[''''FIILraPIUP HIT DO\C KIE\ Tlilt \ B l Oi\li i i m c m HOAT m GIAI HUYET l i \ DE TRÔ G M H i lii\ll HOC Kli''''G G1A\ 6 TRUNG HOC PHO THONG GS TS DAO TAM* 1 Khi dung tn/dc mdt van de ndi ehung, mdt bai[.]
Trang 1['FIILraPIUP HIT DO\C KIE\ Tlilt \ B l Oi\li iimc
m HOAT m GIAI HUYET l i \ DE TRO^G M H i lii\ll HOC Kli'G G1A\
6 TRUNG HOC PHO THONG
GS TS DAO TAM*
1 Khi dung tn/dc mdt van de ndi ehung, mdt bai
toan hinh hpc ndi rieng, hpc sinh (HS) can phal biet
each tra Idl eac cau hdi sau: - Dua tren CP sd nao de
h/a chpn dung cac tien de 'Iri thue da bief n h i m giai
quyet van dedat ra; - Huy dpng kien thdc nao de van
6$ dupe giai quyethpp li, don gian i]hat; • Caeh bien
iSi vS'n de nhu the nao de cd the de dang huy ddng
cac kien thuc da biet trong quatrinh giai quyet vain de
datra.^
Be tra Idl cac cau hdl tren, ehung ta ed the khai
thac tu tudng su phgm cua G Polya trong hoat dpng
tim tdi \di glai cac bai toan Tuy nhien, cho den nay
vi|ic nghien cdu cu the cac phuong phap huy ddng
kien thuc nh^m gitjp HS giai quyet eae van de trong
dgy hpe hinh hpe khdng gian (HHKG) mdt each chu
dpng, tich cue, sang tao ehua dupc nghien cdu can
ke,h$thd'ng.D3cbi§t,chuaquanjam nghien cdu cac
phUdng phap huy dpng diing d^n cac kien thuc ed
v§n dyng tu tudng cua li thuyet day hpc hieti dai, tu
tudng eija tam li hpc nhan thde va chua khac phue
dupc nhdng khd khSn, sal lam^cua HS khi chuyen tu
vi$c nghien cdu hinh hoe phang sang nghien cdu
HHKG
Mue tieu nghien cdu trong bai viet nay la de xua't
cac phuong phap huy ddng kien thue theo hudng dd'i
m6< phuong phap day hpe, dae biet la dinh hudng tiep
cSn phat hien nang It/c glai quyetvande cho HS,kh§c
phi^c nhi>ig khd khdn, sai lam cua cac em khi hpc tap
HHKG dtrung hpc pho thong (THPT)
2 V i ^ nghien cdu, de xuait eae glai phap dua tren
m$ts6eosdli luan ehuyeu sau (dupc phan anh trong
cac cong trinh nghidn cijru cua cac tac gia: Nguyin Ba
Kim;lu.M.Koliagln; A N Lenonchiev; Phan Trpng
Ngp; G Polya; Dao Tam): - Kha nang lua ehpn dting
eac tiln de eho lap luan giai quyet van de, trong dd,
tien de dupc hie'u la: cac tien de, menh de da chthig
minh, cac khai niem da biet; - Luan diem vevaiUdcua
tri thuc, dae biet la tri thuc phuong phap vi/a la cfieu
ki^n, vda la mtjc tieu eua hoatdpng; - Cai mdi thudng
dupe phat hien thdng qua viec ehuyen hda cae lien
tudng tdddi tupng nay sang ddi tupng khac Ngoai cac co sd li luan cae blen phap de ra tren
eo sdtht/c tiln khao sat nhdng khd khan, sai lam cua
HS Dudi day, ehung tdi trinh bay mpt so phuong phap huy dpng kien thdechu yeu khiday hoc HHKG dtrudng THPT
Phuang phap 1 Luyen tap eho HS xac djnh tri thuc coi ngudn cua tri thue can tim an chua trong cae van dedua ra nham dinh hudng dung cho cac boat dgng xam nhap vao dd) tugng nghiin euu Viec xae dinh cac tri thdc edi ngudn de
lam sang to quan he nhan qua gida tri thue da bietva tri thue can tim; eac tri thdc cdl nguon ddng vai trd djnh hudng, dieu chinh hoatdpng xam nhap vao ddi tupng lam sang td cac dd'i tupng toan hpc, cac quan he can kham pha Dd la eP sd de HS hoat ddng chiem finh kien thdc Phuong phap nay cd the thuc hien trong day hpc cac djnh li, quy t^c va day hpc giai eac bai tap toan Giao vien (G V) cd the xay dung he thd'ng cac cau hdi supham,giup HS huy ddng kien thuc va djnh hudng hoatdpng glal quyet van de
