JOURNAL OF SCIENCE OF HNUE Educational Sci 2012, Vol 57, No 9, pp 59 67 CHAN DOAN MOT SO SAI LAM CUA HOC SINH TIEU HOC KHI Sir DUNG p n i p SUY LUAN T U O N G T U TRONC; H O C TOAN Do Van Hung Truifng[.]
Trang 1Educational Sci 2012, Vol 57, No 9, pp 59-67
CHAN DOAN MOT SO SAI LAM CUA HOC SINH TIEU HOC KHI Sir DUNG p n i p SUY LUAN T U O N G T U TRONC; H O C T O A N
Do Van Hung
Truifng Dgi bgc Ddng Thdp
E-mail: dvhung@dlhu.cdu.vn
Tom tat Bai bao uinh bay ve viec chan doan mpl so sai lam ciia hoc sinh lieu
hpc khi sfl dung phep suy luan tUdng tu Iiong mon Toan nham gop phan boi duilng nang lUc chan doan trong day hoc mon Toan cho sinh vien nganh Giao due tieu hoc
va nang cao chai Iflpng, hieu qua dao tao giao vien d trudng sU pham
Tifkhda: Chan doan, nang.luc chan doan, suy luan tUOng lU, sai lam trong hoc
toan
1 Mol dau
C h ^ doan (CD) la mpt thuat ngU dUdc dilng pho bien trong y hoc nbUng nhUng nam g§n day no da dUdc diing trong nhi6u linh vUc, nganh nghe khac nhau Trong cuoc s6ng, trUde kbi dUa ra mpt quyet dinh hay ihuc hien mot cong vice nao do (du ldn hay be,
du quan trpng bay khong quan trpng) ngUdi ta deu dUa vao nhQng dau hieu dieu kien hien
tai de dUa ra nhiing CD nhSt dinb: CD nhiing thuan idi va kbd khan; CD nhiing linh hu6ng
CO tbe xay ra; CD kha nang, miic do thanb cong hoac thSt bai; Mat khac, thuc liln cho
thay nhi^u sU vat, hien tupng khac nhau nhUng chung lai co nhUng dac diem, thupc ti'nh giong nhau, co moi quan be vdi nhau Cho nen, trong nhieu trUdng hpp khi biet (hoac chi bi6t) m6t so dau hieu dac diem, thupc ti'nh giong nhau ciia nhung d6i tupng nay co the suy
luan tUdng tU (SLTT) dua ra dU doan \& nhiing dac diem, thupc ti'nh giong nhau khac cua
chung Hoat dpng day hpc (DH) ciing khong n^m ngoai quy luat va each lam do Nhiing kien thiic (KT) trong chUdng Irinh mon Toan lieu hpc (TH) tuy cd ban va ddn gian, nhUng no lai thiet thttc trong cupc song va co y nghla chuan bi cd s6 nen tang cbo viec xay dung cac KT toan hpc 6 cac bac hpc sau Dong thbi, dac diem phat u-ien
tu duy (TD), trf tue cua hpc sinh (HS) liia tuoi TH thi TD d giai doan nay la TD cu the,
thUcJng tri giac tren tong the; tri nhd trUc quan - bmh tudng va tri nhd may moc pbat trien hdn tri nhd logic; hi^n tUdng, hinh anh cu the dl nhd hdn ngon ngii vi6t, ky hi^u toan hpc trCtu tUdng; kha nang phan ti'ch, tdng bdp, trutu tUdng hoa, khai quat boa, suy luan (SL), phan doan cung nhU kha nang dien dat bang ngon ngii noi, viit, sil dung ky bieu va thuat ngiJ toan hpc con ban che; cac KT, ky nang (KN) toan hpc cua HS con qua it nen nhan thdc toan hpc chUa co tfnh hoan chinh; (theo [I; 11], [5; 7-14]) Cho nen trong qua trinh
Trang 2ni 1 mdn Toiin gi.io vicn (CIV) phiii vda cung cap Irang bj KT, vda quan tam ren luyen cac IIKIO lac i n bdi dudnj: klui miiig SL vil sfl dung ngdn ngfl loan hpc hpp ly cho HS
M.il kliiic Dl 1 Tniiii I'l 1 killing chi dflng lai d vice cung cap, Irang bi KT, ren luyen
KN uiiiii hoc clin IIS ma dicu quan Irpng hPn lil liini cho IIS hicu thau dao ndi'dung, pluiiliii; pluip liiim hoc cii y Ihflc, KN vfin dung KT mdt each lUOng ddi linh hoat trong qua uinh kicn lao KT ira'li vii lain cho I IS bfldc dilu bicl van dung KT, KN vao thflc tien cuoc sniis; [I; 13] Vi viiy, Irong qua Irinh DII mdn Toan GV can phai nam vung sfl phat Iricn CO quy luiil TD cuu 1 IS; cd n.ing lUc (Nl.) pliiit hicn dUpc kha nang, mflc dp linh hdi
