REN LUYEN Kl NANG SlEU NHAN MCm HOC SINH LOfP 7 TRONG DAY HOC TOAN VE Tl IE THIJfC O ThS NGUYEN V A N THANH* Tpdn hpc Id ntdn khoo hpc co bdn, cd tfnh huu tupng coo nhung cd nhllu ung dyng hong mpl ll[.]
Trang 1REN LUYEN Kl NANG SlEU NHAN MCm HOC SINH LOfP 7
TRONG DAY HOC TOAN VE Tl IE THIJfC
O ThS NGUYEN V A N THANH*
Tpdn hpc Id ntdn khoo hpc co bdn, cd tfnh
huu tupng coo nhung cd nhllu ung dyng
hong mpl llnh vpc cuo ddl sdng xd ndl u
nhllu nude hfin t h i gtdt hl|n nay, vl|c dpy hpc
todn f^S thdng khdng d\] Id hong bj cdc kiln thuc
CO bdn vd rin luv^n kr ndng gidl bdl tdp hong
SGK, sdch tham wido md cdn rdt chu hpng d i n
vl|c rfin luy|n kTndng sifiu nh^n thue (NT) eho hpc
sinh (HS) Chfing hpn, hong chuong hinh todn d
THCS cuo Singapore Irong tdl ll|u (1) thi «sifiu
nhdn thue' metoeognltton hodc «tu duy v l lu duy*
(thinking about thinking) d l cdp d i n ndng Ipc klem
sodt qud trinh suy ngnT cua cd nhdn, ode bl$t Id
t ^ v l v i ^ lyo chpn vd su dyng cdc chll^ lupc gidi
glup cdc em hieu dupe bdn chdt cdo qud trinh
(QT) hoc todn vd gidl todn, bllt h/ khdm phd h-i
ndng vdn kiln thuc da hpc vdo ihpc liln
D l rfin luy|n kr ndng slfiu NT cho HS, chung
tdl xdc djnh cdc glal dopn (GD) KT euo HS nhu
hong sodd 1 Mdl hong nhung diiu quon trpng
khi rfin khd ndng slfiu NT cho HS h-ong dpy hpc
todn chinh Id khd ndng Hip cdn Idl gidl mdl bdl
todn cdo ede em Khi HS bllt vdn dyng m^t cdch
thfch hpp cdc h-l thuc dd hpc vdo QT gidl h:>dn
nghTo Id cdc em dd phdt triln dupe h; duy sdng
tpo Khu vdy, HS cdn cd m^l qud h'lnh, dl h> vdn
d l (VD) don gidn d i n phdc h?p d l hinh thdnh kT
ndng slfiu
KT Ddl vdl
HS, d l dpi
dupe md^ kr
ndng slfiu
NT, ede em
edn hdl quo
mdl sd budc
t l ^ cpn V D
theo cdc
cdp dd khde
nhou nhv:
,1 J uiHi man arveuf
- Nhdn a l | n i^myii 4MM»V
vdldm sdng SadSl
G D I
T M M M O t u
NTthOo
T»a tun Huing
+
*
Ucumn
V
G 0 2
M o a c a Mtu d t f M M
+
X t y N n g g l t
Lipklnofcti MnnOOng
^ V ^
0 0 1
•MnhgM
M l klfn titiOcina
V ^ '
Id nhOng V D cdn qugn tdm; - Dua ra nhOng dd nghj ho^c gidi phdp djnh hudng cho QT gIdi quyitt VD; - Ddnh gid, phdn tich, cdc gidl phdp
od d^ hinh thdnh kr ndng nghlAn cOu VD; - Thu ih^p cdc gidl phdp dd dSlilnh thdnh kr ndng situ IMTcOaHS
Dgng todn K1$ thi}c Id phdn ki^n thik rdt quan trgng trong chucmg trinh mdn Todn Idp 7 Khi
