Q N6HieNCt)(ULfLUAN HOAT DONG SIEU NHAN THUTC TRONG QUA TRINH KHAM PHA BAI TOAN KET THUC M d NGUnNTH! HUDNG LAN Truimg Bai hpc Tin Trdo Email ngif]renianGiltqeBmall GO Tdm tit Trong nhdng ndm gan ddy[.]
Trang 1HOAT DONG SIEU NHAN THUTC TRONG QUA TRINH
KHAM PHA BAI TOAN KET THUC M d
NGUnNTH! HUDNG LAN Truimg Bai hpc Tin Trdo Email: ngif]renianGiltqeBmall.GO
Tdm tit: Trong nhdng ndm gan ddy sieu nhdn thdc dd thu hut sa quan tdm eua nhieu nhd gido due todn Mdfmmg
nhij-ng vdn di md cdc nhd nghien edu todn hoc theo duoi Id tim hieu vai trd eua sieu nhdn thdc den khd nang gidi quyft vdn de todn hoc eua hoc sinh Bai viit tap trung vdo viec tim hieu hoat ddng sieu nhdn thdc trong qud trinh khamphibH todn kit thuc mdcua hoc smh cung nha dnh hadng eua sieu nhdn thdc den khd ndng gidi quyet thdnh cdng cdc bdito&i kit thuc md Ben canh dd tde gid cdn chi ra moi taang tdc gida hoat dong sieu nhdn thde eua hoe sinh vd khd ndnggi^ quyet vdn de eua ede em
Tdkhod: Sieu nhdn thdc; khdm phd bai todn ket thuc md
(Nhan bai ngdy 07/7/2016; Nhdn ket qud phan bien vd chinh sda ngdy 20/8/2016; Duyet ddng ngdy 27/9/2016)
I D a t v S n d e
V i o khoang nhdng nam 80 cua the ki trude, eae
n h i g i i o due t o i n nghien cdu ve g i i i quyet v i n d l b i t
dau quan tam den q u i trinh sieu nhan thde (SNT) eOa
hoc smh (HS) khi tim k i l m d d lieu de t r i ldi eho e i u hdi
lieu eac h i n h vi SNT co vai tro n h u the nao doi vdi q u i
trinh giai quyet van de Nghien cuu cua [Lester, 1982)
da chi ra r i n g h i l u biet cua HS ve hoat dong nhan thdc
truoc, trong va sau khi g i i i quyet van de eung vdi cac
hoat dpng mang tinh d i l u h i n h nhU theo doi va t u d i e u
ehinh i n h hudng Idn d i n viee g i i i q u y l t thanh cdng
cac van de t o i n eua ngudi hoe, Mdt so nghien edu sau
g i i l quyet bai t o i n cd ldi van (Pennequyn va nhdm t i c
( K r a m a r s k i v i n h d m t i e g i a , 2002), giai q u y l t van de t o i n
nhdng nghien cdu ve h i n h vi SNT trong q u i trinh kham
trong khuon kho b i l vilc nay, ehung tdi trinh bay ket q u i
qua tfinh kham pha bai toan ket thue m d eua HS trung
hoc pho thong,
2 Sieu n h i n thdc
T h u i t n g d SNT b i t nguon tU Hi Lap Trong tieng
H I Lap thuat ngd"meta" cd nghia la "sau" Do do, SNT l i
n h i n thdc ve hoat ddng nhan thde eua ea nhan Theo
Flavell (1979), SNT la hieu biet cua e i n h i n hen quan
kl nang mang tlnh dieu hanh nhU theo ddi, dieu chinh
tieu dat ra Cu t h l trong q u i trinh hoe t i p cua HS theo
biet ve q u i trinh nhan thdc va nhdng hoat ddng m a n g
inh dieu hanh b i c eao n h u phan tieh nhiem vu hoe tap
len ke hoach, theo ddi, k i l m tra va danh gia ve sU thanh
cong eua viec hpc VI t h l , SNT eo eae d i e trUng sau: N h ^
t h d e v l q u i trinh t u d u y eiia b i n t h i n ; Theo doi tichcyc
Dieu ehinh qua t r i n h nhan thde t r o n g moi quan h?viS(
e i c nhiem vu hoe t i p ; Tu t i m k i l m p h u o n g phipgiJI
q u y l t vi'n d e ; D a n h gia ve q u i trinh g i i i q u y l t vSn d^vi ket q u i dat duoe
