CONBHIINCDU VAN DE MO HINH HOA TRONG CHU0NG TRINH SACH GIAO KHOA MON TOAN PHO THONG TS NGUYlN DANH NAM TrUAog Bal hoc SU pham, Sal hoc Thdi N ThS HA X U A N THANH Bfi BMa due vd Bdo tao I DatvSndl Chd[.]
Trang 1VAN DE MO HINH HOA TRONG CHU0NG TRINH
SACH GIAO KHOA MON TOAN PHO THONG
TS NGUYlN DANH NAM - TrUAog Bal hoc SU pham, Sal hoc Thdi N
ThS HA X U A N THANH - Bfi BMa due vd Bdo tao
I.DatvSndl
Chddng trinh (CT) giio due phd thdng eua nhieu
nude tr§n t h l gicM dddc xay dimg theo hddng hinh thanh ki
nang, do dd CT sich giio khoa (SGK) mdnToan va h i thdng
vio cic tinh hudng trong thifc tiln cudc sdng Tl^u chuan
"bieu diln" trong CT toin hpc pho thdng cCia Hoa Ki neu
rd: "HS edn tao vd s& dung cdc iogi bieu diin khdc nhau de t6
chdc thiit tdp vd giao tiip cdc y tudng todn hoc; lUa chon, dp
dung vd phlin dleh cdc dang bieu dien todn hoc khdc nhau de
gidi quyit vdn di; sd dung bieu dien de mo hinh hda vd hieu
cdc hiin tUpng vdt II, xd hoi vd todn hpc" [11 Vi the, bd sach
"Toin hoe trong ngd cinh" eua Hoa Ki duac rat nhieu giao
viln (GV) sd dung d l phit triln CT day hpc mon Toin gin
lien vdi ngd cinh thuc t l Ddi vdi Cf cda Ha Lan, khoing
tilp cin theo hudmg gin tlln vdi thue tien Khung CT dUa
tren quan nilm ring toin hpc I i boat ddng va HS can ddpe
tril nghldm d l khim phi tai nhiing trI thdc toan hoc bang
cich eCia chfnh minh hay ndi each khic ti toin hpc hda sudt
qui trinh hpc Vin d l toin hoe trong SGK nham giiip HS
hudng eho HS thye hinti "phuong phip tilp can khoa hoe",
trong dd HS phii bllt: M Quan sit, dit cau hdi, trinh biy
mdt gii thuylt v i hpp thdc hda nd, tranh tuan, md hinh hda
theo cich ca bin; 2/ Hilu sU ll^n he glBa cic hien tUdng tu
md t i cic hidn tupng niy" [2],
Nhd viy, vin d l md hinh hda va gin toin hpc vdi thue
tien rit dUpc coi trpng trong CT SGK ciia nhilu nUde tr§n t h l
gidi Dae bi^t, d cic nddc Hoa K), Australia, Ddc Canada va
thdc phit hinh d t i t ei eic cap dp tU tieu hoe den trung hoe
dddc nhOtig vf du, nhiing tinh hudng cu t h l de ho trd GV
trong vlfie triln ktiai day hpc md hinh hda Tuy nhien, trong
SGK mdn Toin eCia V\iX Nam, viec thiet ke eae md hinh toin
hpc v i cic bii toin ed ndi dung thUc tien phue vu cho viee
Trong SGK v i cie t i i ti?u tham khio ve mdn Toan thudng chi
ehii y tip trung lim rd nhutig van d l , nhiing bai toan trong
ndi bp toin hpc Mdt sd bii tip md hinh hda chi mang tfnh
hinh thdc khdng khuyin khich HS tim tdi, khim phi van d l
tip tnjng vio bddc giii bii toin trong ngdeanh toin hoe [3]
eic tinh hudng gii dinh ma ehud xuat phit tif nhifng tinh
hudng thuc t l sinh ddng
2 Dua vin d l md hinh hda vio ehuong trinh sach
gido khoa
Toin hpc cd ngudn gdc td thdc tiln, phin anh thue
tien v i cd dng dpng trong thdc tien Tif dd, ed t h l thay moi
quan h | mit thilt gida toin hpc v i thUe tiln, do do viec day
hpc toin khdng t h l tich rdi vin d l ll^n he vdi thdc tien [4]
Chiing ta cd t h l liet kd mdt sd y tddng vin dung toan hpc
giii quyet vin d l thdc tiln trong CT SGK eCia Viet Nam hifn eua mdt chit diim chuyin ddng thing; khii ni§m ticliplian
