DAY HOC KHAM PHA CONG THDC TINH KHOANG CACH Tif MOT DIEM JIEN MOT MAT PHANG (HINH HOC 12| HANG SUY LOAN TlTONG TO ThS BUI P H D O N G UYEN" Ngay nay, phuong phap (PP) day hpe kham pha(DHKP)vaphepsuy l[.]
Trang 1DAY HOC KHAM PHA CONG THDC TINH KHOANG CACH Tif MOT DIEM JIEN MOT MAT PHANG (HINH HOC 12| HANG SUY LOAN TlTONG TO
ThS BUI P H D O N G UYEN"
Ngay nay, phuong phap (PP) day hpe kham
pha(DHKP)vaphepsuy luan tuong ty'{SLTT)
dugc van dung nhieu trong day hgc (DH)toan
Hon niia, neu giao vien (G V) biet ket hpp hai yeu to
nay vao DH thi khong nhiing giup hgc sinh (HS) on
tap dupc kien thirc cu ma con tao co hpi cho cac em
xay dyng kien thdc mdi Mo hinh DH tuong tutdnq
quat (GMAT) cho phep ngudi hpc su'dyng SLTT de
kham pha kien thdc mdi mgt each hieu qua Trong bai
viet nay, chiing toi van dyng mo hinh GMAT vao DH
cong thirc tinh khoang each tdmgtdiem den mpt mat
phing thong qua mgt thuc nghiem su pham
1 Quan niem v e D H K P , SLTT v a m d i quan he
giua Chung
1) Ouan niem veDHKP DHKP li mgt PPDH
khuyen khich HS dua ra ciu hoi vi tutim cau tra Idi,
hay rut ra nhdng nguyen tac tdnhdng kinh nghiem
thucfiSn TrongDHKP, noi dung DH khong dugc gidi
thieu trudc mi dugc HS tukham phi nhim tao cahgi
cho cac em tham gia tich cue vao qua trinh day hoc
(1; 24-26)
DHKP CO ba dac diem: HS khao sat va giai quyet
van de de hinh thanh, khai quat hoa kien thii'c; HS
dupe thu hilt vao cac hoatdpng hpe tap; khuyen khich
HScosulienketgidakien thuc mpi va kien thde cu
Khi su dung PPDHKP, co the giiip HS phat trien tu
duy vi doi hoi ngudi hpc phai danh gia, phan doan,
phan tich, tong hop, Ben canh do, HS hpc dupc
each kham pha tri thuc mdi va phat trien tri nhP thong
qua hoat dgng huy dpng kien thii'c da c6; ti) do, giup
HS hieu bai nhanh va khic sau dupc kien thde
2) Quan niem veSLTT Danh tir "tuong t d ' co
nguon gdc tir "ava).0Yia", mpt tir toan hpc cua Hi
Lap.Tunayc6 nghTa l a s u b l n g nhau cua haitiso' Vl
d[/.'3:4::9:12,tii'clahehais63va4tuongtuvPihehai
s d 9 v a 1 2 ( 1 ; 81-82)
SL TT li phep suy luan cin cd vao mgt sg thugc
tinh gidng nha u cua hai dgi tugng derut ra ke't luan ve
nhdng thugc tinh gidng nhau khac cua hai ddi tugng
dg (2; 87-88) SLTT con dugc dinh nghTa nhula "su
so sinh gida nhimg vit noi chung khac nhau nhung
[ Tap chi Giao dye so 338
noi bat len a su giong nhau dvai khia canh thich hgp"
(3; 163-165) Vat lam eo sP eho phep tuong tu (ddi tupng de so sanh), dUPe goi la nguon; vat dupc giai thieh nhd su'dyng phep tupngtu gpi la dich Trong DH toan, mue tieu eua viec sir dung phep tuong tula ehuyen nhdng tu tudng td kien thirc nguon thanh kien thde dich Ngoai ra, SLTT cocac irng dyng: xay dung gia thuyet, phat hien va khac phye sai lam eho HS; HS sudyng phep luong tu vao giai bai tap (BT)toan
3) Md'i quan he giua DHKP viSLTT.TrongDH
toan, GV co the sd dyng phep SLTT de kham pha kien thuc mdi, nghTa la sddung SLTT theo thugc tinh hoae theo quan he gida cac ddi tuong de dua ra gia thuyet, sau d6 tien hanh chdng minh hay bac bo Mpt trong nhung mo hinh DH tuong tu phd bien la m6
hinh giang day tuong tutong quat (The GeneralModel
ot Analogy Teaching - GPJIAT) dupc de xuait he'l
Hassan Hussein Zeitoun nam 1984 Mo hinh nay la mpt mo hinh tieu bieu bdi n6 dudng nhu la suke't hpp
gida cac y tudng cua cae mo hinh hien co Mo hinh GMA T gom ba giai doan: giai doan tie'p nhan, giai doan tuang ticva giai doan xac nhan (4; 164) Theo
chung toi, cac giai doan nay eo thedupe ey the qua sP dosau:
Hinh 1 Sa do cac giai doan eda mo f)inh Gh/IAT
va cao kis
'rm
nthu 7 vol kicn thuc dich
ho cua HS vekien Ihu quan nKuon
•GVdira
• HS Ihp Ihuc nguo ni"S
