II DIEN DAN PHAH TICH idl GIAI BANG DAI SO DE BOI DUdNG KY NANG CHO GIAO SINH VA GIAO VIEN DAY GIAI TOAN d BAC TIEU HOC TS Ta Ngpc Tri TrUdng DHSPHd Ngi 2 Phfldng phap dgt an sd mi dye ti^u hpc), cic[.]
II DIEN DAN PHAH TICH i d l GIAI BANG DAI SO DE BOI DUdNG KY NANG CHO GIAO SINH VA GIAO VIEN DAY GIAI TOAN d BAC TIEU HOC TS Ta Ngpc Tri TrUdng DHSPHd Ngi Phfldng phap dgt an sd mi giii phUdng trinh, he phUtfng trinh (ta se gpi la phfldng phap dgi sd d bii viOi nay) ihudng khdng dupc su dyng cho hoc sinh tieu hpc Mdi gan day bao chi dUa tin mpt sd phy huynh hpc sinh thic mac vi kien nghj Ifn Sd Giao dye Thinh phd Hd Chi Minh, rdi sau dd li len Bd Giao dye va Dao tgo Uen quan din nhflng ldi giai dgi sd di khdng dflde chap nhgn cCia mpt sd cac HS mpt bai toin de thi vio ldp trUdng Tran Dgi Nghia (xem d dUdng link http:// tuoitre.vn/Tuyensinh/Tuyensinh/445316/Khong-chamdiem-cho-cach-giai-eao-hontrinh-do-lop-6.html vi d dUdng link http://giaoduc.net.vn/ Tuyen-sinh/Truong-Pho-thong/ Phu-huynh-kien-vi-bai-thi-vaolop-6-dung-ma-khong-duoediem/7368.gd, thing 10/2011) Hpc sinh tieu hpc dUde yeu cau giii toin bing lgp luin Id-gie li ehinh de tang eUdng kha nang suy luin, lap luan va tfl dd li rf n luyfn tfl cho cac em Tuy nhien mpt thfle te cho thay vifc giii toin theo phfldng phip lip luin Id-gic cua bac hpc tieu hpc thudng hay giy nen khd khan khdng nhflng cho hpe sinh tieu hpe m i eho ehinh cic giio sinh (sinh vien sfl pham nganh giip dye ti^u hpc), cic b^ic phy huynh muon giiip eon hpc toi mdn lodn vi ihgm ehi ca ddi vdi giao vien ticu hpc dgy tren ldp Qua khao sat vdi nipl so giao sinh tgi khoa Ticu hpc-TrUdng DHSP Hi Npi thi phan ldn giio sinh cd the giii dUpe bai loan bang phUdng phap dgi sd, song lgi rat lung tiing vi thgm ehi khdng the giii dflpc bang phfldng phap lgp lugn Id-gic: phfldng phap dflpc dung dgy d tieu hpc Chinh vi vgy giio sinh nganh Giio dye Tieu hpc va giio vien dang dgy tieu hpc can phai dUpc trang hi mpt sd cic ky ning de cd the giing dgy thinh cdng mpt so cac bai toan dUpc ggp trUdng tieu hpc, nhat li cic bai toin bdi dUdng hpe sinh gidi toan Mpt ky ning sd dd se dUde bin tdi bii viet niy: ky nang tim hieu cic ldi giii bing lgp lugn Idgic tfl nhflng ldi giai dgi sd hay quen diing Trong bii viet tdng ket sau chin nam sfl dyng chUdng trinh vi sich giio khoa mdi d bgc tieu hpc (tfl nam hpc 2002-2003) eie tic gii Le Tien Thinh vi Hoing Mai Le (Vy Giio dye Tieu hpcBp Giio dye vi Dao tgo) d i de xuat mpt sd cic giii phip de ning cap chat Ifldng dgy hpc mdn Toin d trfldng Tieu hpc (xem Le&Hoing (2011)) Trong dd cic Nhdn bdi ngdy 2/2/2012 > TAP CHi T H I ^ BI GlAO DMC- Sd 78 - 2/2012 tic gia de cap den van de dgy hpc tich cflc va nang cao nang lUc ciia ddi ngu giao vien bdi theo cac tic gii thi "Trong dqy hgc, gido vii^n Id nhdn to quyit dinh chdt lUdng gido due" Cac tac gii cung khuyen cao cac trUdng sU phgm cd dio tgo giao vien tieu hpe " cdn ldm tdt hdn nda cong tdc ddo tqo gido vien, ddp Ung yeu cdu ddi mdi chUdng trinh, ngi dung, phUdng phdp dqy hgc mon Todn giai doqn mdi" Bii viet niy cung thdng bao ve mpt chUdng trinh bdi dUdng thudng xuyen cho giio vien tieu hpc giai dogn 2011-2015 da dUdc Bp Giio due va Dao tgo ban hanh Tat