KT cuu IIS; phiil hicn dfldc nlidii.s ihuan lpi va khd khiin, nhdng sai lam va nguyen nhan lian den sai lam mil IIS ci) Ihc iii.ic phai trong qua trinh nhan thflc; dong thdi cung phal hicn dupc khii ming dm ldi, khai thac phiil Iricn KT, KN uiail hpc cua I IS Tfl dd, cd nhiing bicn phiip Slf pham Ihich hpp vdi Irinh dp phal Iricii liim ly vii phu hpp vdi viiic nhan thiic cac Ki loan hoc cua I IS d TI 1
2, Noi dung nghien cti'u
2,1, Mot so khai nicin
2.1.1, Phep suy luan tuong t u
Theo Dgi lil dien tieng Vict SL cd the hicu: Mpl 111, rut ra mpl hay nhieu phan doan
mdi tren cp sd mpl hay nhicu phan doan san cd Hai lii suy ra dieu nay dicu np mdt each thiSu logic, thidu can cfl thflc lc [7; 1403] Va tuong tU la gidng nbu die, d mat, phfldng dien dflpc ndi den [7;17I7] Nhfl vay, Phep SLTT dUOc hieu la phflOng phap luan (each thflc) xac dinh sfl gidng nhau trong mdt sd mat, tinh chat va quan he giua nhflng ddi tfldng khdng ddng nhit vdi nhau
Trong loan hpc, Phep tflPng tfl (hay phep SLTT) la SL trong dd tfl chd bidt hai doi IflOng toan hpc gidng nhau d mpt sd dau hieu, thudc tinh, la rut ra kcl Iuan rang cac doi tupng nay gipng nhau d nhflng dau hieu, thudc linh khac Phiip SLTT cung la mdt dang cua SL quy nap khdng hoan loan, cac kel luan dfloc rut ra nhd sd dung phep SLTT chi co tinh chat la gia thuydt |4;88-89]
Phep SLTT cd vai trd rat quan Irpng trong viec kham pha, giai thich nhflng kham pha khoa hpc va trong viec giai quyet van de Nd cd the giup phat hien ra van de, de ra nhflng gia thuyet va sau dd dm each chflng minh gia thuyet de xac lap tinh dung dan hoac bac bd
Trong DH mdn Toan TH, sd dung phep SLTT giup HS cd Uie phat huy dudc sang kidn, dm tdi nhflng hieu biet mdi, each giai nhiing bai loan mdi [6;33] va dUa vao nhflng
KT da biet cua mpt ddi tflOng dfla ra phan doan ve u'nh chat nao dd ciia doi tflOng khiic
ma gifla chung da cd mdt so thupc tinh giong nhau Tuy nhien, cflng can Iflu y rang mflc
dp sfl dung SLTT cua HS bac TH cdn thap so vdi nhOng bac hoc khac (theo cam nhan, mang tinh UUc quan cu the, theo kieu "bSt chudc"), cho nen nhflng phan doan ma HS dfla vao SLTT dUa ra chi mdi la gia thuyet Nd can phai dUdc GV xac lap tinh chan thflc bJng
Trang 3each thich hdp hoac bac bo bang each dUa ra phan vf du
2.1.2 Chan doan trong day hoc mon toan
Theo Dgi tif dieh tiing Viet CD la lim hieu nhan xel cae irieu chdng ciia benh bang
each nhin, nghe, hoi, xem mach, r6i quyet doan ve nguyen nhiin, cd che cua benh vii each
chiia [7;245] Con theo tii dicn tieng Viet, CD la xac dinh bcnJi dUa theo trieu cbUng va
ket qua xel nghiem [6; 159] Nhu vay, cd Ihe hieu CD mpl sU vat hicn lUdng irong ihUc liln la tim kiSm, xem xel phal bicn, phan doan ve sU vat, hien IUdng lii sU phan loai linh chat va nguyen nhan ciia sU vat, hien lUdng Va no ihuimg dUdc sir dung dudi nhieu bien the khac nhau de phat hien ra moi lien he nhan qua hoac xac dinh nguyen nban ciia Irieu cbdng, van d6 va giai phap cho cac irieu ebUng van de nay
TU do, chiing toi dUa ra quan niem "Chan doan irong DII la mot qua trinh hoat dpng tri tue gom cac hoal dong thanh phan: ihu thap vii xii ly dicing tin lien quan den noi dung DH; du doan cac linh huong, kha nang co the xay ra irong qua irinh DM; de ra each ihUc
DH thieh hdp vdi tiing linh huong, kha nang xay ra de dai dUpc muc lieu Dl!"
