang cang gin vdi dau hieu ban chit va Iren qua trinh dd khdng tranh khdi nhflng quan niem sai, nhflng khd khan, viec giai quyit cac van dl ddi hdi HS tich eflc suy nghi tim hfldng giai quyet va cin sfl trd giup cua GV bang viec gdi y, ySu cau HS thflc hien cac boat ddng can thilt de doi tfldng bdc Id diu hieu cin nghien cflu va kiem tra dfldc tinh dung dan cua mpt quan niSm Trong viec giai thich ti'nh dung dan cua cac quan niem, ntn yeu clu HS sfl dung nhilu hinh thflc khac 27 Pham Sy Nam iihau cd the sfl dung md hinh triic quan cd the sfl dung suy luan day cung^can lflu y riing vice ihau lac vdi md hinh trflc quan cho chung ta nhflng diu hieu dfldc dien ta bang ldi dudi hinh thflc md l.i lii chinh, BUiic Nhfin hiil thugt ngU, ki hieu vd phdt bieu khdi niem Cd mpl khd khan nhal dinh ve mat lam li vice hinh mdt bieu tfldng diing dan ve khai niotii day sd /:„ co giili ban Trtfc giac cua chung la ddi hdi mpt tfl tudng "ddng" cua gidi han xem nhfl lii kel qua cua mpl qua irinh "chuyen ddng": n nhan cac giii Hi lang dan Iheo diiy so iflnhien 1.2 ;i n va quan sat hanh vi cua day ii„ Ta chd ddi sai sd gifla so u„ va 11 cjing nhd Nhflng quan dicm "ti; nhicn" dd khdng thich hdp vdi SL( diln dat vc mat loan hpc Muon dat tdi mdl dinh nghta chinh xac, can phai dao ngUpc qua trinh lap luan dang le phai chu y irUdc lien den bicn n roi mdi chu y din biln ((„ vande dat lil muun kiem tra dUPc u„ > la can lam the nao? Dc tra ldi cau hdi nay, irudc hcl phai chpn mdl doan nhd liiy y chfla rdi xem xel vdi vice chpn n du Idn, lieu ta c(') the liim chu //„ rdi vau khoang dd hay khdng Sau dd bang each dfla vao cac ki hiey • vil n,) dc bieu thi "mdl doan luy y nhd" vii "n du ldn", la se dat den dinh nghia chinh xac cua gidi han hflu han Muc dich cua vice dfla cau hdi nham thuc hien dieu De HS cd the phal bieu dUdc djnh nghia chinh xac GV yeu cau HS chu y vao kit qua Ua ldi cua cau hdi 3: " vdi mdi sd dUdng e be y cho trudc, chung ta ludn lim dUdc sd tU nhien iiQ dc vdi moi n > iio thi khoang each gifla u„ va sd 1) nhd hdn a " Hay phat bieu tfldng dudng "vdi mdi sd dUdng e be y cbo IrUdc, mpl sd hang cua day, ke tfl sd tu nhien no trd di khoang each gifla ii„ va sd nhd bdn e " GV cung d p them " trUdng hdp ngUdi ta ndi day so (u,,) cd gidi han va viel lim ii,, - Ohoac (/„ -^ " GV yeu clu HS phat bleu khai niem day so cd gidi han 0, sfl dung kl hieu de dien dat khai niem GV dilu chinh phat bieu cua HS neu cd sai sdt hoac dung tfl chua chinh xac De lfl dd cd dfldc dinh nghia chinh thflc ve khai niem "Ta ndi rang day sd {itn) cd gidi han nlu vdi mol so dfldng nhd y cho irudc mpi sd hang cua day sd ke lfl mot so hang nao dd trd di, deu each mpt khoang nhd hdn sd dUdng dd" Khi ta viit lim Un ~ hoac u„ -+ Hay viit dfldi dang ki hieu " lint u„ = 0, BTIO cho Vn > no//i!"ii| < £• " GV cho HS phat bieu khai niem dfldi cac hinh thflc khac de thdng qua dd HS co dfldc y nghia cua khai niem " ddy so {u„) cd gidi hgn cd nghia Id vdi la so s dUifng nho tiiy y Ta cd the chgn mgt si) nguyen dut/ng UQ cho mgi so hgng eda ddy so vdi n > no diu ndm dtfgn I ddi le VA tdm Id diem 0" Budc 5: CUng co vd van dung khdi niem t Vl du 1: Chflng minh cac day so sau cd gidi han a) lim -T,k€ R.b) lim -• n'= n +1 Thdng qua cac trai nghiem tren, GV yeu clu HS neu cac bfldc chflng minh day so cd gidi han bang dinh nghia va neu rd bfldc then chot chflng minh Dieu giup HS kien tao dfldc tri thflc phfldng phap cho ban thSn 28 Van dung ly thuyit kiin lao vdo viic dgy hge khdi niim ddy sd cd gidi hgn hifu hgn Budc 6: Md rgng vd he thdng hda khdi niem - GV yeu cau HS phat bieu khai niem day sd cd gidi han L, GV chfnh sfla nhflng sai sdt (nlu cd) cua HS va yeu clu HS lam vi du sau: Vi du 2: Trong cac day sd sau, day so nao cd gidi han diiy sd niiu khdng? Tai sao? Neu cd hay tim gidi ban dd? a) Ihn - ^ b) liin(^-l)'\ c) lim i n i ^ Thdng qua cae trai nghiem tren, GV yeu cau I IS neu cac budc chflng minh day sd cd gidi ban L bang dinh nghia, cac dau hieu de nhan biel day sd khdng ct) gidi han - GV yeu cau HS ve ,sd dd the hien