ca nhflng dieu niy cho thay giio sinh va giio vien tieu hpc can dUde chuan bj vi bdi dUdng nhflng phfldng phip day hpc Toin tich cflc de cd the lim tdt cdng vifc giing dgy d trfldng tieu hpc Tuy nhien mdt thfle tf cho thay li ky ndng gidi todn phdi dUdc quan tdm ddu tiin vi gido viin dUng ldp phdi biet gidi bdi todn dd trUdc mudn thUc hien viic truyin dot nhU the ndo de giiip hgc sinh ciia minh hieu dUdc vd sau Id gidi dUdc bdi todn Theo quan diem eua ehung tdi can bdi dfldng nhieu hdn eac ky ning giii toin vi ky ning sfl phgm, nhat li cic ky ning de thfle hifn cic phfldng phip dgy DIEN D A N hpc tich cflc cho cac giao sinh nganh Giao dye Tieu hpc cua cac trUdng sU phgm va cac khda bdi dUdng chuyen de cho giio vien Tieu hpc theo tinh than chi dgo cua Bp GD&DT nhfl Le&Hoang(2011) Ve cic phfldng phap va ky nang dgy hpc tich cflc d bgc tieu hpc cd the tham khao cic tai Ufu cua dfl an Vift Bi (dUdng link: http://ati.edu.net.vn/), dfl in ve dgy hpc tich cflc cua td chflc WOB; Td chflc Hpp tic Phat trien va Hd trp Ky thugt vung Fla-mang, VUdng qude Bi (dudng Unk: http://www.wob be/vietnam/?q=vi), hoge cac bai bao Tri(2011), Tri(10/2011) Trong bii viet niy chung ta tgp chung vio vifc phin tich de hinh mpt ky nang cd the giflp giio sinh vi giio vien tieu hpc dgy hpe sinh giai toan vi tfl dd cd the ket hpp vdi eie bifn phip khae thfle hifn phfldng phip dgy hpc tich cflc Bii toin (xem Dd(1998), Tr 153): Cd mdt bin hdp ddng sin xuat dyng cy hpc tap Nhdm thfl nhat ed the hoan thinh hdp ddng sau ngiy lim vifc, nhdm thfl hai cd the hoin thinh sau 15 ngiy lim vifc Thdi gian dau chi rifng nhdm thfl nhat lim vifc, roi sau dd chi rieng nhdm thfl hai lim tiep cho den ket thfle cdng vifc Ci hai nhdm di lim het ngiy thi ket thue bin hdp dong dd Tuih xem ei hai nhdm di lim dxigc bao nhieu dyng cy, biet rang nhdm thfl nhat da lim nhieu hdn nhdm thfl hai la 150 dung cu? Neu giii bing dgi sd ehung ta cd the nhanh chdng tim dfldc ldi giii nhfl sau: Gpi x la sd ngiy ma nhom thfl nhat da lim, y la sd ngiy mi nhdm thfl hai da lam Tfl bii ta se cd hf phUdng trinh: x + y = 9(l) x/6 + y/5 = (2) Khi giiihf (1) &(2) chiing ta the (1) vio (2) bang each tach x/6 = x/15 + x/10 va tfl ta cd x/10 = 2/5, hay x-4 vi y=5 Sd phan cdng vifc ma nhdm thfl nhat lam la 2/3, va 2/3 nhdm hai lam la 1/3 Do dd nhdm thfl nhat lam hdn nhdm thfl hai 1/3 cdng vifc va gia thiet da cho la 150 dyng cy \'ay tong so dyng cy se li 450 dyng cy Vifc tim hieu ldi giai bang phfldng phap dgi sd de ed the giflp ich cho giao sinh, giao vien tieu hpc phuong hUdng de tim ldi giai bang lgp lugn Id-gic dgy cho bai toan Day cung la van de ma chung tdi mudn ban den bai viet Vgy cy the ddi vdi bii toin chflng ta se sfl dyng ldi giai dgi sd tren de dinh hudng cho ldi giii Id-gic nhfl the nio? Chung ta se khdng the dung ngdn ngfl cua phfldng phap dgi sd; tfle li an x, y d diy dUdc nfla Suy nghi tfl (2) vi ed the thay rang: -Phan sd 1/6 xuat hifn the hifn khdi lUpng cdng viec m i mdt ngiy nhdm thfl nhat se lim dfldc Tfldng tfl 1/15 the hifn khdi Ifldng cdng vifc mi mpt ngiy nhdm thfl hai se lim dflde -Phep tich de the sau dd dUdc hieu bang ngdn ngfl Idgic li: Nfu gii sfl ning xuat cua nhdm thfl nhat cung nhU nhdm thfl