II HyONGDANQUANLV SCrDUNG ^ TO CHIJrC HOAT OONC NHilN THllfC CHO HOC f INH TRONG DAY HOC DAI TOAN QUY TiCH TRONG KHONG GIAN Vdl SUTR0 GIUP CUA PHAN MEM GEOSPACW TrUdng Dgi hgc 1 Dgt van df Hifn nay, k[.]
II HyONGDANQUANLV.SCrDUNG ^ TO CHIJrC HOAT OONC NHilN THllfC CHO HOC f INH TRONG DAY HOC DAI TOAN QUY TiCH TRONG KHONG GIAN Vdl SUTR0 GIUP CUA PHAN MEM GEOSPACW Tr^n Viet CUdng Dgt van df Hifn nay, khdng phii nhgn vai trd to ldn cua eie phan mem day hpe dgy hpe Toan Tuy nhien, vifc sfl dyng phan mem dgy hpc nhfl the nao de dgt dfldc mue tieu dgy hpe li van de dang thu hut sfl quan tam cua ddng dio nhflng giio vien (GV) dgy Toin Bai toan quy tieh ndi chung vi bii toan quy tieh khdng gian ndi rieng li mpt nhflng dgng toin khd ddi vdi hpe sinh (HS) Trong bii viet nay, ehung tdi de cap den vifc td chflc hoat dpng nhin thfle trpng dgy hpe bii tpin quy tich khdng gian eho HS phd thdng vdi sfl trd giup eua phan mem GeospaeW Mpt sd vi dy minh hoa vifc td chflc hogt dpng nhin thfle dgy hpc bii toin quy tich khdng gian cho HS vdi s\t trgf giup cua phSn mem GeospaeW Vi dv Cho hinh lang tru dUng ABCAB'C ddy la tam gidc cdn vdi AB = AC = a, BC = bvdAA'=h Ggi P Id diem bdt ki trin dogn AA', E Id hinh chieu cua C lin BP Tim quy tich cua E P chgy trin doan AA' ' TrUdng Dgi hgcSUphgm - Dgi hgc Thdi Nguyin quy tich E li thupc logi trdn va se hfldng vio dd de chflng minh (Hinh 2) + Chuyen ve xet bdi todn hinh hgc phdng: Di thuin ldi eho vifc quan sat, chflng minh GV sfl dyng chflc nang "plan isole" cua phan mem de tich rieng mat phang (ABA') khdi hinh ling tru dflng {Hinh 3) Dfla vio hmh ve vi gii thiet cua bai toin HS de ding nhin thay BP H'E (H' li hinh chieu vudng gdc cua C len A'B') Viy quy tich Hmh I eua diem E P di ddng tren Di giup HS giii quyet bai AA' la thupc cung trdn HjHj toin niy, GV cd the khai thie eua dudng trdn dfldng kinh phan mem GeospaeW de hd B H ' ( H , v i H , lan Ifldtli hinh trd qui trinh td chflc cic hogt chieu vudng gdc eua H' len AB dpng nhin thfle cho HS vi BA') {Hinh 4) dgy hpc nhfl sau: • Hogt dgng 1: Tim hiin bii toin Md file" Vidu l.g3\V"HS quan sit hinh ve, ve hinh, xie djnh yeu td cd djnh, yeu td di dpng vi yeu td qui tich {Hinh 1) • Hogt dgng 2: Tim hfldng chflng minh bii toin + Du dodn quy tich: GV cho diem P thay ddi vj tri den mpt sd diem dgc bift, HS quan sat vj tri cua diem E Khi dd, bing trfle quan HS dfl doin Hlnh Nhdn bdi ngdy 2/2/2012 ll • TAP CHi THI^BI GIAO DUC-S6 78-2/2012 HUOINGDANOUANLV,SI)DUNG Hmh Hmh • Hogt ddng 3: Chflng minh bii toin Dfla vio hogt dpng vi sfl dyng suy lugn Idgie, HS de dgng chflng minh dflpc quy tich eua E P di dpng tren AA' li thupc cung trdn H^H^ eua dudng trdn dfldng kinh BH' (H, vi H^ lan Iflpt la hinh chieu vudng gdc cua H' len AB va BA') • Hoqt dgng 4: Minh hog qui tieh Sau HS xie dinh dvigc quy tich, GV eho diem P chay tren dogn AA' vi de lgi dau vet cua diem E HS se dUdc quan sit cich trfle quan quy tieh {Hinh 5) Quy tieh E tren hinh hoin toin trung vdi ket qui m i HS d i ehi dfldc chflng minh