NGHIEN CIIU 1 ^ sur DONG DIEO D I I N TRUC OUAN Hd TRO DANH GIA NANG LOC TJNH TOAN COA HOC SINH TIED HOC I O I tvande Ning lye tinh toin (NLTT) I I mpt nang Iflc (NL) quan trpng trong tam NL chung cot[.]
Trang 1sur DONG DIEO D I I N TRUC OUAN
Hd TRO DANH GIA NANG LOC TJNH TOAN COA HOC SINH TIED HOC
I O I t v a n d e
Ning lye tinh t o i n (NLTT) I I mpt nang Iflc (NL) quan
trpng trong tam NL chung cot ldi ma Chflcmg trinh Giio
mdt trong nhflng thanh td cua NLTT cd nhieu phUOng
bilu dien trye quan Qua do, hpc sinh (HS) dfldc trii
nghifm vfla tim phflong I n g i l l quylt vin di (GQVD)
vfla bdc Id cic b i l u hifn cua NLTT l i m co sd phan bie
cho thang OG Ddng thdi HS dupe phit triin NL ehuyen
doi gifla ngdn ngfl thdng thfldng vdi ngdn ngfl trye
quan va ngdn ngfl ki hieu
2.JC3C quan niem v l nang lu'c tmh t o i n cOa hpc
sinh tieu hoc
Cle nghifn cu\j v f NLTT trfn t h i gidi cd tfl rit l i u
O Anh, ed quan nifm ve NLTT ciia Crowther (1959),
Coekeroft (DES, 1982), DffiE (1998) Cic quan nifm v f
NLTT ed diem tUong dong la sy hifu bilt v i khi ning
lim vifc vcri nhflng eon so, nhan thfle khdng gian hinh
thj, b i l u dd, ti If phan trim, Chiln Iflpe d i thifn NLTT
cCia Alien giai doan 2011 - 2020 md t i NLTT bao gom
GQVO, d i p flng nhu d u cupe sdng trong mdi triidng
xa hdi phfle tap Quan niem v l NLTT d Oc (2013) la kiln
t o i n hpc trong nhieu tinh hudng, Theo OECD (2008),
NLTT l i khi nang sfl dyng, giii thieh va giao tiep thdng
Theo Chflong trinh Gilo due pho thdng tong the cfla Bd
GD&OT (2015), cic thinh t6 cfla NLTT bao gdm:
- Sfl dung eic phip tfnh v i do Ifldng cO b i n : Sfl
dyng dupe d c phep tinh sd hpc trong hpc tap; do Ifldng
dflpc kich thflde, khdi lupng, thdi gian trong d c trfldng
hop don giin v i bflde d i u b i l t flde Iflpng
- Sfl dung ngdn ngfl toan: Nhin bift v i sfl dung
duoc eic thuit ngfl, ki hifu toan hpc, tinh chat dPn giin
cHa sd t y nhien, mdt sd hlnh dOn giin; bflde d i u biet sfl
dyng t h i n g kf trong hoc t i p ; hinh dung v i vf phie hinh
dang cfla cic hinh hinh hpc co b i n ; nhan bift v l bilu
d i l n dflpe mdi lifn hf t o i n hpe gifla d c y l u td trong d c
tinh hudng ddn g i i n hay b i i t o i n cd ldi van
- Sfl dyng cdng cu tfnh toan: Sfl dyng dflpc d e
dyng cy do, ve, tinh trong hpe tap; sfl dung dfldc miy
trong hoc t i p v i eupc
song-Nguyen Thj Kilu Oanh da de xuat quan dilm phit
triin NLTT d t i i u hpc gdm d c thanh td sau [1]:
-Thyc hifn thinh thao bdn phep tfnh sd hpe, tu tin
flde IflcJng trong hpe tap v i cudc song; hiiu v i ed t h i
sfl dyng eic kien thflc kT nang v l do Ifldng trong nhi
trfldng v i cudc sdng hing ngay;
- Sfl dung chfnh xac, hifu q u i ngdn ngfl toin hpc
nhfl d c thiiit ngfl, ki hifu t o i n hoc tfnh chit don giin
cfla d c sd, tinh chat mot sd hinh hinh hpe, thdng tin
thdng kf t o i n hpe d l GQVD niy sinh trong hpc tap v i
cudc sdng; cd khi ning tfldmg tupng khdng gian nhU
GS TS DAO 1AM - TniiMg 6al hoc Vinh ThS PHAM TH! KIM CHAU - Tnriung Bai hpc Bdng Thip
hinh dung, xle djnh v l sip xep, ve phic hinh dang d c ddi tuong don giin trong mdi trudng xung quanh, nim dupe tinh chit eo b i n eCia chflng;
- Bilt vin dung suy luan logic, phan tfch va lya chpn dupe phuong an toi uu de GQVO ddn giin; xiy dyng md hlnh toan ve mdi quan he gifla d c dat Iflong, yeu td d l GQVD trong hpe tap va cudc sdng;
