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/ SAI LAM LIEN QUAN DEN PHlTONG TRINH MAT PHANG T f CACH TIE? CAN CUA SUY LUAN Tl/OfNG TlT VA HOP DONG DAY HOC BUI PHLraNG UYEN'''' TOM T A T Du dodn sai ldm lien quan den mpt tri thiec vd xdc dinh nguo[.]
\/ SAI LAM LIEN QUAN DEN PHlTONG TRINH MAT PHANG T f CACH TIE? CAN CUA SUY LUAN Tl/OfNG TlT VA HOP DONG DAY HOC BUI PHLraNG UYEN' TOM T A T Du dodn sai ldm lien quan den mpt tri thiec vd xdc dinh nguon goc cua cdc sai ldm la cdn thiel qud trinh dgy hpc (DH) Tie cdch tiep can cua suy ludn tuang tu vd hap dong day hpc, chung toi trinh bay mpt nghien cuu ve sai ldm cua hpc sinh Hen quan den phuang trinh mat phdng thong qua mot ihuc nghiem suphgm Tir khda: suy ludn tuang tu, sai lam, hgp dong day hpc, phuang Uinh mat phdng ABSTRACT Errors related to the plane equation through analogy and teaching contract approach Predicting possible errors related to the knowledge and finding their causes are necessary in the teaching process From analogy and teaching contract approach, the ; researcher presents a sludy of errors of students related to the plane equation through a j pedagogical experiment Keywords: analogy reasoning, errors, teaching contract, plane equation Bat van de I Suy luan tuong tu la phep suy ludn quy nap khdng hoan toan nen khdng phdi mpi J ket ludn deu diing Do do, dimg suy ludn tucmg tu day hpc todn ciing ed t h i ddn , den sai Idm Khi dd, cd nhung quy tac cua hgp ddng day hpc d hpc sinh (HS) lien quan den kien thuc mdi dugc suy mpt each tuong tu tir cdc quy tac cua kien thiic cii, nhung nhung quy tac mdi khdng hoan toan diing mpi tinh hudng Vdi each tiep can nay, chimg tdi tien hdnh nghien ciru mdt sd sai ldm cua HS hpc phuang J,, trinh tong qudt (PTTQ) cua mat phang i) 2.1 Cor sd li thuyit Suy ludn tuvng tu' Danh tir tuong tu ed ngudn gde tir "ovaXoyia", mdt tir todn hpc cua Hi Lap Tir t cd nghTa la su bdng cua hai ti sd Chdng han, 3:4::9:12, tiic la he hai sd va tuong tu vdi he hai sd va 12 vi - = — [5, tr.81-821 t ^ • • 12 ^ ' ^ Theo G Polya (1977), tucmg tu la mot kieu gidng nao dd Nhiing ddi tugng & phii hgp vdi nhung mdi quan he dugc quy dinh la nhirng ddi tugng tucmg i ty Hai he la tucmg tu neu chiing phu hgp vdi cdc mdi quan he xdc dinh rd " NCS Trudng Ogi hpc Su pham TPHCM; Email: bpuyen@ctu.edu.vn TAP CHi KHOA HOC BHSP TPHCM S6 6(72) nam 201S rang giOa nhOng bp phan tucmg ung Vi du tam giac mat phang tuang ung Hi dien khong gian [6, tr 24-26] Vat lam ca so cho tuang tu, la phan tii de so sanh goi la nguon; do, nhitag vat duoc giai thich, duoc hoc nho su dung tuong tu goi la dich Trong DH toan, vice sir dung tucmg tu la chuySn nhitag tu tuong tCt kiSn thtic ngudn kien thiic dich Do do, suy luan tuong tu co cac iing dyng: Xay dung mot nghla