Dieu c3n lUu y ii day la boat dong CD irong DH khong chi difng lai d viec lim ki6m
ihu ihap, xU ly cac thong tin, xac nhan cai hien cd tai mpt thtii dicm cu ihe nao do ma no con bao gom ca sU phal bien cac v3n d^ liem ain, dU doan kha nang co ihe xay ra, xu hUdng
phat trien trong tUdng lai de tii do co nhiing banh dpng, ke sach giai quy^l thich hdp vdi tUng IrUdng hpp Va kSl qua ciia boat dpng CD trong DH la tong hdp ket qua ciia cac boat
dpng thanh phin da thuc hien
Vi vay, trong DH mon Toan thi mpt trong nhung yeu cSu quan trpng dat ra la ngUdi
GV pbai cd nang lUc chan doan (NLCD) phal hien, du doan dUdc nhung loai sai l§m va
nguyen nhan dSn d&n sai lam, tii do dua ra dupc each han che, phong tranh nhUng sai ISm
ma HS CO the mac phai irong qua trinh nhan ihUc
2.2 C h a n d o a n m o t s o s a i l a m thUcfng g a p k h i H S d i i n g S L T T
Trong mon Toan TH cd kha nhi6u KT toan hoc khong dupc va cQng khong the chiing minb chat che theo SL suy dien ma phai hinh thanb KT cho HS qua viec dung SLTT de phu hdp vdi dac diem tam ly lUa tuoi va Irinh dp nhan tbUc cua HS (dac diem
TD ciia HS giai doan nay la TD cu Ihe, nhan ihUc chii yeu la tbeo cam nban dUa vao iriic quan) Vi vay, khi DH mon Toan GV can quan tam to chUc cho HS hoat dpng hpc loan qua cac vf du (bai lap, bai toan), tim nhiing d§u hieu, thupc tinh gi6ng nhau ve mat nay hay mat khac, tim m6i quan be giiia cac doi tUdng loan hpc va yeu cau HS huy dpng KT,
KN, kinh nghiem de SLTT dua ra cac phan doan, riit ra cac kh luan c§n thiet (can lUu y
rang HS d TH chua hpc ve phep SLTT ma chl thuc bien mot each tU nhien theo I6i "bat chudc", nen GV pbai co trach nhiem xac lap tfnh diing hoac sai ciia ket luan, b6i vi HS chUa the tU chUng minh dUpc)
Khi hpc mon Toan, HS co thi m5c nbi^u loai sai lam khac nhau Sau day la mot s6
CD ve nhiJng sai lam va nguyen nhan dan din sai lam ciia HS d TH thudng mac phai khi
Trang 4diing SLTT, dong ihili JO xual ciich han clic vdi tflng loai sai lam
2.2.1 Hoc sinh mac sai lam khi diing SLT'l' ma khnng dua vao thuoc ti'nh, dau hieu biin chat cua cac doi lining loan hoc (hoac cd nhung khong day du)
t liung han kin IIS ldp 4 hpc vc "Dau hicu chia hcl cho 2" cd the qua viec xet "cha
sd uin cung" i) mpl sd vi du cu Ihi!' |2;94|, I IS rut ra dflpc ket luan dung "Cac sd cd chS
sd uin cimg lii 0; 2; 4; 6; K llii chiu hcl cho 2" vil "Cac sd cd chfl sd tan cung la I; 3; 5; 7;
9 Ihi khdiip chia hit cho 2" Tuy nhicn, neu IIS dung SLTT de dUa ra cac ket luan tfldng
uiis; vdi die dau hicu chia hcl cho ^ (hoac 9, hoac 3) |2;95-97], ihi khi dd se dfldc ket luSn
dung vdi dau hic'u chia hcl clio 5 vii sc co ciic ket luan sai vdi dau hicu chia het cho 9
(hoac 3)