Vi du Cho hinh chdp S.ABCD cd ddy Id hinh vudng ABCD cqnh a, SA vudng gdc vdi mat phdng (ABCD) vd SA - a Ggi M la diem bdt ki trin doqn BC, ggi K Id hinh chieu vudng gdc cua S lin DM Tim quy tich diem Kkhi M thay doi tren BC II Di giflp HS giii quyet bii toan niy, GV ed the sfl dyng phan mem GeospaeW de hd trd qui trinh td ehfle cic hoat dpng nhin thfle eho HS dgy hpc nhfl sau: • Hoqt dgng 1: Tim hieu bai toan Md file "Vidu2.g3W" HS quan sit hinh ve, ve hinh vi xae dinh yeu td cd dinh, yeu td di dpng va yeu td qui tieh {Hinh 6) • Hoqt dgng 2: Tim hfldng chflng minh bai toin Hmh + DU dodn quy tich: GV eho diem M thay ddi vj tri den mdt sd diem dge bift, HS quan sit vj tri cua diem K Khi dd bang trfle quan HS dfl doan quy tieh K li thudc logi trdn vi se hfldng vio dd de chflng minh {Hmh 7) + thuin chflng Chuyen ve xet bdi todn hinh hgc phdng: Di ldi eho vifc quan sit, minh GV sfl dyng ehfle Hmh TAP CHi THIET BI GIAO DUC-SO - / 2 • U II HU'OlNGDANQUANLV.SCrDUNG nang "plan isole" eua phan mem de tich rieng mgt phang (ABCD) khdi hinh ling try dflng {Hinh 8) Dfla vio hinh ve vi gii thiet cua bii toan HS de ding nhgn thay AK DM Tfl dd dfl doan: Quy tich cua diem K M di dpng tren BC li thupc eung OD (O li giao diem cua AC vi BD) nhin AD dfldi mpt gde vudng • Hogt ddng 3: Chflng minh bii toin N^i dung HD cua giio vifn Dfla vio hogt dpng vi sfl dyng suy luin Idgi'e, HS de dgng chflng minh d\i0c quy tich cua diem K M di dpng trfn BC li thupc cung OD (0 li giao diem eua AC vi BD) nhin AD dUdi mpt gdc vudng • Hogt ddng 4: Minh hog qui tich Sau HS xae dinh dUpc quy tich, GV cho diem M chgy tren dogn BC vi de lgi dau vet eua diem K HS quan sit trfle HD ciia hpc sinh HD 1: Tim hieu bii toan Md file "VD3.g3W" de HS quan sit HS quan sit hinh ve, ve hinh vi xie djnh yeu td ed djnh; yeu td di ddng vi hinh ve {Hinh 9) yeu td qui tieh HD2:Dfl doin quy tich Quan sit vi tri diem P qui trinh Cho diem M thay ddi vi tri den mpt sd diem die bift tren dpgn SA de HS quan diem M thay ddi tren dogn SA sat vi tri cua diem P (hinh chieu cua S Dfl doin quy tich P Ii thupc logi trdn len mat phlng (CDM) {Hinh 10) HD 3: Xiy dflng chfldng trinh giai bii toin GV sfl dyng ehfle nang "plan isole" eua PM de tieh rieng mat phlng (SHK) khdi hinh chdp yeu cau HS quan sit vj tri tfldng ddi cua SP vi KN tfl dd dfl doin quy tieh eua diem P M di dpng tren SA(Hin/iii) HD 4: Thfle hifn chfldng trinh giii Dfla cac yeu cau cy the tien hinh Dfldi sfl hfldng dan cua GV, bang suy chflng minh phan thugn, phin dio lugn logic, HS tien hinh chflng minh phan thugn, phin dio va ket luan qui tich HS quan sit hinh ve vi dfla cic nhan xet: Vi SP KN hay gdc SPK = 90° nen quy tich cua diem P thupc dfldng trdn dfldng kinh SK mgt phlng (SHK) Mgt khic, M chi thupc SA nen N (N li giao diem cua SH vi KP) chi di dpng tren dogn SH Vgy P chgy tren cungSH HD5:Khao Sfl dyng chflc nang cua GeospaeW eho HS quan sat trfle quan hinh inh quy sit ldi giii da diem M chgy tren dogn SA vi de lgi dau tich trfn hinh vi nhin thay quy tieh diem