Vidu /.-Cho hinh lap phuong ABCD.A,BjC,D,
Gpi cac diem M; N; P lan lupt la trung die'm cua cac eanhAD;BB,;C,D,.Haydt/ngthietdlencuahinhlap phuong tao bdi mat phing (M NP)
Khi giai baitoan nay, HS gap khd khan trong viec xac dinh giao cua mat phang (MNP) vol mdt mat eua hinh lap
phuong de
td do xac dinh giao cija mat phang nay vdi cac mat edn lai
Trithuc edi ngudn can chua'n
*Tni0ng Dai hoc Vinh
Tqp chi Gido due SO 307 | 51
Trang 2matphang;-Quytrinh tim giao cuamptdudngthSng
vtifi mdt mat phang; - Cach xac dinh mat ph&ng: mat
phang di C|ua ba diem; mat ph|ng xac djnh bdi hai
dudng thang edt nhau; mat phing xac dinh bdi hai
dudng thang song song; mat phdng ehua iiidt dudng
thang va mot diem khdng thupc dudng thang do
T d dd, HS cd the huy dpng kien ttidc thdng qua
hethd'ng cau hdi do G V dat ra ching han nhu: - Neu
quy trinh dt/ng giao cua dudng thang^MN vdl mat
phang (A,B,C,DJ; -Xac djnh mat phing (a) chda
MN, do la mat phang chda hai dudng song song BE,
va MM,, trong do M, la trung diem eua canh A,D,;
-Xacdinhglaotuyen cua mat phing (a)vtiflmat phang
day(A,B,C,D,),ddladUdng thing B M , ; - T r o n g mat
phang (a), xac djnh giao diem S cua dudng thing
M N v a B , M ,
GV yeu eau^HS xac dmh giao cua mat phing
(MNP)vamatphing (A,B,C,D,)cuahinh lap phuong
Nhd cac kien thuc da biet, HS tim dupc giao la doan
PQ (xem hinh /) Cae giao diem cdn lai HSed the tu
xac djnh nhd he thdng kien thdc da biet va tim dupc
thiet dien la lye giae deu MTNQPR; trong d d Q , R , T
lan lupt la trung diem cac canh B,C,; D,D va AB
Phuang phap 2: Chuyin viec nghien cuu, tim
tdi cac tinh chat eua hinh khdng gian qua viec
nghien ct/u tinh chat bg phan trong hinh hge
phing, tu do huy dgng kiih thue da biet trong
hinh hgc phang degiai quyet yah de cila hinh
khdng gian Phuong phap 2 nham tao si/ ket nd'i
gida viec hoc tap, nghien euu HHKG vdi kien tht/c
hinh hpe phang da biet, tranh st/dt/t quang ve phuong
dien tam li cua HS HS nghien cuu hinh hpe theo
phuong phap nay la eo hdi de tiep can, phat hien each
gial quyet cac bai toan khdng gian nhd viec chuyen
hda each gial cua bai toan H H KG ve bai toan phang
C h i n g han nhu: - Chuyen bai toan tim tam va ban
kinh mat cau ve bai toan tim tam va ban kinh eua
dudng trdn Idn trong mpt mat phang xae djnh di qua
tam; - Chuyen hda bai toan quy tich khdng gian ve
baitoan quy tieh trong mat phang; - Chi/ng minh mpt
dinh lieua HHKG dupc chuyen vevan dyng djnh li da
biet trong mat p h i n g
Sau day.ta xet eae bai toan HHKG nhd st/dung
kien thuc trong hinh hpc phan^ da biet
Vidu 2:Cho hai dudng thang cheo nhau a va b
Gpi A; B la cac diem CO dinh lan lupt thupc cac dutifng
thSng a; b Cae diem M; N lan lupt di dpng tren a, b,
sao cho AM = BN Tim quy tieh tmng die'm I eua doan
thing MN
521 Tap chi Giao due so 307
tl s d ' ^ = - ^ nen cac diem 0 va 1 thupe mat phing (a)di qua 0 va (a)song song vdi cae dudng thang a
