CHAN DOAN MDI SO SAI IJIM COA HOG SHIH TIEH HOC KHI HllHG SHY lUAN OOY NAP K H Q N E HOAN IBJUITROHG BAY HOG MON TOAN O ThS O O VAN HUNG* 1 Mdt trong nhirng ndng lye (NL) quan trpng dnh hudng trye t i[.]
Trang 1CHAN DOAN MDI SO SAI IJIM COA HOG SHIH TIEH HOC KHI HllHG
O ThS O O V A N HUNG*
1 Mdt trong nhirng ndng lye (NL) quan trpng
dnh hudng trye t i l p d i n chd't lupng, hiiu qud
day hpc (DH) mdn Todn d tilu hpc (TH) Id NL
chdn dodn cuo gido vien (GV) Thyc tiln cho thdy,
neu mpt sy kien, hien tupng ndo dd xdy ra vd
ldp di ldp Igi nhilu Idn thi GV cd the duo ro dy
dodn «quy ludt" xud't hien cuo su kien, hien tupng
dd Kit qud dy dodn cd the dOng hope sal (ehi Id
mdt gid thuylt) nhung trong nhilu trudng hpp nd
vdn cd mdt vol trd rdt quan trgng
O TH, phdn Idn kiln thuc (KT) todn hgc (ede
khdi niem, quy tdc, tinh chd't) dugc hinh thdnh
cho hgc sinh (HS) nhung Igi khdng dugc djnh nghTo
hodc khdng the chung minh chdt che do dde diem
Kr duy cOa HSTH Khi DH nhung KT ndy, thdng
thi/dng mdt kit ludn chung, tdng qudt dupe rOt ro
dya tren viSc xem xet kit qud cuo mdt sd trudng
hpp rieng le Qua dd, HS ed the phdt hien vd
ndm bdt KT mdi mdt cdch chu ddng, trdnh tinh
frgng GV dp ddt ddi vdi HS Tuy nhien, vdi edeh
thuc DH ndy, nhung kit ludn md HS rut ra cd t h i
Id sol Idm, vi vdy, GV cdn phdi kiem nghiem vd
xde djnh tinh dung hodc sai trude khi cho HS su
dyng Ddy Id cdch DH dd dung phep suy ludn
quy ngp khdng hodn todn (QNKHT)
2 Mdt sd' khdi niem
1) Phep suy ludn quy ngp khdng hodn todn
Suy ludn Id nhdn thuc biin thuc mgt each gidn
tiip Id qud trinh hr duy cd quy ludt, quy tac nhd't
dinh, xud't phdt tif mdt bay nhieu van di dd biet
ngudi ta di den phdn dodn md/ ( 1 ; tr.85) Hodng
Chung dd djnh nghTa, suy ludn Id qud trinh suy
nghi dilu mgt bay nhiiu phdn dodn dd cd rut ra
phdn dodn md/(2; fr.58) Trong (3; tr.3), suy ludn
Id qud trinh suy nghT trong dd, hj mgt bode nhiiu
minh di dd ed, ta rut ra minh di mdi
Cd rdt nhilu quan niem v l phep QNKHT:
QNKHT Id logi quy ngp trong dd, kit ludn dugc
rut ra nbSm khdng djnh thudc tinh A thudc ve td't
ed cdc phdn tu ciJa tap bap dang xet, tren co sd
dd mdi biet thudc tinh do thudc ve mgt sdphin tu
md thoi (1; tr.88) Hodc QNI<HT Id phep suy luan
di tu mat vdi h-udng hop rieng di nhgn xet vd riit
ra kit ludn chung (3; tr 14) Tuy nhien, ede each
djnh nghTa ndo thi chung cung cd nhirng diem
gidng nhau co bdn Id suy ludn di hf cdi cu thidi rut ra kit ludn tdng qudt, di tir cdi riing din cdi chung vd kit ludn ch! mang tinh gid thuyit (mudn
dp dyng, cdc kit ludn cdn phdi dugc kiem nghiem, chung minh)
Trong DH todn d TH, phep QNKHT dupe dung
d hdu hit cdc bdi hpc vd nd ed voi trd rdt quan trpng trong viee giOp HS tim tdi, dy dodn cdc quy ludt, thudc tinh cOa dd'i tugng todn hpc; tu
dd, hinh thdnh KT vd tim cdc cdch gidi bdi tdp todn Nd pho hop vdi dde diem tdm li vd nhdn thuc cuo HSTH (vi frinh do hieu bilt cuo HS cdn hgn che vd qud frinh nhgn thuc KT mdi cung phdi dya tren viee xem xet ede trudng hgp ey thi, phdi quo thyc nghiem) Vi vdy, ngay tu Idp 1, khi hpc mdn Todn, HS dd dupe Idm quen vdi phep QNKHT mdt cdch rdt Kr nhien Tuy nhien, GV cdn luu y,