\r
^
itn
d i H S Ihao luan G V u
i n m g d l n t h o H S :h diinu SLTT de lien thjcdich Tudo, kliam Ihe dira ptia roi
>
2 S i i dung SLTT de DHKP djnh li ve khoang each t i i m o t d i a n de'n mot mat phang (Hinh hoc 12) flinh li khoang each tOf mot diem den mat phlng
dugc SGK Hinh hoc 12trinh bay trong bai: Phuang
' Khoa Sir phaiD, Inrairg Dai hoc Can Tho
Oii2-7/2014)
Trang 2cua mat p h l n g Day la mpt trong nhiing cong thdc
dupe su dung nhieu vao qua trinh giai toan chuong:
Phuang phip tga do trong khong gian Dudi day,
chiing toi de xuat mot hudng DHKP cong^thuc tinh
khoang each td mot diem den mot mat phang bang
mo hinh GMAT:
3.ThiJcnghiem s u p h a m
6a>«i]fn
3
-Ir
(hing a m '
|BT1 sau Tiotie lifl6Aff g
plWu>â<cua (o)
na M W'
i ( ^ ) » 2 j 2 r - 2 0
Du flifm Me(™) r-ir AxVflj'-f ( i ' - , / ) 11
= 41,^,-1,4)+fl(>„-fc8H((.-,-*£•)*«-0
_|TTT7T|_Ky/^.-'>;'^
" "* p"-«-«-13-l 4
-Li,Af(ClO-l)E(/J) ,.\„)liailt6^
illlaUmi^''W ton
_|0.2ll-2(-l).N| ,
Chung toi da tien hanh thuc nghiem supham d lop
12A8, Tnj'dng THPT Chau Van Liem, TP Can ThP
(ngay 15/3/2013) Ldp 12A8 gom 45 HSva dupc chia
thanh 15 nhom Sau tiet day, chung toi ghi nhan duoc
mptsdketquasau:
Trong giaidoan tiép nhin, HS n h i c lai dung cong
thdc tinh khoang each td mpt diem den mpt dudng
thang da hgc dIdp 10; tuy nhien, nhieu em khong nhd
each chting minh cong thdc naỵ Nguyen nhan cothe
la do HS chl van dyng cong thdc vao bai tap, it su
dyng den each chung minh cong thuc nen nhanh
quen.KhidupcGVnh§clai,HS da nhd lai each ehdng
minh.Dieu nay tao dieu kien thuan lpi eho HS khi xay
dung cong thdc tinh khoang each td mpt diem den
mptmatphing
dg'iaidoan tuang tie, G V den tdng nhom theo doi
quatrinh cac nhom thao luan.9a so cae nhom dua ra
day la ghi nhan qua trinh thao luan cua nhom 7:
HS An: Khoang each nay hinh nhu tuong tu voi cong thdc tinh khoang each td mpt diem den mgt duong thang Do c6 them thanh phan z nua nen c6ng
thdcc6thela: < / ( w , ( « ) ) = l ^ ^ ; ^ i ^ ; ^ l ^
HS An: Ggi M' la hinh chieu cua M len (a) Vay, khoang each td M den («) la dp dai M M ' va each tinh
|ArM| cung se tuong tucach chiing minh khoang each
td mpt diem den dudng thang trong matphingdọ
HS Khanh: Ta co T7n7 wa s cung phupng:
M-M=knMa \n\ = ^Á + B'+c\ nen chi can tinh k
nua la xong
„-ý = kB<^ \ý = y„~
HS Phat: Ta co:
:> MXx,,-kA;y„-lcB:z„-l(C)
Do diem M ' e ( a ) nen: Ax'+Bý+Cz'+D =
>Ặx„-liA) + B{y„-kB) + C{z„-kC) + D = \J
+ By„+C:., + D
HSKhanh:* =
-+ fl +r'
(ki2-7/2014)
HS An: Tu do, tinh dupc khoang each:
_\Ax„ + By„ + Cz„ + D\
ylÁ +
B'+C'-|Ax„ + By„+Cz, + D|
HS Khanh:Vay: d(M.(a)) = ^ ", / " \ \
' V^' +
B'*C-Qua phan thao luan cua cic nhom, chung toi nhan
thay nhd su hgp tae, cac em da phan tich BT va dua
ra duoc hudng giai Nhdng y tudng giai BT dupc lien
he vdi each chdng minh cong thuc tinh khoang each
td mpt diem den dudng thang trong mat phang 0 day, HS datu luc xay dung dupc eong thirc mcfl thong qua viec sudyng phep SLTT
dgiai doan xac nhan, eae nhom da phat bieu
dugc eong thuc tinh khoang each tu mgt diem den mgt mat phing.GV khang dmh ket qua va phat bleu dinh lị HS d i dang ap dyng cong thdc vao cae vi dỵ Oieu nay chiing to HS da nam vung e6ng thiíc va biet van dyng vao giai bai tap
Nhuvay, bang each sudyng phep SLTT, HS dlop thyc nghiem on tap lai kien thuc vec6ng thiic tinh khoang each tdmptdiem den dudng th^ng Tuc6ng thuc nay,
HS kham phacong thifcmpituong ti/nhutrong khong
•Tap chi Giao dye so 338 | 55
Trang 3moiquan he giua kien thiic cu va kien thdc mcfl ma con
ren luyen cho cac em khanang sang tao Vivay, DHKP
cong thiic tinh khoang each tii mot die'm den mpt mat
