Kieu Thu Linh
Day hpc phat trien nang life Toan cho hpc sinh trung hpc cd sol
Kieu Thu Linh Wen Khoa hoc Giao dye Viet Nam 101 Trah HUng Oao, Hoan Mm, Ha Noi, Viet Nam Email' I([email protected]
TOM TflJ: Toin hgc li mdn khoa hgc cd bin, cong eu quan trgng trong giao due de phit triin td duy, cich suy nghT vi giii quyit van de hieu qua. Nhieu nghien cdu quic tida khang dinh rang, thanh cdng trong hge Toin vao nhdng nam d trudng pho thdng co vai fro quan trgng cung cap cho hgc sinh cic kT nang cin thiit di hgc tiip d nhdng bac cao hdn hoae tham gia IUc IUdng lao dgng cd chat lugng tot hdn. Vi vay, d cic quoc gia, van de nghien cdu giing day Toan hieu qua ludn dUOc chu trgng. Nhiiu nghien cUu da chl ra rang, hoc sinh hoc Toin tot nhat khi cd cd hgi lim Toan hgc, giai quyit cac van de, chia si suy nghT cua minh vdi ngddi khic vi sCt dung suy nghT ciia hg de xay ddng va hiiu siu hdn cac kiin thde. Bai viit gidi thieu mdt so dinh hudng day hgc phat triin nang luc Toin cho hgc sinh Trung hoc co sd.
TLf KHOA: Nang life Toan; Day hgc Toan.
• * Nhan b^i 14/8/2019 ^- Ntian ket qua plian bien va chinh sila 20/9/2019 - i ' Duyet dang 35/11/2019,
1. Dat van de
Toan hgc ia mon khoa hoc ca ban, la cong cu quan trong trong giao due (GD) de phat trien tir duy, each suy nghi va giai quyet van de hieu qua. Nhirng kien thiic va kl nang Toan hoc ca ban da giiip con nguoi giai quyet cac van de trong thuc te cupc song mpt each co he thSng va chinh xae, gop phan thuc day xa hpi phat trien. Nhieu nghien ciiu quoc te da khang dinh rang, thanh cong trong hoc Toan nhung nam hoc pho thong co vai tro quan trpng cung cap cho hpc sinh (HS) cac kT nang can thiet de hpc tiep d nhung bac cao hon hoae tham gia luc luong lao dong co chat lugng tot hon. 0 truang pho thong, mon Toan gop plian hinh thanh va phat trien cac pham chat chu yen, nang lire (NL) chung va NL Toan hgc cho HS; Phat trien kien thiic, kT nang then chot va tao ca hoi de HS dupc trai nghiem, van dung loan hgc vao thuc tien; Tao lap six ket noi giiia cac y tuang Toan hgc, giiia Toan hpc vai thuc tien, giiia Toan hoc v6i cac mon hgc va hoat dpng GD khac, dac biet voi cac mon Khoa hpc, Khoa hgc tu nhien, Vat li, Hoa hgc, Sinh hpc, Cong nghe. Tin hpc dl thuc hien GD STEM [1, tr.3j. Th^ nhimg, lam thg nao da day hpc phat triln NL (PTNL) Toan cho HS van dang la mpt van de dang dugc quan tam nghien ciiu trong day hgc a quoc te va Viet Nam.
2 . N o i d u n g n g h i e n cuTu 2.1. Quan niem ve nang liTc va nang IUc Toan 2.1.1. Nang ILTC (Competence)
Theo CT GD .pha thong (GDPT) t5ng thi (2018): "NL la thupe tinh ca nhan dugc hinh thanh, phat trien nha to chat sin co va qua trinh hpc tap, ren luyen, cho phep con nguoi huy dpng tong hgp cac kien thtic, ki nang va cac thtigc tinh ca nhan khac nhu hiing thii, niem tin, y chi,...
thirc hien thanli cong mpt loai hoat dgng nhlt djnJi, dat ket qua mong mu6n trong nhu'ng dilu kien cu the" [2, tr.37].