v i bii toin tfnh diln tfch, t h l tfch; khdi nilm cap sd nhin ^ bii toin v l gijrt tiln t i l t kilm, Ngoii ra, SGK edn dda vio niim bit phUdng trinh v i bii toin kinh t l ; xie suit, t i i %
ke md t i v i h i thdng cic bii t i p thdc hinh, Tuy nhiln, s6 lUcffig tinh hudng, md hinh toin hpc v i bii toan thuc tien eon qui it v i ehda thi/c sd trd thinh quan diem chi dao, xuyen sudt qui trinh day hpc
Theo kit qui khio sit chung tdi thu th?p ddpe cho thay dai da sd HS dlu mudn bilt nhdng md hinh toan hoc trong thuc tiln nhdng cic em dlu khdng thucftig xuylntM minh tlm hieu dilu niy VI v|y, HS mong mudn trong S(^ can ed nhilu vf du, hinh ve, md hinh sinh dpng hdnxuJi cung quan t i m din vile day hpc theo hddng tang ediHn^ mdi lien h i toin hoc vdi thuc t i l n nhdng sd quan tam n^
chi ddng lai d eip dtf thip v i chua thudng xuyen Nhieu t\(j\
dung kiln thUe trong CT ning v l tfnh hpc thuit khdng c6 nhilu vi dp, md hinh toin hoe thifc tien Cd khoing 50% sj
GV dUde khio sit cho ring lip khdng thudng xuyfin c h o ^ giii quylt nhdng tinh hudng thUe te ngoii SGK-Thitv^
md hinh toin hpc de minh ho? eho bii giing ddi h d i - ^ phii cd SL( tlm tdi, suy nghT tfch cife v i mIt nhieu thM gian trong khi sif am hilu eic ITnh vyc eiia cudc sdng cCia n h ^ GVcon han ehl v i thdc trang "thi gl, hoe nay" van cdnMn
tai, Chfnh tutddng niy ciing vdi eic de thi khdng ed b i i f "
ed Mdn quan din thifc t l l n ndn dan din viec day hpc cd Iffl ghep cic md hinh toin hpc bj xem nhe, thim chi bd gt
mac dii ed mdt sd md hinh la din xuat de gitip HS hieu d%
bii tap ed lien quan din xay difng md hinh toin hpc ddi r djnh v l chinh cic tinh hudng thUe tien eua md hinh dd Chiing tdi quan nilm bii toin ed not dung thi^ec ^
cd hai loai chinh, dd t i : bdi todn cd tinh hudng gid dinh vi bdi todn chUa tinh huSng IhUc Bii toan cd tinh hudng ^;
cHnh I i nhGtig bai toan cd ndi dung liln quan den thdeti^ chf mang tfnh chit md phdng, theo :^ chu quan eua ngiiS bien soan, cic dd kien khdng phin inh dung hoin to^
diing vdi hi§n thdc t d dd, chdng tdi de xuit tang cuim
dda cic tinh hudng thUe tien vio CT SGK mdn Toin thS
Cd, tao hdng thu eho HS va giup GV dUa ra tinh hudngi^ vin de" trddc khi tilp cin mdt khil nldm mdi hoac ndi d^unc
mdt dinh ly mdi; 2/ Hoat ddng md hinh hda dddc thilt ke sat
khi hoc xong mdt ddn vi kiln thdc giiip HS tjllt v|n du^ lien he v i sddung nhifng edng eu toin hpc phii hdp tt
giii quylt vin d l thdc tiln; 3/ Bdi tdp md hinh hda d\
bii hoe giiip HS cCing c6, dio sau va md rdng kiln thCfel
gi^i bii toin trong nhutig ngd cinh khic nhau; A/DUdn n hinh hda giiip HS ed dilu ki|n lim viec theo nhdm trdtig
Trang 2thdi gian khoing hai ngiy va trinh bay bio cao ket qui tai
cie budi xemina hoac ngoai khda toin hoe; 5/Bdi doc them
d cud) bii hoac cudi chddng giiip HS tim hilu v l Ijeh sdtoan
hpc v i ngudn gdc eua cdc;/tudng toin hoc quan trpng Ddi
v ^ cdc hinh thdc 1,4,5, can tang edcmg dua vio cic tinh
cCia HS); vdi eic hinh thdc 2,3 thl cie tinh hudng gii dinh
cd the chilm du t h l Ngoai ra, SGK can dim bao tinh tham
mi, trinh bay nhieu hinh inh v i md hinh toin hpc sinh ddng
gan gijl vdi cudc sdng xung quanh HS
3 Tich hop md hinh hda trong qud trlnh day hoc
Tfch hop md hinh hda trong qua trinh day hpc toan
