v u VAN TAM* Chuang trinh mdn Toandtieu hpc la eo sd, nen tang eho eae bae hpc tie''''p theo; trong dd, mach kie''''n thifc hinh hpe cd vai trd quan trpng trong chuong trinh mdn Toin Nhung nam gan day, nen[.]
Trang 1v u V A N TAM*
tang eho eae bae hpc tie'p theo; trong dd, mach
kie'n thifc hinh hpe cd vai trd quan trpng trong
chuong trinh mdn Toin Nhung nam gan day, nen
giao due Singapore dupe thegidi danh gia, cdng nhan
la mpt trong nhifng nen giao due phat trien tren the
gidi Vi vay, viee nghien cifu chii de hinh hpc trong
chuong trinh va sach giao khoa (SGK) mdn Toin
eiia Viet Nam va Singapore nhim tien hanh so sanh
mdt sd ndi dung co ban ve: muc tieu, eau true ndi
dung de tha'y dupe nhirng diem tuong ddng va khac
biet giifa chuang trinh mdn Toinaim hpe ciia nude
ta va Singapore ve ehii de hinh hpc
1 Chu dehinh hpc trong chuang trinh vaSGK
mon Toan dtieu hpc tai Singapore
1) Quan diim day • hgc toan a Singapore Md
hinh ngu giic ciia Toan hpe Singapore la chuong
trinh khung (SMCF Singapore Mathematics
Curriculum Framework) tuyen bo lan dau tien vao
nam 1990 Ldi ciia md hinh nay la giai quyet cic van
detoan hgc Md hinh ngu giae gom: khii niem (ndi
dung), quy trinh (phuong phap), kJning, thii do va
siiu nhan thu'c (tu duy) Md hinh nay the hien cac
nguyen tie ea ban eiia mdt chuang trinh toan hpc cd
hieu qua dupe ap dung eho tat ea eac cap hpe tai
Singapore
Monitoring one's
^ i L \ own thinking
Estimation and
Mental calculation
Communication
Use of mathematical tools
Arithmetic manipulation
Algebraic manipulation
Handling data
dehinh hgc trong chuang trinh mdn Toan dtieu hgc My Pals are here Maths la mdt bd SGK mon
Toin d tieu hpe d Singapore, dupe thiet ke dua tren
eac hoatddng hpc tap cua hpe sinh (HS) nhim trang
bj nhiing kie'n thifc toan hpc co sd va phat trien kT nang tu duy phe phan, sang tao, giai toan hieu qua cho cac em
Chuang trinh SGK d mdi khd'i Idp gom 2 tap (tap
1, tap 2) danh cho hai hpc ki, ehia lam hai eud'n A va
B Mdi eud'n sach duac ehia thanh cac chu de, cac mach ndi dung nhu sau: (bang 1)
3) Ngi dung chu dehinh hgc trong chuang trinh va SGK mdn Toan a tieu hgc Npi dung
hinh hpc trong chuong trinh va SGK toan tieu hpc a
Singapore dupe sip xep theo cau true hinh xoay trdn de, ehia thanh cae tieu ehii de khac nhau nhu: hinh, mau hinh, khdng gian 2-D, 3-D, gdc, diem, doan thang, dudng cong, mat phang, phuang hudng va dupe sip xep rieng biet thanh tung chii
de nhd, ed su bd' sung, hd trp lin nhau Vidu:6e
hinh thanh kie'n thu'c ve HCN tuong dd'i day dii thi
can nhieu kie'n thuc a cac khd'i Idp cung phd'i hpp 0
Idp 1, HS dupe hinh thanh bie'u tupng ban dau ve HCN thdng qua cac hoat ddng nhu: dat ten, quan sat hinh d mifc dp don gian, ghi nhdhinh anh, mota HCN gdm ed 4 dinh va 4 canh Len Idp 2, HS dupe hpc ve dudng thang, dudng cong, mat phang, eac
em cd su hieu biet rd han ve HCN va nim dupe HCN gdm 4 doan thang, trong dd, ed 2 canh dai bing nhau va 2 canh ngin bang nhau 0 Idp 3, su
md rdng hieu biet ve HCN lai dupe phat trien hPn nifa; khi hpe ve gdc, gdc vudng, HS se phan tich va tha'y ring, HCN cd4 gdc vacac gdc deu la gdc vudng; khi hpc ve hai dudng thing vudng gdc va hai dudng thSng song song thi lai hie'u them dupe ring: trong HCN ed 4 cap canh vudng gdc va 2 cap canh song
48
2) Kehoach phan phd'i ngi dung day hgc chu * Trading Oai hpc sir pham Ha Noi 2
Tap chi Gido due so 327
(kil-2/2014)
Trang 2Bang!