hai thi sau ngiy lUpng cdng vifc dfldc hoan thinh chi li 9/15 = 3/5 cua toan bd cdng vifc NhU II vay lupng cdng vifc 2/5 lai (chuyen ve sau the song d phuong phap dai sd) da dUpc hoan nhd nhdm thfl nhat cd nang xuat cao hdn' Nhu vay chiing ta cd the dgt van de lai xem moi ngiy da bdt di lUdng cdng vifc cua nhom mpt di 1/10 lupng cdng vifc (1/6 - 1/15 = 1/10) Lupng hdn moi da giup hoan cdng vifc; tfle li da giiip lim het lupng cdng vifc 2/5 cdn lai Moi la 1/10 lUpng cdng vifc Do dd sd ngiy nhdm thfl nhat da lim li 2/5 : 1/10 = (ngay) Phin cdn lai cua lap luan hoan toin dupe the hifn each giai dai sd: Sd phan cdng vifc ma nhdm thfl nhat lam la 2/3, va 2/3 nhdm hai lim li 1/3 Do nhdm thfl nhat lam hdn nhdm thfl hai 1/3 cdng vifc vi gia thiet da cho li 150 dyng cy Vay tong sd dung cy se li 450 dung cu Qua vi dy tren chung ta thay rd la 'suy nghi tfl ldi giai bang phfldng phap dai sd "cua ngUdi ldn" cd the giup ich cho vifc dgt dUdc mdt Idi giii bang lip luin Id-gic ma cic em hpc sinh tieu hpc can Bii toin (Bii toin cd): Vfla gi vfla chd Bd lai cho trdn Ba mUdi sau Mdt tram chin chan Hdi bao nhieu eon ga? Bao nhieu chd? Bang phUdng phap dai sd chflng ta ed the giii nhfl sau: Vdi li sd gi vi sd ehd can tim chung ta cd hf sau x + y=36(3) 2x + 4y=100(4) The (3) vio (4) chung ta cd: 2(x+y) + 2y = 100 (5) TAP CHi THIET BI GIAO DUC - S6 78 - 2/2012 • II DI£N DAN Hay 2.36 + 2y = 100 Tfl dd ehung ta ed 2y = 100 - 72 = 28, dp dd y = 14 (con chd) vi x = 22 (con gi) Tfl ldi giii niy chung ta cd Uie phin lieh de dan den mpt ldi giii bing lgp lugn nhu sau: Phep the dUpc x + y vio (4) de viet dUpc (5) thfle chat la chung ta da gii sfl ga va chd cung cd chin NhU vgy 36 la sd chin cua cd 36 vgt sau gid sfl Phep ehuyen ve vi trfl de dfldc 100-72 thf hifn sd chin chd bj hyt di gii sfl vgy Phfldng trinh 2y = 100 - 72 = 28 the hifn mdi eon cho bj hyt di chin mi tdng sd chin hyt di li 28 Tfl dd ta ed sd chd li 14 vi sd gi la 36-14=22 nhu di giii d tren Bii toin (xem Dd & Lf (2003), Tr 174) Hifu cua hai sd bang 15 Tim hai sd dd, biet rang neu gap mpt sd Ifn hai lin vi gap sd len lan thi dUpe hai sd mdi cd hifu bing 51 Dieu thu vi nghien cflu ldi giai dgi sd cho bii toin niy li ldi giii dd se giup djnh hUdng rat tdt eho ci eie ldi lip luin cd the hpc sinh giii bii toan dd O diy neu chung ta gpi hai sd chfla biet li X, y tfldng flng thi ta se cd trUde het: x-y= 15 (6) Neu chfla suy nghi can thin, dfl kifn edn lgi cua bii toin se dUdc the hifn bdi phUdng trinh li 2x-5y=51 Giii hf niy ehung ta se dfldc ket qui y=-7, khdng phai li sd chflng ta chd ddi d bic Tieu hpe! NhU viy ehung ta ein nhin lgi giii thiet vi thin trpng hdn: bii toin cho hai sd mdi cd hifu li 51 Do dd dan den hai trfldng hdp cd the xiy 2x57=51 hoic 5y-2x=51 chfl khdng chi li mdt trfldng hdp di xft vi khdng thich hdp vdi bgc tieu hpc d tren Vifc the vio se dUpc the hifn nhfl sau: 5y-2x = 51=>3y-2(x-y) = 51 =>3y-2 15= 51=>3y= 81 vi y= 27, tfl dd x= 42 Nhin nhin lgi tfl ldi giii bing dgi sd chiing ta cd the giup cho hpc sinh lap luin ring dfl kifn thfl hai se phdi li lin sd thfl hai trfl di lan sd thfl nhit bing 51 Biy gid chflng ta cd the sfl dyng cic phfldng phip trfle quan giiip hpc sinh tU bii toan niy