phii dat ddpe hai muc dich cd bin sau diy: l/MdhJnhhda
ho trd viec hpc eae y tddng va khii niem toin hpc cda HS,
vi du nhdtao ddng cd, cOng ed, vdn dung khai niem va lien
he vdi kien thdc cua cic mdn hpc khic; 2/ Hpc todn de md
hinh hda cd nghIa la coi md hinh hda ta mdt muc dich cua
viec hoc toan, qua dd bdi dUdng cho HS nang life giil quylt
va ngdn ngd toan hpc de md t i , giii thich hien tuong thdc
tien Ngoai ra, day hpc gin vdi mo hinh hda I i mpt cich
thdc tdt de thdc hien day hoc lien mdn, day hpc tfch hdp
v i truyen thu "vin hda toin hpc" [5].Tfch hdp md hinh hda
trong day hpc toin giup chuan bj tdt cho HS budc vio cudc
sdng da dang sau bac hpc phd thdng, cd khi nang nhln mot
van de dudi nhilu gdc dp khic nhau khi giil quylt van de
vdi nhuTng kiln thdc tdng hpp ciia nhilu mdn hpc Cach tiep
deu tdn tai vdi tU each mpt thife the thdng nhat hdu cd Td
nghidn eUu thUc tien chiing tdi de xuat mdt sd bien phap
sau diy trong day hpc mdn Toin:
o) Bien phdp 1: Tdng cuiatg gcrf dpng ca md dSuxudt
phdt tCr tinh hu6ng thUc tien vd yiu cdu HS thudng xuyen
iiin hi vdi thUc tien
Vile gpi ddng cd md dlu trong day hoe ed the xuat
phdt td van d l trong thuc tien hoic trong ndi bd toin hpc
Khi gpi ddng ea xuat phit td thuc tien GV ed the nlu ten:
7/ Thur tegdn guixung quanh cudc song cua HS; 2/ Thuc ti
xd hdi rdng Idn (kinh ti, ki thudt, quoc phdng, ); 3/ Thdc re d
nhdng mdn hpc vd khoa hpc khdc (vdt ii, hda hoc, sinh hoc, ki
thudt, ) Viec xuat phdt td thuc te gin giji xung quanh HS
se giup cac em thay dUdc sU tdn tai khai nilm toan hpc an
ehda trong thi/c tiln, td do ed dUdc nilm tin va huTig thii
de khim phi l<hii niem toin hpc Hem nda, HS thddng da
cd sd trdi nghidm ve thdc te gan gui xung quanh v i diy la
ed sd d l HS cd them thuan lot trong viec hinh thinh khii
tic dung gpi d^ng cd m i edn gdp phin hinh thanh t h l gidi
quan duy vat bien chdng Nhd dd, HS nhin rd vile nhin
thdc v i cii tao thigicrt da ddi hdi phdi suy nghi v i giii quylt
bat ngudn t d nhdng nhu eiu ciia ddi sdng thdc t l
Viec y^u du HS lidn he den thue tien trong qui trinh
hpc Id cin thilt bdi vi&e lam niy tao ed h^i de HS sd dung
nhdng trii nghilm trong cudc sdng, nhin thay dddc kien
thue hiln dddi cac hinh thdc nhd Tim hinh dnh, xdy dung
md hinh trong thUc tien phdn dnh kien thCtc todn hoc, tim cdc
ling dung cua kiin thdc todn hpc dd hpc vdo thuc tien hoac
dua vdo so liiu thuc t/ln de phdn tich vd dU bdo ve van de
trong tuong lai gdn
b) Ken phdp 2: Chd trpng phdt triin ndng lUc gidi
quyit vinde thUc tiin trong qud trinh day hoc
Day hpc phat trien nang luc ddi hdi phii tang eudng
yeu eau HS md hinh hda toan hoc, van dung kiln thdc vao giai quylt nhiing van d l thUe tien Khi giii quylt van de thdc tdng hpp liln quan din nhieu mdn hpc nhd vat Ii, sinh hpc hda hpc kT thuat Nhilu md hinh toin hpc cung ddpe GVcac mdn hpc khdc sddung de giii thfch v i dd bao ve cac hien tupng trong tif nhien, xa hpi v i mdi trddng
Vi du 1: Do hien tuang tan bdng, nUdc bien ddng nen dien tich mdt hon dda tren Thdi B'inh Duang mdi ndm bi chim thim 2% Gid sit ndm 2015 diin tich ddo Id 1.200 km', hdi ndm
2030 diin tich cua ddo con bao nhieu?
