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20 4i ^ '''' l i i a r m n n i ^ u ^ H ) 30 112011 D^MvaHQC , „, J/NGAY NAY Mpt so bien phap thifc hien phiTtfng phap day hpc tich cifc khi day toan cho hpc sinh tieu hpc TS TA NGQC TRf Trddng DHSP H[.]
20 4i ^ ' l i i a r m n n i ^ u ^ H ) 30 112011 D^MvaHQC , J/NGAY NAY „, Mpt so bien phap thifc hien phiTtfng phap day hpc tich cifc day toan cho hpc sinh tieu hpc TS TA NGQC TRf Trddng DHSP HaNdi2 T rong bai viit ehung toi phan tfeh mdt sd ed sd ly luan v l phddng phap day hpe tich eye d bac t i i u hpe Chung toi cung d i l m Igi mpt sd nhdng bi^n phap d l tich cdc hda viec dgy va hpe toan d trydng T i i u hpe qua mot sd cdng trinh nghien cdu g i n day ciia cae bgn ddng nghiep Cudi cung ehung tdi xin d l xult them mpt sd bien phap nufa, thdng qua nhOng vl du eu t h i d l xay ddng ddpc nhdng bai giang giup eho hpc sinh tieu hpc hpc Toan mpt each tfeh cdc Hpe sinh t i i u hpc d day ddpc hieu la hpc sinh d Ida tudi td 6-11; dda tre bat dau di hpc ldp d i n h i t Idp Day la giai dogn d i u tien eua chddng trinh giao dye phd thdng cho tre "Van sd khdi d i u nan" cho nen viec hpe tap, nha't la hpc mdn Toan cua da sd cae em chic chan se cd nhilu khd khan Viec tim ddpc nhdng phdPng phap day hpe tdt nhat va nhdng each lam de khuyin khich viec hpe eua eae em eOng nhd tgo mpt mdi trddng hpc tap tdt, mang Igi hieu q u i eao eho tre la eye ky c i n thiet Day la t i l n d l tdt de chuan bj eho tre hpc tap d eae bac hpc tren cung nhdcupesdng nghi nghiep tddng lai Lam the nao de tao nhdng tilt dgy va hpe toan mpt each ti'ch cdc? Phddng phap tich cdc dgy hpe d day ddpc h i i u la "nhdng phddng phap giao due hoac dgy hpe theo hddng phat huy tfnh tfeh eye chu ddng cua ngddi hpe" (xem Tran (2007)) Cung theo Tran (2007) thi cac dgc trdng eiia phddng phap tieh eye la: day hpe I i y hpc sinh lam trung tam, dgy hpc thdng qua id chdc cac hogt dpng eua hpe sinh, dgy hpe chu trpng viec ren luydn phdPng phap ty hpc, day hpe ea t h i va day hpc hpp tac, va danh gia va ty danh gia Dang Thanh Hdng (trich lai Bui (2010), trang 95) lai eho rang: "Day hpe tieh cdc hay cdn gpi la day hpc hddng vao ngddi hpe, lay chCi the hpc sinh lam trung tam ddpc coi la tdu hien dgi ciia Au-My" Tren thdc te phddng phap dgy hpe tich eye cd ngudn gde td xa xda, khdng phai I I s i n pham rieng eiia Au-My, ma "Id sin phim cua nhin to?