dgy ngc todn vi phdn H /^ ihik, HS ihudng ^ [ gidl di/gc cdc bdi todn 6art thudn, cdn nnOng
bdl khd hon, c d c a m c d t h j r o i vdoih^b<)dc, khdng bl^t thdo gd nhu th^ ndo vd khdng bl<t cdch d|nh hudng gidl q u y ^ V D Khi dgy hgc cdc bdl todn v4 tr If thuc, gido viin (GV) thudng duo
ro to nhChig bdl todn ttm m$t ihdnh phdn chuo bi^t cho d^n cdc bai todn Km bo hoOc bdn thdnh phdn chua bl^t cdo tf 1$ thuc hoy cuo ddy K sd odng nhau NhOng dgng todn ndy ddu trang b| ki^n thi>c cho HS d muc d$ thdng nllu Dudi ddy Id mft sd vi dv;
Bdt Iodn I : T l m x b i l t ^ = | j
HutSngdaaTO ^ ' ^ ^ " ^ - ^ •
Muc d$ NT cuo HS du<7C ndng coo ddn ihdng qua ydu cdu ciJa cdc bdi todn, khdng chi hlS thdng hllu It thuydt v l t< If ihOc dd dp ck/ng vdo Idm bdi tdp md cdn dua ra gidi phdp gtdt quylt cdc bdl todn phuc tgp hon
Bdt todn 2: Tim x , bid't: o^ -4^'—;
bl ''±
49
Hudng dSn: a) ^ r r - -3 (-27)
blT-81 =>x = 9 h o d c x - 9
4
-»= = (-9)
49 • x 2 = :
• I1M« eiio llx - Mo t ) ! laqKl Sic SN • m Nti
Tjp Chi Blao dgc s6 2 9 0 (w a 7/toi«i
Trang 27 ~ 7 • glol bdl toon theo cdch sou:
To cung co bdl tgp tuong ti/ sou: _^ fx = 5k
Bd/(o<in3:Tlmxthodmanlilf thuc: ' ' ' ' ? ' 9 * ^ Iv =9*' ^ " y ™ ° '''^'' ''^'''^
i : l = i : : ^ 2 x - y = l , 4 = > 1 0 k - 9 k = l , 4 = > k = l , 4 V d y , x
' + 2 -t + S = 5 x l , 4 = 7 ; y - 9 x l , 4 = 1 2 , d
, , j j - l _ i - 2 D l glup HS hllu bol nhonh, GV cdn Dm ra
Huing o " " ' , + 2 " < + 3 mOt phuong phdp dgy hgc lot nhdt Neu HS ndm
=> |x - 1 )(x +3) = (x - 2)|x + 2) => x^ + 2x - 3 ™"g ^'^" ^<": * ' cdc em sS bill vdn dvng vdo
= x' - 4 => x= - x' + 2x = • 4 + 3 viec gidl cdc bdl tgp todn
_, Bd/(odnd(tr 31 •Todn7|:Tlmhalsdx, y
=> 2x = - 1 => X = —
Nhu v§y, sou khi gidl bdl todn ndy, HS si '"^'- j ° J ™ 'V - 10
ndm vung cdc Mnh chdt cOa tl 1$ thiic, kr ndng Oa'l vdl bdl todn ndy, nhllu HS rdt hay mdc
gidi todn cuo HS se dugc ndng Idn vdl dgng bdl
tim hgl thdnh phdn chua bllt cuo ti If thuc hoy sol Idm khi dp dgng T = \-—: rdl gidl tim x, y
Clio ddy H sd bdng nhau g y ^ ^ ^ ^ g j 5 „ ^5 giaj rt,eo nhllu cdch d l
Bdt Iodn 4: Tim x, y bllt: o) 5x = 7y vd x + y giOp cdc em trdnh dugc cdc sol Idm thudng gdp,
12 23 ddng thdi, r6n luyfn cdc kr ndng gidl cdc bdl
= 4,8;b) — - y v d y - x 5 5 todn v l H If thiic
{xsVc
, mdxy =
' '' • 1 0 n 8 n 2 k x 5 k = I 0 o l 0 k ^ = i 0 = > k ' = l = > k
