TRUQNG DAI H O C DONG THAP Tap Chi Khoa hoc so 27 (08 2017) MOT SO BIEN PHAP B 6 I D U ^ O N G NANG LlTC PHAN TICH TIM LC« GIAI " BAI TOAN CHO HOC SINH THONG QUA 0 A Y HQC GIAI BAI T A P CHU DE PHirON[.]
Tap Chi Khoa hoc so 27 (08-2017) TRUQNG DAI H O C DONG THAP MOT SO BIEN PHAP B I D U ^ O N G NANG LlTC PHAN TICH TIM LC« GIAI " BAI TOAN CHO HOC SINH THONG QUA A Y H Q C GIAI BAI T A P CHU DE PHirONG PHAP TOA DO TRONG M A T P H A N G - H I N H HOC 10 • Nguyen Thj Xuan Mai'*', Nguyen Diidng Hoang^'J Tdm tat Bdi bdo trinh bdy tdng quan ve nang luc todn hgc, ndng luc gidi todn, ndng luc phdn tich tim lai giai bdi todn, tit dd di xudt mot sd bien phdp nham bdi duang ndng luc phdn tich tim ldi gidi bai todn cho hoc sinh thdng qua dgy hgc chu de "Phuang phdp tog mat phang-Hinh hgc 10 " Tit khoa: Ndng luc phdn tich, bien phdp, hgc sinh, bdi tap, tga mat phang Dat van de trudng phd thong, day toan la dgy hogt ddng toan hpe cho hpe sinh (HS) [5, tt 206], ttong dd gidi toan la hinh thiic chu yeu Do vay, dgy hpe giai bai t ^ toan cd tam quan ttpng dac biet va tir lau da la mpt van de ttpng tam cua phuong phdp day hpc todn d trudng thdng Theo Polia [2], ed budc de di den Idi giai bdi toan: 1) Tim hieu ndi dung bdi toan; 2) X ^ dpng chuong trinh gidi; 3) Thue hien chuong trinh giai; 4) Kiem tia nghien eiiu ldi gjai Nhu vay ttong giai bdi toan, edng viec tim tdi ldi gidi bdi toan la khau quyet dinh Dii cd ky thudt eao, cd thdnh thao ttong vipc thyc hien cac thao tae va eac phep tinh nhung chua ed phuang hudng hogc phuong hudng chua tot thi chua the cd ldi giai hope ldi giai ehua tot Tim tdi ldi gidi bdi todn ciing chinh la co sd quan ttong vipc ren li^en khd ndng lam viee ddc lap, sang tgo cua HS Van de dat Id bdi dudng nhu the ndo cd hieu qua de cho cac em cd nang lpc dimg trudc mdt bdi todn cd tiie giai duoc mpt each hop li Bai viet de xuat mdt so bipn phap de boi duong nang lpe phan tich tim dudng loi giai bai todn cho HS thdng qua dgy hpe gidi bai tgp chii de "Phuang phdp tga mdt phangHinh koc 10" Nang Inc phan tich tim Icri giai bai toan 2.L Nang Iprc toan hoc Theo V A Krutecxki [6, tt 13], nang lpe toan hpc dupe hieu theo y nghia, miic dp Mdt la, theo y nghia nang lpe hpe t?^ (tai tgo) tiic la nang lue doi vdi viec hpe Toan, doi Hgc vien cao hpc, Tnrdiig Dai hgc D6i^ Thap Tru6ng Dai hoc D6iig Thap vdi viee ndm sach giao khoa mdn toan d tmdng thdng, nam mdt each nhanh va tdt cac kien thiic, ky nang, ky xao tuong iing Hai Id, theo y nghTa ndng luc sang tao (khoa hoc), tuc la nang luc hopt dpng sang tgo Toan hpe, tao nhimg ket qua mdi, khach quan co gia tri doi vdi xa hpi loai ngudi Ong dua dinh nghia "Ndng luc hpc t ^ toan hoc la ede dae diem tam ly ea nhdn (trudc het