Tran Viet Cufmg vd Dtg Tap chi KHOA HQC & CONG NGHE 103(03) 151 154 B O I D l / O f N G K H A N A N G P H A T H I E N V A S L T A C H L T A S A I L A M T R O N G L C n G I A I B A I T A P T O A N C H[.]
Trang 1B O I D l / O f N G K H A N A N G P H A T H I E N V A S L T A C H L T A S A I L A M
T R O N G L C n G I A I B A I T A P T O A N C H O H O C S I N H
T r a n Vi^l Cu-6ng'', Lc Van Tuyen^
'Truong Dai hpc Supham - DH Thai Nguyen 'So Gido due vd Ddo lau Tuyen Quang
TOM T A T
N6u hpc sinh (HS) co kha nang phat hi^n va sua chiJa sai lam trong giai loan thi sg khac phuc dugc nhihig sai lam trong giai loan va phat trien cac nang luc tri tue cho ban than Bai bSo nay, chung toi Uinh bay mot so vi dy theo hudng boi du&ng kha nang phat hien va sira chOa sai lam trong giai bai tap loan cho HS
Til' khoa Hoc smh, sai ldm, bdi dudng, bdt lgp todn, sira chira
Giai loan c o the xem la mgt trong nhirng hinh
thiic chii yeu cita hoat d o n g loan hgc ciia HS
Cac bai loan la p h u o n g ti^n hieu q u a trong
viec lam cho HS nam viing cac Iri thirc, phat
trien kha nang t u duy, hinh thanh cac kT nang,
kT xao cho ban than Viec giao vien ( G V ) to
chirc day hge mon T o a n cho HS hieu qua se
gop phan nang c a o chat l u g n g day hgc Toan
ndi rieng va phat trien kha nang giai quyet
van de noi c h u n g cho H S
Thuc liln day hgc da cho thay, c h i t l u g n g hgc
loan ciia HS c o n c h u a c a o , bieu hien q u a nang
luc giai tgan con han c h e d o HS con mac
nhieu sai lam trong qua trinh giai toan Vi
vay, kha nang phat hien va sira c h u a sai lam
ciia HS la mgt trong nhiing m i u chot de gop
phan tang tinh hieu q u a ciia g i o hoc
Tu duy sai l i m t r o n g hoat d g n g nhan thirc,
trong cugc sgng noi c h u n g , trong giai toan noi
rieng dem den nhij-ng tac hai Ion Vi vay,
trong day hoc, viec phat hien som nhirng sai
lam ciia HS trong t u duy noi c h u n g , t u duy
giai loan noi rieng d e g u i p cac H S kip thai
sua chiia co mpt y nghTa ral quan trgng HS
nSu CO d u g e kha n a n g nay thi viec hgc tap
mon loan tro' nen hieu q u a h o n
Mo ta eho kha n a n g nay, c h u n g t6i minh hoa
bang mgt sg vi dy sau:
Vi d u I "Giai b i t p h u o n g trinh
•hx- -(ix + ^<2x+l ( 1 ) "
Mot sd HS giai nhu sau:
Loi gidi thir nhat Tii' (1) ta c o
' Tel 0978 626727 Email: tranvielcuong20Q6(wgmad com
2 v ' - 6 T + 4 < ( 2 ; f + 2 ) '
> A = + 7 x > 0
rx>o
^ |_;c < - 7
Vay nghiem ciia bat p h u o n g trinh Va x>Q va
x < - 7
Ldi gidi thir hai' Tir (1) ta co
2 x ' - 6 x + 4 > 0
2 : C ' - 6 A : + 4 < ( 2 X + 2 ) '
x<-l
0 < ; c < I
X > 2
(*)
Vay nghiem ciia bat p h u o n g trinh (1) la nhung gia trj ciia x thoa man (*)"
Hay nhan xet hai loi giai tren, chi ra cho chua hgp ly trong m6i each giai va trinh bay lai loi giai dimg ciia bai giai
Qua viec G V cho HS nghien ciin hai loi giai tren va phan tich tinh dimg sai ciia hai loi giai bai loan do, HS se nhan thay d u g c
Q loi giai Ihii n h i t , HS d o da khong nam ro