7 5
Ap dyng h'nh chd't cuo ti If thiic, to cd: ^ ^ hodc k = - 1
j : _ y _ x + y _ 4 , 8
y
V d l k = l t h i r _ r ; v 6 l k = - l t h i x = 2 , , rjr = - 2 , ; vol k = - 1 thi i
T u ^ = 0 , 4 = > x = 2,8;7=0,4=>y=2.V§y, , ;t y 2y ^
7 ' ' 5 ' ' '"• C d c A 2 T u - = ^ = > 5 x = 2 y = > x = - ^ T h a y
b) Tuong ty, HS cd thi gidl duoc de ddng 2y ,« „ , r „
vdo cdng thuc xy= 10=> "r-y= 1 0 = > 2 / = 5 0 Bd//odn5;Timx,yblSj = ^ v d 2 x - y = l , 4 - y i , 25 =>y = 5 hodcy =-5
Ddl vol dgng todn ndy, GV cdn hudng dSn [^ = 2 f^ = -2
HS sii dvng Knh chdt cdo ti If thiic d l gidl Vdy, j 5 hodc L , 5
T i £ = > - 2 £ > Z = 2 £ , 2 £ - y ^ i 4 , , 4 ^ „
5 9 10 9 10 10-9 1 Cdc/i5:Tacdxy=10=> j = ^ ( d o c d x v d
V d l - = l , 4 = > x 7 ; v d l | = l , 4 = y = 1 2 , d y phdl khdc 0)
Nhilu HS cdn lung lung vl bllu lhiic2x-y= 1,4 ^ d | = ^ => ^ = ^ = ^ => ^ = 7 =•
khdng cd trong tinh chd't CO bdn ciia Hid Ihuc GV 2 5 2 2y 5 2y 5
cdnn8urachoHSthdydo<7Ccdchbilnddigldng 2y2 = 50 a y = 5 hodcy = • 5
nhu tfnh chdt cua phdn sd: 'Kht nhdn ho^c chta fj: = 2 jx = -j
cd tli vd nSu cuo mpt p/iSn so' vnH mpt sd ihdc ^^' \y = 5 • ' [ ) • = - 5 '
khong thi duoc mdt phdn so mdl bdng phan sd' Tu bdt hdn 6 se glup HS tim ro cdch gidl bdl
ton ddu', khi dd, HS se bilt dp dvng mft cdch todn sou:
Trang 3Bdl todn 7: Tim X, y bllt 7 = , vd x ' - y ^ « 1
5 4
Trong cdc cdch gidl d bdl Iodn 6, HS cd thi
chgn mgt cdch ndo dd d l gidl bdl todn 7 Tuy
nhldn, HS cdn chgn cdch gidl ndo nhonh nhdt,
ngdn ggn vd d l hllu nhd't Chdng hgn, HS cd thi
gidl theo cdch sou:
[^ = 5*
D d l ; Thay vdo bllu thiic
' - y = - l , t a c d :
15k|' • (4k)' - 1 =j 25k' - 1 dk= - 1 =: 9k^ 1
> k ' ^ = k i h o « c k - i ;
N l u k = i t h i x t v d y ^ ; n l u k 4 l b l
duy sdng tgo Nhu vdy, trong QT dgy hgc todn,
HS dugc rf n luyfn tu duy sdng tgo vd cd thi gidi quylt cdc VD mdl, duo ra cdc phuong phdp gidl mdi khdng chudn mi/c; ddng thdi cho phip HS dugc gidl phdng khdl cdc cdch gidl khudn mdu, cdc tifu chudn cd sdn
Vifc rdn kf ndng sISu NT cho HS Id rdt cdn thilt trong QT dgy hgc todn Vdl mft dgng todn bdt kl, vifc HS rdn luyfn kindng sifu NTcd nghTa
Id cdc em dd hgc cdch thiic phdt hifn, tllp cdn vd gidi quylt VD mdt cdch khoa hoc; gdp phdn bdi dudng cho ngudi hgc nhung dlic Knn cdn thilt cuo ngudi HS nhu Knh chO dfng, sdng tgo, Hdi cvc, kiln tri vugt khd •