Ldp
1
2
3
4
5
6
NOI dung
L6p 1: Duac chia thSnh 19 chu d4 Cu6n A c6 10 chu d6;
cudn B CO 9 chu d4: trong do, not dung hinh hpc \k chu d^ 6:
Hinh va miu hinh (Shapes And Patterns)
Ldp 2: C6 17 chu d6 Cuon A co 9 chu dS, cuon B co 8 chu
d^ Trong C6, no! dung hinh hpc co 2 chu dS, g6m chu de
16: Dudng t h i n g va mSt phIng (Lines And Surfaces) va chu
66 /7:Hinh va mau hinh (Shapes And Patterns)
L6p 3: C6 18 chij d6, cuon A c6 9 chu d^; cuon B co 9 chu
dfi Trong do, co 3 chu d ^ co npi dung hinh hpc la chu d^
16, 17 yjk 18; ChLj dS 16: G6c (Angles); chu dS 17: Di/dng
t h i n g vu5ng g6c va ducmg thdng song song (Perpendicular
And Parallel Lines); chu de 18: Dign tich v^ chu vi (Area And
Perimeter)
Ldp 4: C6 14 chu d^ Cuon A co 8 chu de, cuon B co 6 chu
d6 Trong d6, npi dung hinh hpc dupe th^ hi6n trong cac chu
6& 6, 7, 8, 12, 13 va 14; gom: chu 64 6: Goe (Angles); chu
66 7: Dudng th&ng vuong g6c va dudng t h i n g song song
(Perpendicular And Parallel Lines); chu dS 8: Hlnh vuong v^
hinh chtr nhat (HCN) (Squares And Rectangles); chu 66 12:
Difin tich vk chu vi (Area And Penmeter); chu d6 13: D6i
xi^ng (Symmetry); chu66 14:BQ ghep hinh (Tessellations)
Ldp 5: C6 14 chu d6 Cuon A co 6 chu d ^ , cuon B co 8 chu
d^ Trong do, npi dung hinh hoc dupe t h i hien trong cac chu
d 6 : 5 , 1 1 , 1 2 , 1 3 v^ 14 C/7iJ cf^ 5; Difin tich cua mot tam gi^c
(Area Of A Triangle); chu dS 11: Goe (Angles); chu d6 12:
Tfnh chat cua mpt tam giac va hinh td giac (Properties of
Triangle and 4 - Sided Figures); chu de 13: Di/ng hinh
(Geometrical Construction); chu 66 14: Jh$ tich eua hinh l$p
phuong vk hinh hop chQ nhat (Volume Ot Cube And
Cuboid)
Ldp 6: C6 11 chu d6, cuon A c6 6 chQ d6, cu6n B c6 5 chu
dS Trong 66, npi dung hinh hpc t h ^ hifin trong cac chu d6:
2, 3, 8, 10 vS 1 1 Chu 66 2: So do cOa g6c (Angles In
Geometric Figures); chu dS 3: Mang lucfi hinh hpc (Nets);
c/?tJ 66 8: Hinh tr6n (Circles); chu 6e 10: Di$n tich va chu vi
(Area And Perimeter); chu d6 11: Thg tich chS't rSn va chSt
I6ng (Volume Of Solids and Liquids)
song; khi hpc ve dien tich va chu vi eiia eac hinh, HS
dupe hinh thanh bieu tupng ban dau ve ehu vi va
dien tieh HCN (ehu vi la td'ng dp daicua 4 canh, dien
tich la phan mat phing chifa trong HCN, dupe do
bing eac ludi d vudng (cm^)) Len Idp 4, HS da hinh
thanh cdng thuc tinh ehu vi va dien tich HCN mpt
each rd rang, chu vi ehinh la td'ng dp dai eac canh
bao quanh ben ngoai hinh dd, edn dien tieh ed the
citgheptif mdt hinh phifc tap de thanh cac hinh CO
ban nhu HCN va hinh vudng 0 Idp 5, HS hie'u dupe