nao cho tri thlic, xay dtmg gia thuySt, dung tuang tu de giai bai tap toan cho HS Suy luan tuong tu giup HS tim toi, kham ph4 kiSn thiic mai Tuy nhien, khong phai moi suy luan tuang tu dSu cho k a luan diing Di6u la suy luan tuong tu la suy luan quy nap, khong phai la suy luan diln dich, nen nhimg ket luan du kien chi la gia thuySt Thuc ti diing dan ciia nhitag suy luan tuong tu khong duoc bao dam, ma phai duoc kilm chiing Vi vay, su dung suy lujln tucmg tu, HS co thS mJc phai sai ISm qua trinh hoc tap 2.2 Quan nifm vi sai ISm Theo thuyit hanh vi, sai 13m phan anh su thiSu hieu biet hay su vo y ma thoi Ngugc lai, hpc thuyjt kiln tao cho rtag sai ISm va nhan sai lam dong vai tro xay dung hoat dgng nhan thirc, bai vi tao su mat can bSng he tu cua chli thl, viec nhan sai ISm tao didu kien thuan lgi de vugt qua no va lam sinh mgt thl can bang gia moi Sai lim khong phai la mgt su kien thit ylu xay mot qua trinh: no khong nam ngoai kiln thiic ma la mgt bieu hien ciia kien thtrc G Brousseau (1976) nhan manh: ^Sai ldm khong chi dan gidn la thieu hiiu biel, ma hd hay ngdu nhien sinh , md cdn la hgu qua mot kien thtrc truac ddy timg td CO Ich, dem lgi thdnh cdng, nhtmg bdy gia lal td sal hogc dan gidn la khdng cdn phii hap nUa Nhihig sai ldm thuoc logi ndy khong phdi thdt thttang hay khdng du dodn duac Chiing tgo thdnh chudng nggi.'' (dan theo [1, tr.57]) G Brousseau cho rang duong di cua HS phai trai qua viec xay dtmg (tam thai) tir mgt so kien thirc sai hoac chua hoan chinh, boi viec y thirc dugc dac trung sai lam se la yeu to cau ndn nghia ciia kien thirc ma ta muon xay dung cho HS 2.3 Ll'Ihuyet nhdn chung hgc Quan he the che, quan he cd nhdn Quan he ciia the che I vdi tri thiic O, R(I, O) la tap hgp cac tac dgng qua lai ma the che I co vai tri thirc O No cho biet O xuat hien o dSu, nhu the nao, t6n tai sao, CO vai tro gi I [l,tr 317] Quan he ca nhan X vai tri thiic O, R(X, O) la tap hgp cac tac dpng qua lai ma ca nhan X co voi tri thirc O No cho bilt X nghi gi, hieu nhu thl nao vl O, co thl thao tac O Viec hgc tap cua ca nhan X ve doi tugng tri thiic O chinh la qua trinh thilt lap hay dieu chinh m6i quan he R(X, O) Hiln nhien, d6i vai mgt tri thiic O, quan he ciia the che I, ma ca nhan X la mgt phan, luon luon de lai dSu Sn quan h? R(X,0) Muln nghien cim R(X, O) ta cdn dat no R(I, O) 40 I A P CHI KHOA H O C D H S P TPHCM Biii Phiromg Uyen To chuc lodn hpc Hoat ddng toan hpc la mpt bp phdn ciia cac hoat dpng mdt xa hpi, thuc te todn hpc cung la mdt kieu thuc te xa hpi nen can thiet xdy dung mdt md hinh cho phep md td va nghien ciiu thyc t i Chinh quan diem dd ddn d i n khdi niem praxeologle Ddn theo [1, tr 319], Chevallard chi mdi praxeologie la mdt bd gdm phdn \T, T, 0,0], dd T la kiiu nhiem vy, r la kT thuat cho