HS d TH rdt d l mde sal Idm khi dung QNKHT trong qud trinh hpc tdp
2) Chdn dodn trong DH mdn Todn Di qud
trinh DH dgt hieu qud coo, GV cdn xde djnh dOng ndi dung, myc tieu DH; ndm dupe dpc diem phdt trien tu duy, muc dp iTnh hpi, khd ndng tim tdi, phdt triln KT todn hpc cOo HS; dy dodn dugc nhirng khd khdn, sol Idm vd nguyen nhdn ddn
d i n sal Idm md HS cd t h i mde phdi frong hpc tdp; d l xud't cdc bien phdp su phgm phO hpp vdi
sy phdt then tdm sinh li cOo HS; khde phye khd khdn, trdnh nhi/ng sai Idm thudng gdp cho HS
Vi vdy, ed the hieu: chdn dodn trong DH Id mdt qud trinh boat dgng (HD) tri tui gom cdc HD thdnh phdn nhu: tim kii'm, thu thdp vd xu li thdng tin lien quan den ndi dung DH; du dodn cdc tinh
* Phong Quai h kboa kfc n sau dai kfc, Tnriinj Bai kfc B o i | Tkap
Tap chi Glao due so 3 0 0 (ki a • la/aoiai
Trang 2budng, khd ndng cd thi xdy ra, tim dugc cdch
thuc DH phu hgp vdi tifng tinh budng, khd ndng
ed tbi xdy ra nbdm dgt dugc muc tieu DH
3 Ch£fn dodn mdt so' sal Idm cue HS khi
dOng QNKHT
Ode dilm phdt friln tu duy, fri tue cOo HSTH
Id K/ duy ey f h l , theo kilu «bdt chude"; tri nhd
trye quan - hinh tupng vd tri nhd mdy mde phdt
triln hon fri nhd logic; hien tupng, hinh dnh cy
f h l de nhd hon ngdn ngu v l l t vd cdc ki hieu todn
hpc truu Krpng; khd ndng phdn tieh, tdng hpp,
fruu h/png hod - khdi qudt hod, suy ludn, phdn
dodn vd khd ndng dien dgt bdng ngdn ngu ndi,
ngdn ngi/ vllt cdn hgn che; nhdn thirc chO y l u Id
theo edm nhdn, dya vdo trye quan; (4; tr.7-14)
Vi vdy, d l phu hpp vdi dgc d i l m tdm li Iua Kid'i
vd trinh dg nhdn thuc cua HS, trong DH mdn Todn
d TH, GV cdn quan tdm d i n viee td chuc HD DH
thdng quo cdc vi dy (bdi tdp, bdi todn) ey thi
Yeu cdu HS tim nhirng ddu hieu, thudc tinh vd
bdn chd't gidng nhau, tim mdi quan he giua cdc
dd'i K/png todn hpc vd huy ddng nhung KT, kT
ndng dd ed d l rut ro phdn dodn, kit ludn cdn
thilt GV phdi xde ldp tinh dung - sal cOa cdc
phdn dodn vd kit ludn vdn de (kit ludn khdng
chung minh md giai thich, li gidi hodc dung cdc
phdn vi dy); djnh hudng cho HS trong viee dua
ro kit lugn dOng vd chdn dodn dugc nhi/ng sai
Idm eua HS trong DH d l ed bien phdp khdc phye
Dudi ddy, chOng tdi de cdp tdi mdt so nguyen
nhdn ddn den viee HS mde sai Idm khi dOng
QNKHT; tir dd, d l xud't cdch udn ndn, phdng frdnh
vdi h/ng logi sal Idm:
1) Do khdng ndm vifng ibudc tinh cua dd'i
Iugng todn hgc
Vidu /: Khi hgc ve phep nhdn, phep chia cdc
sd ty nhien, mdt so HS nhpn xet thdy mdi quan
hf gii/a hai phep tinh trong mdt so frudng hgp
cy the: «2x 3 = d tbi d: 2 = 3 vd d: 3 = 2"vd «5
x3=15 tbi 15:5=3vd 15:3 = 5" TO do,
HS se suy ludn vd duo ro kit ludn chung Id: «h>li'u
axb = ethie:b = avde: a = b" £)dy Id kit ludn
sai Idm (frudng hpp cd o = 0 hodc b = 0)
NguySn nhdn dan den sai Idm khi dOng
QNKHT d tren Id do HS khdng ndm vung npi
hdm khdi niem phep chia Id frong phep chia thi