Vdl n h d n g d i e trUng d d , SNT dUoe p h i n bl§t mffl
e i c h ro rang vdi nhan thde, Ve npi d u n g , SNT bao g&n
m o t phan cua the gidi t r i tue, t m h than, Trong khi 66,
nhan thdc bao g o m hieu b i l t c i c d d i tuong, eon ngi/ii,
su kien, hi&n t u o n g t i m li va e i e ki n i n g d l xd II eicvSn
de n i y Do do, SNT k h d n g eo n g u o n goe t d thUe t l bfei ngoai chil the m i g i n vdi hoat d o n g t n tue v i tinh ihJn cua ehu t h l , no cd t h l bao g o m n h d n g gi m i c i nhSn
b l l t v l q u i trinh h u d n g n d i , c i c h thde thUc hien v i cSdi
ehdc nang g i i i quyet van d l v i mang lai k i t q u i khi giii
d m h h u d n g nhan t h d c cua ea n h i n trong qua trinh giil
q u y l t van de,
3 M d hinh sieu nhan thdc ciia Tobias v^ Evn«n
C6 n h i l u m o hinh ve SNT da duoc nghien eiilivi
ap d u n g v i o hoat d d n g t a m If hoe va day hoc, Trong dft
/ L J P ke boach \ \
/ Lira chpu chiin hr^c
/ E>inh ga Mfc b ^
\ / ^ S
^^\
/ Tbto ddi hieu brfl \
Hlnh 1: ft/Id hlnh phdn cdp vequd trinh SNT
Trang 2mo hlnh SNT theo kieu phan cap cua Tobias va Everson
tnnh day hoe Tlieo cic dng, SNT la sd ket hop gida cic
yeu to nhd ki ning, kien thdc (hieu biet «e nhin thdc)
theo doi qua trinh nhin thdc cua ngudi hoc cung nhu
dieu khien qui trinhdd theo md hinh !
- Ldp klhoach: Cong viec dau tien cua HS trong
• hoat dong SNT l i lip ke hoaeh, bao gom xac dinh mue
tieu hoe tip thdi gian hoc tap, ddklen ket qui dat duoc
-/('"^''oncWerr/i/crcr Sau khi lip ke hoach, ngudi
ftl hoc cin lua chon ehien Idoc, phddng phap phil hdp de
% thuc hien nhiem vu hoc tap dd
iff -Odn* gid vlec hpc: Khi thuc hien xong ehien Iddc
V! hoc tap, ngddi hoc can dinh gii ve viec hoe cua minh
<h: baa gom danh gla qui trlnh v i dinh gii ket qui dat
dddc so vdi muc tieu dat ra Danh gia l i hoat ddng quan
minh
- Theo ddl hiia bietiTheo ddi mde dd hiiu eua bin
than dtung giai doan khie nhau, theo ddi hieu qui coa
' cic phuong phip duoc sd dung de Ida chon phdong
u bin than biet nhdng gi vi khdng biet nhdng gi Neu
!, HS khong phan biet duoc ehlnh xie nhdng gl ho bidt
-.: va nhdng gi ho khdng biet thi khd eo the tham gia vio
i, cie hoat ddng mang tinh SNT nhd danh gii viee hoe cua
chinh minh, lip ke hoaeh hay di^u khiin qui trlnh hoe
:- tap do Nguoc lai, nhdng HS cd ki nang SNT se nhin bie't
- duoc kien thdc cua bin thin, cic em nhan bift duoe dau
li kien thue trong tim mi bin than can dat den Td dd
, cic em cd the sd dung mot cich eO hieu qui thdl gian'
tim kiem duoe bien phip de thuc hien nhiem vu cua
minh, giup cho viec hoe cd hieu qua hon VI the, theo ddi
hlfu biet duoc xem l i hoat ddng nen ting, lam eo sd cho
Vlec cho cac hoat ddng khac
- Klim sodt: Veu to chl phdi ea oua trinh SNT ehinh
la Sd kiem soit Kiem soit nhim dieu phdi qui Irinh hoc
tap hay thuc hien nhlim vu cua ngudi hoc, khi do ngddi
hoe CO the dua ra quyet dmh tiep tue hay ddng lai khi
hudng di nao dd khdng cdn phu hop vdi muc tieu."