Dinh nghia nay the hien; NL la su ket hgp giCta to chat san CO va qua trinh hpc tap, ren luyen ciia nguoi hpc; NL la su tich hgp cua kien thiic, kT nang va cac thupe tinh ca nhan khac nhu hiing thii, niem tin, y chi (ma nguai hgc co dugc n!id qua trinh hpc tap, ren luyen), ...; NL dugc hinh tlianh, phat trien thong qua hoat dpng va the hien a sir thanh cong trong hoat dpng thuc tien (la cai co the quan sat, do luong).
Nhu vay, NL la kha nang thuc hien, biet lam va Iam co hieu qua Noi toi NL la phai gan vai y thiic, thai dp, kien thiic, kl nang, su hieu qua.
2.1.2. Nang life Toan (Mathematical competencies]
Theo Morgan Niss [3; tr.4]: NL Toan hpc nhu kha nang ciia ca nhan de sir dung cac khai niem Toan hgc trong mgt loat cac tinh huong co lien quan den Toan hgc; de hieu, quyet dinh, va giai thich. Niss cho rang, de hpc Toan tot ckn phai co nhung NL Toan hgc va da xae dinh 8 thanh phkn Clia NL Toan nhung co the chia thanh hai cum [4, tr.7]. Cum thii nhat: De hoi va tra loi ve Toan hgc. Bao gom cac NL; Tu duy Toan hgc (Thinking mathematically); Lap luan Toan hpc (Reasoning mathematically); Mo hinh hoa (Modelling mathematically); Dat ra van de va giai quyet cac vkn dk (Posing and solving mathematical problems).
Cum thii hai Kha nang xu li, quan li ngon ngu Toan hgc va cac cong cu. Bao gom cac NL. Bieu diln (Representing mathematical entities); Su dung ngon ngii ki hieu, hinh thitc (Handling mathematical symbols and formalisms); Giao tilp hkng ngon ngir Toan hpc (Communicating in, with, and about mathematics); Sir dung cac d6 dimg ho trg va cong cu (Making use of aids and tools).
Voi quan dilm ciia NCTM (Hpi dong Quoc gia giao vien (GV) Toan ), NL loan la each thirc nam bat va sii dung ngi dung kiln thiic Toan, bao g6m; Giai quyet van de (Problem Solving); Lap luan va chiing minh (Reasoning and Proof);
So 23 thang 11/2019 63
NGHIEN CIJU LILUAN "•'^^^^IK -
Giao tiep (Communication); Ket noi (Connections); Bieu dien (Representations) [5, tr. 39].
N h u vay, co sir chong cheo dang ke giiia cac NL Toan . Day la ket qua tir nhirng each thirc ma cac NL quan he vai nhau trong iing dung ciia Toan hgc de viec giai quyet mpt van de.
6 Viet Nam, CT GD mon Toan (2018) dat ra muc tieu;
Gop phan hinh thanh va phat hrien cho HS NL Toan hpc (bieu hien tap trung nhat ciia NL tinh Toan) bao gom cac thanh phan cot loi sau; NL tu duy va lap luan Toan hpc; NL mo hinh hoa Toan hgc; NL giai quyet van de Toan hgc; N L giao tiep Toan hgc; N L su dung cong cu, p h u a n g tien hpc Toan [2, tr.52]. Voi cap Trung hpc CO sa (THCS), yeu cau can dat ve vai cac N L do la: Neu va tra loi dugc cau hoi khi lap luan, giai quyet van de; Thuc hien dugc viec lap luan hgp li khi giai quyet van de; Chiing minh dupc menh de Toan hgc khong qua phiic tap; Su dung dugc cac mo hinh Toan hpc (cong thirc Toan hpc, phuong trinh dai so, hinh bieu dien,...) de mo ta tinh huong xuat hien trong mgt so bai Toan thuc tien khong qua phirc tap; Sir dung dupc ngon ngii Toan hgc ket hgp vcri ngon ngii thong thuong de bieu dat cac not dung Toan hpc cGng nhu the hien chimg cii, each thirc va ket qua lap luan; Trinh bay dugc y tuong va each su dung cong cu, phuong tien hpc Toan de thuc hien mgt nhiem vu hpc tap hoae de dien ta nhirng lap luan, chimg minh Toan hgc [1, tr 7].
