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