3 3
-4
vd y
-BAI todn 8: Tim x, y bllt: x-t-y _x-y vd
6 10
X + y = 12
D l gidl bdl todn 8, GV cd thi hudng ddn HS
gidl theo cdch sou: to nhdn thdy, tu sd cdo cdc
phdn sd Id m$t bilu thiic cuo x vd y ndn cd thi
blln ddl v l « I f Ihiic chi cd chiio thdnh phdn Id x
x + y x-y x + y + x-y 2x x x + y _ x - y
™ ' ' ' 6 ~ 10 ~ 6+10 " 1 6 " 8 ' 6 i0~
x*y-x*y 2y y , X y
= 6-10 -r^-n;ta'uyraj-3^vax +
y = i 2
Bdi todn trd v l dpng ban ddu GV edn hudng
ddn HS khi Idm ede dpng todn v l H l | thuc, cdc
em ed thi su dpng cdc cdch gidl sou: + Cdch 1\
Ap dyng h'nh chdt cua ddy tl sd bdng nhou:
a t e _a + c + e a + c — e , ,
rr7'i;77Vf'JT7:rj'-;*Cdch2:tch,
khdng su dpng dupe ttnh chdt cua H l | thue th) to
k; + Cdch 3: Blln ddl x theo y hoflc y theo x d l
thay vdo ddng thde lifin h | glua x, y
Nlu HS Hm ra quy ludl cuo cdc bdl todn v l tf
1$ thuc se glup cdc em cd dupe cdch gidl tdng
qudt eho cdc odl todn cung dpng Ti> vi|c gidl
bdl todn Hm x, y, la duo ra cdc bdi todn phuc
tap hon Idit flm 3 hodc 4 thdnh phdn chuo bill
ddu, nlu HS ndm vung cdch gidl thi cdc em cd
thi Hm ra dupe cdch gidl cOa cdc bdi todn khdc
(I) Secondary Mathematics Syllabuses, Singapore,
2007
Tdi li^u tham khio
1 Phan Dik Chfnh (ting chu bien) Toin 7 (t9p 1) NXB GMorfi^c.H 2007
2 Nguyin BA Kim Pfauong phip d«y b ^ inOn Toia
NXB Dpi hpc suphpm, H 2004
3 Bill van Nghi Vfn dvng If lufn vio thvc Mn dfy
b9c mOn Toin d truiVng pbl tbfing NXB Dpi hpc su
phpm, H 2008
4 Metacognition: Study strategies Monitoring, and Motivation, William Peirce, 2003
SUMMAITK
Training metacognltlve skills for students in ttie process of teaching genercimathemetkis at sctKX^ Is currently much concerned wtth In ttie worki Ttilsarltele prments an approach to training metacognlttvesl^ tor grade 7 - students m teacNng proportkin
THONG BAO
Tap c h i C U o due ra I tlung 2 ki,
d$t mua ttiuan tif n t ^ cac buu qic dja pliuoi^ (Ma sd C192), IKI^C d|tt mua tivc tiep tjd Toa s o ^ (sd lugng Ion) theo
dja du': TAP CHf ClAO DVC, 4 M n h
HoAl Dlic quan D6ng Ba, Hi N6L
Kinti md4 b^ dgc, cac don v} glao
due, trudng tigc tiep tyc d$t mua Tap
c h i C U o due 6 t l i ^ cudi n i m 2012
Mgl lien tif xin gul ve dja d l l tren hofc lien l(ic qua sd d i f n thofJ: 04.3734S3d3i fax: 04.373453d3 _
Xin tran trgng cam on
TAP CHJ GIAO PyC^