2.2. Day hoc phat trien nang liTc Toan cho hpc sinh trung hpc cti SDI
2.2.1. Kinh nghiem quoete
Trong hau het cac CT GD mon Toan o pho thong, NL Toan dugc xae dinh la kha nang, ki nang, quy ninh hay la kl nang thuc hanh de hgc tap va ap dung Toan. Moi CT lai xae dinh he thong cac NL Toan kliac nhau, song co ban thong nhat trong cac N L cot loi chung nhu; Giai quyet tinh huong CO van de; Giao tiep bang ngon ngil Toan hpc; Mo hinh hoa,...
Jeremy Kilpatrick va cac c6ng su [6; tr. 407] xem viec day va hgc Toan la san pham ciia su tuong tac giiia GV, HS va Toan hoc. Su chac ehan kien thirc, niem tin, quyet dinh va hanh dpng cua GV anh h u o n g den nhung dieu dugc day va cu6i ciing la nhiing dieu HS dugc hpc Tuy nhien, su ki vpng, kien thirc, so thich va phan hoi ciia HS ciing dong vai tro quan trpng trong viec dinh hinh nhiing gi dugc day va hoc. HS CO the giai thich, dat cau hoi, tra lai, tham chi la hoan thanh theo nhirng each khac nhau cho cimg mgt nhiem vu Toan hgc Hon niia, viec day hoe dien ra trong boi canh ia mpt loat cac y l u to moi trirong va tinh huong. VI du, chinh sach G D , danh gia cua HS va GV,. (xem Hinh 1).
N C T M cho rang, d l day hpc Toan hieu qua, GV ckn b i l t nhirng gi HS ckn hgc, ket n6i dugc vai nhirng gi HS da bilt;
GV dat can hoi tap trung vao phat triln su hieu bilt khai mem, kinh nghiem va kien thirc da biet se tao dupc nen tang cho viec hoc l o a n . HS trinh bay (noi, vilt) dugc cac chiln luge giai quylt vkn de [5, tr.l6]. D6ng thoi, can man thii t6t nhit cac ySu cau sau day de thuc hien bai hpc Toan hieu
Hinh J: Sa dd tam gidc GV, HS, Todn hgc vd bdi cdnh (Ngudn: Cohen vd Ball, 1999, 2000) (Chii thich: Contexts- Boi cdnh; Teacher: GV; Students- HS;
Mathematics- Todn hgc)
qua: Su tham gia ciia HS a miic cao; Nhiem vu dugc xay dung dua tren nhiing kien thiic da biet ciia HS; Tao ket noi dSn cac khai niem, N L va hieu biet; Tang cuong mo hinh hoa; HS se giai thich suy nghT va lap luan; Can doi thai gian thich hgp danh cho cac nhiem vu [7, tr. 346]. Viec to chirc day hpc 6 MT thuang thuc hien theo quy trinh 4 huge: B u a c 1: Quan sat cac tlnh huong thuc te va phat hien ra van de can giai quyet; B u o e 2: Tim kiem mgt m o hinh Toan hgc the hien dupc ban chat cua van de thuc te do; B u o e 3: Giai quyet mo hinh Toan hpc tren va tim ra dap an; B u o e 4: Ap dung ket qua co dugc vao tinh huong thuc te de giai quyet van de. Co hai kT nang dugc chii trpng la; 1/ Kha nang tim ra mo hinh Toan hpc phii hgp ap dung vao tinh huong thirc te CO van de; 2/ Kha nang ap dung ket qua co dugc vao giai quyet van de mang tinh thuc t l .