\k b i t p h u o n g trinh t u o n g d u o n g , cac phep
bidn d6i t u o n g d u o n g va viec HS d6 lam
d u g c n h u vay g i n n h u la ban nang tu nhien
Do do, lai giai thu n h i t chua chinh xac
Q lai giai Ihir hai, HS do da lap luan nhu tren boi hg nghT, voi b i t p h u o n g trinh dang
Jf\x)<gix), dieu kien ciia x la f{x)>0
Do v€ trai kh6ng am, ma v^ phai khong nho hon va trai nen ve phai cung khong am Vi vay, hai v8 dSu k h o n g am, do d o co the binh
151
Trang 2phuang hai \e dc dugc bat phuang trinh
| / ( v ) > 0
tuong duong J , Vai lap luan
[f{.\-)<{g{x)]-nhu Ihe 1 IS se tia lim dugc
.\ < - 7 ; 0<.V< 1.1 -2 Ci loi giai thir hai, dt)
thay khi \ < - 7 khong Ihiia man bfil phuang
irinh (1) do khi do Zx + 2 < 0 Do do, lo^i giai
Ihir hai la chua chinh \ac
Nhung IIS CO nnic i.\d nhan thirc cao hon sc
nhan ra ngu\en nhan sai lam la "Neu vc trai
duang, \c Irai nho ban hoac bang ve phai ihi
\c phai se duong" chi diing vai nhii'ng gia Irj
cua \ la nghiem cua bai phuong trinh do do
JYiy)<g{x) luong duong vo'i ••"'^'^^
\f{x)<[g(x)]
tren tap nghiem ciia bat phuang Irinh chir
khong phai la tuong duong tren tap xac djnh
Trong bai toan tren thuc ra he dieu kien day
dil nhu sau
f / ( ^ ) > 0
x/7WsxW« «W>o
Ldi gidi dung: Tap xac djnh ciia bat phuang
trinh ( l ) h
[x>2
Ta CO (I) <=>
x>2
x<\
2x 6;r + 4 > 0
2.r -f 2 > 0
2:<-'~6;c + 4 < ( 2 ;
0 < ; r < l
x>2
Va> nghiem ciia bai loan la 0<.v<l va
x>2
Vi du 2 -'Cho AABC biet AB - 3cm, AC =
5cm va BC = 7cm Tinh gia tri tich v6 hirong
AB.AC , do Ion goc A va do lan goc giua hai
duo'ng Ihang AB va AC
Mgt vd HS gidi nhu sau:
Ldi gidi thii-nhdt: Ta co 'AB.AC = 3.5 ^ 15
p ABAC , Suy ra cos A = ^ r- = I •
\AB\.\AC\
Vay so do ciia goc A bang O" hay g6c giii'a hai duo'ng thang AB va AC la O"
Ldi gidi thir hai Ta co AB.'A'C = ^{AB' + AC' - BC' ) = - — 2^ ' 2
"1 AC 1
Suy ra cosA
-\AB\.\AC\ 2
Vay goc A bang 120" hay goc giiia hai duong Ihang ABva AC bing 120""
Hay binh luan \ e hai Idi giai tren, chi ra eho chua hop ly trong moi each giai \a trinh bay
lai \b\ giai dimg cho bai giai
Qua viec GV tien hanh to chiic cho HS nghien ciru hai loi giai tren va phan tich linh dung sai ciia hai tai giai bai loan do, HS se nhan thay dugc
Neu HS CO kha nang ve giai loan se nhan thay
a lgi giai thir nhat, HS do da khong nam chac
cac kien thiic ve vecto, do dai vecta va tich
v6 huong ciia hai vecto Do do \o\ giai thir
nhat la chua chinh xac
Neu HS CO kha nang ve giai loan se nhan thay o' lai giai Ihir hai, HS do da c6 sy nham lan ve each xac dinh goc giCra hai vecta va goc giira hai duong thang Do do lo'i giai thii hai la chira chinh xac
Ldi gidi dimg: Ta co
| ^ S | | ^ C | 2 Vay goc A bang 120" hay goc giira hai duang thing AB va AC bing 60°
Vi du 3 Cho AABC biat CA = a, CB_^b Lay
hai diem A', B' sao eho CA'-ma,CB' = nb
Ggi I la giao digm cua A'B va B'A Hay bieu
thj vecto ci theo hai vecta a,b
Trang 3103(03): 151- 154