Vice diin ddn I IS cii nhflng phan doan, nhdng kcl luan sai lam d trong trudng hdp niiy lil do KT vii khii niing SL phan lich, tdng hop cua I IS cim han che Khi sfl dung SLTT dii khdng nhiin Ihay mdt dau hicu dac bicl quan trpng la vdi cac sd trdn chuc thi chac chan chung chia hi:! cho 2 (hoac 5) iicii chi can xel dau hieu cua chfl sd d hang "dOn vi" (chflso
tan cung) cdn vdi cac sd trdn chuc thi khdng chac chiin chia hel cho 9 (hoac 3)
De ban che nhdng sai lam tren, GV cd the td chde cho IIS xet mdt so vi du deHS nhan th5y cd Irfldng hpp chfl sd tan cung chia het cho 9 (hoac 3) nhung sd dd khdng chia hel cho 9 (hoac 3) va cd nhflng trfldng hpp chfl sd tan cung khdng chia het cho 9 (hoac 3) nhflng sd dd van chia hcl cho 9 (hoac 3), Ngoai ra, GV cd the id chflc cho HS hoat dpng (Irong trfldng hpp cd the) dc I IS nhan thay cfl mdi chuc, tram, nghin, khi chia cho 9 (hoac 3) thi deu dU I, cho nen dan ddn vice (SL) chi can xet vdi tdng cac chfl sd d cac hang don vi, chuc, tram, nghin, khi xet dau hieu chia het cho 9 (hoac 3)
2.2.2, Hoc sinh mac sai Iam khi diing SLTT ma khong hicu rd hoac chua nam virng ban chat khai niem sd tren cac tap hop so
Khi HS thuc hien phep chia tren tap Sd lfl nhien nhan thay rSng 63 : 15 = 4 (dfl 3) thi day la mdt ket luan dung NhUng khi hpc "Phan sd va phep chia sd tfl nhien" [2; 108-110],
HS dung phep SLTT cung dfla ra cac ket luan 3 : 4 khdng chia dupc va 5 : 4 = 1 (dfl I) thi day la nhflng kdt luan sai Hoac khi HS hpc "Chia mdt sd thap phan cho mpt so thap phan" [3;7I], neu HS cung dua ra cac ket luan 23,56 ; 6,2 = 2 3 5 , 6 : 62 = 3 (du49,6) va 36,3 ; 1,5 = 363 : 15 = 24 (du 3) thi day cung la nhflng ket luan sai
Khi HS hpc thflc hien viec "So sanh hai phan sd" [2; 119J hoac "So sanh hai so diap phan" [3,41 ], HS mac sai lam thflc hien viec so sanh tUOng tU nhu so sanh cac so tfl nhiSn:
- So sanh tfl so vdi lit so, mau sd vdi m§u so cua phan so:
»l ^ ^ ^ M -^ ^ 3 13 1,5 , 1 3 8
a ) j < 7 b ) - > - ; c ) - < _ ; d ) - > - ;
- So sanh cac sd khdng quan tam den vi tri "dau phay" cua so thap phan: a) 35,7 < 3!;,69 ; b) 25,71 > 25,8 ; c) 31,57 < 31,569 ; d) 13,17 > 13,6 ; Mdt so HS m5c phai nhflng sai lam tren la do HS da SLTT tii cac KT, KN cua phep chia cdn du, so sanh cac so tren tiip hop So tu nhien da biet la dung chuyen sang ap dung
Trang 5vao vific thttc hien phep ehia, so sanh pban s6, so sanh sO ihap phiin uong khi HS cbua
hieu ro cac khai niem ve phan so [2; 106], kbai niem ve so Ihap phan [3; 36] vii chUa nam
viing cac quy tic so sanh phan so [2; 119-121], so sanh so ihap phan [3; 41-42]
De han chfi nhUng sai lam nay ihi khi day nhiing KT vfi pbiin s6, so Ihap phan trUdc
het GV can pbai lam cho HS hifi'u ro cac khai niem, y nghia ctia phan so, so ihap phan (la
nhiing loai so mdi khac vdi s6 IU nhicn), each bie'u dien mol phiin so, so ihap phan, dong
thcfi phai lam cho HS nam vUng khai nifim ciia phep chia hel phep chia con dU vit cac quy
tac UiUc hien so sanh pban so, so sanh so thap phan