- Sfldung hifu qua cdng eu, dyng cu do ludng, tfnh
t o i n nhfl d c loai thude, eke, compa, miy tfnh d m tay; bilt tinh t o i n vdi cac so do
3 Quan niem ca nhan ve nang liic tmh t o i n cila hoc sinh tieu hpc
Tit c l nghifn eflu tren cd y nghTa quan trong trong vifc hinh thinh va phat triin NLTT efla HS t i i u hpe Tuy nhif n, de phfl hc^ vdi mue tifu OG, chflng tdi quan nifm NLTT gdm eae NL thanh to sau:
3.1 Ndng liic tinh nhanh
Cic bilu hifn chu yeu cua NL tinh nhanh bao gdm: Sfldungthanhthaoeic bifn phip tinh nham, biet ehuyen ddi hdp li d c h tinh phfle tap ve each ttnh ddn giin
3.2 Ndng luc sifdunp cdc ki thugt ttf duy Cac bleu hifn chii yeu cfla NL sfldung eic ki thuit
tu duy bad gdm: Bift suy luan logic; bift dy doan v l kilm nghifm; bilt so sanh, phin tich, tong hpp, khai q u i t , d l tim phUdng i n tdi flu trong GQVD; bilt quy la v l quen
di tinh cac bieu thflc phfle tap
3.3 Nang lucsCrdung ngon ng&vd kihieu todn hge
v l ki hifu toan hoc bao gdm: Biet ehuyin doi gifla ngdn ngfl thdng thfldng vdi ngdn ngfl trfle quan v i ngdn ngfl
ki hifu; sfl dyng chfnh xae, hifu qui cic thuit ngfl, ki hlfu t o i n hpc, tinh chat ddn giin ciia cac sd va mdt sd hinh ddn giin; budc dau biet sfl dung thdng kf trdng hpc tap; hinh dung va ve phac hlnh dang eac ddi tfldng ddn giin trong moi trudng xung quanh
3.4 Ndng liicsitdung cdc phep tkih, quy tdc cong tfidt
tfnh, quy tic, edng thdc bao gom: D i m ; thiie hifn thinh thao bon phep tinh sd hpc; van dyng dupe cic quy tie, hiiu v i sfl dung cic kien thfle, kT nang vf do Ifldng trong
n h i trfldng v i eude sdng
3.5 Ndng Iticsddung cdng cu tinh todn
Cle bilu hien chti y l u cua NL sfldung edng ey tfnh toan bao gdm: Thuc hien thinh thao d e thao tic td, d t Ike, tranh inh, true sd, tia sd, sd dd, hinh ve, bing, bilu cae cdng cu tinh toan de GQVD
NLTT cd nhilu NL thanh td vdi nhieu bilu hifn d
d e mflc dp khae nhau Khi tinh t o i n d l gill quyet tinh hudng hpc t i p , HS phii trai qua rit nhifu hoat dpng
v i thao tic tfnh toan Do do, viee phan hoach NLTT ra nhien, vife phin chia nay la cd sd cho viec xly dung d c tifu chi cung nhfl hlnh vi trong OG NLTT eiJa HS cudi
d p Tiiu hpe
Trang 24 Tinh toin qua bieu dien trUc quan trong Toan
tiiu hoc
4.1 Biiu diin todn hge vd edc hinh thdc eda bieu
diin todn hge
Theo PISA, NL t o i n hoe phd thdng gdm nhilu NL
thanh phin ma bleu dien t o i n hpe II mdt NL cd bin v i
quan trpng Bilu dien toin hpc phin thinh 3 pham trfl
nhfl saii: ThUc tf Gdm cic bilu dien thye t l d mfle dp
thip, thao tic trfle t l l p bing tay; Bieu tugng: Cae bilu
diln true quan sti dung cle hinh Inh, dd thj, sd do, bieu
bing, ; Kl hiiu: Gdm d e btlu diln ngdn ngfl v i bieu
dien kf hifu [2] Bilu difn tnic quan ddng vai trd trung
gian k i t ndi bilu dien thyc t l vdi bleu diln kf hifu
Tadao phin loai cle bilu diln trong giao due Toan
t h i n h 5 dangsau:
- Biiu diin thuc ti: Cic bilu dien dUa tren trang thai
thyc cfla ddi tUpng, tic ddng tnic tiep, cu t h i v i tfl nhien
- Biiu diin bang md hinh thao tdc dugc Chflng nhfl
nhflng cdng cu hd tro day hpe Dd l i sy thay the hay cie
md hinh^il ve doi tfldng m l HS t i c ddng trye tilp