Diy la b i i toin HS phii huy ddng kiln thdc v l toan hpc v i kiln thdc v l ^ a Ii, mdi trudng Kit qui thdc nghiem toin sddung eip sd nhin ma khdng gap bat ki trd ngai nao
fte.«i ,.^.(if' is t> t^.Ai^, L d^ J.XJ^U^TX
^ il7i:^ i \ iJ .: L, t- P £, IL HI tnff £i£M'.n^ c£^.S^'.-JM dM a //» Sw imu ibf J
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I- U-l-s Jtittfl, Ittj dew tfel f(i Iqi Inwa noft tOiO Id Wf'^9 lew' HJnh 1: HS phdn tich, mo hinh hda va gidi bdi todn
Tuy nhien, khi nang phin tich, tdng hdp, lien he ket qui Idi giii bai toan v i ddi chilu thifc te cua nhieu HS edn han ehe Chi mpt sd ft HS cd the dUa ra nhutig bien sd inh hudng den k i t qui eua bdi toan trong thue tien nhu bien dng nhi kinh, lUdng khi thii tang, tupng mua, sU bdi dip hayximlan,
c) Bien phdp 3: Gido due tich hap t/idng qua cdc mo
hinh todn hpc
Trong qua trinh day hpc toin, GV can tang cddng sd dung cae md hinh toin hoc d l tich hap giio due cac vin d l
v l din sd, moi trudng, sdc khde, the thao, cho HS thdng qua eae dU an hpc tap tam viec theo nhdm vdi thdi gian hoin thanh du i n khoing 2 ngay Do dd, khi thilt ke chu sdng, khi nang van dung kiln thdc Men mdn, nhiing ndi dung HS td khim pha va nhdng ndi dung GV ed t h l h6 trp
Trang 3ca NGHIEN C D U
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massj^^i
0
1 S N
Hinh 2
nhU: ylu cSu dpe kT vin d l , phic hoa md hinh, xie djnh muc
tieu, sd lieu can t h i l t thu thap them so lieu, ehpn toe sd lieu,
y nghTa cua ket qua trong thdc tien,
Vf du 2: Su tdng đn so duac Udc tinh theo cdng thdc
S = ^ e ' " , trong do A Id đn so cda ndm idy Idm mdc tinh, S
lds6đnsauNnam,rldtIs6tdngđns6hdngndm.Biitndm
2001, đn so Viit Nam id 5 = 78,685.800 ngUdi va tl le tang
đn so nam do id r = 1,7% Hdi din ndm ndo đn so nUdc ta
dmiiclOO triiu, niu tl so tdng đn so khdng dSỉ
GV dUa mo hinh bai toin v l din sd sau khi hpc xong
bii him sd mu nhim giOp HS v|n dung toin hpc trong
nghiem cho thiy da sd HS da bleu dien dUpc md hinh toan
mdclOOtrieu ngđị
Tuy nhien, rat nhieu HS chua cd thdi quen dot chilu
kit qua tinh toan vdi thdc t l v i nhanh chdng đa ra kit ludn
rang din nam 2015 dan so Viet Nam se dat 100 trieu ngudi
ta ehda dat den con sd da đpe tinh toan v i ehda đa ra
dupe nguydn nhan vl sao lai cd sit khac biet gida tinh toan
trir\ md hinh toin hpc v i sd lieu thue tẹ
Mpt sd it HS lien he thue te rat tdt v i đa ra nguyen
nhan ed nhdng sal sd trong qua trinh tinh toan dUa tren mo
hinh toan hpc: "Hl§n nay, dan sd nUdc ta khoing ttin 90
trieu ngđị Sai sd da tinh toin t i do tl le gia tang dan sd da
thay đi qua tdng nim.Tr^n thdc te thl ti le tang dan sd con
phu thupe vio mdt sd yeu to khic nhU tl \i td, di eU nhip
ed, chiln tranh, ctiinh sach k l hoach hoa gia dinh, Vi vay,
kit qud đdc tinh d tren chi mang tfnh chit tdOng đị Tuy
hôeh hda gia dinh trong thdi gian gan day"
Nhu vay, thdng qua cac mo hinh toan hpc, GV co the
Idng ghep vin de giao due din sd v i giao due mdi trUdng rat
ed hieu qui va co tinh khi thl caọ Vi the, can tang eUdng đa
eic md tilnh toan hpc ve cac van de tu nhien v i xa hdi vao
trong SGK d l gdp ptian giao due toin di^n eho HS 6 bic hoc
phd thdng Ngoai ra, GV ed t h l sdu tam cac bai toan v i mo