2.2.3 Hpc sinh m a c sai lam khi dung SLTT ma khong nam virng quy tac thufc hicn
phep ti'nh, tinh ch4t cua phep tinh (hoac co nhifng khong day du)
Vf du hpc "Cac phep tfnh vdi phan s6'" [2; 126-139) hoac "Cac phep linh vdi so ihap
phan" [3;49-73] Ihi HS cd die' m5c sai lam khi sU dung phep SLTT:
- Sai lam kbi ibuc hifin cac phep tinh vdi pban so (IhUc hicn tif s6 vdi tii so, mau so
vdi mau so):
2 J _ 2 + 5 _ () _ 3_
^*5 "^ 3 ^ B T S " 8 "" 4 '
5 _ 3 _ 5 - 3 _ 2 _ j
^ 8 ~ 2 ~ 8 - 2 ~ 6 ~ 3 '
4 2 _ 4 : 2 _ 2
'^ 9 • 3 ~ 9-1-3 ' 3 •
- Sai Um khi thuc hien cac phep tfnh vdi so thap phan (khong chu y den vi trf "dau
phay" trong so thap pban):
a) 75.8 + 249.19 = 256 77 ; b) 50,84 - 19, 2 = 48,92 ;
c) 4.34 X 3,6 = 156,24 ; d) 23.56 : 6, 2 ^ 3.8;
- Sai lam khi ap dung SLTT vdi cac tfnh ch§t cua phep ti'nh:
a) Tii cac ket luan da bifit la dung a + b = b + a hoac axb = b:ra nfiu ap dung SLTT
dUa ra cac ket luan A — 6 = 6 — a va a : 6 = 6 : a thi day la nhiing ket luan sai b) TU cac
a t i X c a Cl ' c r
kit luan da bifit la dung, vdi c ?^ 0 tbi - := va - ;— -r— neu ap dung SLTT dUa
b b X c 0 b : c
, ' , a a - | - c a a — c , , ^ ,, , _ , ^ ,
ra cac ket luan - := va - := tbi day la nhung ket luan sai
' 0 R-l-c o b~ c
Mpt so HS CO the' mac phai nhiing sai 15m tren la do HS da van dung SLTT nhflng
KT, KN thuc hifin phep ti'nh (cac kfit luan, tfnh chat, quy tac) iren tap hdp So tU nhien dUdc
trang bi da bifit la diing sang thuc hien phep tfnh vdi loai so khac la phan so, so thap phan
De ban che nhflng sai lam nay thi khi day GV phai to chflc cho HS nhan th§y su
khac nhau khi thUc hifin phep tfnh giiia cac loai so va tiT do HS phai n^m vflng cac quy tac
thflc hifin phep tfnh vdi cac phan s6, s6 thap phan
Trang 62.2.4 Hoc sinh mac sai lam khi diing SLTT ma khong hicu ro ban chat gia thilt bai loan {hoac khong nhan thay sir thay doi gia thiet bai toan)
Chang ban khi IIS dfi hoc each giai bai loan "Tmi bai so kbi bicl long va bifiu ciia
hai sd do" |2;47] ihi US co the' van diing mol irong hai each giai vao giai bai loan cho
dling dang "Tuoi bo va luoi con cong lai dUdc 58 luoi Bo hdn con 38 tudi Hoi bo bao nhicu ludi, con bao nhicu ludi?" [2:47| NbUng neu chi thay ddi gia ibict bai loan Ihanh biii loan nuii "Ba nam IrUdc anh bdn eni 5 ludi Ba nam sau nfla tdng sd tudi ctia hai anh
cm ,se la 27 lioi hicn nay anh bao nhieu ludi, em bao nhifiu tudi?" thi mot so HS kh6ng giai dUdc hoac la se ap dung may mdc mpl irong hai each giiii (Hai lan ludi cm la: 27-5
= 22 (tudi): Tudi em lii: 22 : 2 = 11 (ludi); Tudi anb lii: 27 - 11 = 16 (tudi)) Day la mot lili giiii sai
Sai lain Clia I IS if day lii I IS chi mdi nhan thay mot sd thupc tinh co ve giong nhau
\c gui ihiel "Tdng", "'Hieu'" cua dang bai loan quen ihupc "Tim bai sd kbi biel tdng va hieu Clia hai so do" vii dimg ngay SLTT dc ap dung each giai da biet mii khong nban diay