ia cae dgc diem boat ddng tri tue) dap ung yeu eau hoat ddng toan hoc va giiip cho viec nam giao trinh Toan mdt each sdng tao, giiip cho viec ndm mdt each tuong doi nhanh, de dang vd sau sdc kien thirc, ky nang vd ky xao toan hpc" [7, tt 14] Theo Le Ngpc San [9, tt 21], neu coi qua trinh hpc t ^ Id qua trinh thu nhan va xii li thong tin thi ndng luc toan hpc ciia HS bao gom: - Ndng lpe thu nhan thdng tin toan hoc: nang lpe tri giac hinh thiie hda tai lieu toan hoc, ndm eau tnie hinh thiie cua bai toan - Nang lpc ehe bien thdng tin toan hpe: nang Ipc tu dio' logic ve quan he so luong va hinh dgng khdng gian bang ki hieu toan hoc; nang iuc khai quat hda eae doi tupng toan hpc, quan h^ toan hpe va eae phep toan; nang lyc tu di^ linh hogt bdng riit gpn qua tiinh suy luan va cau true toan hpc nit gpn; nang lpe chuyen hudng qua hinh tu - Nang lue luu trii thdng tin todn hpc: nang luc ghi nhd (tri nhd khai quat, dac diem ve loai, so suy lugn va chimg minh, phuong phdp giai bai toan), Ndi den HS cd ndng luc toan hpc Id ndi den HS cd tri thdng minh tiong vipc hpe Toim, Tat ca moi HS deu ed kha nang vd phai ndm duoc chuong trinh tnmg hpc, nhung cac khd ndng * TE.UC3NG DAJ H O C DONG THAP khac tii HS qua HS khdc Cac khd nang ndy khdng phai co dinh, khdng thay doi Cdc nang luc khdng phdi khdng the thay doi md hinh thdnh vdjyhdt trien qud trinh hoc tap, luyin tgp de nam dupe boat dpng tuong iing, vi vay, can nghien cim de nam dupe ban ehat cua ndng luc va cac dudng hinh thanh, phat trien, hoan thi^n nang lue 2.2 Nang luc giai toan Ndng luc giai toan Id gi? Chung tdi quan niem nhu sau: Nang lue gidi toan la mdt phan cua nang lpc toan hpc, la to hop cac ky nang ddm bao thuc hien cac hogt ddng giai toan mpt each cd hieu qua cao sau mot so budc thuc hien Mpt ngudi ed nang lpe gidi todn neu ngudi ndm vung tri thiic, ki nang, ki xdo cua hogt dpng gidi toan vd dat duoc ket qua cao so vdi trinh dd trung binh cua nhimg ngudi khdc cimg tien hanh hogt ddng gidi toan ttong eae dieu kien tuong duong Tir dgc diem boat dpng tri tue cua nhiing HS cd nang lpe toan hpe vd khdi nipm ve nang lyc giai toan, ed the rut mdt so dgc diem va cau true cua nang lue giai toan nhu sau: - Khd nang liiih hpi nhanh chdng qiQ' trinh giai mpt bai toan va cac yeu cau ciia mdt ldi giai dep va rd rdng - Sp phat trien manh eua tu day logic, tu sang tao the hien d khd ndng \^ lugn ehinh xac, v4 quan he giiia cae du kipn eua bai toan, - Cd nang Iuc phdn tich, tong hop ttong linh vuc thao tdc vdi edc ki hipu, ngdn ngir toan hpe Khd nang chuyen doi tir i^eu kien cua bai toan sang ngdn ngu: ki hieu, quan h§, phep toan giua cdc dai lupng da biet, ehua biet vd nguoc lai - Cd tinh dpc lap va dpc ddo eao ttong gidi