phep giai quyit T, Id I cdng nghe giai thich cho kT thudt r , la li thuyit giai thich cho Mot praxeologie , md eae phan deu mang ban chat toan hpc dugc gpi la mdt td chiic toan hpc Do do, viec phan tich eac td chitc toan hpc lien quan d i n mdt ddi tugng tri thiic la i cdn thiet qua trinh day hpc tri thirc bdi nd cho phep vach ro mdi quan he the che va quan he cd nhdn ddi vdi tri thu:c Tir dd, cd the tim hieu ngudn gdc ciia nhung sai Idm m a HS gap phdi hpc tap tri thuc 2.4 Hap dong dgy hgc J H g p ddng D H la tap hgp nhtrng quy tac phdn ehia va gidi han trdch nhiem cua , mdi ben, giao vien (GV) va HS, ddi vdi cdc ddi tugng tri thirc toan hpc dugc gidng day Nd la tap hgp cdc quy tac boat ddng, cac dieu kien quy dinh mdi quan he giiia GV va j., HS [l,tr.339] Hgp ddng D H dugc xem n h u la cdng cy de nghien ciiu sai lam cua HS va d u : doan nguyen nhdn cua cdc sai lam jjj Ldm thi ndo de xdc dinh cdc hieu luc cUa hap dong dgy hgc ilj Mdt phuang phdp nghien ciiu ed hieu qua cua hgp ddng DH la tao su bien loan jf he thdng gidng day cho cd the dat GV va HS mdt tinh hudng khdc la dugc gpi Id tinh hudng phd vd hgp ddng [1, tr 339] jjf T[[i oH D e tao r a m d t tinh h u d n g p h d v d h g p d d n g cd t h e tien h a n h theo cdc cdch sau: Thay ddi dieu kien sii dyng tri thiic; - Dat HS ngoai pham vi hgp thirc cua tri thirc dang ban tdi hoac nhtrng tinh hudng m a tri thiic dd khdng glai quyet dugc; Dat GV trude nhiing ung xir ciia HS khdng phii hgp vdi nhiing dieu ma G V mong IJ dgi Chang han dd la nhung cdu trd ldi khdc la cho cho mdt tinh huong jjj Thiet ke nhung tinh hudng n h u vay va quan sat iing xir ciia G V va HS, phdn tich sdn phdm ma hp tao de thay hieu luc ciia hgp ddng: viec cdc quy tac cua hgp ddng ^ vdn chi phdi ling xir ciia ho ^j, Xac dinh cac sai lam lien quan den phuong trinh tdng quat cua mat phang lijii ddy, chung tdi xet ddi tugng O la '"PTTQ ciia mat phang", the che I la the chi j,f, DH toan ldp 12 Sach gido khoa (SGK) dugc sit dyng la Hinh hpc 12 (Ca bdn vd Ndng a cao) TAP CHi KHOA HOC DHSP TPHCM S6 6(72) nam 2015 3.1 Cdc kiiu nhiem vu liin quan den phwang trinh tong qudt cua du&ng thdng va mat phdng Ddu tien, chimg tdi xin de cap hai kieu nhiem vu ve phuang trinh dudng thdng •4 Kieu nhiem vu T l : Viit PTTQ cua dudng thdng di qua hai diim A, B phdn biet KT thudt r,: Chpn VTCP ii = ~AB = {a\b), suy VTPT « = (b;-a) Thay tpa dp diem A va n vdo phuang trinh (PT) A(x -Xf,)+ B{y-yj = «i- Kiiu nhiem vu T2: Viit PTTQ cua dudng thang di qua diim A va song song vdi dudng thang d (diem A khdng thude dudng thang d) KT thuat TJ : Chpn VTCP M = {a; b), suy VTPT h = (b; -a) Thay tpa dp diem A va n vao PT A{x-x^)+B{y-y^) = Q Hai kieu nhiem vy ndy khd quen thudc ddi vdi HS hpc PTTQ ciia dudng thdng KT thudt r, vd