II DIEN DAN PHAH TICH idl GIAI BANG DAI SO DE BOI DUdNG KY NANG CHO GIAO SINH VA GIAO VIEN DAY GIAI TOAN d BAC TIEU HOC TS Ta Ngpc Tri TrUdng DHSPHd Ngi 2 Phfldng phap dgt an sd mi dye ti^u hpc), cic[.]
Trang 1II DIEN DAN
PHAH TICH i d l GIAI BANG DAI SO
DE BOI DUdNG KY NANG CHO GIAO SINH VA GIAO VIEN
DAY GIAI TOAN d BAC TIEU HOC
TS Ta Ngpc Tri
TrUdng DHSPHd Ngi 2
Phfldng phap dgt an sd mi dye ti^u hpc), cic b^ic phy huynh tic gia de cap den van de dgy hpc giii phUdng trinh, he phUtfng muon giiip eon hpc toi mdn lodn tich cflc va nang cao nang lUc ciia trinh (ta se gpi la phfldng phap vi ihgm ehi ca ddi vdi giao vien ddi ngu giao vien bdi theo cac
dgi sd d bii viOi nay) ihudng ticu hpc khi dgy tren ldp Qua tic gii thi "Trong dqy hgc, gido khdng dupc su dyng cho hoc khao sat vdi nipl so giao sinh tgi vii^n Id nhdn to quyit dinh chdt sinh tieu hpc Mdi gan day bao khoa Ticu hpc-TrUdng DHSP lUdng gido due" Cac tac gii nay
chi dUa tin mpt sd phy huynh Hi Npi 2 thi phan ldn giio sinh cung khuyen cao cac trUdng sU hpc sinh thic mac vi kien nghj cd the giii dUpe bai loan bang phgm cd dio tgo giao vien tieu
Ifn Sd Giao dye Thinh phd Hd phUdng phap dgi sd, song lgi rat hpe " cdn ldm tdt hdn nda cong Chi Minh, rdi sau dd li len Bd lung tiing vi thgm ehi khdng the tdc ddo tqo gido vien, ddp Ung Giao dye va Dao tgo Uen quan giii dflpc bang phfldng phap lgp yeu cdu ddi mdi chUdng trinh, ngi
din nhflng ldi giai dgi sd d i lugn Id-gic: phfldng phap dflpc dung, phUdng phdp dqy hgc mon
khdng dflde chap nhgn cCia mpt dung khi dgy d tieu hpc Chinh Todn trong giai doqn mdi" Bii
sd cac HS mpt bai toin trong de vi vgy giio sinh nganh Giio dye viet niy cung thdng bao ve mpt thi vio ldp 6 trUdng Tran Dgi Tieu hpc va giio vien dang dgy chUdng trinh bdi dUdng thudng Nghia (xem d dUdng link http:// tieu hpc can phai dUpc trang hi xuyen cho giio vien tieu hpc tuoitre.vn/Tuyensinh/Tuyen- mpt sd cic ky ning de cd the giai dogn 2011-2015 da dUdc Bp
s i n h / 4 4 5 3 1 6 / K h o n g - c h a m - giing dgy thinh cdng mpt so cac Giio due va Dao tgo ban hanh diem-cho-cach-giai-eao-hon- bai toan dUpc ggp trong trUdng Tat ca nhflng dieu niy cho thay trinh-do-lop-6.html vi d dUdng tieu hpc, nhat li cic bai toin bdi giio sinh va giio vien tieu hpc link http://giaoduc.net.vn/ dUdng hpe sinh gidi toan Mpt ky can dUde chuan bj vi bdi dUdng Tuyen-sinh/Truong-Pho-thong/ ning trong sd dd se dUde bin tdi nhflng phfldng phip day hpc Phu-huynh-kien-vi-bai-thi-vao- trong bii viet niy: ky nang tim Toin tich cflc de cd the lim tdt lop-6-dung-ma-khong-duoe- hieu cic ldi giii bing lgp lugn Id- cdng vifc giing dgy d trfldng diem/7368.gd, thing 10/2011) gic tfl nhflng ldi giai dgi sd hay tieu hpc Tuy nhien mdt thfle tf