/"(Bui Thi Huong, xem Bui (2010), trang 95) CQng Bui (2010) tac g i l cho rang "bin chit cua d^y hgc tich cdc Id mot qui trinh ngddi thiy biit ti chdc, diiu khlin hgc sinh ti/ biin dSl nhdng kinh nghiem bin ngoil thdnh kinh nghiem bin cua cac em, kim theo ndng biit van dung, sang tao' c a c bipn phap eiia giao vi§n se cd vai tro quan trpng vi§c tgo n§n mpt phdPng phap dgy hpc tich ciic, lam d l hogt dpng hpe tap eiia hoc sinh co nhOng dac trdng ciia mdt phddng phap dgy hpc tfeh epc nhd tren Co nhilu each d l ed t h i tao n§n nhOng bai giang bang phdPng phap tich eye cho hpc sinh tieu hpc Trddc het Chung ta d i l m Igi m^t sd phUdng phap da dupe de xuat bdi eae nha nghien cdu ma ehung tdi cd dip gap hoac tham khio Vu&Hoang (2011) de x u l t vi^c phd nhgc cac chO s6, cac cdng thdc toan hpc eae p h i p cdng trd, nhan va chia, phd nhgc cac bai toan vui de tich cpc hoat dpng hQC toan cua hpe sinh tieu hpc Tuy nhi§n ehung ta hlu nha cdn xem nhp each lam thye tien giang day nhi/ cac tae g i l da nhgn x§t: "d bic hgc mim non, cac em da tdng hit "Mot vdi wot Id hai" - ding tiic nhdng bil hit nhd vay it thay xuat hien d TH Ngay ci cic bil hgc thude ldng c6 "tinh nhae" (nhil bing cufu chddng) cung da khdng dddc sCt dung nda vl bi cho li "miy mdc", nghe nhd "cudc kiu" Thdc ra, theo Chung tdi, niu cic noi dung dddc phi nhae mot each nhuin nhuyin, chic chin viec hgc toin se co hieu qua hon ri't nhliu" Mpt nhufng myc ti§u ciia viec day toln la viec hinh ky nang tfnh toan Ddi vdi hpc sinh TH thi "cac hinh thdc td chufc day hpc cung ed tae dpng khong nho d i n viec ren luypn k9 nang tfnh toan eCia tre" (Nguyen (2011)) Nguyen (2011) cQng d l xuat den viec td chiJc cae trd chdi hpc tap; mpt hinh thiifc de tfeh cue hda hoat ddng hpe toan eho hpc sinh tieu hpc Tac g i l cho rang; "Diy li mdt h)nh thdc day hgc rat phd hdp vdl hoc sinh TH, thu hut dddc sd tham gia cOa hgc sinh, gdy hdng M 'VrtI14/^ s o 11-2011 vd glim sd met moi hgc tap" Viec sd dung ngdn ngO cua trd chdi de tim hieu idi giai cho bai toan cd sau da de lai tam tri tre nhdng ky de khd phai; tao nen sd thfch thu hpc toan Ban than tac gia mpt eau chuyen rat khd quen, ma tae gia mudn viet lai d day Dd la dddc hddng d i n giai bai toan: Vda ga vda chd Bd Igi cho trdn Ba mddi sau Mpt tram chan chan Hdi cd bao nhieu ga? Bao nhieu chd? Khi ddpc t h i y hddng dan thong qua nhdng hogt dpng h i t sdc "tre con" tac gia da rat an tupng va each lam da di cung tae gia d i n tan bay gid: Bddc 1: Hay cho tat c l ga va chd xep hang san Bddc 2: Hay yeu cau tat c l ga va chd mdi eon gid mpt chan len Cd tat ea bao nhieu chan dddc gid len? (36) Bddc 3: T i l p tyc yeu c l u t i t ea ga va chd mdi gid them mpt chan nOa len! (Cddilil) Cd tat ea bao nhieu chan sau ca hai lan ddpc gid len? (72) Bddc 4: Sd chan ddng cdn Igi la bao nhieu chan? (28) Cd chan ga khdng?