- Bieu dien bdng hlnh dnh (bieu dien true quan): Cie
btlu dien sfldung tranh minh hpa, sO do, d ^ thj, bleu do
Diy l i loai bilu difn giiu tinh true quan v l sinh ddng
- Biiu diin bing ngdn ngd: Cic bilu difn sfl dung
ngdn ngfl hing ngiy d l dien dat Loai bleu dien nay bj
chi phdi bdi cle quy udc nhflng thilu tfnh ngan gpn
Bieu dien cd tinh md t l va tao d m giac quen thupc
- Biiu diin bdng ki hiiu: Cic bilu difn sfl dyng kf
hifu t o i n hpc nhfl sd, ki tu, bieu tupng
Trong ChUpng trinh Toin tifu hpe, phan Idn cac
kiln thflc dupe trinh biy dfldi dang trfle quan (tranh i n h ,
trtic sd, tia sd, sd dd, hlnh ve, bing, bleu do) cung d c yfu
d u vf thao tic (dim, td, e l t ghfp, gIp, ve, flde Iflpng,
do, lufmg)
4.2 Quan niim cd nhdn vi Biiu dien trUc quan
trong Todn tiiu lige vd tinh todn qua biiu dien trde
quan trong Todn tiiu hgc
Tfl cic kit q u i nghifn eflu vf bilu difn toan hoe v i
dac dilm chuong trinh Toin t i i u hpc neu trfn, chung tdi
d l xult hai quan nifm sau:
- Biiu diin tn/e quan trong Todn tiiu hoc la viec md
t i hay bilu diln cie doi tflpng Toan tieu hpe qua cae md
hlnh trye quan nhU:Tranh Inh, true sd, tia sd, so do, hlnh
ve, bing, liilu dd bing cic thao tie dim, td, d t ghep,
gap, ve, flde Iflpng, do, Ifldng
- Tfnh todn qua biiu dien tn/c quan trong Todn tiiu
hgc l i vile thflc hifn nhung thao tic dfm, td, d t ghfp,
gap, ve, flde Ifldng, dd, ludng; sd sanh, ddi chilu, phan
trfn mien g i i tri eua md hinh trye quan; cie thao tie
t o i n hpc v i ngdn ngfl trfle quan tren md hinh trye quan
Can sfl dung tinh toan qua bilu diln trye quanpt trong OG NLTTcfla HS tieu hpc vi nd phfl hpp n g u j ^ | j nguyen t i c day hpe tfl true quan sinh ddng den tu duy trflu tflpng v i giii quylt nhflng khd khin cua HS tieu hpc troiig vifc tim nghTa cua tri thflc Vife tinh toan tren bleu dien trfle quan khdng chi l i eo hdi deOG NLTT eda
HS m l cdn l i tinh hudng giflp HS phat trien NL sfl dung ngdn ngfl toin hpc
5 OInh gii nang lUc tinh toan cua hoc sinh tieu hoc qua bilu diln trUc quan
Mi^c dfch cfla Chflong trinh OG HS quoc te (PISA) la
DG NL ciia HS nhfl; NL sfl dung ngdn ngfl toin, NL mfl hinh hoi va d c kT nang GQVO O Vift Na_m, NL sfldung ngdn ngfl t o i n dflpe xem l i mdt thanh td cfla NLTT Mit khic, dfla vio d c bilu hifn cfla NLTT, ngdn ngfl toan hpc dfldc hieu khdng chi gom cie thuit ngfl, kf hieu toan hoc m i cdn md rdng tdi cic lo^i ngdn ngfl so dd, hlnh
vf, tranh Inh, bing, bilu dd Do do, vife thiet ke cic tinh mdt sd thinh td NLTT ciia HS t i i u hpe vfla dip flng muc tieu OG cOa PISA
Vidu: Vnh hudng phdn sdtrin dogn thang
(vdi 2"= 2.2.2 2 gdm n thfla sd 2)
Vdi HS trung hpe pho thdng, bai t o i n nay giai bing cich sfl dyng gidi han khi n d i n tdi vd eUc Trong tinh ctia bieu dien trye quan trong viec ^ n h hfli^g HS tiiu hpc quy la v l quen d l tim k i t q u i Chiing tdi minh hoa gia trj phan sdqua bieu dien trfle quan, HS tfl vife quan sit • thao tie - dfl doin - khii quit se nhin thiy ket qui bai toin
Hlnh 1: Cde md Mnh bdng gidy trdng
Gil sfl Idp hoc ehia thinh 04 nhdm, phat cho moi nhdm 01 md ninh trong 04 md hlnh d Hlnh l.Yeu clu
md hlnh cua nhom minh, sau dd trinh biy kit qui v i giai thich each lam
Hinh 2 Hlnh 3 Hinh 4