Hpc sinh tieu hpc dUde yeu cau quen diing cho thay li ky ndng gidi todn phdi giii toin bing lgp luin Id-gie li Trong bii viet tdng ket sau dUdc quan tdm ddu tiin vi gido ehinh de tang eUdng kha nang chin nam sfl dyng chUdng trinh viin dUng ldp phdi biet gidi bdi suy luin, lap luan va tfl dd li rf n vi sich giio khoa mdi d bgc tieu todn dd trUdc khi mudn thUc hien luyfn tfl duy cho cac em Tuy hpc (tfl nam hpc 2002-2003) eie viic truyin dot nhU the ndo de nhien mpt thfle te cho thay vifc tic gii Le Tien Thinh vi Hoing giiip hgc sinh ciia minh hieu dUdc giii toin theo phfldng phip lip Mai Le (Vy Giio dye Tieu hpc- vd sau do Id gidi dUdc bdi todn do
luin Id-gic cua bac hpc tieu hpc Bp Giio dye vi Dao tgo) d i de Theo quan diem eua ehung thudng hay giy nen khd khan xuat mpt sd cic giii phip de ning tdi can bdi dfldng nhieu hdn eac khdng nhflng cho hpe sinh tieu cap chat Ifldng dgy hpc mdn ky ning giii toin vi ky ning sfl hpe m i eho ehinh cic giio sinh Toin d trfldng Tieu hpc (xem phgm, nhat li cic ky ning de (sinh vien sfl pham nganh giip Le&Hoing (2011)) Trong dd cic thfle hifn cic phfldng phip dgy
Nhdn bdi ngdy 2/2/2012
> TAP CHi T H I ^ BI GlAO DMC- Sd 78 - 2/2012
Trang 2DIEN D A N II
hpc tich cflc cho cac giao sinh
nganh Giao dye Tieu hpc cua
cac trUdng sU phgm va trong
cac khda bdi dUdng chuyen de
cho giio vien Tieu hpc theo tinh
than chi dgo cua Bp GD&DT
nhfl trong Le&Hoang(2011)
Ve cic phfldng phap va ky nang
dgy hpc tich cflc d bgc tieu
hpc cd the tham khao cic tai
Ufu cua dfl an Vift Bi (dUdng
link: http://ati.edu.net.vn/), dfl
in ve dgy hpc tich cflc cua td
chflc WOB; Td chflc Hpp tic
Phat trien va Hd trp Ky thugt
vung Fla-mang, VUdng qude Bi
(dudng Unk: http://www.wob
be/vietnam/?q=vi), hoge cac
bai bao Tri(2011), Tri(10/2011)
Trong bii viet niy chung ta tgp
chung vio vifc phin tich de hinh
thanh mpt ky nang cd the giflp
giio sinh vi giio vien tieu hpc
dgy hpe sinh giai toan vi tfl dd
cd the ket hpp vdi eie bifn phip
khae nhau thfle hifn phfldng
phip dgy hpc tich cflc
Bii toin 1 (xem Dd(1998),
Tr 153): Cd mdt bin hdp ddng
sin xuat dyng cy hpc tap Nhdm
thfl nhat ed the hoan thinh hdp
ddng sau 6 ngiy lim vifc, nhdm
thfl hai cd the hoin thinh sau 15
ngiy lim vifc Thdi gian dau chi
rifng nhdm thfl nhat lim vifc,
roi sau dd chi rieng nhdm thfl
hai lim tiep cho den khi ket thfle
cdng vifc Ci hai nhdm d i lim
het 9 ngiy thi ket thue bin hdp
dong dd Tuih xem ei hai nhdm
di lim dxigc bao nhieu dyng cy,
biet rang nhdm thfl nhat da lim
nhieu hdn nhdm thfl hai la 150
dung cu?