Tren co so cac tieu chuan ngi dung va nang luc ciia quoc gia, cua cac tieu bang, GV o MT se thilt k l bai hgc, xae dinh ro rang nhung gi HS nen hgc d moi c4p, moi lap, m6i bat hgc. Bai hgc dugc thiet k l d l giai q u y l t cac khai niera hoae kT nang dua tren nhung yeu cau cu t h i : HS lam trung tam hoat dgng hpc tap; Tap trung yeu can va giai quyet van de bai hpc; T u duy phe phan va ki nang iing dung k i l n thtic;
Dli thoi gian, khong gian va vat lieu d l hoan thanh nhiem vu; Danh gia da dang, lien tuc, dugc thilt k l d l danh gia ca tien bo ciia HS va hieu qua cua GV, Ngoai viec dam bao HS tich cue tham gia, GV can man thii cac nguyen tSc sau:
Tao mgt moi tarong hgc tap an toan noi HS cam thdy thoai mai; Thiet lap cac quy t5c va thoi quen ro rang; Cung c i p cac nhiera vu va san sang ho trg; Sir dung cac nhora hoc tap hop tac dugc phan cong va quan li tot, Thuong xuyen k i t noi bai hoc voi thuc te; Su dung cac phuong phap giang day tich hpp; Ket noi sinh dpng cac kien thiic da bilt ciia HS tdi nhung k i l n thtic mdi; To chirc cho HS lam viec thong qua cac boat dpng va chia se cac san phara [7, tr348]
64 TAP CHi KHOA HOC GIAO DUC VIET NAM
w^^mm.
Kieu Thu LinhV^ cac cong nghe ho trg day hgc, NCTM cho riing, chiing nhu m6t c6ng cu thiet yeu trong day hgc loan. Sir dung cong nghe phii hgp co the ma rpng ca phara vi ngi dung va cac tinh huQng co vSn dk cho HS. NCTM khuyin nghi riing, HS va GV nen dugc tiep can voi nhilu cfing cu cong nghe giang day. Cac lap hpc ciing cong nhan va dap img cac phong each hgc tap da dang ciia HS, xay dung each thirc de thu hiit HS voi cac phong each hpc tap khac nhau, phSn nhom linh hoat, ca nhan hoa huong din cho HS gap kho khan, phin loai bai t3p, du an va dieu chinh miic do ciia cau hoi [5, tr.l8].
2.2.2. Mpt SO dinh hiJ0ng day hoc phat trien nang life Toan cho hpc sinh trung hpc cti scl
DI dat dugc muc tieu CT mon Toan (2018), cin co nhilu doi moi vl phuang phap day hgc Toan o truong ph6 thong, nhtmg truac het theo chiing t6i, cac bai hpc can tuan thii cac yeu cau ca ban sau:
Thic nhdt: Giiip HS co nhiing hilu bilt virng ch5c, phat trien dugc von kien, ki nang Toan hpc nen tang.
Thu hai: HS phai biet sir dung cae kiln thiic Toan dl giai quySt cac van de thuc tg.
Thu ba: Viec day hge Toan can gan vai viec hinh thanh cac pham chat: Tinh ki luat, kien tri, eham chi, chu dpng, linh hoat, dgc lap, tu chit va hgp tac.
Vifc trien khai day hgc mon Toan can dugc to chiic thong qua mgt chuoi cac hoat dpng tich cue, dpc lap, sang tao ciia HS, quan triet tinh than lay HS lam trung tam vai sir ho trp hop li ciia GV: GV la nguoi djnh huong, dieu chmh va thiic day sang tao, tao moi truang hpc tap an toan, coi ma...;
Chii trpng sir dung cac phuang phap day hgc tich cue; Dam bao tao dieu kien cho HS thuc hanh, trai nghiem, van dung kien thiic, ki nang vao cac tinh huong thuc tiln; Chii trgng cac hoat dpng mo hinh hoa Toan hgc va ren luyen cac hoat dOng giao tiep bang ngfin ngil Toan hgc (noi va viet); Phat huy vai tro ca nhan trong hgp tac va boat dpng nhom, ca nhan hoa nguai hpc; Ren luyen tu duy phan bien va sang tao; Tang cuong su dung cac cong cu, thiet bi day hgc thong minh trong day va hgc; Boi duong phuang phap tu hpc. De dilt dugc ket qua do, GV can thiet ke bai hgc theo cac buoe sau:
Bif&c 1: Xdc dinh muc tiiu bdi hgc vd lua chgn ngi dung dgy hgc trong tdm
Xdc dinh muc tieu: GV can bam sat ylu cau can dat da dugc quy dinh trong CT.