(0) Mdi eon ehd cdn may chan ddng? (2) Vay sd chd se la bao nhieu? (14) Sd ga cdn lai la bao nhieu? (22) "Dgy va hpc tfeh eye" la mpt cae myc tieu quan trpng eua dy an Viet Bf "Nang cao chat lypng dao tao bdi dddng giao vien tieu hpe, THCS eae tfnh miln nui phfa Bac Viet Nam" Trong tai lieu tap huan sii dyng d hpi thao td chde khudn khd cua dy an da d l xuat mpt sd md hinh day hpc tich cdc: dgy hpe dya tren hdng thu, hpe qua lam, hpe tap "da giac quan" (xem tren dddng link td trang web c u a Bp giao due va Dao tao www.moet.edu.vn) Mdt nhOng y i u td tgo nen dpng cP hpc tap, mpt each d i l n dgt khae eiia hpe tap dya tren hdng thu la ngddi hpc p h i i thay li thu vd hap d i n D i l u lai eang can thiet cho hpe sinh tieu hpe: Ida tudi ma viec hpe va viec chdi p h i i ludn ludn ddpc nhin nhgn nhd la hai cdng viec song hanh, Idng ghep vao bai hpe eua hpe sinh t i i u hpe Trong bai viltTri(2011) ehung tdi d l cap d i n phddng phap thilt k l cac bai toan nhd day mpt bai toan khd nao dd each lam nham nhan mgnh quan d i l m dgy toan eiia Polya (xem Polya(1958)); Dd la: ngddi t h i y p h i i ddng vai trd ciia mpt ngddi trp giup gidi; giup khdng qua nhilu ma cung khdng qua it Neu ngddi t h i y giup nhieu qua thi khdng giup ddpc hpc sinh phat triin ddpc nang ldc suy nghT (day toan la dgy each nghT; xem Polya(1958)) Tuy nhien neu ngddi thay khdng gidp "dii" hoac khdng giup gi hpc sinh (va nhat la hpe sinh t i i u hpc) se sinh chan n I n va khdng cdn dpng cd d l hpc toan nda Trong bai v i i t ehung tdi d l xuat them mpt sd bien phap nda ed t h i giup tieh cdc hda hogt ddng hpc tap mdn toan ciia hpc sinh t i i u hpc: Thd nhat, hay dung trye quan minh hpa d l hpc sinh hinh dung va lien he eae dCf kien cua bai toan Con dddng nhgn thdc eiia ngddi nhd ehung ta da biet la di td trde quan sinh dpng den tU triu tddng Chfnh vi vay viec cy t h i hda nhdng sd khd khan nhtfng hinh anh ed the thay dddc so sanh ddpc la rat quan trpng ddi vdi viec day hpc mon toan, nhat la ddi vdi day toan tieu hpc Chang han cac loai bai toan tim hai dai Idpng biet tdng (hieu) va thddng m (m la sd nguyen dddng) cua ehung Chung ta ed the hddng d i n cae em hpc sinh Idp 4-5 suy nghT nhd sau: Bddc 1: Neu dai Idpng nhd hdn ddpc bieu d i l n bang mpt doan thang thi dai Iddng Idn hdn ddpc bieu dien bang may doan thang? (m) Bddc 2: Tdng (hieu) ciia ca hai dai Idpng dddc bieu d i i n bang may doan thang? m-i-1 (m-1) Bddc 3: Vay mpt doan thang la bao nhieu? Dai Iddng nhd hdn la bao nhieu? Oai Iddng Idn hdn la bao nhieu? Thdc te tdi lam nghien cdu vdi tdi, chau hpc ldp va Idp cho thay chau hoan toan hiiu va nam ddpc dang toan sau vai vf du cy t h i Thd hai, hay sap xep cac bai toan cho hpc sinh theo thd ty td d i den khd, sap xep d l hpc sinh thay ddpc sd phat trien ciia bai toan dd Chang han khdng nen sap xep bai toan dddi day trddc cac bai toan dang tim hai dai Idpng biet tdng (hieu) va thddng ciia hai dai Idpng dd Hieu ciia hai sd la 33 Lay