r, ndi tren la chien lugc tdi uu Vi vdy, HS cd the thuc hien hai kT thudt tren cho cdc bai todn thudc kieu nhiem vy Tl va T2 Tiep theo, chiing tdi xin de cap hai kieu nhiem vy lien quan din O i- Kieu nhiem vy T l ' : Viit PTTQ cua mat phang di qua ba diem A, B, C phdn biet KT thudt r,': Chpn2VTCP «,-^^B, w, = : ^ , suy VTPT h = [u„U^] Thay tpa dp diim A va h vao PT A{x-x^)-i-B{y-y^) + C{z-z^)^Q 4- Kieu nhiem vu T2': Viet PTTQ ciia mat phang di qua diim A va song song v6i hai dudng thdng d, d' phan biet KT thudt TJ ': Chpn VTCP H,, U,., suy VTPT « = [«^, w^ ] Thay tpa dp diim A va h vao PT A{x~x^) +B(y-y^) + C{z-z^) = Bang Thong ke s6 luang bdi tap theo cdc kiiu nhiem vu a SGK Kieu nhiem vu T, So lugng Kieu nhiem vu T,' So lugng TI Tl' T2 T2' 42 aut irnuung I r\r \_fni r\nurt n u o r^nor i rnoivi u^cn 3.2 Phdn tich cdc sai lam lien quan din cdc kieu nhiem vu Tl' vd T2' Chiing ta da biet giua dudng thang va mat phang cd dac diem tuang tu: deu la sieu phang khdng gian Euclide hai chieu va ba chieu, deu xdc djnh biet diem di qua va VTPT, cd PTTQ tuang tu Do do, cdch tim PTTQ cua mat phang cting tuong tu each tim PTTQ ciia dudng thang: hai kT thuat giai r,' va TJ 'ciia kieu nhiem vuTI', T2'neu d tren tucmg tukT thudt r, va r^ eua kieu nhiem vuTl,T2 O kieu nhiem vy Tl, HS thudng khdng cdn thuc hien viec kiem tra nao bdi sy phdn biet eua hai diem A, B la rd rang KT thuat r,' cho phep HS dua ldi giai dung A, B, C khdng thang hang Tuy nhien, diem A, B, C thang hang thi nd khdng phil hgp niia, bdi HS se liing tiing tinh W = [U,,MJ] = Trong trudng hgp nay, HS cd the cho rdng GV da cho de sai, ma khdng the dua dugc ket ludn phu hgp O kieu nhiem vy T2, kT thudt r^ mang Iai ldi giai diing, vi the HS cd the dp dyng vao ldi giai ma ciing khdng can su kiem tra nao Cdn d kieu nhiem vu T2', kT thudt TJ ' cho ldi giai diing trudng hgp d\k d' cat hoac cheo Khi d song song d' thi kT thuat khdng cdn phii hgp niia Tir cho phep chiing tdi dy dodn hai sai lam sau day: SLI: HS sie dung cong thiec VTPT n ^[«|,«,] md khong kiim tra linh thdng hdng cda ba diem da cho thuc hien kieu nhiem vu Tl' SL2: HS su dung cong thuc VTPT h = \uj, w^.] ma khong kiim tra vi tri tuang doi cua hai du&ng thdng dvdd' Ihuc Men kiiu nhiim vu T2' Viec HS khdng kiem tra tinh thang hang ciia ba diem (SLI) hay vi tri tuang ddi eda hai dudng thdng (SL2) Id cdch trinh bdy cdc bdi tap dang d cdc SGK Chiing tdi nhdn thdy rdng nhiing bai tap d SGK 12 khdng bao gid cd trudng hpp cho diim thang hdng va hai dudng thang song song Do vdy, mdt each ngam dn, HS khdng cd trdch nhiem kiem tra tinh thdng hang ciia ba diem A, B, C ddng trudc kieu nhiem vu Tl' va kiem tra vi tri tuang ddi cua hai dudng thdng dung trudc kieu nhiem vu T2' Ndi each khac, tdn tai nhihig quy tdc ngdm