nhifng ung dung rpng rai cua HCN; HCN ed thephd'i
hop vdi cac mat phing khac hoac phd'i hpp vdi nhau,
phd'i hop vdi hinh vudng va hinh tam giac detao
nen cac miu vat hinh khd'i 3-D nhu: hinh hop chif
nhat, hinh lap phuang, hinh kim tuthap
Cae yeu to hinh hpe trong chuang trinh va SGK
toan tieu hpe d Singapore dupe sap xep, phat trie'n
tang dan theo vdng xoay trdn d'c, ndi dung dupe dan xen trong cac khd'i Idp debdtrp cho nhau nhim dat dupe mue tieu giao due toan tieu hpc ndi chung, muc tieu day hpc ehij de hinh hpc ndi rieng
2 Chu dehinh hpc trong chuang trinh va SGK mon Toan dtieu hpc ciia Viet Nam
1) Ke hoach, phan phd'i ngi dung day hgc chudehinhhgc.Chuangtr'mhSGK mdn Tointu
Idp 1 de'n Idp 5 dupe bien soan theo quan diem ddng tam, tieh hop; trong dd, sd hpe la hat nhan, chiem thdi lupng bai hpc Idn nha't Chinh vi quan diem dd
ma SGK dupe bien soan theo tung ehu de, cae npi dung ed sutich hpp trong mdi chu de, tham chi tich hpp trong ca mdt bai hpc SGK dupe bien soan theo tiet hpc, mdi nam hpc cua tifng khd'i Idp gdm 35 tuan hpc vdi khoang 5 tiet/tuan Nhu vay, khoang 134 de'n 175 tiet hpe toan eho mdt nam hpc theo phan phd'i chuang trinh
Ldp
1
2
3
4
5
Bd>
Liip 1: c6 134 l\6V n^m Mdi bii trong SGK tuong i2ng vdti m6t tiSt hpc
Trong (16, nO' dung hinh hoc l i cfic ban Hinh vu6ng, hinh trin; Hinh tam giic: Luy^n t^p; Diim; Doan thing; Di} dii do^n thing; Vd doan thing cd
dO dai cho trude, D\im 6 tronq, difi'm cf nqoii mftt hinh Ldp 2 cd 168 ti€t/ nim hpc Trong dd, ndi dung hinh hpc l i cic bii: HCN
- Hinh ti^ giic; Oudng thing; On t^p vd hinh hpc; Dudng gSp khOc - D$ dii dudng g£p khuc; Luy$n t$p; Chu vi hinh tam giic - Chu vi hinh lit giic; Luyfin tip; dn tip v& hlnh hpc; 6n tip v6 hlnh hpc (liSp theo) L6p 3: 175 tifit/ nim hpc Trong <J6, n$i dung hinh hpc th^ hi$n qua cic bing 6 ke; HON; Hinh vudng; Chu vi HCN; Chu vi hinh vudng; DIfi'm d
giifa Trung diim ciia do^n thing; Hinh trdn, tim, dudng kinh, bin kfnh;
ve (rang tri hinh trdn; Di^n tich cua m$t hinh; Di$n tich HCN; Luy$n t$p:
DiSn tfch hinh vudng; Luy^n tSp; On tip v6 hlnh hpc; 6n t^p v6 hlnh hpc
(tiSp theo)
Ldp 4 cd 175 tilt/ nim hpc Trpng dd, ni>i dung hlnh hpc thi hi$n qua cdc
bii: Gdc nhpn, gdc tu gdc b^t; Hai dudng thing vudng gdc; Hai dudng thing song song; Vg hai dudng thing vudng gdc, Vg hai ducmg thing Hlnh binh hinh DiSn tfch hlnh binh hinh; Luy$n tip; Hinh thoi; Dt$n tich hinh thoi, Luy$n tip; Luy$n tap chung, On l i p v l hinh hpc; On tip v l hlnh hoc (tiip theo)
L<Sp 5: cd 175 till/ nim hpc Trpng dd n^i dung hinh hpc dUi?c bifin soan