Xae dinh ro npi dung, NL can hinh thanh cho HS trong bai hoc do, lien ket vgi nhiing kien thiic da biet ciia HS, chu j den cac hoat dpng giiip hinh thanh phSm chat cho HS.
Bu&c 2: Lua chgn phuang phdp. ki thudt vd hinh thuc dayhpc
Cac phuang phap day hpc dam bao phu hgp voi tien trinh nban thiic cua HS, chu y each tilp can dua tren kinh nghiera va trai nghiem cua HS. C3n tl chiic qua trinh day hpc theo huong kiln tao, trong do HS dupc tham gia tim toi, phat hien, suy luan va giai quyet van de, giiip HS co su hieu biet
vung chac, phat tnln dugc v6n kiln thiic, ki nang Toan hpc nen tang. CSn su dung hieu qua cac phuong tien, thilt bi day hpc toi thieu theo quy dinh doi vcri mon Toan. Khuyin khich sii dung phuong tien nghe nhin, phuang tien ki thuat hien dai ho trg qua trinh day hpc, ddng thai coi trpng viec sir dung cac phuong tien truyin thing (co thi true tilp cktn, nam, sap xep, dich chuyen); Tang cuong thilt bj day hgc tulam.
Bu&e 3: Lua chgn mdi truang hgc tap, tu lieu, hgc lieu Cac hoat dong day hgc Toan hgc da phin la diln ra tai lap hpc. Ngoiti ra, GV eo the to chirc cho HS hgc tap voi nhilu hinh thitc khac nhu: Thuc hien nhung dl tai, du an hpc tap ve Toan, dac biet la tihiing de tai va du an ve img dung Toan hgc trong thuc tien, To chirc tro choi hpc Toan, cSu lac bp Toan hgc, dien dan, hgi thao ve Toan ,... Khi do, moi truong hgc tap dugc ma rgng hon ra ngoai lop hgc nhu Iam a nha, lam o thu vien, san truang, bo ho, cong vien, truang pho th6ng hoae dai hgc, moi truong hoc true tuyln,...Cac tu lieu, hpc lieu dugc GV va HS chuan bi phii hgp voi muc tieu bai hgc va moi trudng to chiic day hgc. Vi vay, GV nen huang dan HS each tim kiem thong tin, tu lieu tren hitemet hoae CT truyen hinh co uy tin ve GD de md rgng von hilu bilt va NL tu hgc.
Bu&c 4: Thiit ki hogt ddng hgc, bao gom:
Hogt ddng khdi dpng: De tao hiing thii eho HS, GV co the khdi dpng bai hpc bang each sir dung cac trd choi, xem video hoae neu mpt tinh hudng ed van de lien quan den bai hpc.
Hogt dgng hinh thdnh kien thue: Day la phan trpng tam cua hoat dgng hgc giiip hinh thanh kien thirc mdi cho HS.
Cac npi dung trong hoat ddng nay can neu ro muc dich, each thiic tien hanh va san pham ciia HS. Vdi cac tinh huong co van de, GV se dua HS thuc hien 3 budc co ban: Tim hieu van de; Len ke hoach giai quyet; Giai quyet van de.
Hogt dpng luyen tap: Lua chpn nhiing bai tap, hoat ddng tuang tu vdi kien thiic vira hinh thanh d hoat ddng trudc, ket hgp sir dung cac phuong phap day hgc tich cue; Td ehiic hoat ddng nhdm; thuyet trinh san pham;...
Hogt ddng van dung: GV td ehiic cho HS lien he thuc te de van diing kien thiic da hgc thdng qua cac tinh hudng cu the, chii y den kha nang tich hgp lien mon. Co the xuyen sudt ca thiet ke hoae the hien tap trung d hoat dgng van dung nay.