ban chai sii khac nhau ciia giii thiel sU bicn ddi moi quan be gifla cac gia thiet "Tong",
"Hicu" (irUdc sau, hicn lai) vdi cau hdi cua bai loan
Muon tranb sai lOm kbi giai biii loan tren can yfiu cAu HS phan tfch de nhan Ihly moi quan he ban chAl ciia gia thiel bai loan "Neu ba nam trUcJc anb hdn em 5 tudi thi hien nay (cung nhU ba nam sau nfla) anh van hdn em 5 ludi" va "Ba nam sau tdng sd tudi ciia hai anb em sc lang them 6 tudi so vdi tdng sd tudi hifin nay" Khi dd HS cd the SL dedi tim tudi Clia moi ngucii sau ba nam nfla hoac tim tdng sd tudi cua hai anh em bien nay va tfl dd tim tudi hien nay cua mdi ngUtJi
Hoac sau khi HS hpc each giai dang bai loan "Tim hai so khi bifit hieu va li sdciia hai so do" [2; 150] ihi I IS co thfi^ van dung ngay vao giai bai loan "Ngudi ta dung sd bong den mau nhifiu hdn sd bdng den U'ang la 250 bong den Tim sd bdng den mdi loai, biet rang sd bdng den mau bang - sd bdng den trang" 12;151] Tuy nhicn neu thay ddi gia thiel bai loan trfin thanb bai loan mdi "NgUtii ta dung sd bong den mau nhieu hdn sd bong den trang la 250 bdng den Tim so bdng den mdi loai hicn tai, bi^t rang neu mdi loai si
dung thfim 50 being nfla thi sd bong den mau bang - sd bong den tring" thi co the co mot
so HS khong giai dUdc hoac HS se ap dung each giai (theo mau) da biet: So ph5n bong den mau nhieu hdn sd phan bong den tring la: 5 - 3 = 2 (phin); So bong den mau la:
250 : 2 X 5 = 625 (bong); Sd bong den trang la: 625 - 250 = 375 (bdng) Day la m6ll6i giai sai
Sai lam cua HS khi sfl dung SLTT each giai bai loan da biet vao giai bai toan trong trudng hdp nay la do HS mdj chi nhan thay mot sd gia thiel tUdng ttt gifla hai bai toan cu tbe la "Hieu" va ' T i sd" ma kh6ng nhan thay sU thay ddi quan he gia thiet ("Ti sd" sau khi them) ciia bai loan mdi "Neu mdi loai sfl dung thfim 50 bong nfla thi sd bdng den mau bang - so bong den trang" va cung khong phat hien ra mdi quan he gifla "Hieu" ban dAu
Trang 7Hinh 1 Hinh 2
vdi "Hifiu" sau khi mdi loai da sfl dung thfim 50 bong den van khong thay ddi Dfi' han che nhflng sai lam cua HS trong qua irinh giai cac bai loan co su gan gidng nhau vfi mat cau true (nfin cijng co sU gan gidng nhau vfi each giai), IrUdc kbi giai bai loan yfiu clu HS phai lU phan lich ky cac dfl kien cua biii loan lim ra cac mdi quan he gidng nhau va co the diing SLTT chuyfin chung ve dang da biel ciich giai (dang bai loan m5u)
Cung can lUu y cac bai loan sau khi da thay ddi giii thifil danh cho hpc sinh kha, gioi Con cac bai loan d lai lieu 12;47,151] dinih cho hpc sinh dai tra
2.2.5 Hoc sinh mac sai lam khi dung SLTT ma khong nam virng bieu tUdng \h ddi
tuTdng, dai liTdng hinh hoc
Chang ban, kbi cho HS on tap ve nhan dang vii nhan bict so lUdng cac hinh da boc:
- Hinh 1 cd bao nhieu hinh vuong?
- Hinh 2 co bao nhieu hinh chfl nhat?
- Hinb 1 cd bao nhifiu hinh chfl nhat?
