Bgch Phuong Vinh Tap chi KHOA HOC & CONG NGHE 86(10) 227 23 I iTNG DUNG BAN DO TlT DUY TRONG DAY HOC GIAI TOAN HINH HOC 9 GOP PHAN REN LUYEN CHO HOC SINH MOT SO HOAT DONG TRI TUE Bach Phuong Vinh Tnrd[.]
Bgch Phuong Vinh Tap chi KHOA HOC & CONG NGHE 86(10): 227-23 I iTNG DUNG BAN DO TlT DUY TRONG DAY HOC GIAI TOAN HINH HOC GOP PHAN REN LUYEN CHO HOC SINH MOT SO HOAT DONG TRI TUE Bach Phuong Vinh Tnrdng Dgi hoc Sir pham - DH Thdi Nguyen TOM T A T Ban dd tu (BDTD) cdn goi la so dd tu duy, lugc dd tu duy, la hinh thiic ghi chep nham tim toi, dao sau, md rpng y tudng, he thdng hda mpt chii de hay mpt mach kien thiic bang each ket hgp viec sii' dung ddng thdi hinh anh, dudng net mau sac, chu' viet phii hgp vdi cau triic, hoat dong va chirc nang ciia bo nao, vdi sir tu tich cue khdng nhung tao cho hoc sinh (HS) sir hirng thii hoc tap ma cdn gdp phan thuc hien doi mdi phuang phap day hoc (PPDH) a trudng thong Do vay, cd the iing dung BDTD day hpc giai loan hinh hoc Idp gdp phan phat trien cho HS mot sd hoat dong tri tue (HDTT) Til' khoa: hogt dgng tri tue, phdn tich, tdng hgp, chieng minh, hoc sinh Phat trien tu cho HS va giang day kien thirc ve toan hge ludn la mdt nhung nhiem vu quan trgng hang dau ciia ngudi giao vien (GV) day toan Nham hudng HS den mdt phuo'ng phap (PP) bgc tap tieh cue vii tu chu, ngudi thay khdng chi ciin giiip HS kham pha cac kien thire mcVi ma cdn phai giiip HS he thdng dugc nhung kien thirc dd Viec xay dung dugc mdt "hinh anh'' the hier mdi lien he giii'a cac kien thirc se mang lai nhung lgi ich dang quan tam ve cac mat: ghi nhd, phat trien nhan thirc, tu duy, dc tudng tugng va kha nang sang tao Mdt nhung cdng cu het sire huu hieu de tao nen cac "hinh anh lien ket" la BDTD Bai viet nham gidi thieu tdm luge nguyen ly nen tang ciia BDTD, irng dung BDTD day bgc giai toan hinh hge sir dung phan mem ve BDTD Concept Draw Mindmap Pro.v5.2.2 (tai tir mang internet), gdp phan ren luyen cho HS mgt sd HDTT KHAI NIEM, NGUYEN LY VA CACH LAP BAN DO TU DUY BDTD (Mind Map) la mgt binh thirc ghi chep su dung mau sac \a hinh cinh de md rdng va dao sau cac y tudng [5] Ky thuat tao loai Email: bachvinhtniayahoo.com biin dd ggi la Mind Mapping va dugc phiit trien bdi Tony Biizan vao nhung nam 1960 BDTD la mdt cdng cu td chirc tu Day la PP de nhat de chuyen tai thdng tin viio bd nao cua ban rdi dua thdng tin ngoai bg niio Nd lii mdt phuong tien ghi chep day sang tao vii rat hieu qua theo dimg nghTa ciia nd "Siip xep" y nghT eua ban BDTD la mdt lugc dd dugc sir dung de tiie hien tii' ngu' y tudng, nhiem vu, hay cac muc dugc lien ket va sap xep tda trdn quanh tir khda hay hinh anh trung tam BDTD la mdt PP dd hga the hien y tudng va khai niem Trong BDTD, thdng tin dugc ciiu tnic hda theo each gidng nhu bd nao HD BDTD cd the dugc tao bang nhieu each khac nhau: tren giay, tren bang hoac tren may tinh vdi cac phan mem irng dung hay cac phan mem tao BDTD Vo'i each the hien gan nhu- cc che HD ciia bg nao, BDTD cd y nghTa quan trgng day bgc vi nd dem lai mdt each tiep can mdi, phi tuyen viec kien tao y tudng, kien thirc va suy nghL nen nd lam chuyen bien tich cue mdi tuong tac giua giao vien vii HS, se giup cho viec day bgc sang tao hon, tiet kiem thai gian, ghi nhd tdt hon, nhin thiiy birc tranh tdng the, biet td chirc va phiin loai 227 Bgch Phuang Vinh Tap chi KHOA HOC & CONG NGHE suy nghT Tony Buzan lii ngud'i di dau viec nghien cuu tim HD cua bg nao Theo Tony Buzan thi "mot hinh anh cd gia