3j<i>« ddng SNT trong qua trinh khim phi bai
toin ket thdc md
IJeo Nguyen Thl Duyen (2014), bai toin kft thue
mdlibaitoin mang den eho HScohgi detlm kiim duoe
VI cie bai toan kft thuc md thudng eo cau true khdng
chat che nin ddl hdi HS phii xem xft cie ye'u t d khii
niem toan hoe Nen quan den vin de can giii quyft tim
kiem cae phddng thde giii quyft vin de, dua ra cie ciu
tri ldl khae nhau cd the cd va tim kie'm eich thdc de giao
tiepeae ket qui thu duoc, khdng don thuan chl la viic i p
Qiil quyft vin de khi lim vlec vdi cac bai toin ddng (ed
mot eau tri Idl duy nhit dung)
,-,„„,?" ''""^ """ '''"'' ^'" ""' '''>>"" ™ Everson
(2002) vao qui trlnh khim phi bii toin kft thuc md si
glupcho ngudi hoc ed dinh hddng rd rang trong viec tim
klim phddng i n giai quyft van de dit ra trong bai toin
ban dau Cu the hoat ddng SNT se dinh hddng qui trlnh khim phi bai toin kft thuc md bing cic hoat ddng thinh phan cuthe sau:
- Lap ke hoach: Cdng viic dau tiin cua HS trong
hoat ddng SNT la len ke hoach di' fim hieu tinh hudng toan hoe dit ra trong bai toin kft thuc md Viec lin ke hoach dUde bit dau bang eie edng viic cu the la dit ra ddng cic gii thuyft de khim phi tlnh huong ban diu -lu-ocftonc/iienJi/ocrSaukhidatraeacciuhdI.gii thuyft v i mue dich di' khim phi tlnh hudng ban dad ngddi hoc tim kiem phdong an giai quyft van de thdng qua viee phin tich va xd (i dd lieu, tim kiem phuong i n giil quyit van de, kiem chdng hay bac bd cie gii thuyft
- Bdnh gid viic hgc: Dinhgiieicphddnginkhim
pha bai toan ket thue mft kft gui khim pha bil toin kft thuc md so vdl muc tieu ban dau de ra
- Theo ddi hliu biit: Theo ddi hieu biet eua bin
than ve eic kien thde vi kl ning toan can thiet di' khim pha bil toan kft thue md, theo doi tinh hliu qui eung thuc mode tim kiem hddng khim phi phu hop nha't
- Klim sodt: Ngddi hoc kiern soit qui trinh khim
pha bai toan kft thuc md, quyft dinh ddng lai hay tiin hanh md rdng bai toin ban dad dit ra cic ciu hdl va van
de mdl de tien hinh kham phi xa hdn
4 Phddng phap nghien cihi
Di' tim hieu boat dong nhin thde trong qui trlnh kham pha bii toin kft thuc md eua HS ehung tdi da nen hanh quan sit tren ddi tuong gom 40 HS Idp 11 cua mot trudng trung hoe phd thdng d mien nui phia Bic cua Met Nam Nhdng HS nay dUde chia thanh 10 nhdm
mo trong ehu de xac suit vi yiu cau cac nhdm trlnh biy hunng kham phi cua nhom minh Sau dd chung tdi quan sat eac pha trong hoat ddng SNT cua cic nhom HS khi cae em khim phi eic bii toin kft thiJe md dd
Bai todn I: Lan va Hong d i md mdt quay nude giii
khat vao dip hoi trai dtrudng Lan gdp van 500.000 donq
va Hong gdp vio 1.000.000 ddng di' mua nguyen lieu
fnnn n'nnT"' ' ? ' " " ' ' " " ^ ' ° " " " ""' *"•""' " " " ^ '^
duocnhuthenio?