Neu giii bing dgi sd ehung
ta cd the nhanh chdng tim dfldc
ldi giii nhfl sau:
Gpi x la sd ngiy ma nhom thfl nhat da lim, y la sd ngiy mi nhdm thfl hai da lam Tfl bii ra
ta se cd hf phUdng trinh:
x + y = 9 ( l ) x/6 + y/5 = 1 (2) Khi giiihf (1) &(2) chiing
ta the (1) vio (2) bang each tach x/6 = x/15 + x/10 va tfl do ta cd x/10 = 2/5, hay x-4 vi y=5 Sd phan cdng vifc ma nhdm thfl nhat lam la 2/3, va 2/3 nhdm hai lam la 1/3 Do dd nhdm thfl nhat lam hdn nhdm thfl hai 1/3 cdng vifc va gia thiet da cho la 150 dyng cy \'ay tong so dyng cy se
li 450 dyng cy
Vifc tim hieu ldi giai bang phfldng phap dgi sd de ed the giflp ich cho giao sinh, giao vien tieu hpc phuong hUdng de tim ra ldi giai bang lgp lugn Id-gic dgy cho bai toan nay Day cung la van de ma chung tdi mudn ban den trong bai viet Vgy cy the ddi vdi bii toin 1 chflng ta se sfl dyng ldi giai dgi sd tren de dinh hudng cho ldi giii Id-gic nhfl the nio?
Chung ta se khdng the dung ngdn ngfl cua phfldng phap dgi sd; tfle li an x, y d diy dUdc nfla
Suy nghi tfl (2) vi ed the thay rang:
-Phan sd 1/6 xuat hifn the hifn khdi lUpng cdng viec m i mdt ngiy nhdm thfl nhat se lim dfldc Tfldng tfl 1/15 the hifn khdi Ifldng cdng vifc mi mpt ngiy nhdm thfl hai se lim dflde
-Phep tich de the sau dd dUdc hieu bang ngdn ngfl Id-gic li: Nfu gii sfl ning xuat cua nhdm thfl nhat cung nhU nhdm thfl hai thi sau 9 ngiy lUpng cdng vifc dfldc hoan thinh chi li 9/15
= 3/5 cua toan bd cdng vifc NhU
vay lupng cdng vifc 2/5 con lai (chuyen ve sau khi the song d phuong phap dai sd) da dUpc hoan thanh nhd nhdm thfl nhat
cd nang xuat cao hdn'
Nhu vay chiing ta cd the dgt van de lai xem moi ngiy da bdt di lUdng cdng vifc cua nhom mpt di 1/10 lupng cdng vifc (1/6
- 1/15 = 1/10) Lupng hdn moi ngay nay da giup hoan thanh cdng vifc; tfle li da giiip lim het lupng cdng vifc 2/5 cdn lai Moi ngay la 1/10 lUpng cdng vifc Do
dd sd ngiy nhdm thfl nhat da lim li 2/5 : 1/10 = 4 (ngay) Phin cdn lai cua lap luan hoan toin dupe the hifn trong each giai dai sd: Sd phan cdng vifc ma nhdm thfl nhat lam la 2/3, va 2/3 nhdm hai lim li 1/3 Do do nhdm thfl nhat lam hdn nhdm thfl hai 1/3 cdng vifc vi gia thiet da cho li
150 dyng cy Vay tong sd dung
cy se li 450 dung cu
Qua vi dy tren chung ta thay
rd la 'suy nghi tfl ldi giai bang phfldng phap dai sd "cua ngUdi ldn" cd the giup ich cho vifc dgt dUdc mdt Idi giii bang lip luin Id-gic ma cic em hpc sinh tieu hpc can
Bii toin 2 (Bii toin cd): Vfla gi vfla chd
Bd lai cho trdn
Ba mUdi sau con Mdt tram chin chan Hdi bao nhieu eon ga? Bao nhieu con chd?