sd' chia phdi khdc 0 (Todn 2; tr 133) nen cdc em
dd khdng xet frudng hgp so chia bdng 0 Vi vdy,
frong phep chia, GV cdn luu y cho HS v l d i l u
kl$n cua so chia phdi khde 0
Tap chi Glao due s6 3 0 0 (ki a la/aoiai
2) Khdng ndm vung diiu kiin di dp dung cdc tinh chd't todn hgc
Vi du 2: Khi DH v l Phdn so bdng nhau
(Todn 4 ; tr 111), HS xet mdt so vi dy ve thyc hien phep nhdn (hodc chia) ed tu so vd mdu so cOa mdt phdn sd vdi cung mpt so ty nhien thi thu dupe phdn sd mdi bdng phdn sddd cho:
3x5
4 x 5 '
15 3 ,, 6:2 3 6
25=4 '^°'?^ 771=2 = 4'
2x3 5x3"
6:3
9 : 3 "
1 5 ~ 5 '
- = - ) 3 9 '
TO dd, HS dung QNKHT duo ro cdc kit ludn tdng
, axe a ,, a.c a, , , ,
quot 7 — = T hodc -— = y vd ddy Id mdt ket
^ bxc b - h:c b '
ludn sal Idm (trudng hpp c = 0)
Nguyen nhdn HS mde sal Idm tren Id do ede
em khdng ndm vOng ve d i l u kien khi nhdn (hope chia) ed tu so vd mdu so cOo mdt phdn so vdi eOng mdt so thi so dd phdi khde 0 Vi vdy, de giOp HS trdnh dupe nhirng sol Idm tuong ty, GV cdn dua ro cdc phdn vi dy (nhdn vdi 0, chia cho
0 thi khdng thyc hien dupe) vd luu y cho HS ve dieu kien ndy
3) Khdng biiu rd (hodc biiu sal) ngdn ngif dien dgt trong todn hgc
Vi du 3: Khi DH v l dien tich hinh chi/ nhdt
(Todn 3, tr.l52), khi xem xet v l mdi quan he giua cdc egnh vdi dien tieh cua mdt hinh chi/
nhdt, HS d l ddng nhdn thdy «A'lpt binh chif nhdt
CO chieu ddi Id a, chieu rang Id b Ni'u tdng chieu rdng thim mgt don vj tbi dien tich hinh chif nhdt tdng thim a don vl Neu tdng chiiu ddi thim mgt don vj tbi dien tich hinh chif nhdt tdng thim b don
vj' TO dd, mpt sd HS dOng QNKHT rOt ro kit
ludn chung «Mgt binh chif nhdt ed chiiu ddi Id a, chiiu rdng Id b Ni'u tdng chiiu rdng thim mgt dan vi vd tdng chiiu ddi thim mdt don vj tbi dien h'ch binh ehu nhgt tdng them a + b don vj" Ddy Id
mdt kit ludn sal
Nguyen nhdn mde sal Idm cua HS khi su dyng QNKHT trong frudng hpp ndy Id do cdc em dd hieu sai ngdn ngu dien dgt cuo todn hpc HS ve hinh tdng them theo K/ng chieu eua hinh chir nhdt
theo cdeh hieu eua cdc em (binh 1) Vdi cdch diln
dgt d kit ludn thu hai, HS phdi hieu Id «Neu mdt hinh chu nhdt dd cd mdt chieu ndo dd tdng them mdt don vj vd chieu cdn Igi tdng them mdt don vj thi duong nhien hinh chir nhdt dd phdi dugc md
rdng cdc egnh theo kich thudc mdi (binh 2f
Trang 3a
b
4) Do mdi chi xem xet dd'i tugng todn hoc
trong nhung trudng hop dde biet
Vi du 4: Khi DH v l Dd'u biiu chia hit cho 3
(Todn 4 ; fr.97), cd f h l Kr KT v l ddu hidu chia hit
cho 2 (hodc 5) dd hgc vd qua viec xet mdt so
trudng hpp rieng, HS nhdn thdy ede so: 3, d, 9,
33, 3d, 39, 123, 12d, 129 chia hit cho 3, h> do
cdc em dOng QNKHT rut ro kit ludn: «Cdc sded
chif sdtdn cung Id 3, d,9tbi chia hit cho 3" Ddy
Id mdt kit ludn sal Idm
Nguyen nhdn ddn d i n sai Idm Id HS dd xet
cdc frudng hpp dde biet De hgn che sai Idm, khi
DH, GV cho HS xet them mdt so vi dy d l cdc em
ty phdt hifn ra sai Idm Chdng hgn, xet cdc sded
chir so tdn cOng Id 3, d , 9 nhung khdng chia hit
cho 3 vd cdc sd Kiy khdng cd chu sd tdn cung Id