trpng chuong ba thdng qua cic bii: Hinh tam giic; Di§n Kdi hlnh tam giic, Hlnh thang, DiSn lich hinh thang; Hlnh trdn Dudng trdn; Chu vi hinh trdn; Didn lich hinh trdn; Gidi thiiu bilu do hlnh quat; Hinh h$p chi} nh§t Hinh lap phuong; Didn tich xung quanh v i di$n tich toin phin cua hlnh phuang; Thi tich cua m^t hlnh; Thi tich hinh hftp chiJ nhit; Thi tfch hlnh Idp phuong; Gidi Ihldu hinh tn,i Gidn thi$u hlnh cdu
Ngoii ra cdn cd 20 bii luydn tip, luy$n tip chung v i bii h$ trp khic; bin cgnh dd, n^i dung hlnh hpc cdn dui?c tich hop trong cic mach kiln thiJrc khic tronq sudt nim hpc
2)Ndidung chu dehinh hgc trong chuang trinh vaSGKmdn Toan Ndi dung chii de hinh hpc
mdn Toandtieu hpc tai Viet Nam cung dupe sip xep theo hinh xoay trdn d'c, theo cap dp md rdng va nang cao dan Vi du: de hinh thanh kie'n thifc, kl nang ve HCN, ndi dung nay dupe sip xep theo cap dp md rdng, tang dan tif Idp 2 de'n Idp 5 0 Idp 2, HS hpc ve
(kil-2/2014) Tap chi Giao due so 327 49
Trang 3HCN vdi muc dp, yeu eau don gian, dd la: hinh thanh
bie'u tupng ban dau ve HCN thdng qua viee gidi thieu
HCN va hinh tii'giac, eho ehiing diing lien ke vdi nhau
de HS phan biet giira HCN va hinh [it giac Sau dd,
HS dupe thuc hanh nd'i cac diem tren ludi d vudng
nhim tao dupe HCN, day la hoat dpng giiip HS the
hien su hie'u biet eua minh de nhan biet HCN nhd
hinh ve HS dupe hpe each dpe ten HCN eho diing
HS tie'p tue dupe ciing ed ve bieu tupng HCN thdng
qua eac hoatddng hpe tap, ching han nhu: chia hinh
hoac nhiing HCN vao mdt hinh khac Nhu vay, didp
2 khdng yeu eau HS md ta ve HCN nhu sd dinh, sd
canh, sd gdc
Len Idp 3, HS dugc hpe nhieu han eac yeu tdlien
quan de'n HCN Lan dau tien, HS dupe lam quen vdi
viee md ta, phan tich mdt hinh ca ban Sau khi HS
da hpc ve diem, doan thang, gdc, dp dai eiia doan
thing, eae kie'n thuc ve HCN eiing dupe tang cudng
HCN khi ay dupe HS md ta, phan tich gdm nhieu
yeu td lien quan, dd la: HCN ed 4 gdc vudng, cd 2
canh dai bing nhau, 2 canh ngin bing nhau; dp
dai cua canh dai gpi la chieu dai, dp dai canh ngan
gpi la chieu rdng HS tie'p tue nhan dang ve HCN
thdng qua eae hoat ddng do dp dai eae canh HCN
ed chii'a trong mdt hinh phire tap, vede tao ra HCN
Tie'p dd, HS dupe hpe edng thue tinh ehu vi HCN
dua tren ca sd tinh dp dai dudng gap khuc va bit
dau lam quen vdi tu duy triiu tupng Khi hpe de'n
dien tich cua mdt hinh, dan vj do la xang-ti-met vudng,
HS dupe hpc ve dien tieh HCN va hinh thanh edng
thiJctinh dien tich HCN Sau dd, HS dupe phattrien
kTnang phan tieh, ehia eitdien tich cac hinh de tinh
dien tich cac hinh phii'c tap ed chifa HCN