mdi quan he gifla cac khai niem; day ,sd, diiy sd cd gidi han, day so khdng cd gidi han, day so khdng bi chan Vl du 3: Hinh dfldc cho dudi day cd id dam eac hinh chfl nhal cd kich thudc cho tren hinh ve, gpi S„ la dien tich cua n hinh chfl nhal diu lien (tinh tfl trai sang) Em hay tinh lim S„ Hinh Hinh Trong vi du HS phai van dung kien thflc de tinh dfldc tdng 5,i tfl dd dfldc ket ' , ' roi van dung ket qua d vi du b) qua 5^ = n, + ' • GV cd the dat yeu clu HS sfl dung hinh anh de giai thich kit qua, dilu tao cho HS mpt cd hpi phal huy sfl sang tao, phat trien tu true giac BSng viec sap lai cac hinh chfl nhat nhfl Hinh HS cd the thiy dfldc kit qua Ket luan Day s6 cd gidi han hiiu ban la khai niem cd linh trflu tupng cao va khd khan vifc td chflc day hpc de hinh nd Vi6c hieu ban chat khai niem la lien dl quan trpng cho viec nam vflng cac khai niem Giai tich sau Trong qua trinh giang day theo tien trinh tren, chung tdi thay riing: Viec van dung Ly thuyit kiln tao cung vdi sfl ho trd cua md hinh dong da tao eho HS cd hpi kham pha Toan hpe, HS dfldc thflc hanh nhieu hdn va cd cd hpi the hien nang Iflc cua ban than, de tii cd nhflng dfl doan dung ve dac diem cua khai niem cin linh hoi, xay dflng cho minh hieu biet dung dan ve khai niem 29 Pliiiiii Sy Nam Ben eiinli iilnins ciiii tni ldi mil CIV mong dpi, cung xuat hicn nhflng cau Ira ldi cd the sai liim, hoije ehflii day dti diiy ehinh lii ed bpi de' GV cd hoiit ddng thich bpp nham giup HS ei liilde luen hiel dung v.i Hiinh dflpc eiie sai liim Md hinh dpng thflc sU la cau nli quiiii imng vice day vii hpc nhflng khiii niem trflu Iflpng TAI 1-IKU THAM KHAO 111 Doiiii Quynh Trail Nam Dung Nguyen Vu l.Kdng, Diing Hung Thang , 2010 Tdilieu chitven Imin Dtii Sii vci Gidi lich 11 Nxb (inin due Ha Npi |2] Doiin Quynh Triin Nam Dilng Nguyen Vu Lfldng, Dang Hung Thang, 2010 Tai lieu chuyen imin hdi lap Dm sii vd Gidi lich 11 Nxb Gian due, llii Nfii P I Nguyen I Iflu Chiiu 2006 NhCing viin de co hdn vc chtliing irinh vd qud trinh dgy hpc Nxb Giiio due, I Iii Npi |4| Vii Quoc Chung Nguyen Viin Khai, Gary J.TrcxIer, James Cameron, John Timothy Denny Nguyin Uii Kim, Norm Kaui, Peter Thursby Scan McGough, Ryuichi Sugiyama Teresa San Buenaventura, 2011 Tdi lieu hudng ddn tdng cuiing ndng lilc sit phgm cho gidng vien cdc iriliing ddo Igo gido vien trung hpc phii thong vd Irung cdp chuyen nghiep [5] Phiim Minh Hiic, 1997, Tdm ly hoc Vu-giil-.xki, Nxb Giiio due, Hii Npi [6] Phuc N D M & Nam P S., 2012 Experimeni school mathematics in constructing knowledge of infinitesimal small quantities Proceedings of the SthAnnual Conference ICER 2012, Intemalional Conference on Educational Research: Challenging Education for Future Change Khon Kacn University, Thailand, page 309-319 ABSTRACT Using constructivism to teach the concept of a sequence is unlimited among grade 11 students in gifted high schools Ones of the greatest difficulties in leaching and learning the limit concept lies nol only in its richness and complexity, but also in the extent to which the cognitive aspects cannot be generated purely from the mathematical definition In this paper, we designed basic mathematical tasks which will guide students who are learning of the limit of sequence It has been shown that experiments that use dynamic manipulation enable students to more easily forming hypotheses, verifying them, rejecting wrong hypotheses and come to a full understanding of limit of sequence 30 ... cd pham vi long hdn 2.3, Vl tiu ap dung: Day hoc khai niem day so co gidi han hfi''u han cho HS 16p 11 THPT chuyen Budc 1: Urn iinh nhu ciu nhgn thtic d HS thdng qua hoal dpng trtfc quan Gidi... niem trflu Iflpng TAI 1-IKU THAM KHAO 111 Doiiii Quynh Trail Nam Dung Nguyen Vu l.Kdng, Diing Hung Thang , 2010 Tdilieu chitven Imin Dtii Sii vci Gidi lich 11 Nxb (inin due Ha Npi |2] Doiin Quynh... de kel ndi lien he nhflng dau hieu da dUdc tach nhUng chung cho ca mot ldp cac doi tfldng GV phan tich va dua thuat ngfl, ki hieu cho khai niem mdi HS sfl dung cac thuat ngfl, hudng dan ma GV