Tfl phUdng trinh (6) chiing ta bieu dien sd nhd hdn li dogn thang, sd ldn hdn li ddoajn thing dd vi them 15 nhU mpt dogn nhd hdn (nhfl hinh ve) |— j — —| | NhU vgy lan sd nhd vi lan sd ldn se dUde bieu dien nhu sau: | | —| | | | | |— | | Do dd hifu gifla lan sd ldn vi hai lan sd nhd dflpc bieu difn bing ba dogn bieu dien sd nhd vi can bd bdt di thfm hai dogn bieu di^n cho 15 nfla Do dd ba lin sd nhd bdt di 30 li hifu 51 Tfl dd ba lan sd nhd li 51-H30=81 vi sd nhd li 81:3=27, sd ldn li 27+15=42 Cd mpt nhgn xft li bii toin cd thi quy ve tit ci mdt an nio dd thi vifc giii bing lip lugn se rit thugn ldi nhd vifc bieu dien chinh an dd qua mpt dogn thing de hpc sinh hinh dung Tren thfle te vifc sfl dung TAP CHi THI^ BI GlAO DMC- Sd 78 - 2/2012 cic hinh inh trfle quan li cich rit tdt de giup hpe sinh tieu hpc tu ve bii toin (xem them d Tri(10/2011)viTri(2011)) Ta xet them mpt vi dy nfla sau diy: Bii toin (xem Dd 8c Le (2003), Tr 21) Tdng sd tudi cua ba ngUdi li 115 Tudi eua ngUdi thfl nhit bing hai lan tudi cua ngUdi thfl hai cpng vdi 10 Tudi eua ngfldi thfl hai bing ba lin tudi cua ngfldi thfl ba trfl di Hdi mdi ngfldi bao nhieu tudi? Neu nhu phfldng phip dgi sd chung ta chpn mpt dgi lUdng nio dd cin tim hogc tfl dd giiip ta giii dUde bii toin li x thi lgp lugn Id-gic chiing ta se chpn mpt dogn thang de minh hpa cho dgi lUpng dd Trong trfldng hdp niy ehiing ta cd the ehpn tudi cua ngUdi thfl ba li x vi nhu vgy dfldc bieu dien bang mpt dogn thing Hay bieu dien tuoi cua nhflng ngfldi cdn lai qua dogn thing dd vi tfl dd gin ket vdi giii thiet eua bai toin di eho Cy the nhu sau I thflba I Tudi ngUdi I I I |///5//| Tudi ngfldi thfl hai Vi cudi cung li tudi ciia ngfldi thfl nhat I —-I I|///5//| I —I I |///5//| I-5 I 5-I Nhfl viy tdng sd tudi eua ei ba ngfldi se li 10 dogn thing (tudi efla ngfldi thfl ba) bdt di Tfl dd mfldi dogn thing hay tuoi ngfldi thfl ba se li 115+5=120 Do dd tudi cua ngfldi thfl ba la DIEN O A N 12 tudi, ngudi thfl hai li 31 tudi vi ngfldi thfl nhat li 72 Practice makes pefect! (Luyfn tip se tgo sfl hoin hao!) cd le la phfldng chim tdt cua mdn toin Rat nhieu cic vi dy cic sich toin bdi dudng vi cic de thi hpc sinh gidi cd the sfl dyng cic phep phin tich nhu trfn de dan den nhflng ldi giai thich hdp cho hpc sinh tieu hpc Chung tdi cho rang neu dflpc bdi dUdng ky nang phin tich niy cung nhU mdt sd ky nang dgy toin tieh cflc khic chac chin eie gid dgy hpe mdn toin d cic trfldng tieu hpc se hap dan cic em hpc sinh (xem them d Tri(2011)) Rd ring vdi nhflng cich phin tich vi lgp lugn Id-gic hpc sinh tieu hpc se ed cd hpi ren luyfn vi ning eao nang tU sau hpc nhflng bii giing nhfl vgy Tai lifu tham kliao Dd & Le (2003); Dd Trung Hifu vi Le Tien Thinh, Tuyen tip De thi Hpc sinh gidi bgc Tieu hpc mdn Toan, Nhi xuat bdn Giiodyc(2003) Dd(1998); Dd Trung Hifu, Cic bii toin dien hinh ldp 4-5, Nhi xuat bin Giao dvc(1998) 3.Le8cHoing(2011);LeTien Thinh vi Hoing Mai Le, Dgy hpc mdn Toin d Tieu hpc: Thfle trgng vi Giii phip, Tgp chi Giao dye, Sd 269(ky 1-9/2011), Tr 41-42 Tri(2011); Tg Ngpc Tri, Thiet ke cic bii toan nhd de dgy hpc sinh tieu hpc gidi mpt bii toin, Tgp chi Dgy hpc Ngiy (07/2011), tr 24-26 Tri(10/2011); Tg Ngpc Tri, Mpt sd bifn phap