Hogt dpng ddnh gid tdng kit, dinh hudng hgc tap tiip theo: Trong mdi bai hgc, GV ed the sir dung nhieu hinh thiic danh gia khac nhau, cd the la nhirng bao cao san pham, bp SUU tap san pham ciia HS, to chirc cho HS tu danh gia, danh gia Ifin nhau va GV danh gia, nhan xet... hay sir dung cac bai tap ngin, phieu danh gia,... GV se chdt lai ndi dung bai hpc va CO nhiing dinh hudng vl viec chuan bi bai tiep theo.
Vi dy:
Ten bah Ghi s6 tu- nhien (Toan 6).
Muc tieu: HS hilu dugc thi nao la he thap phan, phan biet sd va chd sd trong he thap phan Hieu ro d he thap phan gia tri cua mdi chS s6 trong mgt sd thay ddi theo vi tri. HS thay So 23 thang 11/2019 65
NGHIEN ciru Lf LUAN
dugc uu diem eua he thap phan trong viec ghi sd va tinh Toan. Biet dpc va viet cac so La Ma khong qua 30.
Ren luyen tinh can than, nhanh nhen, gop phan PTNL giai quyet van de, NL mo hinh hoa, NL giao tiep Toan hgc.
Cdc hogt dgng dgy hpc chinh:
a. Kh&i dpng
GV trinh chieu cho HS xera 2 video va neu nhiem vu:
Tim hieu cac each ghi sd trong lich sir qua website:
https://www.youtube.com/watch?v=cZHOYnFpjwU.
https://www.youtube.com/watch?v=cy-81PVKLIo Chia nhdm HS thao luan, trinh bay.
b. Hinh thdnh kiin thuc Vdng 1: Nhdm chuyen gia
GV chia Idp thanh 1 nhom theo each dem so. Nhiing HS cimg so thii tu la mdt nhdm. Cac nhdm cd 3 phiit de di chuyen va dn dinh td chiic; bau nhdm trudng, thu ki. GV giao nhiem vu cho cac nhdm nhu sau:
Nhdm I: Phdn biet so, chusd
HS tim hieu tai lieu de ve so dd tu duy md ta dugc cac ndi dung: Phan biet sd, chu so; Ditng 10 chil sd de ghi sd: 0; I;
2; 3; ...9; Cach viet so, dgc sd: Viet so tir trai sang phai. Vdi cac sd cd 5 chii sd trd len thi viet taeh, phan biet cae ldp.
Dpc sd tir trai sang phai, theo Idp (dpc sd c6 3 chii sd), cudi mdi ldp CO kem theo ten ldp. Ldp don vi khdng can dpc ten ldp; Phan biet sd chuc vdi chir sd hang chuc, sd tram vdi chii so hang tram...
Nhom 2: Tim hieu ve hi thdp phdn
HS tira hieu tai lieu tham khao (GV cd the dinh hudng cho HS) de ve so do tu duy rad ta dugc cac ngi dung sau:
Ghi sd theo he thap phan la nliu the nao? Td chirc so ra sao?
Td chiirc sd theo hang va ldp la nhu the nao? Gia tri cua mdi chir sd trong rapt sd phu thuoc vao yeu td gi? Minh hga, phan tich sd theo don vi hang. Ghi cdng thiic tdng quat,
Nhom 3: Cdch ghi sd bdng chit sd La Md HS tim hieu tai lieu tham khao de ve so dd tu duy md ta dugc ndi dung: Cac chil sd La Ma co ban: I, V, X. Quy tac viet so La Ma (den 30): Chii sd dupc ghi vao ben phai sd gdc la sd cpng them, chii sd ghi vao ben trai sd gdc la sd trir di. Sd trir ludn la sd nhd hon sd bi trir; Cach ghi sd bang chO sd La Ma GV phat tai heu, phieu hpc tap da chuan bi cho cac nhdm. Cac nhdm lam viec duoi su dieu khien ciia nhdm n-udng va hudng dan ciia GV.