Bang phUdng phap dai sd chflng ta ed the giii nhfl sau: Vdi
li sd gi vi sd ehd can tim chung
ta cd hf sau
x + y=36(3) 2x + 4y=100(4) The (3) vio (4) chung ta cd: 2(x+y) + 2y = 100 (5)
TAP CHi THIET BI GIAO DUC - S6 78 - 2/2012 •
Trang 3II D I £ N D A N
Hay 2.36 + 2y = 100 Tfl dd chi li mdt trfldng hdp di xft vi
ehung ta ed 2y = 100 - 72 = 28, khdng thich hdp vdi bgc tieu hpc
dp dd y = 14 (con chd) vi x = 22 d tren Vifc the vio se dUpc the
(con gi) hifn nhfl sau:
Tfl ldi giii niy chung ta cd 5y-2x = 51=>3y-2(x-y) = 51
Uie phin lieh de dan den mpt ldi =>3y-2 15= 51=>3y= 81 vi y=
giii bing lgp lugn nhu sau: 27, tfl dd x= 42
Phep the dUpc x + y vio Nhin nhin lgi tfl ldi giii
(4) de viet dUpc (5) thfle chat la bing dgi sd chiing ta cd the giup
chung ta da gii sfl ga va chd cung cho hpc sinh lap luin ring dfl
cd 2 chin NhU vgy 2 36 la sd kifn thfl hai se phdi li 5 lin sd
chin cua cd 36 con vgt sau khi gid thfl hai trfl di 2 lan sd thfl nhit
sfl Phep ehuyen ve vi trfl de dfldc bing 51 Biy gid chflng ta cd the
100-72 thf hifn sd chin chd bj sfl dyng cic phfldng phip trfle
hyt di do gii sfl vgy Phfldng trinh quan giiip hpc sinh tU duy bii
2y = 100 - 72 = 28 the hifn mdi toan niy
eon cho bj hyt di 2 chin mi tdng Tfl phUdng trinh (6) chiing
sd chin hyt di li 28 Tfl dd ta ed ta bieu dien sd nhd hdn li 1
sd chd li 14 vi sd gi la 36-14=22 dogn thang, sd ldn hdn li ddoajn
nhu di giii d tren thing dd vi them 15 nhU mpt
Bii toin 3 (xem Dd & Lf dogn nhd hdn (nhfl hinh ve)
(2003), Tr 174) Hifu cua hai sd |— 1
bang 15 Tim hai sd dd, biet rang j — —| |
neu gap mpt sd Ifn hai lin vi gap NhU vgy 5 lan sd nhd vi 2
sd kia len 5 lan thi dUpe hai sd lan sd ldn se dUde bieu dien nhu
mdi cd hifu bing 51 sau:
Dieu thu vi khi nghien cflu | - |
ldi giai dgi sd cho bii toin niy li 1 —|
ldi giii dd se giup djnh hUdng rat | |
tdt eho ci eie ldi lip luin cd the | | | —
khi hpc sinh giii bii toan dd O | |
diy neu chung ta gpi hai sd chfla Do dd hifu gifla 5 lan sd ldn
biet li X, y tfldng flng thi ta se cd vi hai lan sd nhd dflpc bieu difn
trUde het: bing ba dogn bieu dien sd nhd
x-y= 15 (6) vi can bd bdt di thfm hai dogn