an cua hgp ddng day hpc HS thuc hien hai kieu nhiem vy T l ' vd T2' tucmg tu nhu cdc quy tdc ngdm dn thuc hien kieu nhi?m vy Tl vaT2 Bdng Cdc quy tdc cua hap dong day hpc Quy tac thuc hien Tl va T2 Rl: HS khdng cd trdch nhiem thuc hien vi^c kiem tra nao thuc hien kieu nhiem vuTl R2: HS khdng cd trach nhiem thuc hien viec kiem tra nao thuc hien kieu nhi?m vu T2 Quy tdc thuc hien Tl' vd T2' Rl': HS khdng cd trdch nhiem kiem tra tinh thdng hang cua ba diem A, B, C thuc hien kieu nhiem vu Tl' R2'; HS khdng c6 trach nhiem kiem Ua vi tri tuong ddi ciia hai dudng thang d \k d' thuc hien kieu nhiem vy T2' 43 I ttr wni r\nwtt n v ^ t ^ n o r i rnwivi j ( / u( / * / ' Tir nhung phan tich tren cho phep chiing tdi hinh mdt gid thuyet: Gia thuyit H: "Tdn tgi mol s6 sai ldm (SLI, SL2) cua HS hpc tap cdc kieu nhiim vu lien quan din PTTQ cua mat phdng co nguon goc tic su dp dung suy ludn tuang tu vd su ldn tgi cdc quy ldc cua hap dong dgy hpc gdn lien v&i kien thuc nay" Kiim dinh gia thuyit thong qua mot nghien ciiu thuc nghiem 4.1 Mo td th tec ngh iem Tinh huong sau day dugc thyc hien nhdm kiim nghiem gia thuyit H neu tren Tinh hudng duge thuc hien vdi HS ldp 12 da hpc bai PT mat phang vd PT dudng thang chuang trinh Hinh hpe 12 Pha HS giai bai toan sau thdi gian 30 phiit va nop lai bai lam cho GV Bdi todn 1: Cho diim A(4;l;2), B(5;-2;l), C(3;4;3) Tim mat phdng di qua diim A, B, C (x = l-2t Bdi todn 2: Cho hai du&ng thdng d:\ y^5-t , ^ ' ^ ^ - - = — Viil PTTQ [z=3+l cua mat phdng {a) di qua A(3;2;-4) vd song song v&i d, d' Pha GV va HS ciing sua bai 10 phiit: HS phat bieu, cac em khac nhan xet, bd sung va GV danh gid sau cimg 4.2 Phan tich tien nghiem 4.2.1 Cdc chiin luac Bdng Cdc chien luac cua hai bdi lodn Bai toan Bai toan S2-1: VTPTH,„,=[S„!;,.] Sl-1: A, B-C thing hang si-2: vTPTn,^^ J=[;4s,;5c] S2-2: VTPT>i|.|=[n"j,MA/'] voi M ed.M'^d' 4.2.2 Cdc bien dgy hoc VI: Bgc diem cdc diem A, B, C: thang hdng hay khdng thing hdng Ba diem A, B, C thang hang cho phep xem xet sai ISm thir nhit V2: Bgc diem duang thdng d, d': song song hay khdng song song Hai duang thang d//d' tao dilu kien xem xet sai I t o thir hai V3: Bgc diem mat phdng cdn tim Trong bai toan 1, mat phjng cin tim di qua dilm A, B, C thang hang nen co vo so mat phang bai toan 2, mat phfag (a) xac djnh nen HS cin tim dugc PTTQ ciia mat phang 4.2.3 Cdc ldi glal co the quan sdt duac i- Bai toan Sl-l:Tac6 AB = (l;-3-l), ^ C = (-l;3;l) nen A, B, C thing hang I AP CHI KHOA HOC DHSP TPHCM Bui Phwang Uyen Den ddy, HS cd the dua hai ket luan cho bai toan nhu sau; • Ket luan 1: Cd vd sd mat phang di qua diem A, B, C Ddy la ket ludn dung cho bai todn • Ket ludn 2: Khdng cd mat phang nao di qua diem A, B, C Ket ludn khdng diing Sl-2: l4B = (\;-3-\), ^ = (-I;3;I) => VTPTwj^^^j = []4S,]4C] = Vdy PTTQ cua mat phdng (ABC) la 0(x - 4) + 0(y -1) + 0(z - 2) = VTPTw^^, = [wrf,A^'] = (9;-7:11) Vdy PTTQ ( a ) : ( x - ) - ( y - ) + Il(2 + 4) = < » x - y + I Iz + - Ddy la ldi gidi diing cho bdi todn 4.3 Phan tich hgu nghi&m Chiing tdi tien hanh thir nghiem d ldp 12A8, Trudng THPT Chdu Van Liem, thdnh phd Can Tho vdo 20 thdng nam 2014 thdi gian 30 phiit Ldp 12A8 gdm 45 HS dugc hpc theo chuang trinh ndng eao Sau day la ket qua thuc nghiem 4-Phai Bdng Thong ke cdc chien luac cua HS doi v&i bdi todn Chien luac Sl-1 Ket luan Ket luan (6.67 %) (17,78%) Chien luoc Sl-2 34 (75,55%) Chien lugc khac (0%) Chien lugc uu the bang thong ke la chien lugc Sl-2 (75,55 %) Nhu vay, hau het cac em diu tinh VTPT n = r.4S,BC] rli suy PTTQ cua mat phang (ABC) ma khong kiem tra tinh thang hang ciia cac diem A, B, C truoc Dieu dan den sai lam tim mat phang Bai lam ciia HS Nguyen Thy minh hga cho trugng hgp la: " ^ = (l;-3;-l),fiC=(-2;6;2) £»«,„., = [ I B , S C ] = (0;0;0) Mat phdng (ABC) di quaAvg cd VTPT n = (0; 0; 0) la 0(:t-4) + 0(>'-l) + 0(z-2) = 0c=.0jr + 0>'+0z=0 " 45 I f\r uni r\nuM n u u u n ^ r i n-iuM Si) (>{/£) nam £ui Bang Thong ke cdc chien luac cua HS d6i v&i bdi todn Chiln luac S2-1 Kit luan Kit luan Khong ket luan Chien luoc S2-2 Chiln lugc khac 13 (28,89 %) 21 (46,67 %) (11,11%) (13.33%) (0%) Chien lugc chiem da so bang thong ke la S2-1 (86,67 %) Hau het cac err deu tinh VTPTw^^j =[wj,u^,] = ma khong kiem tra vi tri tuong doi ciia hai duonj thang d vkd' Do do, cac em da bo litag ma khong ket luan hoac ket luan sai Bai lam Clia HS Yen Vy minh hga cho truang hgp nhu sau: "Tacd: 5^ = (-2;-l;-l) S^, = (2;1;-1) =>S|_, =[i/j;i7^,] = (0;0;0) => khong tdn tgi {a)." Chi CO HS (13,33 %) nhan ta dugc ducmg thang d song song voi d' va giai diing PTTQ cua mat phang theo chien lugc S2-2 J-Pha Sau HS da giai hai bai toan va nop lai bai lam, GV va HS cimg thao lu|n S tim lcri giai dung cho bai toan Kit qua dli thoai giita GV va HS (dugc trinh bay phu luc) cho thiy cac em da mic phai sai lim vilt PTTQ cua mat phing Cac sai lam ton tai mpt quy tac ngim in thuc hien cac kilu nhiem vu T l ' va T2': tinh VTPT dieo cac cong thlic da bilt ma khong thuc hien viec kilm tra nao Vi cac bai tap truoc day SGK khong co Uuong hgp gilng vol hai bai tap da cho nen n£u vin thtrc hien theo each lam thi khong lai loi giai dung cho bai toan Han ntra, cat cau tra lcri cua HS nhu "day la cdch em da ldm nhitng bdi ldp truac", "tuangty nhu cdc bdi todn truac day, " cho thiy ling xii cua cac em vin khong thay dli dimg truoc mgt tinh hulng mai Mat khac, thoiig qua qua trinh thao luan cho thiy HS da timg buac nhan dum dac diem cua ba dilm A B, C thitig hang va khong thl tinh VTPT dua vao tich co huong hai VTCP cira hai duong thing song song Tii