Vong 2: Mdnh ghep
Sau khi hoan thanh san pham, GV sfi dung kT thuat manh ghep de ddi cac thitnh vien trong nhdm. Thanh vien ciia nhom cii co nhiem vu trinh bay ket qua liim viec cua nhdm minh. Thanh vien cac nhdm khac nghe va ghi chep lai viio phllu hpc tap. Hoae GV sii dung kT thuat manh ghep, phdng tranh, di chuyen theo tram de cac nhdm dugc trinh biiy kit qua va ghi chep lai nhiing gi nghe dugc, neu thae mac nlu cd. Cudi cimg, GV nhan xet va kit luan nhirng npi dung da tim hieu.
c. Luyen tap - Thuc hdnh
HS lam cac bai tap sau: Hoat ddng theo nhdm, thuylt trinh, trung bay san pham.
Bai tap 1:
Dien vao bang sau So
da cho 6980
So nghin
So hAng nghin
5 S6 tram
89 So bang tram
4 So chuc
So hang chuc
3 5
s6
don vi
So h^ng dtfn vj
1 0 Bai tap 2: Viet cac sd sau bang so La Ma 81;30;27; 12.
d. Vdn dung
HS thao luan nhirng irng dung trong thuc te cua viec ghi sd tu nhien vao giai quyet cac van de ciia eudc sdng; Ghi chep sd lieu, tinh Toan, ghi menh gia tien te. Sd tu nhien edn dimg trong danh sd thii tu, danh sd so nha, danh sd cac trang sach, tao cac sd dien thoai.,,Ket hgp tap hgp sd tu nhien vdi tap hgp cac chii cai {A; B; C; D, E..}, danh sd phan biet cac ddi tugng; ...
GV td chuc bang k! thuat day hpc tich cue (khan trai ban):
Hoat dpng theo nhdm; Tap trung viio cau hdi; Viet vao 6 mang sd ciia minh eau tra ldi hoae y kien cua minh. Mdi ca nhan liira viec ddc lap trong khoang vai phut. Ket thiic thdi gian lam viec ca nhan, cac thiinh vien ehia se, thao Iuan va thdng nhat cau tra ldi; Viet nhirng y kien chung cua cii nhdm vao d giiia giay AO
e. Tdng kit. ddnh gid
HS tu nhan xet, danh gia qua trinh va kit qua lara viec;
HS neu cam nhan vS bai hgc; GV danh gia chung sau tilt hgc. Giao nhiem vu chuan bi cho bai hgc tiep theo.
Qua td chiic tnln khai bai hpc tren tai Trudng Tilu hgc, THCS va Trung hgc phd thdng Thuc nghiem Khoa hpc GD - Vien Khoa hge GD Vidt Nam, chiing tdi nhan diiy ring, bai hpc dugc thiet ke phii hgp vdi tiln trinh nhan thiic ciia HS. HS cd ca hpi dugc sii dung vdn kinh nghiem, su trai nghifim ciia minh ve npi dung bai hgc. HS duge [a trung tam trong ldp hpc, phat huy tinh tich cue, tu giac, chu ddng ciia HS Cac boat dgng hge tap theo quy trinh hpe kiln tao, trai nghiem, su dung cac kJ thuat day hgc tich cue: I^dra ehuyen gia, khan trai bim, day hgc hgp tac... tao dilu kien cho HS cd CO hpi tim tdi, thao luan, chia se, thiy dugc each thuc hien va y nghTa cua viec ghi sd tu nhien trong cugc sdng. HS c6 dugc CO hpi PTNL giai quylt vin dl, md hinh hda Toan hgc, phat tnen nang luc giao tilp bing ngdn ngii Toan hpc... Bai hpc tao ca hdi cho HS dugc ket ndi kinh nghiem v6 kiln thiic s6 tu nhien da hpc d tieu hge, phat trien va md rdng them hilu biet Clia cac em Caeh lara nay giiip HS hilu ro ban chit tir dd nam vimg dugc kien thiie cua bai hpc. Ben canh do HS ciine duoc giao nhiera vu giai quylt cac vin dl eua cupc sdng gin vdi kiln thiic trong bai hgc, giiip HS hmh thanh va phat triln NL giai quylt vin de, van dung kiln thiic Toan hgc vao thuc tlln. Cac hunh thiie td chiic day hgc dd cilng da gop phin phat trien va ren luyen cac phara chat can cd cua HS- Hem tac kien tri, chu ddng, hnh hoat,..