Moi HS giai nhu sau:
Taco CA'^ma<:i'CA'= mCA
CA
CA'
=> =
A'A
Taco CB
=>CB^^
CB
BB'
CB
m
l - m
' - « 6
C/1'
c^CB'' = n
CB-BB'
n =>
CB
1
Vay B chia doan B'C theo ti s6 / - n A' chia
doan AC theo ti so JH- va I chia doan AB"
l - m
theo ti le x
Ta CO B, I, A' thang hang, ap dung djnh ly
Menelauyt, ta c6:
l - m AI
0-") - ; c = l
m(\-n)
IB-mil-n)
m(\-n)
m ( l - « )
Hay binh luan ve lo'i giai bai loan tren, chi ra
cho chua hgp ly trgng loi giai bai taan va
Irinh bay lai loi giai bai giai cho hoan chinh
Qua viec GV eho HS nghien ciru va phan tich
tinh dung sai ciia loi giai bai toan tren, HS se
nhan thay dugc:
Trong qua trinh giai bai toan tren, HS do da
xac djnh nhim vj tri diem / (/ nim trong
A/i6C) Mac dil ket qua cuoi ciing trong lo'i
giai la dimg, nhung lai giai nay van chua
chinh xac, vi da lam "thu hep" dieu kien ciia
m, « la m > 0, « > 0 Mat khac, HS da xac
dinh nham: Tir ti s6 ciia hai doan thing
= \-~n da suy ra ngay diem B chia doan thang B'C theo ti s6 7 - « va ciing lam tuong
ty nhu the doi voi diem A\
Ldi gidi dung Vi I nam tren A'B va AB' nen
ton tai cae s6 x va y sao cho:
CI = x.CA' + {i-x)CB
= yCA + (l^y)CB' hay x.m.a + (1 - x)b = ya + (\- y)nb
Vi hai vecto a, b khong ciing phuang nen
ta CO
\mx = y \-n
\ hay x = [ ! - J : = n{\-y) \-mn -^r, m(\-n)- f, ]-n ^r Vay: CI = — -a + \ I \b
\-mn \ \-mn) _ m{\n) n{\~m)
Tom lgi, qua phan tich mgt vai vi du tren
buac dau cho chiing ta thay, b6i duong cho
HS kha nang phat hien va giai quyet van de trong giai bai tap toan se giiip cho viec hoc tap mon loan tra nen hieu qua, HS se khac phuc dugc nhu'ng sai lam trong giai bai tap toan va giup HS nam vihig cac tri thirc, phat trien tu duy, hinh thanh cac kT nang, kT xao can thiel cho ban than
TAI LIEU THAM KHAO
[ I ] Le Thi Thu Ha (2007), Ren luyen ky nang gidi loan cho HS bdng phuang phdp vecta Irong chuang trinh hinh hoc 10 (chuang I, 11 - Hinh hoc
10 sdch gido khoa ndng cao), Luan vSn Thac sy
Giao due hgc
[2] Nguyin Ba Kim (2004), Phuang phdp day hoc mon Todn, Nha xuit ban Dai hoc Su pham Ha N6i [3] Tir Dij-c Thao (2012), Boi duang ndng luc phdi hien vd gidi quyit vdn de cho hoc sinh trung hoc phd thdng trong day hgc Hinh hoc, Luan an
Tien sTGiao due hgc
153
Trang 4SUMMARY
FOSTERING THE ABILITY TO DETECT AND REPAIR MISTAKES
IN MATH SOLUTION FOR STUDENTS
Tran Vie) Cuong'', Le Van Tuyen^
'College of Education - TNU 'Education and Trainnmg Deparlmenl ofTuyenquang
If the student has the ability lo detect and repair errors in computing will overcome the mistakes in the settlement and development of intellectual capacity for themselves This paper, we present some examples in the direction of fo.stering the ability to detect and correct mistakes in solving the exercises for students
W^'sworA Students, mistakes, fostering, math, correct mistakes
Ngdynhdnbdi 31/1/2013, ngdy phdn bien.22/2/2013 ngdy duyel ddng-26/3/2013
Te! 0978 626727, Email, tranvietcuong2006@gmaii.com