va b Dieu nay suy ra tudjnh li Thales dao trong khong gian HS dl^dang chdng minh dupc I la tnjng diem cua doan thing M,N,, trong d d M , ; N , lan lupt la cac hinti chieu cua M; N len mat phing (a) theo phuong chieu AB, Tudd suy ra duoc quy tieh can tim
Vidu3:Qho tddien OABC cd gdc tam di?n dinh
0 la gde tam dien vudng.Vedudngeao GHctjatudien.Gpil
la tmng die'm cua doan OH; ki hieu Sj,;
S^j S^; S^ lan lupt la dien tich eua cae mat ddi dien vd^ eae dinh
0 ; A ; B : C Chdng minh ring:s/,7o+5]M+5j7s+5,'.7c = 0 Baltoan dupegialduatren ketqua bai toan phing
sau: 'Cho tam giac ABC vudng tai A Vedudngcao
AH Ggi I la tmng diem doan AH Chdng minh ring
° f l ' Z i + A'7s + c ' 7 c ==d" van dyng vao haitam giac vudng ADM vudng tai 0 ; ed dudng eao OH va tam
giac vudng BOC vudng tai 0 , cd dudng cao OM, vdl
M la giao cua AH vdl BC {hinh 2)
Phuang phap 3: Luyen tap cho HS chuyen hda cac lien tudng tudoi tugng nay sang doitugng khac nhdm cau true lai hinh thuc va ngidung cda van decan nghien cuu dedi dang xac lap m oilien hivdikiih thucdabiit, tudd huy dgng dung din cac kiih thuc degiai quyet van de
Phuong phap 3 giup HS khie phue khd khSn khi ehua xac lap dupc md'i lien he gida dd'i tupng can kham pha vdi cac kien thue da ed; giup HS blen dd'i thong tin
an cht/a trong vain de can giai quyet, biet xem xet cac van de eua HHKG theo nhieu each khae nhau va ren luyen tuduy linh hoat cho cac em trong viec phat hien cae each gial quyet van de
V/'di/4.Cho hinh lap phuong ABCD.A,B,C,D, Gpi 0 la tam cua hinh
lap phuong Dt/ng thiet dien eua hinh lap phuong tao bdi mat phing (a) di qua O v a (a)vudnggdcvdiACj
Neu dyng true tiep thiet dien eua hinh lap
Trang 3xac djnh qao cua (a)vcncac malcOa hinh iap phi/ong
GV c6Ihe luyen tap cho HS chuyen »iec xac (Jinh thiet
dien vuong goc veviec xac djnh thiet dien teo b i j mat
phang diquaOvasong song vaihaimatphang(BDA,)
va (CB,D,) nhd lien tudng cac mat phang nay lan lifot
vuong goc vdi di/dng cheo AC, tai cac diem HvaG Khi
dd, 0 la tnjng diem cua doan HG Vjn dung kien thdc
ve djnh ti Thales dao dechungtdthietdiendiqua tnjng
demcaccanhBC;BB,;A,B;A,D,;DD,:DC(/j//i/j3)
Phuang phap 4- Khao sat, nghien cm cac
dang sal lim cua HS khiday hgc HHKG va lao ca
hgi sua chua sai tam cho cac em trong qua trinh
huy dgng liien thuc giai quyet van dedat ra Ivlot
sddang sai iam thudng gap cua HS trong day hpc
HHKG dd la:-Do chudng ngai sir pham khi chuyen tir
hpctap hinh hpc phjng sang H HKG ;• Do khdng giai
quyet can ddi quan he gida cu phap va ngu nghTa;
- Do khdng n^m vung djnh nghTa cac khai niem va
quy t^c: • Do HS thieu cac bie'u tucfng khdng gian, l u
duy khong gian cdn yeu
Xet «i du sau ve sai lam cua HS do khdng nam
dupc cac djnh nghla tuong duong va thieu kha nang
hinh dung hinh khdng gian qija hinh bieu dien
Wdu5;Cho hai dudng thing cheo nhau a, b va
mpt diem _M khdng thupc cac dudng thing dd Dung
dudng thing qua M va cSt cac dudng thing a va b
Vdi bai toan nay, cd HS da thuc hien theo quy
Irinh: dung m j t phang (a)qua M va dudng thing a;
dung mat phing (P) qua M va dudng thing ID Sau
dd, HS dua ra ket luan: giao tuyen cua matphSng(a)
va C/? M dudng thing can dung Sai lam d day la H S