do, cac em da tiln hanh A chinh de tim loi giai dung cho bai toan Dilu chimg to cac em da nhan va sin chtia sai lam nha nhimg thong tin phan hli tir moi Uuong Qua hai pha tinh hulng thuc nghiem cho phep khing dinh tinh diing dSn cua gia thuyet H 46 TAP CHI KHOA HOC D H S P TPHCM Biti Phwang Uyen K i t luan Sai lam la mpt phuang dien cua kien thuc va nd tdc dpng trd lai qua trinh boat dpng cua HS Qua dd, HS cd the tien hanh nhiing dieu chinh can thiet de xay dung nghia cua kien thiic thu nhan dugc Cdch tiep can suy ludn tucmg tu va hgp ddng D H cho phep giai thich ngudn gdc ciia mdt sd sai Idm qua trinh hgc tap hpc ciia HS De khdc phuc sai lam, theo hpc thuyet kien tao, nen ddt HS vdo nhimg tinh hudng mdi gdn lien vdi sai lam Tinh hudng ndy tao cho HS nhiing xung dot nhdn thiic, cho phep hp khdng chi tu nhdn sai lam ma cdn nhdn cac quan niem ma hp da van dyng dan den nhiing ket qua mdu thudn Dieu dd giiip hp dieu chinh nhiing quan niem cii cua minh de xdy dung kien thiic mdi Va nhu vay, HS se chu ddng ban viec sua chiia sai ldm TAI LIEU THAM K H A O Annie Bessot, Claude Comiti, Le Thi Hoai Chdu, Le Van Tien (2009), Nhieng yeu to ca bdn ciia Didactic todn, Nxb Dai hpc Qudc gia TP Hd Chi Minh Bp giao due va dao tao (2009), Kinh hpc 10, SGK ndng cao, Nxb Giao due Ha Npi Bd gido dye va ddo tao (2009), Hinh hoc 12, SGK ndng cao, Nxb Giao due, Ha Ndi Bp giao due va dao tao (2009), Hinh hpc 12, SGK ca bdn, Nxb Giao due Ha Ndi Nguyen Phii Lpc (2010), Dgy hpc hieu qud mdn Gidi tich tru&ng thong, Nxb Gido due Viet Nam, Ha Ndi G Polya (1977), Todn hpc vd nhuTigsuy ludn cd li, quyen 1, tap 1, Nxb Giao due Ha Npi G Brousseau (1976), Les obstacles espistemologiques et les problemes en mathematiques In : (1983) Recherches en didactique des mathematiques, 4(2), pp.164-198 PHU LUC Bien ban doi thoai gitra GV va HS pha GV: Nao, bay gid chiing ta se giai lai hai bai toan nhe Nhung trudc neu each giai, em nao co the nhac lai bai toan da hpc Uong hinh hpc 10 tucmg tu bai toan ? HS Tnic: Thua cd, bai toan "Viet PTTQ cua dudng thSng di qua diem phan biSt" GV: Bai toan giai bang each nao? HS True: Tim VTCPu ='AB = {a;b) => VTPTn = (6;-a) rdi thay vao PTTQ dudng thing GV: Tucmg tir, em nao co the cho cd biet em gial bai toan nhu the nao? Vi sao? HS Thy: Em tim VTCP la ^ , ^ ^ V T P T n ( ^ ^ ^ j = [ l s , ^ ] , rii em thay vao PT mat phdng Day la each em da lam nhiing bai tap trudc GV: Vay em tim VTPT dugc vecta nao va dirge PTTQ cita mat phang la gi? HSThy;Da, ^i^^^^^^=VAB,~AC~\ = Q va PTTQ cua mat phing (ABC) la Ox + 0>' + Oz = GV: Theo dinh nghTa, VTPT ciia mat phang phai la mot vecto khac Ci day em tim VTPT cua mat phdng bing nen chua phai la VTPT dau Em nao co each giai khac? IAP GHI KHUA MUU yMbh* I KHUM SO 6(/^J nam HSNhi: Em thay ^ - ( l ; - - l ) , ^ C = (-];3;l), suy AB = -AC hang, vi vay khong cd mat phang di qua A, B, C .iuij nen A B, C thing GV: Em da phat hien dimg diim A, B, C thang hang Nhung co mat phing nao di qua diem thing hang khdng cac em? HS Tiin: Da, ba diem A, B, C thang hang nen tao dudng thang Ma co vd so mat phing di qua dudng thang Vay co vd sd mat phang di qua A, B, C GV: Em Tiin phat biiu diing rdi eac em Cach giai ciia em Thy diing ba diem A, B, C khdng thing hang Vi vay, cac em nen kiim tra tinh thang hang ciia ba diem da cho trudc ap dung eong thdc ii,^f^.-\AB,AC\ GV: Bay gid ehung ta xet bai toan Em nao eo thi neu dugc mdt bai toan da hoc tuong ty bai toan HS Minh: Da, bai toan "Viet PTTQ ciia dudng thang A di qua diem A va song song vdi dudng thing d\ GV: Em co the nhac lai each giai bai toan khdng? HSNhi: Taed VTPT w^ =nj =(b\-a), sau thay vao PT dudng thang GV: Vay, em nao hay phat biiu each giai bai toan 2? HS Vy: Tucmg tir nhu cac bai toan trudc day, em tinh o, , =[w^;"j']- Nhung d day K(^, = nen suy khdng tdn lai mat phing (or) GV: Em nao co y kien khac? HS WM'^{\;-5;-A) Ngpc: Em liy M(l;5;3)e^,A/'(2;0;-l)ef/', suy Uj=(-2;-l;l) va la VTCP ciia [a], roi ti'nh VTPT«,^j-[M^,WM^] = ( ; - ; 1) Em dirac PTTQ 9;c-7>'+n7 + 3l = GV: Em eo the giai thich ro han tai phai diing cong thiic VTPT«, , = \uj,MM''\ ? HS Ngpc: Vi d//d' nen u^ va M^ ciing phucmg Niu dung cong thiie n , -[w^;w^.] thi "(«) =0 va se khong tim dugc VTPT day, vi [a] song song vdi d va d' nen {a) song song vdi mat phing tao bdi d va d' Niu liy M, M' thupe d va d' thi [a) song song vdi MM' Hai dudng thang dva MM' cit nen c6 thi tinh dupe VTPT «, ^{H/^aA^O GV: Dimg roi cac em Khi dudng thing d va d' eit hoae cheo thi cong thdc oj^j =[«j;«j.] se giup cac em tim dugc VTPT, nhung d/Zd' thi cdng thirc khong dung niia Cac em phai diiu chinh lai each tim VTPT thi mdi giai duge bai toan Do do, trudc tinh VTPT eae em nen kiim tra vi tri tuang ddi eua d va d' trudc d i biit diing cong thirc nao cho phii hgp Bay gid, co mdi Tiin va Ngoc len bang giai lai bai toan nav (Ng^y Tda so$n nhSn diroc b^i 17-6-2014; ngdy phan bien d^nh gi§: 01-8-2014; ngdy chip nh$n aSng: 22-6-2015) ... suy luan tuong tu khong duoc bao dam, ma phai duoc kilm chiing Vi vay, su dung suy lujln tucmg tu, HS co thS mJc phai sai ISm qua trinh hoc tap 2.2 Quan nifm vi sai ISm Theo thuyit hanh vi, sai. .. ph4 kiSn thiic mai Tuy nhien, khong phai moi suy luan tuang tu dSu cho k a luan diing Di6u la suy luan tuong tu la suy luan quy nap, khong phai la suy luan diln dich, nen nhimg ket luan du kien... thirc sai hoac chua hoan chinh, boi viec y thirc dugc dac trung sai lam se la yeu to cau ndn nghia ciia kien thirc ma ta muon xay dung cho HS 2.3 Ll''Ihuyet nhdn chung hgc Quan he the che, quan