Neu chfla suy nghi can thin, bieu di^n cho 15 nfla Do dd ba
dfl kifn edn lgi cua bii toin se lin sd nhd bdt di 30 li hifu 51
dUdc the hifn bdi phUdng trinh Tfl dd ba lan sd nhd li 51-H30=81
li 2x-5y=51 Giii hf niy ehung vi sd nhd li 81:3=27, sd ldn li
ta se dfldc ket qui y=-7, khdng 27+15=42
phai li con sd chflng ta chd ddi Cd mpt nhgn xft li khi bii
d bic Tieu hpe! NhU viy ehung toin cd thi quy ve tit ci mdt
ta ein nhin lgi giii thiet vi thin an nio dd thi vifc giii bing lip
trpng hdn: bii toin cho hai sd lugn se rit thugn ldi nhd vifc
mdi cd hifu li 51 Do dd dan den bieu dien chinh an dd qua mpt
hai trfldng hdp cd the xiy ra 2x- dogn thing de hpc sinh hinh
57=51 hoic 5y-2x=51 chfl khdng dung Tren thfle te vifc sfl dung
cic hinh inh trfle quan li cich rit tdt de giup hpe sinh tieu hpc
tu duy ve bii toin (xem them d Tri(10/2011)viTri(2011))
Ta xet them mpt vi dy nfla sau diy:
Bii toin 4 (xem Dd 8c Le (2003), Tr 21) Tdng sd tudi cua
ba ngUdi li 115 Tudi eua ngUdi thfl nhit bing hai lan tudi cua ngUdi thfl hai cpng vdi 10 Tudi eua ngfldi thfl hai bing ba lin tudi cua ngfldi thfl ba trfl di 5 Hdi mdi ngfldi bao nhieu tudi?
Neu nhu trong phfldng phip dgi sd chung ta chpn mpt dgi lUdng nio dd cin tim hogc tfl
dd giiip ta giii dUde bii toin li x thi khi lgp lugn Id-gic chiing ta
se chpn mpt dogn thang de minh hpa cho dgi lUpng dd Trong trfldng hdp niy ehiing ta cd the ehpn tudi cua ngUdi thfl ba li x
vi nhu vgy dfldc bieu dien bang mpt dogn thing Hay bieu dien tuoi cua nhflng ngfldi cdn lai qua dogn thing dd vi tfl dd gin ket vdi giii thiet eua bai toin di eho
Cy the nhu sau
I I Tudi ngUdi thflba
I I
I |///5//| Tudi
ngfldi thfl hai
Vi cudi cung li tudi ciia ngfldi thfl nhat
I
I-—-I |///5//|
I I
— I |///5//|
I-5 I 5-I
Nhfl viy tdng sd tudi eua
ei ba ngfldi se li 10 dogn thing (tudi efla ngfldi thfl ba) bdt di 5
Tfl dd mfldi dogn thing hay tuoi ngfldi thfl ba se li 115+5=120
Do dd tudi cua ngfldi thfl ba la
TAP CHi THI^ BI GlAO DMC- Sd 78 - 2/2012
Trang 4DIEN O A N II
12 tudi, ngudi thfl hai l i 31 tudi
vi ngfldi thfl nhat li 72
Practice makes pefect!
(Luyfn tip se tgo ra sfl hoin hao!)