65 TAP CHI KHOA HOC GIAO DUC VIET NAM
3. Ket luan
Day hpc PTNL Toan cho HS la yen cau cap thiet hien nay theo xu the quoc te va de dap iing yeu cau eua CT mon Toan (2018). Day hgc PTNL Toiin cho HS c i n d u g c t l chiic thdng qua cac boat dgng; HS la trung tara trong Idp hpc; Chu trpng cac hoat ddng giai quyet van de, lien he thuc tiln; giiip HS co k i l n thiic nen tang virng chac va phat huy tinh dgc lap, linh hoat, chit dpng, hgp tac, sang t^o, t u d u y phan bien... De nang cao chat lugng day va hpc loan d THCS, chiing toi khuyen nghi: Can chii trpng dao
dao GV day Toan T H C S ve eae ddi mdi trong CT GD mon Toan mdi, giiip GV nam ro m u e tieu, phuong phap day hpc Toan d cap hpc nay; Tang cudng bdi duong p h u a n g phap.
Id thuat day hgc tich cue ddi vdi GV de hp cd the ap dung linh hoat trong mdi bai day nham dat rauc tieu tdi uu; Gidi thieu cac ngudn tai nguyen giiip xay dung thiet ke cac bai hpe da dang den tat ca GV day Toan tren toim qudc; M d rpng nghien ciiu, hpc tap kmh nghiem qudc te ve phuong phap, m o hinh trong day hpc va danh gia trong giang day Toan dap img duoc yeu can PTNL cho ngudi hpc.
Tai lieu tham kh^o
[1] Bp Giao due va Dao tao, (2018), Chucmg irinh Gido due pho thong (Chuong trinh mon Todn).
[2] Bo Giao due va Dao tao, (2018), Chucmg trinh Gido due phd thong (Chuang irinh tdng the).
[3] Niss, M, (2003), Mathematical Competencies and the Learning of Mathematics- The Danish KOM, Project. In:
Gagatsis, A./Papastavndis, S (Eds), 3rd Mediterranean Conference on Mathematical Education. Athens:The Hellenic Mathematical Society, pp. 115-124.
[4] Nguyen Thi QuS, (2019), Nghien cuu thiet ke dgy hgc cdc mdn hgc vd td chirc hoat dpng trdi nghiem theo Chuong
trinh Gido due phd thong m&i, Nhiem vu thudng xuyen theo chirc nang, Vien Khoa hpc Giao due Viet Nam.
National Council of Teachers of Mathematics, (2003), Principles and Standards for School Mathematics, Reston, VA: National Council of Teachers of Mathematics
Jeremy Kilpatrick - Jane Swafford - Bradford Findell, (2001), Adding u up: Helping children learn mathematics.
Washington DC. USA. National Academy Press Geoff Petty, (2009), Teaching Today, Nelson Thomes.
MATHEMATICAL COMPETENCE-BASED TEACHING FOR SECONDARY STUDENTS
Kieu Thu Unh
The Vietnam National institute of Educational Sciences 101 Iran Hung Dao, Hoan Kiem, Hanoi, Vietnam Emaii i([email protected]
ABSTRACT: Described as the basic science. Mathematics Is an important tool in education to develop problem solving skills. A vast number of international studies have confirmed that success in learning tyfath during school years plays an important role to provide students with the skills necessary to further study at higher levels as well as contribute to high quality workforce. Therefore, the issue of effective research and teaching of Math is recently focused in many countries. The findings have also shown that students will be the best at math when they have opportunity to do Math, learn to solve problems, and share their thoughts with others. This article introduces orientations for teaching based on mathematical competence development for secondary students.
KEYWORDS: Mathematical competence; mathematical teaching.
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