Co the" dung cac each xac dinb sd lUdng
hinh khac nhau, HS dua ra kfil luan "Hinh 1 co
tat ca 5 hinh vuong" tbi day la mpl kfil luan dung
Tuy nhien, neu HS dung SLTT kfil qua nhan dang sd lupng hinh vuong tfl Hinh 1 chuyfin sang Hinh 2 dfi' dUa ra kfit luan "Hinh 2 eo tal ca 5 hinh chii nhat" va cung tUdng tU nhU vay dUa ra kfit luan "Hinh 1 cd lit ca 5 hinh chfl nhal" thi day lai la nhung kfit luan sai ThUc ra irong Hinh 1 va ITinb 2, moi binh dfiu co tit ea 9 hinh chfl nhat
Sd di HS mac nhflng sai lam tren la do HS da van dung SLTT mpl each hinh IhUc, may mdc khi chua nam vflng bifi'u lUdng ciia hinb chfl nhat Khong nban bifit dUdc la bai hinh vuong co cbung mpt canh tbi khong lao thanh mpt hinh vuong, nhung bai hinb chfl nhat co chung mpl canh ihi lao thanb mpl binh chfl nhat va binh vuong ciing la hinb chfl nhat
Cho nen, de han che nhflng sai lim kbi HS diing SLTT trong qua trinh DH nhan dang, nhan bifit sd binh thi GV can chu y tap cho HS co thoi quen pban tfch, tong hdp hinb (cat, ghep hinh), tim mdi quan he gidng nhau va khac nhau gifla cac ddi tupng loan bpc
Hoac khi cho HS on tap vfi chu vi, dien tfch cac hinh da bpc [3;I66-167], de' hinb thanb cac cong thflc tfnh dien tfch hoac phai tfnh dien tfch ciia mot hinh phflc tap tbi thudng dung phfldng phap clt, ghep hinh dfla ve cac hinh quen thupc, ddn gian bdn va da bifit each tfnh difin tfch (chang ban vdi cac hinh 3,4, 5)
Va HS nhan thay rang "N^u mot hinh nao do dfldc chia cat thanh cac hinh thanh
Trang 8phan Ihi dicn (ich cua hinh ban dau can linh bang tdng dicn tich cua cac hinh thanh phai tia difOc chia ra", O.iy ki mdl ket luiin dung Tuy nhicn, neu IIS ap dung SLTT de nitn kcl luiin vtii vice linh chu vi cua hinh ban dau thi di'i lai lii mdl ket luan sai lam Sai lam cda mdl sd HS khi sfl dung SLTT trong Irfldng hop niiy la do HS chi nhar lliay su gidng nhau vi: hinh hinh hoc cdn khdng cd bieu tUOng dung vc chu vi, dien tie! cua mot hinh, Dii:n lich la dai luong hicu thj ve gidi han be mat cua hinh, nen dien tich ciia cac canh chung biing 0 Cdn chu vi lii dai IflOng bieu thi ve tdng do dai cac canh cua hinli nen khi unh chu vi cua hinh Ihi canh chung cua cac hinh thanh phan da dUdc tinh dp dai 2 lan vi vay dan den kel qua sai
Dc triinh sai lam nay, Irong qua trinh DH vc chu vi va dien tich cua mdt hinh cin lam cho IIS hicu id y nghia va phan biet sfl khac nhau vc cac bieu tUOng dien tich, chuvi cua mdt hinh,
2,2,6 Hoc sinh mac sai lam khi diing SLTT ma chira hicu hoac hieu sai ngon ngii dien dat, ngdn ngu toan hoc
Chiing han, khi hoc cac khai niem "sd chSn", "sd le" (2;94|, HS nhan thay "long (hieu, lich) cua cac sd chan la sd chan" la mdl ket luan dung Tfl dd, SLTT dUa ra ket luan
"Tdng {hieu tich) cua hai sd le la sd le" Ihi la mdt ket luan sai lam
Nguyen nhan sai lam d day la HS da khdng hieu ngdn ngfl loan hpc "Sd chia hel cho 2 la sd chan" va "Sd khdng chia hdt cho 2 la sd le" Vi vay khi DH phai cho HS Ihay can phai hieu va xet cac dSu hieu rdi mdi dfla ra ket luan
Hoac khi GV cho HS giai bai loan "Cd 4 diem ndm Iren mot dudng Uon, nju noi cac diem vdi nhau thi duoc bao nhieu hinh tam giac" HS thUc hien va xac djnh dil*