ph§ng thong qua phep SLTT la hoan toan kha thi
PPDHKP mang lai nhieu loi ich doi vdi HS boi n6
giup cac em phat tnen tu duy, tri nho va tao duoc moi
lien he giua kien thdc mdi vdi kien thiic cu Bac biet,
DHKPb§ngSLTTdaehdng minh dupc hieu qua cua
no trong qua trinh hpc tap, kham pha tri thiic mdi ciia
HS Vivay, viec nghien cifu, phattrien vavan dyng
phuong phap nayvao qua trinh DH laeanthiet.Q
{]) Nguyen Phu Lflc Gido tnnh Xii Im&ng day hoe
khdng truyin ihd'ng Truiyng Dai hoc Can Tha, 2010
(2) Hoang Chung L o g k hpc pho thiing NXB Gido
ducH 1994
(3) Nirah Halivah Teaching for effective iearning in
higher education Ktuwer Acadeniie Publishers The
Nelherland.s 2000
Analogical Reasoning for the Concept of Translation,
Joumal of Scienee and IWalhemmalic Educalion in Southeast Asia Vol 31 2 No 164-177 Faculty of
Science & Technology, Sultan Idris University of Educalion Malaysia, 2008
Tai lieu t h a m Ithuo Tran Van Hao {tOng chu bien) Hinh hoc 12 NXB
Giaoduc VietNam H.2010
SUMMARY
Currently, tenching by discovery and analogy are applied a lot in leaching maths Moreover If teach-ers combine these elements into teachmg they not only review the old knowledge but also help students
to build the new knowledge easily The General Model
of Analogy Teaching (GMAT) is used to discover the new knowledge effectively In this article, we applied the GMAT model m teaching the formula of calculat-ing the distance from a point to a plane through an pedagogical experiment
Thiet 1(6 tiettra bai
(Tiep theo trang 46)
Tai liSu tham Ichao
I Dir an ViCl - Bi Day va hpc
tich circ, mpt so p h u o n g p h a p
va lii thuat day hpc NXB Dai
hoe supham, H, 2010
2 Nguyfin Thiinh Thi Chuyen
de btii d u ^ n g giao vien t r u n g
hpc pho thong Soc Trang, 2011
3 Nguyen H6ng Nam 'Thia't k^
cau hoi day hoc Van - M6t thir
thach vai giao viCn" Tap chi
Gido due, %6 147,2006
SUMMARY
In the current schools,
pay-ing for student tests is not
enough attention The
imple-mentation of this class a
per-consistency has led many
stu-dents miss the opportunity to
fix weaknesses, strengths, and
promote the process of writing
office hours pay discourse to
promote the highest efficiency
of this class
Sir dung hinh hoc cao cap
(Tiep Iheo trang 50)
_ 6 ldi giai tren ta thay, cac cap diem ( 0 ' ; M), {N'; R) va {S'\ P) lan lugt
nam tren cac ducftig trung tuyen eua A/1'S'C'nen anh cua chiing qua anh
xa afin / ' la cac cap diem { 0 ; l\4), (A/; fl), (S; P) ciJng n^m tren cac dudng trung tuyen eua AABC vi phep bien doi afin bao toan cac dudng tmng tuyen Day ehinh la co sd cho viec si) dyng S r 2 d e tim Idi giai cho BT1
Trong qua trinh day hpc, neu GV thudng xuyen khai thae cae kien thdc cua HHCC nhim soisang cac kien thde cua HHSC sectiiipSV hieu dupc mpt each ehinh xac, hieu diing ban chat eiing nhu nam dupc cpi nguon cac kien thde eua HHSC; tudo, SV thay dUPc mdi quan he giua HHCCvdiHHSC.Q
Tai lieu tham khao
1 v a n Nhu Cuong - Ta Man Hinh hpc Afin va hinh hpc Euclid NXB
D(ii hoc quoc gia Hd Noi, 1998
2 Trdn Viet Circ>ng - Nguyin Danh Nam G i a o trinh Hinh hpc so-cSip
NXB Gidodite VietNam, 2013
3 Dito Tam Giao trinh Hinh hoc so" cap NXB Dgi hpc suphgm, H 2004
4 Ng6 Viet Trung Giao trinh Dai so tuyen ti'nh NXB Dai hpc qud'c gia
Hd Npi 2002
SUMMARY
This paper presents some ideas of using advanced geometry in sup-porting students learning mathematics From advanced point of view, students would gel insight into some difficult problems in elementary geometry and make it clear the relationship between advanced geom-etry and elementary geomgeom-etry
Tap chi Gido due so 338
(ki 2 - 7/2014)