tri hon ca ngan tii" va "mau sac cung cd tac dung kich thich nao nhu hinh anh Mau sac mang den cho BDTD nhung rung dgng cdng hirdng, mang lai sire sdng va nang lugng vd tan cho tu sang tao" Sir dung BDTD day bgc giiip ngudi hge biet xac dinh va liet ke y tudng quanh chu de cho trudc Sau dd tim mdi lien ket giua cac y tudng va phan loai chiing cho BDTD trd nen cd he thdng va de phan tich Trong in(5t sd trudng hgp BDTD giiip ngudi hge biet xac dinh van de va dua dugc each giai quyet phii hgp Nd cting giup ngud'i hge ghi lai va trinh bay y tudng mdt each true quan Nhiing yeu td lam eho BDTD cd tinh hieu qua cao: BDTD da the hien ben ngoai each thirc ma nao bg chiing ta HD Dd la lien kdt, lien ket va lien ket Mgi thdng tin ton tai nao bg ciia ngudi deu can cd cac mdi ndi, lien ket de cd the dugc tim thiiy va sir dung; Viec sir dung cac tir khda, ehii' sd, mau s^c va hinh cinh da dem lai mdt cdng dung ldn vi da huy ddng ca bcin cau nao phai va trai cung HD Sir ket hgp se lam tang cudng cac lien ket giira ban cau nao, va ket qua la tang cudng tri tue va tinh sang tao ciia chu nhan bd nao Trong day hge mdn toan cd the sii' dung BDTD day hge kien thirc mdi, cimg co dn tap he thdng hda kien thiic, kiem tra danh gia ket qua hge tap va phat huy nang luc sang tao ciia HS kha gidi Cach lap BDTD ([1] tr 12-14) Bu'd'c 1: Chgn hinh anh trung tam hay tir khda Hinh anh trung tam la mdt hinh anh, hinh ve can phat trien hay tir khda (tii' trung tam) la ten ciia mdt bai ten mdt chii de hay mgt ndi dumg can khai thac Bude 2: Ve nhanh ciip mgt Ccic nhanh cap mgt lii ndi dung chinh ciia chii de Bude 3: Ve nhanh cap 2, cap 3, va hoan thien BDTD Cac nhanh cap 2, cap 3, la cac 228 86(10): 227-231 nhanh ciia nhanh trudc no hay la cac y ciia ngi dung cua cac nhanh trudc dd Mgt sd ggi y ve BDTD; - Bat dau tii' hinh anh trung tam hay mdt cum tir ten chu de giiip HS tap trung vao chti de va gay thii cho HS - Su' dung mau sac, vi mau sac cd tac dung kich thich nao nhir hinh anh - Ve cac nhanh chinh cap mgt tir hinh anh trung tam ve cac nhanh cap hai tii' cac nhanh cap mgt bang cac dudng ke thang, dudng cong cd mciu sac khac nhanh mau nao thi chu viet tren nhanh cd mau - Mdi hinh anh hay cum tir lien quan den nhanh nao nen dirng dgc lap va nam gan dudng cong cua nhanh - Tao mgt kieu BDTD rieng cho minh (kieu dudng ke, mau sac, chfr viet ) - Nen dimg cac dudng cong nhieu hon cac dudng thang vi dudng cong thu hiit dugc su chii y ciia mat hon - Bd tri thdng tin deu quanh hinh cinh trung tam - Chinh sii'a, them bdt thdng tin, them bdl nhanh cho hinh thirc dep, chir viet rd U'NG DUNG BDTD TRONG DAY HQC GlAl TOAN GOP PHAN REN LUYEN CHO HS MOT SO HDTT Trong day hoc giai toan co the sir dung BDTD hd trg dn tcip, cung cd he thdng hda kien thire, ren luyen kT nang giai toan va phat huy nang luc sang tao ciia HS kha gidi Chimg tdi trinh bay iing dung BDTD day hge tim Idi giai va khai thac bai toan (BT) hinh hge 9, gdp phan ren luyen cho HS mgt sd HDTT (phan tich, tong hop, tuong tu, khai quat hda, phan chia trudng hgp, lat ngugc van de .xet tinh giai dugc ) va boi dudng kha nang sang tao cho HS kha gidi Cd rat nhieu phan ve BDTD, chimg tdi su dung phan mem Concept Draw Mindmap Pio.v5.2.2 (tai tii' mang internet) &k lap BDTD tim Idi gicii va khai thac BT hinh hoc Bgch Phuang Tap chi KHOA HOC & CONG NGHE Vinh Nham giiip HS nhin thay birc tranh tdng the va chi tiet ciia HD giai toan va phat trien BT Nhd hinh anh ciia BDTD va