sd Idn chia cho sd nhd ddpc thddng la 3, sd dd la Tim hai sd dd Hay phan ti'ch cho hpc sinh thay n i u bd "sd dd la 3" di thi ta dddc dung bai toan dang da hpc: tim hai dai Iddng biet hieu va thddng cua hai dai Idpng dd Tuy nhien gpi y dd se giup cho hpc sinh lien he td sd dd da hpc d dang trddc, suy nghT mpt chut de dda ve dang bai toan da biet Td dd cd the bieu d i i n nhd sau: Sd nhd _3_ Sd Idn Nhd vay hieu eiia hai sd se la hai doan thang vd Do dd hpe sinh se h i i u ddpc hai doan thang la 33-3 va td dd tim dddc mpt dogn thang va sau dd la tim ddpc hai sd dd each dgy cung da ddpc Polya nhae d i n : giii mdt bdi todn hay nhd lai xem cd bdi todn ndo gan gid'ng nhd vay ma da giii (xem Polya(1958)) TdPng td nhd vay ehung ta nen sap x I p bai toan BT 1: Niu viit them mdt chd si vio ben trdi mdt so cd hai chd si thi so dd se thay doi thi ndo? trddc day bai toan: BT 2: Jim mdt si td nhien cd hai chd so, biit rang niu viit thdm chd si vdo ben trdi so dd thi dddc si mdi Idn gi'p 13 lin si ban diu Ly la vi BT se cd djnh hddng giup eho hpc sinh g i l l BT D i l u cung ed the ddpc g i i i thfch bang each da sCr dung d bai v i i t Tri(2011) Mpt vi du khae rat hay la ehung ta can sap x I p cho hpc sinh bai toan BT 3: Mdt si chia cho 11 dd 6, chia cho 12 dd Hoi si dd chia cho 132 thi dd bao nhieu? trddc bai toan BT 4: Mdt si chia cho dd 3, chia cho dd Hdl so dd chia cho 36 thi dd bao nhieu? (3 BT ehung ta hddng d i n hpc sinh v i i t ra: s= l l x t ^ -I- (1) va (2) s= 12xt2 + 5, sau dd nhan (1) vdi 12 va nhan (2) vdi 11 (de tgo sd chia la 132) Trd cho ehung ta ddpc s= 132x 22 DrnvoHoc S6l12011 u.ii(inis M>i nUMUUIMrMMWf'iMiiXa'i^ ~ — v/NG/iY N/tY So phai tim Sd sau them vao b§n trai (t^ 1^)+ 61, va td dd ta cd dupe sd dd can tim I I 61 N i u hpc sinh lam tudng ty nhd BT cho BT thi dan den viec ehung ta khdng ed s ma la 5s va khdng thu ddpc k i t qua mong mudn; s= 4xt, + (3) va s= 9x1^ + 5, (4) Hay phan tich cho hpc sinh thSy m l u chdt cCia van d§ la Chung ta c i n b i i u d i l n dupe s qua sd chia la 36 Do dd viec nhan bay gid can khae di mdt chut; nhan (3) vdi 9, song nhan (4) vdi (!) va sau dd cung trd cho d l cd b i i u dien: s= 36x (t, -21^ -1)+ 23 va td dd sd dd c i n tim la 23 Thd ba vd la bign phap cudi cung ciia bai v i i t dd la: hay k i t hpp eae each khae d tren lai vdi d l cd t h i tieh eye hda ddpc hogt ddng hpe tap cCia hpc sinh Chang hgn hddng dan hpc sinh giai BT d tr§n sau dda BT ehung ta lai t i l p tyc c6 t h i dung trpe quan de minh hpa eho eae em nhd sau: (xem tren) Vdi BT hpc sinh da cd t h i hieu ddpc rang viec them sd vao ben trai sd c i n tim (cd hai chd sd) da lam sd mdi tang len 300, chinh la 12 doan nhd Td cac em nhan biet ddpc sd c i n tim la 25 (mdi doan la sd can tim) Thay eho k i t luan ciia bai v i i t ehung tdi mudn nhan manh la: phddng phap tfeh cdc day toan t i i u hpe khdng phai la eai gi qua xa la; nd cd the ddpc tgo nen nhd nhOng bien phap sang tao vdi cae d i l u kien s i n cd d trddng t i i u hpc Mpt dieu quan trpng la lam cac t h i y cd giao cd nhOng k i l n thdc va ky nang sd phgm d l cd t h i thdc hien cac bien phap dd Chinh vl vay viec chuan bj cho cac sinh vien sd phgm, nganh Giao dye T i i u hpc ed nhOng k i l n thdc va ky nang nay la h i t sdc quan trpng (xem Tri(9/2011)) Xin hpn quay Igi trpng bai v i i t khae va mong ddpc trao ddi cdng eae nha nghien edu, cac t h i y cd giao khae, cae bac phy huynh v l nhCfng bi^n phdp khie nda giup tgo ndn nhufng gid hpc toan tich cpc d bac t i i u hpc TAI LIEU THAIVI KHAO Bui (2011); Bui Thj Thuy Hing; Odng cd hpc tap theo li'thuyet v l sy ty quyit; Tap chl Khoa hgc Giio due, Sd 66 (3/2011) Bui(2010); Bill Thi Hddng; Gido trinh Phddng phdp day hoc mdn Todn d Trung hgc Phi thdng theo dinh hddng tich cdc Nh xuat bin Giao dye Vi§t Nam(2010) Chu(2011); Chu Trpng Thanh, Phan Anh Tai, Nguyin Ode Thanh; Con dddng hinh so dd nhSn thdc khai ni§m dgy hpc mdn toan; T^p chl Gido due, 260, Ky 2(4/2011) Nguyen, 0(2011); Hinh ky n§ng tfnh toan cac sd tif nhiSn cho hpc sinh d tiiu hpc; Tap chl Khoa hgc Gido due, Sd69 (6/2011) Polya(1958); G Polya, How to solve it?, Princeton University Press (1958) Tran (2007); Tran Ba Hoanh; Dii mdi phddng phdp d$y hgc, chddng trinh vd sdch gido khoa; Nha xuat b i n DHSP (2007) Tri(9/2011);Tg Ngpc Trf, Dgy va hpc tfeh eye: Mpt cai nhin tif cac cd sd dao tao giao viin, Ky yeu Hdi thao Quic ti'Giao due Dai hgc: Hiin tai vd Tddng lai", DHSP Ha Npi (9/2011) Tri(2011); Ta Ngpc Tri, Thiet ke cac bai toan nhd de day hpc sinh tieu hpc giii mpt bai toan, Tap chf Day hoc Ngay (Q71 2011),tr 24-26 Trieu(2011); Trieu Thj Thu Hien; Giup hpc sinh tieu hpc hpc tap luyen thao tac khai quat hda dgy hpc giai toan; Tap dii Gido due, 259, K^ (4/2011) Vu&Hoang(2011); Vu Ngpc Tuan Hoang Thi Thanh; Sif dyng am nhgc dgy hpc mdt sd mdn d tiiu hpc; T^p chiGiao due, 264; Ky (6/2011) ... 6, chia cho 12 dd Hoi si dd chia cho 132 thi dd bao nhieu? trddc bai toan BT 4: Mdt si chia cho dd 3, chia cho dd Hdl so dd chia cho 36 thi dd bao nhieu? (3 BT ehung ta hddng d i n hpc sinh v... sinh g i l l BT D i l u cung ed the ddpc g i i i thfch bang each da sCr dung d bai v i i t Tri(2011) Mpt vi du khae rat hay la ehung ta can sap x I p cho hpc sinh bai toan BT 3: Mdt si chia cho. .. hpc ldp va Idp cho thay chau hoan toan hiiu va nam ddpc dang toan sau vai vf du cy t h i Thd hai, hay sap xep cac bai toan cho hpc sinh theo thd ty td d i den khd, sap xep d l hpc sinh thay ddpc