toan va su phdt trien eua nang luc gidi quyet van de - Cd tinh tich cue, kien tri ve mat y ehi vd khd ndng huy ddng tri dc cao ttong gjai toan - Khd nang tim tdi nhieu ldi giai, huy ddng nhieu kiln thue mot luc vao vipc giai bai tap, tir lua ehpn ldi gidi toi uu, - Cd khd nang kiem tia eac ket qua da dgt dupe va hinh mdt so kien thiic mdi thdng qua hoat dpng gidi todn, ttanh dupe nhung nham lan ttong qua trinh giai toan - Cd khd nang neu dupe mdt so bai tgp tuong cimg vdi each gidi (cd the la ^nh hudng Tap chf Khoa hgc so 27 (08-2017) gidi, hodc quy trinh ed tinh tiiudt toan, hogc thuat toan de giai bai toan do) - Cd kha nang khai quat hda tir bdi toan eu the den bai todn tong quat, tir bdi toan ed mdt so yeu to tong qudt den bai toan ed nhieu yeu to tong quat, nhd edc thao tac tri tup: phan tich, so sanh, tcing hpp, tuong tu, trim tupng, he thong hda, dac biet hda, 2.3 Nang lure phan tich tim Idi giai bai toan Xet ve binh dien triet hpc thi "Phdn tich Id phuang phdp phdn chia cdi todn thi thdnh timg bg phdn, timg mat, timg yeu td de nghien citu vd hiiu duac edc bd phgn, mdt, yiu to dd" [8, tt 86] Ngodi cdn ed nhieu dinh nghia khdc ve phan tich Theo Nguyen Ba Kim [5] "phdn tick id tdch (trong tu tudng) mdt he thdng thdnh nhihig vdt tdch mdt vdt thdnh nhirng bd phdn rieng le"; Theo Hodng Chung [1], "Phdn tich Id diing tri 6c chia cdi todn the thdnh edc thdnh phdn, hogc tdch timg thudc link hay khia cgnh riing biit nam edi todn thi do" Tren co sd phan tich edc dinh nghia tien, ed the quan mem ve phan tich nhu sau: "Phdn tich Id dimg tri dc tdch doi tugng tu thdnh nhimg thugc tinh, nhimg bd phdn, cdc mdi lien he quan he de nhdn thirc ddi tugng duge sdu sac han" Cd hai hinh thiic phan tich' Thii nhat, Id tach van de eac bp phgn theo tieu chi, Chang han phan tich khai niem so thdnh hai bp phgn: so chan vd so \i Viec tdch nhu the nao thudc tung dae diem, yeu cau, mue £eh bai toan Thu hai, dd Id tach mot phan, tdp tnmg chii y vao phan dd, thu thap cae thdng tin tir viec nghien cim phan vira tach Chang han, ttong mpt phuang tiinh, tdch ve phai cua phucmg trinh, quan sat, xem xet cae phep todn, edc so ttong bieu thirc ve phdi, tir dua cdc thdng tin ve bieu thirc ndy Theo chung tdi quan ruem: Ndng luc phan tich tim ldi gidi bai toan la khau dau tien ttong qua tiinh gidi toan, ddi hdi ngudi gidi toan phai ed kha ndng nhu dy doan, md mam, dac biet hda, khdi qudt hda, tuong hda, xdc dinh dupe the loai bai todn, vach phuong hudng gidi bai toan, tim duoc cac phuang phap va cdng cp thich hop de giai bai toan Mpt so bi^n phap boi du-ong nang lu-c phan tich tim ldi giai bai toan cho HS thong 21 TB.UC(NG DAI HOC D N G THAP Tgp chi Khoa hpc so 27 (08-2017) qua d^y hoc giai bai