3, d, 9 nhung van chia h i t cho 3 TO dd, dan den
viSc ehi cdn xet tdng ede chir so eua so dd khi xet
ddu hifu chia h i t cho 3
5) Do cbua dugc trang bi ddy du ede KT
todn bgc
VI du 5: TO viec xem xet mdt so phep tinh ey
t h i tren tdp hpp so h/ nhien, HS nhdn thdy mdi
quan he «?0 chia hit cho 2 vd 70 chia hit 5 thi
10 chia bit ebo 2x5" va«12 chia hit cho 2 vdi 2
chia bit cho 3 thi 12 chia bit ebo 2x3" Id nhung
kit ludn dung Mdt so HS dd dua ra kit ludn:
«Ni'u mdt sd'vua chia hit cho a, vua chia hit ebo
b tbi sd dd chia bet ebo a x b" Ddy Id mdt kit
ludn sai Idm (frudng hpp hai so a vd b khdng
nguyen tdeung nhau)
Nguyen nhdn HS mde phdi sol Idm tren Id do
cdc em chl mdi xet phep chia hit vdi cdc so trong
cdc trudng hpp khd dde biet Ddng thdi, do HS
chuo dupe frong bj dO cdc KT, kT ndng v l phep
chia hit, nen ede em khdng biet ddu hieu de nhdn
biet tinh chd't ndy De HS trdnh mde phdi nhirng
sol Idm h/ong h/ khi dung QNKHT, GV cd the
cho cdc em xet mgt so phdn vi dy d l cd the duo
ro kit ludn phu hpp (chdng hgn xet ede frudng
hpp ehia hit cho 2 vd 4; 2 vd d hodc 3 vd 6)
d) Khdng tim dugc cdc quy ludt todn bgc
Vi du 6 (ddnh cho HS khd, gidi): Tinh tdng
12-1-112-1-212+ + 1912 + 2012 Mdt sdHS khdng tim dupe kit qud hodc lief ke hit cdc sd hang d l tinh tdng
Nguyen nhdn ed f h l Id do HS khdng nhdn thdy quy ludt cuo cdc so hgng trong tdng, khdng xde djnh dugc so so hgng cOa tdng De giup HS gidi quyet bdi todn ndy, GV cdn yeu cdu ede em neu nhdn xet v l ede so hgng trong tdng (gdm cdc sd
md 2 chu so cudi hdng chye vd hdng don vj Id 12), khodng cdch giira cdc sd hgng liln nhau, ede sd hgng cdch d l u nhau Id 100 don vj Sd sd hgng eua tdng Id: (2012 - 12): 100 + 1 = 2 1 ; tCr
dd, HS tinh tdng bdng cdeh ghep thdnh nhung cgp ddi: (2012 + 12): 2 x 2 1 =21.252
Viee dung QNKHT frong DH mdn Todn d TH
mong Igi nhieu hieu qud thiet thyc, nhdt Id trong viec tim tdi, phdt hien, hinh thdnh KT mdi tren co
sd chi xem xet mgt so trudng hgp ey the Tuy nhiSn, cdc phdn dodn, kit qud rut ra cuo HS dya vdo QNKHT chi Id mot gid thuylt, cdc em vdn chuo dO
KT, kr ndng todn hpc d l chung minh Vi vdy, GV cdn kiem nghiSm vd xde djnh tinh chdn thyc bdng cdc phuong phdp dgy hpc phu hpp Q
(1) Pham Van Hoan (chu biCn) Giio dye hpc m6n
ToSn NXB Gido dvc H 1981
(2) Hoang Chiing Mpt sili va'n d£ v^ logic trong giing
day toan hpc NXB Gido due H 1962
(3) Pham Dinh Thirc Mat sft' va'n d^ suy luSn trong
mOn Toan * tieu hpc NXB Gido due, H 2001
(4) Ha ST Hd Phinmg phap day hpc Toin (Giao trinh
dao tao giao vien tieu hpc) NXB Gido due, H 1998
Tai lieu tham khao
1 D6 Dinh Hoan (chu bien) Toan 1, Toin 2, Toin 3,
Toin 4, Toin 5 NXB Gido due, H 2008
SUMMARY
In order to foster the diagnostic capacity of
stu-dents majoring In primary education and to improve their awareness of expkiiting students'mistakes In their teaching offvlathematics this paper presents the di-agnosis of primary students'mistakes when applying incomplete induction in their mathematics studying
Tap chi Glao due so 3 0 0 (kt a • la/aoia)