chua xel tdi cac dieu kien de tdn tai giao luyen Chang
h^n, tiong trudng^hop neu diem M va dudng thanfl a
nam tren mSt phang (P) song song vdi dudng Ihang
b Ihi khdng Ion tai dudng Ihang can di/ng
GV can can n h i c va siia chda nhung sai lam,
thieu sdt cua HS dp khdng n i m virng vi tri tuong dd'i
gida cac dudng thing cheo nhau trong khdng gian
3 Trong pham vi bai viet nay, ehung tdi chi trinh
bay boh phuong phap huy dpng kien thuc nham djnh
hudng, dieu chinh hoat dpng giai quyet van de cho
HS Irong day hpc HHKG d Irudng THPT Cac bien
phap nay cd the van dgng vao day hpc cac npi dung
loan hpc khac dcae cap hpc khac nhau Ddc gia can
quan lam them phuang phap xem xet cac linh chat
hinh hpc bat bien qua cac anh xa, dae biet ia phep
bien hinh de lua chpn dung Iri thdc khi giai quyet van
d e t r o n g d a y h p c H H K G a
(Xem Hep ^ng 55)
Giao due hch sir dja phirong
(Tiep theo trang 50}
tra, danh gia qua trinh hpc va day nhim xac dinh ket qua nhan thdc cua HS va hieu qua day hoc cua giao vien Tddd, cd nhung dieu chinh bd'sung kjp thdi ve npidung va phuong phap Can da dang hda cac hinh thuc tuyen truyen tmyen thd'ng LSDP qua nhieu hinh thuc phong phu nhu: xay dung cac phdng tnjyen tfiong nha tnj'dng; toehue eae hdi thi tim hieu ve LS; suu tam
va trien lam tranh anh, tu lieu; eham sdc di tich LS; day manh phong trao dpc sach LS tai tn/dng va trong nhan dan; tuyen truyen ca khtjc each mang va eae hoat dpng van hda van nghe khac
DongThap Mudi la vung dat giau tiem nang Nhan dan Dong Thap Mudi anh dung trong dau tranh chdng giac ngoai xam va can etJ trong lao dpng san xuat Vung dat nay da tao nen mdt tmyen thd'ng dep eho dja
phuong va dan toe Tim hieu, luu tru, tieh cue tuyen
tmyen, giao dtJC gia tri tmyen thd'ng cua vung Dong Thap Mudlchocac the heHSIatraeh nhiem cua nganh giao dtjcva nhung ngutlfi nghien cuu LS Trong dd nha tn/dng phd'thdng, cae glaovien/.Sdwig vaitro tn/c tiep mang kien thucden cho HS;tung budc giup cae the he
HS hieu sau sic hOn que huong, tran trpng nhung thanh qua cua dja phuong minh de khdng ngi/ng hoc tap, tich eye tham gia lao ddng san xuat gdp phan lam giau dep que huong dat nudc.Q
Tai lieu tham khdo
1 Ban Ch^p h^nh Dang bO tinh Ddng Thap Ljch sii Dang ba tinh Ddng Thap lap 3 Ban Tuyfin giao
Tinh uy NXB Ddng Thdp 1997
2 H6i Khoa hoc Ljch sdD6ng Thap Dia danh lich si>
- V3n hoa huyen Thap Mu6i NXB Ddng Thdp 2012
3 Pham Chi NSng Dieu Ira, nghien cihi, bien soan
tai lieu day hoc Lich s d va Dja li dia phmmg tinh
Ddng T h i p tap 1, t^p 2 NXB Ddng Thdp 2004
4 Trdn Thj Kiem "Sudung tai lieu ljch sd dia phircmg
trong day hoc Lich sd Viei Nam d iruong irung HQC
pho thOng Tap chi Ddng Thdp Xua vd Nay, s6 36/
2012
SUMMARY
The education and historical researchers have a big responsibility In searching, keeping, propagating and educating Uie traditanaJ value of Dong Thap Muoi for Oie pupils High-schools play a direct rolein bring-ing the knowledge to the pupils On the basis of Uie actual situation, this article focuses on some of pos-sible solution to improve the etfection of this action
Tap ehi Giao due so 307 | 53