cac y tudng HS biet each lien tudng den nhu'ng kien thu'c can huy ddng de giai BT, biet cimg cd he thdng hda kien thuc, biet tim nhieu ldi giai ciia BT, biet sang tao BT mdi tii' BT da cho, biet hinh khai quat lai tri thuc PP tir tri thirc ndi dung Qua dd HS dugc ren luyen kT nang giai toan va phat trien tu Sau day la hai BDTD tim Idi giai va khai thac hai BT hinh hge 9: 86(10): 227-23 I Cho nira dudng trdn (DTr) tam O cd dudng kinh AB Ggi Ax, By la cac tia vudng gdc vdi AB (Ax, By va nira dudng trdn thugc cimg mdt nira mat phang bd AB) Qua diem M thudc nira dudng trdn (M khac A va B), ke tiep tuyen vdi nira dudng trdn dd, nd cat Ax, By theo thii' tu d C va D Chirng minh rang cob = 90° Cho tam giac vudng ABC (A = 90") cd AB < AC ndi tiep dudng trdn (O), ve dudng cao AH va ban kinh OA Chirng minh ring OAH = B - C BAN 0 Ttr DUY TIM LOI GIAI VA KHAI THAC BAI TOAN GOP PHAN REN LUYEN MOT SO H B H CHO HS LCTP 91 I I ' i - Van d|irH| TC liep tuyen c i t ntiju het hqp vo>: - T ^ cic gdc tiong T.glic hoic long hai goc (uitg phi clii hinh thing vuong; • Hoic TC JUong phan giic cua gdc lie bii B il mis I vunnji ill) I ' Vin dung TC tiep tuyen cit ket hop vdi: TC tiJ'l I giic ngi tiep hoic TC cua hai JI vuong goc, tong tong \ j;nc fii Ch iB Qm dien M M m ili/i'mf,' rri'i nira dumig iron idm H.^ S_r vii nim thug cil duirng dudng nira dirinig Iron (M khiic m STl.l (.hii niia il\tun° trim tiim dm\g kinlj 4B (jfi.ii By / li ck tiu mnnj gk viti iH (.it, Ry VA BUU Dh Ihuk dins ">?' '"'•'' "'^f / _ '""V>-./ \ lam ihtmg i.mh AB Gfi It By lit phang hii ,\Hl Trin It lay dim C hat i i if ditinii lliUni mmg f/ii nn OCtai cil ,-!)• lai D Chiing minh VD la Ikp luyin cua Dir lOj kt fiep luyen minh j riH b& nira rung gi'ic C()f> = h\ (1) OCOD la cac dudng phin giac cuj guc ke bii = > dpcm y ^ Iti^ \ '/ ^ cit iii.i,, \ ^ [7) T« giac ABDC la hinh ^ ^ - - _ _ ^ ' thang vudng = > Tgiac COO vudng tai = > '" iS.I) V.diuig IC soc nnl iltp va gac A tam Cling chin tn^l cun;^ til hinh ro: OJ=Bi ;6^ = \ mill diim nm (ri'Ji r\m dit\')\g trim Im chi/s goc COD -VJn dyngTC •'• ; * " „ iD.Hnhsiiltogik(00 ck lia mnj! ^ik iS (ix, Hy I'li nira DTi Ihu^ ciini; mpt niia mat p ; j/ phki bj.iB) fren ,ix lay tiim C hai iJpcm 15.2) Xel hai tir giac noi Qtp ACMO & BDMO: (i dmti Unh iH va I' In dim bit ii ivim w\ dmin \H Oi^i I \ Hy la ck lie mill; ^oc wi iB Lix Hy iii nira linrni; tron thuoc ciing mgi i\ira mil phiing bit iBj, duirnv (/lanj vuiinj goc m MP tai i/ M/.lc, Bl'lanluijiiMCva0 (/IUTI;'minhraii^ ih-.-^y 1^2.1) O.^ A va 0, - H , (gocDl cimgchfln I -> a 0^ = r ( B , = 180'- (.r^ t £ ) - 90' dpcra: (SJ.2) 0, =.\1 va Oj=.\l, (g6cnl ciing chan Iciingi aptnu '.fl Bl!.} Cho M la moi Jim niim tm nuij dmij^ iron ijm u' drni^ kinh ,-lff vii P w diim hdi ki nam trin dum^ \B liim^ If phia ngooi Jim ihim^ mn^ ih^n'j l S J i l C = A, va D._ = B igoc nl cune rhan cung) C + D = A , + B = ' = apcni ihartj^ AB G()( Ax By la dk Jitipi}; gdc viri iB Jmjo jkaiij^ n/iing ^oc voi MP loi 1/ I'df is Hy !aii lutil (o; C vii D ('bini^ minh rjnj; iTo - v / I-i) tron lm BT 1.4 Cho M /li m{)i diem nim iren nUa iii dirijn^ kinh IB va P la dim duirn" ihaii^ AH (i{ii (.v, Hy la cdc duifn^ duiw^ r hat ki tren lhan» I'Hii/i;; / ^^ L jj/if viri AB Dtrimg thang vuong goc vm MP Igi \f cat -(.v, By Un kifl tgi C va I) Chimg minh rang \ i cT'f)=*r aC ' r /o (.S) HT I.S Cho \l !(i mot tfian luvn trill f)Tr tam () co liii&iif; kinh Mi vo I' la tiiati bat ki iiai dt AH