CI Idp 4, HS da dupe hinh thanh tuang dd'i day dii
eae yeu tdlien quan de'n HCN Khi hpe ve hai dudng
thang vudng gdc va hai dudng thing song song,
HS dupe phan tieh HCN theo ndi dung nay Dd la:
HCN ed bdn cap canh vudng gdc va hai cap canh
dd'i dien song song va bang nhau, eae em cdn dupe
lam quen vdi hai dudng cheo ciia HCN, nhan xet
xem ehiing ed vudng gdc hay bing nhau khdng
Vdi yeu cau cao hon, HS phai ve dupe HCN theo
yeu eau cho trude HS dupe hudng din ve HCN
thdng qua kT nang ve hai dudng thing vuong gdc
va haidudng th§ng song song Nhuvay, de'n Idp 4,
50 Tap chi Gido due so 327
HS da ed dupe tuang dd'i day dii kie'n thue, kT nang lien quan de'n HCN
De'n Idp 5, HS khdng ehii trpng de'n mdt HCN dan
le ni/a ma thay vao dd la su phd'i hpp giifa cac HCN, giifa HCN vdi eae hinh khac detao nen cae mau vat trong khdng gian ba chieu, HS nhan thu'c dupe ve HCN mdt each sau sic han, mang tinh irng dung eao trong cude song
Nhuvay, ndi dung day hpe lien quan de'n HCN dupe sip xep theo mdt trat tu logic phii hop vdi su phat trien nhan thiifc, tam li eiia tre Ben canh dd, nen bd' sung cho tre ve tinh phang ciia HCN thdng qua viee xac dinh mat phang ed ehua trong eac miu vat 3-D, bdsung ve tinh dd'i xirng trong HCN decae
em ed duqc day dii han kie'n thue, kT nang lien quan
de'n HCN
Nghien cifu so sanh npi dung chu de hinh hpc trong chuang trinh toan tieu hpe ciia Viet Nam va Singapore de tha'y dupe su gidng nhau va khac biet giifa chuong trinh toan tieu hpe eua nude ta va Singapore Viee nay cd y nghTa gdp phan dd'i mdi, nang cao chat lupng day hpc eac yeu to hinh hpe d tieu hoc tai Viet Nam •
Tai lieu tham khao
1 D6 Dinh Hoan (chii bien) Toan 1, Toan 2, Toan 3,
Toan 4, Toan 5 NXB Gido due Viet Nam, H 2002
2 Dr Feng Ho Kheong - Chelvi Ramakrishnan
Michelle Choo IVIy Pals Are Here! Maths 2nd Edition
I A, IB, 2A 2B 3A, 3B 4A, 4B, 5A, 5B, 6A, 6B Marshall
Cavendish Education, Singapore, 2007
3 Ministry of Education Singapore Mathematics
Syllabus Primary Singapore, 2006
4 Ministry of Education Singapore N(T)-Level
Mathematics Teaching and Learning Syllabus,
Singapore, 2013
5 http://www.moe.gov.sg/
6 http://www.singaporemath.com/
7 http://www.singaporemaths.co.za/
SUMMARY
The study of the comparative between geometry content in the elementary mathematics curriculum
of Vietnam and Singapore to see the similarities and differences between the elementary math program
In our country and Singapore It makes sense to con-tribute Innovation, to enhance the quality of teaching elementary geometry In Vietnam
(kil-2/2014)