t^p chu de "Phuwng phip toa dp m | t ph^g-Hinh h^c 10" 3.1 Thanh to nang lire giai toan cua chu de "Phmmg phap tpa dp m^t phangHinh hpc 10" Ndi dung chii yeu cua ehu de "Phuang p h ^ tpa dp mgt phdng-Hnh hpe 10" bao gom: Tpa dp diem, veeta; Phuang trinh dudng tiiang; Vi tri tuong doi giua hai dudng thang; Gde; Khoang each tir mdt dilm den dudng thdng; phuong trinh dudng ttdn, vi tri tuong d6i giua dudng ttdn va dudng thdng Can eu vao dac diem ciia nang Ipc gidi toan, can cii vdo ndi dung hp tiiong bai t ^ eua chu de, chiing tdi xde $nh eae to cua nang lpc giai bai toan chu de "Phuong phap tpa dp ttong mat phang-Hinh hoc 10": Ndng luc huy ddng, van dyng edc tinh chdt, cdng thuc, dinh ly vdo viec gidi nhanh vd chinh xdc cdc bdi tgp Ndng luc phdn tich, tdng hgp du kien vd yeu cdu bdi todn de dinh hudng cdch gidi Ndng luc tim ldi gidi bdi todn tga mat phdng bdng nhiiu cdch khdc Ndng luc trinh bdy ldi gidi mot cdch chdt che vd cd ca sd 3.2 M$t so bi|n phap boi dirong 3.2.1 Bien phdp 1: Tap luyen cho HS biit sir dung cdc thao tdc tu nhu dit dodn, md mdm, phdn tich, tdng hap da Men vd yiu cdu bdi todn de dinh hudng cdch gidi Khi diing trudc mdt bdi toan HS can dgt cho minh cdu hdi: De gidi bdi toan ta can nhiing kien thiic nao? Tir giiip hp lien tudng den cac kien thiic hen quan de gidi bdi toan, Mgt khac, gido vien (GV) can dua bai toan ngau nhien, khong xep theo mpt trinh nao dgt trude dl ren luypn eho HS nang luc huy dpng va vgn dung kien thue vao gidi bdi todn Vi dii 1: Trong mgt phang tpa dp Oxy, cho hinh chu nhgt ABCD cd tam / &•) phuang trinh la w = (l;-2); / —;0 Id tam ciia hinh chu nhgt nen d(I,AD) = 2d(I,AB) d(J,AB) = d{I,CD), Hinhl - Ket l u ^ : l,ap phirong tiinh cac cgnh cua hinh chii nhgt (cae dudng tiling AD; BC; DC) Tom tat each giai bai toan: Tir kiln tiiiic da biet: Biet AB//CD, ma phuang trinh AB:x~2y + = sity phuong trinh CD cd dgng x-2y + c = 0(ci^2) Tuong tix, AB±AD;AB1BC; suy phuong trinh AD va BC cddgng 2x+y+c'=0 - De tim dupe c, chung ta can lien he cong thiie khoang each tir mpt cKem den mpt dudng thang Do biet tam —;0 ciia hinh ehu nh§t I ll nen d{I,AB) = d{I,CD) '^\c-\-\=-^ [c=2(i) _'• cgnh AB ed phuong trinh la x - y + = va AB = 2CD L ^ phuang trinh cae canh edn lai eiia hinh chii nhat Phan tich bai toan: Bai todn ed gia tiuet kha phiic tap, ddi hdi HS phdi huy dpng tat cd cdc Itien thiie: tir kien 22 thiie da hpc (tinh ch4t cda hmh chii nhgt) lln kien thiie dang hpc (1§P phuang tiinh duong thdng), Nhimg neu ttong qua trinh gidng dgy (bai phuang trinh dudng tiidng), GV hp tiiong dupe kiln thiic (cac yeu to can thilt de ^ phuong trinh dudng tiiang) va HS nam vung dupe cac kiln tiiuc ^ thi vipc gjai bai toan sS khdng ed gi khd khan - Gia