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MDI 80 BIEN PHAP BOl D U S N I ; Til DDY THDAN N G H I C H CHD HDC SINH '''' TRONB DAY HDC GlAl BAI TAP TDAN H T B D I I N G PHllTHiiNG ThS THAI THI H O N G LAM Trong day hpc toan, dd''''i vdi hpc sinh (HS)[.]
MDI 80 BIEN PHAP BOl DUSNI; Til DDY THDAN NGHICH CHD HDC SINH ' TRONB DAY HDC GlAl BAI TAP TDAN HTBDIING PHllTHiiNG ThS T rong day hpc toan, dd'i vdi hpc sinh (HS), cdthe coi hoatddng giai bai tap toan l i hinh thifc chu ye'u cua hoatddng toin hpe Cae bai toin (BT) la mdf phuong tien rat cd hieu qua frong viec giiip HS nam vifng tri thdc, phit trien tu duy, hinh ki nang, kixao, biet iJng dgng toan hpc vao thuc tlln Bai viet de cap mdf sd bien phip boidudng tuduy thuin nghjch cho HS frong day hpc giai bii tap toan dtrudng phdthdng Hudng dan HS thuc hien cac thao t i c t u phan tich va tdng hpp nham thu nhan them thdng tin, ho tro cho viec tim each giai BT; ddng thdi, HS biet khai thac md'i quan he giira phep phan tich va tdng hpp tim each giai va trinh bay Idi giai mpt BT Phan tieh v i td'ng hgp la hai hoat ddng tri tue trii ngutyenhung lai l i hai mat cua mot qua trinh thdng nha't Chung la hai boat ddng tri tue co ban eua q u i trinh tu duy, nhifng boat ddng tri tue khie deu diin tren nen tang cua phin tich va td'ng hgp De phat frien tri tue eho HS day hpc toan, giao vien (G V) can chii frpng van de ren luyen kha ning phan tieh va td'ngh(;pcho HS Cd the hie'u, hoat ddng giai toin, thao tie tu phin tich va td'ng hgp dugc the hien: - Phin tieh yeu tdda cho, ye'u to can tim va can chdng minh ; - Thue hien phin tieh va tdng hgp xen ke; - Tieh BT da cho (thudng l i khd ban) nhieu BT phan, BT die biet, don gian hon, cud'i cung td'ng hgp lai de'thu dupe ket qua Vidu 1: Cho tam giae ABC Gpi (0,), (0^), (O3), (0 J la cic dudng trdn bang nhau, dd mdi dudng trdn (0,), (Oj), (O3) tiep xue vdi hai canh eua tam giic v i eung tiep xue vdi (0 J Chdng minh ring: cae die'm O^.tam dudng trdn npi tiep, t i m dudng trdn ngoai tiep tam giae ABC thing hing {hinh 1) Day lamdfBTkhakhdGia thief eiia BT chda nhieu ye'u td va HS rait khd djnh hudng de tim cac m i t xich lien kef gjifa gia thief vdi ket luan GV ed the td chdc, hudng d i n HS phan tich vatdng hgp degiai BT 54 Tap ehi Gido due so 325 THAI THI H O N G L A M Phan tich (phin tich gia thief): Hudng 1: Tu gia thiefmdi dudng trdn (9,), (0,), (O3) tiep xue vdi hai canh cua tam giic va bing fa suy dieu gi? Hinh Kef qua mong mud'n: 1) I = AO^ nBO^ r^CO, {V);2)OflJI/^B;Op^ilBC\OpjlAC{2') Hudng2{\6r)g hgp phan 1): Td(1') v i (2>), ta thu dugc dieu gi? Tu(r),(2-)^^.^.^(3') Hudng 3: Td gia thief cac dudng trdn (0,), (0^), (O3) eiing tiep xue vdi (OJ, ta suy dieu gi? T d , , = 0^0^= 030^=>0, la tam dudng trdn ngoai tiep A0,0203 (4') Den day, neu dd'i tugng HS la gidi, GV cdthe tiep tge hudng din cie em khai thac ketqua thu dupe tdcac he thdc (3'), (4') va sudgng phep vj tutim I de giai BT Tuy nhien, hudng tiep can l i khd dd'i vdi HS Lue nay, GV nen dinh hudng cho HS phan tieh kef luan eua BT Phan tich2{phar\ tich kef luan): De'chdng minh 1,0,0^ thing hing, ta can chifng minh dieu gi? Mgc dieh eua eau hdi niy la yeu eau HS xem xet kef luan, neu dugc mdt so cich thudng sd dgng de chifng minh ba die'm thing hang "Khi tap trung tu tudng vao muc dieh vi hudng ta't ei nghi luc vao viec thuc hien muc dieh dd, ehung ta di nhin tha'y cac phuong tien deditc^ketqui"{^; tr 121) Hudng 1: ziOfi = 180°; Hudng 2.