NLTT cfla HS t i i u hpe ehi dupc the hifn qua cie hoat ddng khi giii quylt tinh hudng Chflng tdi thiet ke tinh hudng vdi nhilu hoat ddng trong Bing 1:
Bdng 1: Cde hogt dgng gidi quyit tinh hudng cua HS
cau h6i
cia giio v\in
1, Hay thyc hien thao tic tren
md hlnh d l xic djnh gii trj
phin sd — va ghi cdng thflc
tfnh gii tri phin sfi —,
Hoat dpng cua HS (X^t mo hinh bing giay]
- GIp ddi bang gily
-Tfi mpt phan (Hinh 2)
- Chua nhin ra each tfnh tdng theo edng thflc
O-i)
Bilu hifin tfnh toan cia HS (Lim cd sd phfin bac cho thang SG)
- Lfdc Ifldng, chia bang gily lim 02 phin bing nhau
- Chuyin tfl ngdn ngfl kf hieu sang
ngdn ngfl gii tri phan sfi teen bang
giay
Trang 32 Hay thye hien thao tae tr§n
1 di xic dinh gii tri cfla tdng
gii tri eiia tong nay
- Phin tich: Phan bang gily ehfla td l i — Mudn cd
— phii gap de ehia phan bang giay ehfla td lim 02 phin bing nhau
-Tfi mdt phan (Hinh 3).Tinh tong:
Cich 1:Tinh true t i f p : + i = ^ =
-2 4 4 4
ehUa td la — Phin da td bing 1 trfl phan chua tfi
2 4 4
- Chuyen tfl ngfin ngfl ki hieu sang ngdn ngfl gia trj phan sd tren bang giay
- Chuyfn tfl ngfin ngfl ki hlfu sang ngfin ngfl gia trj phan sfi tren bang gtay
- Cach 1: HS khdng biet chuyen tfl ngfin ngfl gii tri trin bang giay sang ngdn ngfl ki hifu
- Cach 2: HS bift chuyin tfl ngdn ngdn ngfl ki hieu; bift phan tieh edng trfl phin sfi, phin bi^ va eae phan bang nhau eiia don vi
3 Thflc hien thao tie tren md
d l xic djnh gia trj eiia tdng
1 1 1 • ,
-—+ —-i va ghi cong thflc
tfnh gii tri cfla tong nay
Cac hoat ddng cfla HS tfldng ty nhu trong eiu hdi
2 (Hinh 4)
Cac bieu hifn efla HS tUdng t y nhfl trong eau hfii 2
d bflde thfl n, ta cd tdng sau:
- + — + -I- +
2 2.2 2.2.2 2.2 1
(phin sd thfl n eo mau sfi gfir
n thfla sd 2) Hay tinh tdng i
bude thfl 8
•- Cich 1: Tinh trye tifp tfing eua 8 phin sfi theo cieh quy dong mlu sfi
- Cich 2: HS bilu diln tren doan thing lin Iflpt dfn
- Cach 3: HS khdng bifu dien tren doan thing, d e
em phin tich:
Bflde 1 tfing bing ( 1 - ; Budc 2 tfing bing
-Bilu hien nhfltrong cich 1 cua cau hdt 2 Tinh theo d c h nay vat v l , sal sfit mat thfri gian
- Bilu hien nhfltrong cich 2 efla cau hdi 2
- Cieh 3: Nhay bin trong kT thuat tu duy, bilt quy la vf quen de dfla bieu trong each GQVO
Cich gap trfn md hlnh hlnh trdn va md hinh hlnh
vudng thflc hifn tflong t u (Hinh 5,6) Cach gap trfn md
hinh hinh tam giie nhu sau: Gap ddi mdt canh d l cd
trung diem, kf doan thing dl qua dinh cdn lai efla tam
phin bing nhau (Hinh 7) Chung tdi ehi minh hoa cich
gap m l HS t i i u hoc thudng sfl dung
MA
Hinh 5 Hinh 6 Hinh?
Khi quan sat mdi nhdm trinh bay kit q u i v l giii
thieh d c h lim, HS c l ldp phit hifn dii thye hien trfn d e
md hinh khic nhau nhflng d c h GQVO tUOng t y nhau.Tfl
dd, HS khii quit d c h GQVO eho loai t o i n niy
Vidu 1: Tinh hudng ludi tam gidc diu
Hmh 8 Hinh 9 Hmh 10 Hinh 11
Chiing toi thilt ke tinh huong theo cic cau hdi ning dan dp khd trong Bing 2
Vcfl HS t i i u hpe, clu hdi 5 trong moi tinh hudng trfn tuong ddi khd Cach thiet ke d e ciu hdi theo t r i t t y ngu
HS thay van de dOn giin, cd the giii quyft dflOc
6 Kit luan
Chung toi da tifn hinh phin tieh hifu qui cfla vifc sfl dijng bieu dtin tmC quan trong DG NLTT cfla HS cudi d p
(Xem tiep trang 22)
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