hinh toan hpc gin vdi thue tien bang each: l/Tim kiem eic
bai toan td nguon tai tieu tham khio trong va ngoii nudc; 2/
Tim kiem bai toan tdCT SGK cCia eae mdn hoe khic; 3/Tim
kiem bii toan niy sinh tU nhutig van de trong thue tien nhu:
ngan hdng, chdng khoan, bio hilm, giao thong, kinh doanh,
y te, the thao, i m nhac mi thuit ; 4/Tim hilu 'j/ nghTa thUe
tien ciia cic khai niem toan hpc trong SGK v i tdng ghep kien
thdc Ijch sCf todn hpc trong sudt qua trinh day hoẹ
^ ế'*.^.'' _ - Z°fiOfl.QOflQ as A, If ' W^íWo ^ M i ? - fi -= lôg-C-UZhi
^ ,/il, £^ A-a -
.VJM <^ Maw ££«' cl<hi Cs'i^ot fa lạ •i£0'trt&, nq# Hinh 3: Ldi gidi bdi todn cOa HS ve md hinh phdt trien đn so
4 Kit luan Kit qua nghien cdu cho thiy HS hoin toin cd the tham gia vio qua trinh md hinh hda nlu xay dUng dUpc nhulig trinh day hpc Thong qua do, cd the phat triln d HS nang tdc giii quylt van d l va xiy dUng md hinh toin hpc phD hdp vdi thdc tẹ Chiing toi d l xuat mot sd biln phip tang cudng liln he toin hoc vdi thdc tien, long ghep phdOng phap md hinh hda nhim ho trp GV trong day hpc tich hop, liln mdn Trong bdi cinh CT giao due phd thdng dang tilp cin theo hđng phat triln ndng lue HS thl viec van dung kit cic md hinh toan hoc phue vu eho qui trinh day hpc toin la
mdt viee lim rit ed y nghTạ Thdng qua đ, HS thIy dUpc vk
dep ciia toan hoc qua cic litig dung thuetien cCia nd,d6ng
thdi thdng qua cic md hinh toin hoc, HS ed cd hpi đpe g\i\
quyet eic van d l trong thdc tiln đi sdng Day cijng chinh
la mot trong nhdng muc tieu quan trpng cOa qua trinh day hpc mdn Toan d trUdng pho thdng
TAILIIUTHAIVIKHAO
[1] Richard Lesh, Peter Galbraith, Christopher Haines,
Andrew Hurford, (2010), fi/lodeling students' mathematical modeling competences Springer
[2] Qi Dan, Jinxing Xie, (2011), Mathematical modelling skills and creative thinking levels: An experimental studỵ
In G Kaiser et al (eds.) Trends in Teaching and Learning of IVIathematical Modelling, International Perspectives in the
Teaching and Learning of IVIathematieal Modelling Splnger
[3] Nguyen Danh Nam, (2015), Thiet ke hoat đng m6 hinh hoa trong day hoc mdn Todn, Tap chi Khoa hoc, Trđng
Dai hpc SU phani Ha Npi, 60(8A), 152-160
[4] Nguyen Thj Nga, (2014), Sdn vivdn dedgyhocmd hinh hda todn hpc d trudng pho thong Tap chi l<hoa hoc,
Trudng Dai hpc Su pham Ha Npi, 59(8), 69-75
15] Tran Vui, (2009), Sđung todn hpc hda dindng cao hiiubiit dinh lupng cho hoc sinh trung hoc pho thdng, J^pcUl
Khoa hpc Gido due sd 43, Tr 23-26
SUMMARY
The paper ađresses the issue of modeling in the Mathematics textbooks at schools According to the author, students can fully participate in this process within appropriate situations and integrate modeling in the teaching process Then, students can develop competence in solving problems and building mathematical models fit realitỵ The author also proposes a number of measures to strengthen contacts with practice, integrated modeling approach to assist teachers into integrated teaching, interdisciplinarỵ In the context
of general education tovi/ards competence development, provides opportunities for teachers and students to develop mathematical models to serve mathematics teaching is a ver/ meaningful job
Keywords: t\Aodelllng: curriculum; texttbooks