thfle hifn phfldng phip dgy hpc tich cflc dgy toan cho hpc sinh tieu hpc, Bii viet dang gfli ding II Summary Students teachers and teachers are familiar with the method of using unknowns to establish equations to solve mathematics problems, called the equation solution' here However this kind of solutions is not accepted at primary school level That is why student teachers and teachers sometimes meet challenges when teaching mathematics for primary school children This paper shows some examples and then suggests some ways of using the equation solution to obtain the solution to be able to teach primary school children The paper also gives suggestions of when and how to foster these skills to help the implementation of active teaching and active learning at primary school mathematics teaching niiiuiniiiiiMiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiMiiiiiiiiiiiiiiiiiiiiiiiiiiiiiinMiiiiiiiinMiiiiiMM QUY TRiNH THIET KE CONG CU mp,heotrang33) Ghi chfl: / / : rat ddng y; Bii viet niy ehung tdi de cap Ndi (NgUdi djeh: Nguyen Hflu / ddng y; ?: khdng chac chan; quy trinh thiet ke bd cdng cy Chiu), 2011 Vice-Principal, Universty of ^: khdng ddng y; ^x: rat khdng giflp GV ed the thu nhin dflde TTPH ve ket qui hpe tip eua standrews feedback on teaching: ddngy Vi du Bang quan sat de SV, qua dd dieu khien QTDH Student questionaires and peer observation of teaching Approved thu thgp TTPH ve thai dp (xem dgt ket qui tdi flu nhat by Academic Council, 2004 bing 4): Bing quan sat ve thai Abstract: Feedback is a very Tii lifu tham khao dp chuan bj giao in, phfldng Robert J M, Debra J P, Jane important role for improving tifn trfle quan va tap giang E P, Cic phfldng phip dgy hpc learning outcomes To collect it, Ket lu^n teachers need to have the tools This Nhd TTPH m i GV ed the hifu qui, NXB GD, TP Hd Chi paper refers to the process design de cic bifn phip tie dpng Minh, (NgUdi djeh Hdng Lgc), tool receiving feedback in teaching hifu qua vao cic hogt dpng hpc 2005 Tran Thi Tuyet Oanh, Danh the teaching biology method at tgp cua SV, ddng thdi SV cung gii va Ifldng ket qui hpc tip, the University of Pedagogy This tfl dieu chinh vifc hpc tap efla process includes three steps: NXB Dgi hpc SU phgm Hi Npi, mmh cho dgt dflgfc ket qua 1) Determining the goal(s) of 2009 cao nhat De lim dflgfc dieu learning; 2) Analyzing the contents Robert J Marzano, Nghf dd, GV can phai biet thiet ke of learning; 3) Designing the kit to thuit vi khoa hpc dgy hpe, collect the feedback information bp cdng cy thu nhan TTPH NXB Giio dye Vift Nam, Hi TAP CHi THIET BF GIAO our-S6 78-Z/2012 • 41 ... sich toin bdi dudng vi cic de thi hpc sinh gidi cd the sfl dyng cic phep phin tich nhu trfn de dan den nhflng ldi giai thich hdp cho hpc sinh tieu hpc Chung tdi cho rang neu dflpc bdi dUdng ky nang... 1/3 cdng vifc va gia thiet da cho la 150 dyng cy ''ay tong so dyng cy se li 450 dyng cy Vifc tim hieu ldi giai bang phfldng phap dgi sd de ed the giflp ich cho giao sinh, giao vien tieu hpc phuong... the giup cho hpc sinh lap luin ring dfl kifn thfl hai se phdi li lin sd thfl hai trfl di lan sd thfl nhit bing 51 Biy gid chflng ta cd the sfl dyng cic phfldng phip trfle quan giiip hpc sinh tU