-1, , , la anh cila diem thing hing qua mdt phep bien hinh (phep ddng dang, hoic phep ddi hinh); HudngS:^^^ * Khoa Toan -TnTOngDai hoc Vinh (kil /2014) tai phep v j t u V e d tam lampttrong die'm 1,0,0^ v i die'm cdn lai l i cap anh va tao anh tuong ifng; Tong hqp 1: Vdi l i tam dudng trdn ngoai tiep AABC, fa can chifng minh ton tai V ,: ^ , Phan tich 3:1 on tai V,,,,: - > ' )//A => n7-"I = • nhung lai cua ban thin nghia l i c i e em da tu thi'y dugc nhirng diing ke't qua n^,.ii^ = o de ke't luan (P)//A cai dung, eii sai, cai dugc va chua dugc kien *** thdc, kining eua minh Tren day la mdt sdbien phap su pham G V edthe' Wduff.-Trong khdng gian vdi hefpa ddOxy, cho su dgng de giiip HS viec tim tdi each giai BT va m i f e a u ( ) : ( x - l ) ' + ( : i ' - ) ' + ( r - ) ' = v a d u d n g nang cao nang lye giai toan, ddng thdi gdp phan hinh va phat trien cho HS each suy nghi theo hai thing A : i ^ = ^ = ^ Viet PT mat phing (P) chieu ed xu hudng trai ngugc • di qua M(4; 3; 4), song song vdi dudng thing A va tiep xue vdi mat eau (S) (1) G Polya Giai bai toan nhy the nao? NXB Giao diic.H 1997 CdHSgiainhusau:Gpi^(o;A;c)(fl'+A'+e^?iO) (2) Nguyen Ba Kim (chii bien) Phmmg phap day hpc mon Toan NXB Dai hoc supham, H 2004 la vecfophip tuye'n cua (P) Khi dd, PT eua mat phing (3) Dao Tam (chu bien) - Tran Trung Td chirc hoat (P) •.a(x-4)-^ b(y-3)->- c(i -4) = Vi dudng thing ddng nhan thirc day hpc mon Toan or trinrng trung hpc phd thong NXB Dai hpc supham, H 2010 Asongsong vdi mat phing {P)=>n,,.u^ = 0, frong (4) Nguyen Canh Toan Phmmg phap luan vat dd Wi(-3; 2; 2)la vecfochi phuong eua dudng thing bien chirng vdi viec hpc, day, nghien cuu toan hpc, tap NXB Dai hpc qud'c gia H 1997 ASuyra: -3a + 26+2c = O o o = —^—^ SUMMARY Gpi ^ ; 2; 3), R=3 lan lugt la tim va ban kinh cila Fostering and developing thinking for students mat cau (S) Mat phing (P) tiep xiie vdi mat cau (S) are important issues in teaching mathematics in \-3a-b-±_^ ''(''(''»='^«;^?:P^ (kil 1/2014) schools This paper mentions some measures to foster reverse thinking for students in teaching how to solve mathematical problems at high school Tap chi Gido due so 325 57 ... V,,,.: hieu chiu ngoan Bae Hd, dd ed cap anh em sinh ddi Can chpn mpt nhdm HS frong sdso em di duDai hdi chiu ngoan Bic Ho cho nhdm khdng cd cap anh em sinh ddi nao Hdi cd bao nhieu each chpn? A-^0,... nhu: - Thief ke Cd each chpn cap anh em sinh ddi Vdi mdi cac BT m i ktii giai HS phai su dgng phep td''ng hpp; each chpn cap anh em sinh ddi cd 48 each chpn ? ?Cho HS giaicicBT (edcung yeu ciu neu... ludn diing Trong toan BT tren, yeu cau HS giaj bing cich lien he vdi BT hpc, suy luan suy dien logic ddng vai trd chu ye''u ngupe; - Sau HS giai xong mdf BT cd khai thac Trong qua trinh tu duy, quy