thilt: Biet hmh chii nhgt ABCD, suy raAB//CD, AB ±AD;AB LBC Biet AB:x-2y + = 0, suy vl ph^i Vgy phuang trinh canh CD •.x-2y-'i = ^ - Tuong ti; tim c: Do AB = 2AD suy d{I,AD) = 2d(I,AB) o|c'+l| = O _ • Vgy phuong ttinh AD vd BC lan lupt la 2:t + _V + = v d j : + ; ' - = TB.UeJNG DAI HOC DONG THAP 3.2.2 Bien phdp 2: Tap luyin cho HS biit nhin nhgn tinh hudng dgt dudi nhieu gdc khdc va biet gidi quyet van di bang nhiiu phuang phdp khdc nhau, lua chgn cdch gidi toi iru Bien p h ^ giiip HS nhin nhgn bai toan duoi nhieu hinh thiie, nhieu gde dp khac nhau, Tir dd, HS se tim tdi dupe nhieu each gidi khdc cho mpt bdi toan va tim dupe phuang phap giai dpe dao Dieu ren luyen tu diQ' sang tao, dpc Igp giai quyet van de eho HS Vi dy 2: Viet phuang trinh dudng ttdn npi tiep tam giae ABC biet phuang trinh cac canh AB:lx+Ay-6=(y, AC:Ax+3y-\=(i, BC:y=Q Phan tich bai toan - Hudng dan HS ve hinh Tap chi Khoa hgc sfi 27 (08-2017) dung cdng thiic khodng each dyI,ABj = r ta tim duoc tpa dp tam / GV: Hudng thit ba gpi l{a;b) thi xet xem a, b phdi thda dilu kipn gi (dua vao tpa ciia A, B, cy HS Do dudng ttdn ndi tiep tam giac ABC nen t a m / ( a ; ) phdi thda—^(-2;3) 4x + : v - l - [>' = ^ ' Tuong tp,tatim s ( ; ) , C - , 3x+4y-6=0 4x+3y-l==0 Htnb2 - Ddt eau hdi goi y cho HS tim phuang an ttd ldi: GV: Cd till tim dupe ylu to ndo biet phuong trinh ba canh ciia tam giac? HS: Cae dinh A, B, C lan lupt la giao diem cua cae cgp canh AB va AC, AB va BC, AC vd BC Ta tim dupe tpa dp ba dinh A, B, C GV: Tam dudng ttdn npi tiep tam giac ABC duoc xac dinh bang each ndo? HS: Cdba hudng: + Tdm I la giao cua ba dudng phan gidc ttong cua tam giae + Ap dung tinh chat khoang each tir tam I den ba cgnh bang + Gpi l(a;h) la tam dudng ttdn npi tiep tam giac ABC Vi B, C nam tten trpc Ox spy l{a,b),b>ii^l{a;r); Phuong trinh cac dudng phdn giae ttong va ngodi cua gdc A la 3x+Ay-6 _^Ax^3y-\ \x-y + 5^0 0) V3^+4' " U^+Z" [x + ; ^ - l - (2)' Thay lan lupt toa dd ciia B, C vao vl tiai cua (1), ta ehpn duoc (2) la phuong trinh dudng phan giac ttong cua gde A Phuong trinh cac dudng phan giae ttong va ngoai ciia gdc B la 3JC + ; ' - \Zx-y-e = Q (3) — ±—_ ^ + V o ^3^+4^ \x+3y-2 = Q (4) Thay lan lupt tpa dp ciia A, C vdo ve ttdi eua (4), ta chpn duoc (4) la phuong ttinh dudng phan giac ttong eiia gdc B Gpi l{x;yj vd r Id tam va ban kinh dudng trdn npi tiep tam giae ABC Khi dd tpa dp / la nghiem eua he phuang 'x + y-\ = Q trinh J " ' -^ * " Cndi he ta tim dupe [x + 3^- - = = i h a y / [ - , - ] , Suyrar=^(/,SC) = - , S = p.r=> r = - Ap 23 Tap chf Khoa hoc so 27 (08-2017) TRUONG DAI HOC DONG THAP Vgy phuong trinh duong tron ngi tiep tam giac^Cla(^x-ij +[y-^j =i Vay phuang trinh duong tion n^i tiep tam giac ABC »(-3