4 hinh tam giac thi day la mot ket qua dung Tuy nhien, neu HS dflng SLTT tfl ket qua nay dfla ra ket luan "Cho 4 diem thi ve dflgc 4 hinh lam giac" thi day la ket luan sai lam (trudng hop cd it nhal 3 diem cung nam tren mot dudng thang)
Sd di HS mac phai sai lam tren la vl HS khdng nhan biet mot dieu quan Uong la 4 diem njm tren mdt dfldng trdn da "ngam" cho biet mdt dau hieu la khdng cd 3 diem nao cung nam tren mdt dudng thang
De ban che viec xay ra sai lam tren cung nhu nhflng sai lam khi sfl dung SLTT trong
DH mdn loan, GV can bdi dudng ngdn ngfl toan hoc cho HS qua viec tap cho HS each trinh bay dien dat bing ngdn ngfl toan hoc hoac s i dung cac Uiuat ngii, ky hieu loan hoc
3 Kit Iuan
Phep SLTT cd vai ud rat ldn trong qua uinh sang tao toan hoc Trong DH mdn loan
TH viec sfl dung SLTT mang lai nhieu hieu qua thiet thUc Nd thudng dUdc dung de hinh thanh cac KT mdi Uen co sd nhflng KT da biet cua nhflng ddi tuong toan hoc cd sU giong nhau ve mdt sd tinh ch4t va moi quan he, nen nd phu hop vdi quan die'm DH k i k tao Tuy nhien voi cac phan doan ma HS dung SLTT rut ra thi chi mdi la nhiing gia thuyet (cd the dung hoac sa.) nhung HS lai khdng du KT, KN d l chflng minh Do dd, nhflng gia thiiyfc
Trang 9nay can phai dUdc GV kiem nghiem va co trach nhiem xac djnh ifnh diing sai bang nhflng each thfch bdp
Bai bao da dat ra va giai quyet van dfi CD mpt so loai sai lim IhUdng gap kbi HS diing SLTT Irong hoc mon Toan TH Trong thttc le khi hpe mon Toan cd thfi' HS con mac rat nhieu loai sai lim khac ma GV cin phai phal bien va tim each ihi'tc ban chfi, phdng tranb phu bdp Mudn vay, trudc bet GV can phai co NLCD trong DH mon Toan TH dfi' co the'CD dung, phal hien dUdc nhitng sai lamed ihe xay ra vdi I IS TU do co the djnh hudng trong vific giup HS dung SLTT dUa ra cac kel luan dung va giup HS Iranh dUdc nhflng sai lim trong kbi hpc mon Toan, NL nay chii yeu dUdc hinh ihimh va bdi dudng qua qua trinh hpc lap, ren luyen d IrUdng sU pham va lich luy kinh nghiem mot each thudng xuyen, lau dai
TAI LIEU THAM KHAO
[1] Vii Qudc Cbung, 2007 PhUcfng phdp dgy Todn d lieu htfc, Sach dao tao giao vien
Nxb Giao due Ha Npi
[2] Dd Dinh Hoan, 2008 Todn 4 Sach giao khoa Nxb Giao due Ha Noi
[3] Dd Dinh Hoan 2008 Todn 5 Sach giao khoa Nxb Giao due Ha Npi
[4] Pham Van Hoan (Cbii bien), 1981 Gido due hgc mim todn Nxb Giao due Ha Npi [5] Ha Si Hd, 1998 Phuong phdp dgy hgc Todn Giao trinh dao tao GVTH Nxb Giao
due Ha Npi
[6] Hoang Phfi (Cbu bifin), 1988 Tif dien tiing Viet Nxb Khoa hpc Xa hpi
[7] Pham Dinh ThUc, 2001 Mgt sd vdn di suy lugn trong mem ttfdn d tieu hgc Nxb Giao
due Ha Npi
[8] Nguygn Nhu Y (Chu bifin), 2011 Dgi tit dien tieng Viet Nxb Dai hpc Qudc
gia Tp HCM
ABSTRACT
Diagnosing the mistakes of primary students
when they apply analogies in mathematics
The article presents a diagnosis of primary students' mistakes made when they
ap-ply analogies in mathematics, done in order to improve Ibe diagnostic capacity of students majoring in Primary Education and improve teacher training at pedagogical universities