P hoin toin trung vdi ket qua tim dflgfc vet cua diem P mi HS da chi dflgfc hogt dpng {Hinh 12) U • TAP CHi THlA^BI GIAO DUC-S6 78-2/2012 H I T O N G D A N Q U A N LV, Hmh Hmh 10 SCr DUNG II Hmh 11 T i i lifu tham khao quan hinh inh quy tich tren khim phi vi trfle tiep thao tic Tran Vift CUdng, SU hinh vi ket lugn quy tieh vdi eie ddi tfldng hinh hpe diem K hpin toin trung vdi mdi trfldng dpng de tfl dung phdn mem GeospaeW ho ket qui d i chi dflde dd tiep thu kien thfle nen tinh trd dqy hgc hinh hgc ldp 11, tich cflc eua HS qui Ludn vdn thqc sy Gido due hgc, hogt ddng {Hinh 7) Thdi Nguyin, 2006 Vi du Cho tam gidc deu trinh hogt dpng dflde phat huy Nguyen Mpng Hy (ehu SAB vd hinh vudng ABCD cgnh eao dd bien), Khu Qudc Anh, Nguyen a ndm hai mat phdng H i Thanh, Bdi tap hlnh hgc 11, vudng gdc vdi Ggi H, K NXB Giio dye, 2007 ldn lugt la trung diem cua AB, Nguyen Bi Kim, PhUdng CD Ggi M Id diem di ddng trin phdp dgy hgc mdn Todn, NXB Dgi hpe Sfl phgm, 2004 dogn SA Tim quy tich diem P Id hinh chieu cua S trin mat Summary phang (CDM) Organizing awareness Di giflp HS giii quyet bii activities for learner with toin niy, GV cd the sfl dung GeospaeW software in phan mem GeospaeW de hd the teaching geometry of trd qui trinh td chflc eie hogt space in general and in the dpng nhin thfle cho HS teaching math locus in space Hmh 12 dgy hpe nhfl sau: in particular would create Ketlu^n favorable conditions to activate Theo chung tdi vifc flng Vifc tim tdi cic bifn phip the learner The learner could de dgy tdt cic bii toin ve hinh dyng cdng nghf thdng tin, khai explore, discover, speculate hpc khdng gian ndi chung v i thie mdt cich hdp ly cic phan to yield remarks, important cic bii toin quy tieh mem dgy hpc de hd trd GV HS conclusions basing on the khdng gian ndi rieng eho HS vifc dgy vi hpe toin se visual drawings and feedback li rat can thiet Qua eie vi dy gdp phan ddi mdi phfldng phip suggested by the software The cv the ve vifc khai thic phan dgy hpe, ning cao chat Ifldng article suggests some examples ofhow to exploit the GeospaeW mem GeospaeW de hd trgf dgy did tgo vi can dvigc nghien software to organize activities hpc bii tip hinh hpc khdng cflu, trien khai tren phgm vi in the teaching math locus in gian cho HS, chflng ta thay vi tit ci nhflng trfldng phd thdng spacewith students HS dfldc tiep can, nghien cflu, tren toin qudc TAP CHi T H I ^ BI GIAO DUC - SO 78 - 2/2012 • 25 ... Minh hog qui tich Sau HS xae dinh dUpc quy tich, GV cho diem M chgy tren dogn BC vi de lgi dau vet eua diem K HS quan sit trfle HD ciia hpc sinh HD 1: Tim hieu bii toan Md file "VD3.g3W" de HS... speculate hpc khdng gian ndi chung v i thie mdt cich hdp ly cic phan to yield remarks, important cic bii toin quy tieh mem dgy hpc de hd trd GV HS conclusions basing on the khdng gian ndi rieng eho... activities hpc bii tip hinh hpc khdng cflu, trien khai tren phgm vi in the teaching math locus in gian cho HS, chflng ta thay vi tit ci nhflng trfldng phd thdng spacewith students HS dfldc tiep can,