cd le la phfldng chim tdt cua mdn
toin Rat nhieu cic vi dy trong
cic sich toin bdi dudng vi cic de
thi hpc sinh gidi cd the sfl dyng
cic phep phin tich nhu trfn de
dan den nhflng ldi giai thich hdp
cho hpc sinh tieu hpc Chung tdi
cho rang neu dflpc bdi dUdng ky
nang phin tich niy cung nhU mdt
sd ky nang dgy toin tieh cflc khic
chac chin eie gid dgy hpe mdn
toin d cic trfldng tieu hpc se hap
dan cic em hpc sinh (xem them
d Tri(2011)) Rd ring vdi nhflng
cich phin tich vi lgp lugn Id-gic
hpc sinh tieu hpc se ed cd hpi ren
luyfn vi ning eao khi nang tU
duy sau khi hpc nhflng bii giing
nhfl vgy
Tai lifu tham kliao
1 Dd & Le (2003); Dd Trung Hifu vi Le Tien Thinh, Tuyen tip De thi Hpc sinh gidi bgc Tieu hpc mdn Toan, Nhi xuat bdn Giiodyc(2003)
2 Dd(1998); Dd Trung Hifu, Cic bii toin dien hinh ldp 4-5, Nhi xuat bin Giao dvc(1998) 3.Le8cHoing(2011);LeTien Thinh vi Hoing Mai Le, Dgy hpc mdn Toin d Tieu hpc: Thfle trgng
vi Giii phip, Tgp chi Giao dye,
Sd 269(ky 1-9/2011), Tr 41-42
4 Tri(2011); Tg Ngpc Tri, Thiet ke cic bii toan nhd de dgy hpc sinh tieu hpc gidi mpt bii toin, Tgp chi Dgy hpc Ngiy nay (07/2011), tr 24-26
5 Tri(10/2011); Tg Ngpc Tri, Mpt sd bifn phap thfle hifn phfldng phip dgy hpc tich cflc khi dgy toan cho hpc sinh tieu hpc, Bii viet dang gfli ding
Summary Students teachers and teachers are familiar with the method of using unknowns
to establish equations to solve mathematics problems, called the equation solution' here However this kind of solutions
is not accepted at primary school level That is why student teachers and teachers sometimes meet challenges when teaching mathematics for primary school children This paper shows some examples and then suggests some ways of using the equation solution to obtain the solution to
be able to teach primary school children The paper also gives suggestions of when and how
to foster these skills to help the implementation of active teaching and active learning at primary school mathematics teaching
niiiuiniiiiiMiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiMiiiiiiiiiiiiiiiiiiiiiiiiiiiiiinMiiiiiiiinMiiiiiMM
QUY TRiNH THIET KE C O N G CU mp,heotrang33)
Ghi chfl: / / : rat ddng y;
/ ddng y; ?: khdng chac chan;
^: khdng ddng y; ^x: rat khdng
ddngy
Vi du 4 Bang quan sat de
thu thgp TTPH ve thai dp (xem
bing 4): Bing quan sat ve thai
dp chuan bj giao in, phfldng
tifn trfle quan va tap giang
3 Ket lu^n
Nhd TTPH m i GV ed the
de ra cic bifn phip tie dpng
hifu qua vao cic hogt dpng hpc
tgp cua SV, ddng thdi SV cung
tfl dieu chinh vifc hpc tap efla
mmh sao cho dgt dflgfc ket qua
cao nhat De lim dflgfc dieu
dd, GV can phai biet thiet ke
bp cdng cy thu nhan TTPH
Bii viet niy ehung tdi de cap quy trinh thiet ke bd cdng cy giflp GV ed the thu nhin dflde TTPH ve ket qui hpe tip eua
SV, qua dd dieu khien QTDH dgt ket qui tdi flu nhat
Tii lifu tham khao Robert J M, Debra J P, Jane
E P, Cic phfldng phip dgy hpc hifu qui, NXB GD, TP Hd Chi Minh, (NgUdi djeh Hdng Lgc),
2005
Tran Thi Tuyet Oanh, Danh gii va do Ifldng ket qui hpc tip, NXB Dgi hpc SU phgm Hi Npi,
2009
Robert J Marzano, Nghf thuit vi khoa hpc dgy hpe, NXB Giio dye Vift Nam, H i
Ndi (NgUdi djeh: Nguyen Hflu Chiu), 2011
Vice-Principal, Universty of standrews feedback on teaching: Student questionaires and peer observation of teaching Approved
by Academic Council, 2004
Abstract: Feedback is a very important role for improving learning outcomes To collect it, teachers need to have the tools This paper refers to the process design tool receiving feedback in teaching the teaching biology method at the University of Pedagogy This process includes three steps: 1) Determining the goal(s) of learning; 2) Analyzing the contents
of learning; 3) Designing the kit to collect the feedback information
TAP CHi THIET BF GIAO our-S6 78-Z/2012 • 41