^ Bil toan nay ddde lua chon nhim kli'm tra kha nanq phan ehia so tien thu duoc sau khi diu tu bin hang cua
HS nhim dem den cho cac em eo hdl td do ehia si suy
de dua ra cich chia bin mi eie em cho l i phii hop
^ -Phuang dn I: Ba't ke sd vdn ban dau ma mdi ngudi nid- ^'° "^ ™: " " ' "'" " "*" "•" """" * 0 mdl
nguoi Oieu do co nghla l i chia tien thu dude theo ti le 1.500.000ddng.Phuongi„nayedtheehapnhinnh"ng
Trang 3m
no khdng dam b i o duoc tfnh eong b i n g vdi sd von dau
t u ban d i u cua Hai ngudi
- Phuang dn 2: T r i lai sd tien vdn eua mdi ngudi rdi
sau dd chia deu sd tien l i i Do do, Lan se n h i n dUOc so
tien l i 1.250.000 dong va Hdng n h i n dUoc so tien la
1,750.000 d o n g PhUong i n nay co t h l e h i p n h i n dUoe
NhUng tren thue t l , viec phan chia sd tien thu dUoe se t l
le t h u i n vdi sd lien vdn ma hai ben da g d p vao lue dau
Do do, HS ed t h l dl den phuong i n ehia tien t h d ba
- Phaang dn 3: Chia sd tien thu dUoc ti le vdi sd tien
von m i hai ngUdi da g d p ban dau hay chia theo t i le la
1:2 N h u v i y , Lan se n h i n duoe 1,000,000 ddng v i Hong
se nhan duoc 2 000,000 ddng PhUong an n i y n h i m
d i m bao ti'nh cong b i n g vdi su dau t u ban dau cua ea
Lan v i Hdng
Trong ba each chia tlen a b i i t o i n tren thi hai e i e h
dau mang tinh v i n hda x i h d i con each chia t h d b a d i m
b i o duoc tinh cong b i n g trong gdp von kinh doanh Do
dd, c i c h ehia t t l n theo ti le g d p vdn cd the duoc xem
la mot eich t i l p can theo quan diem t o i n hpc de g i i i
quyet c i c van de cd bdi c i n h thUe te,
Bdi todn 2 Nam va H i i ciing t r d b i n b i v i quy dinh
neu ai t h i n g ba van se la ngudi chien t h i n g v i d i n h
duoc t o i n bd 24 vien bi ma hai ban d i dat cUOc ban dau
ddng lai H6i Nam v i H i i p h i i ehia sd vien bi ban dau
n h u t h e n a o '
Bil t o i n t h d hai duoc lUa chon nhSm kiem tra k h i
n i n g p h i n chia so bi da cUoc khi HS tham gia t r d choi
HS ed the tiep can mdt trong ba c i c h chia sd bi d i cuoe
nhusau;
- Phaang dn 1 Chia sd fai theo ti le 1 1 Moi ngUdi
nhan dUoc 12 vien bi ban d i u Phuong i n n i y co t h l
c h i p n h i n nhung nd khong d i m b i o dUoc t i n h cdng
b i n g vdl hai ngUdi choi
- Phaang dn 2 Chia sd bi ti le thuan vdi sd v i n t h i n g
eua hai ngudi hay chia theo ti le la 2 1 C i c h ehia n h u t h e
nay cung khdng dam b i o dUoc tinh edng b i n g vdl ngudi
choi vi neu Iro choi khdng ddng lai thi eo hoi t h i n g eudc
theo d l g i i l q u y l t van de,
- Phuang dn 3: Neu trd choi van tiep tuc thi ehi c i n
tdl da 2 v i n nda trd choi se k i t thuc Hai van choi co 4
dau va H i l t h i n g v i n t h d hai, H i i t h i n g v i n d i u v i Nam
kha nang cuoi cimg mdi t h u i n loi cho H i i , hay khi b i l n
ed do x i y ra thi H i i mdi trd thanh ngudi e h i l n t h i n g Vi
vay Ha, chl cd 1/4 eo hdi ehien t h i n g eon Nam ed d i n
3/4 CO hdl chien t h i n g Do do, ehia so bi theo co hdi
t h i n g eudc eua ngudi ehoi, nghia l i ehia theo tl le 3-1
Day la each chia d i m b i o tinh cdng b i n g vdi hai ngudi
ehoi nhat Lue do Nam duoc 18 vien bi va Hai duoc 6
vien bl,
Trong ba phuong an tren thi phuong an t h d 3 la toi
uu nhat vi nd d i m b i o t i n h c d n g b i n g vdi ngudi chof a chia sd bi theo x i c suat t h i n g cudc cua m o i ngudi
Bai todn 3: Hai d p i eung t h a m gia m d t t r d chcfiltfo
CO Mdl van t h i n g duoc 10 d i l m , d d i n i o duoe 60 dilm tfUde se d i n h dugc toan b d phan t h u d n g l i 1.OOO.000
d d n g Khi ddi t h d nhat duoe 50 d i e m v i d d i t h d hai dugt
30 d i l m thi trdi d d mUa nen tro choi phal ddng l^i.H4i phai ehia sd t i l n t h u d n g eho hai ddi n h u t h i n i o ?
- Phaang an 1: Chia t i l n t h e o ti le 1:1 Moi d$ise
nhan duoc 500.000 d o n g P h u o n g an n i y cd t h l c h ^
vdl hai d o i choi
- Phaong dn 2: Chia t i e n t i le t h u i n vdi sd d i l m cila
hai d p i hay ehia theo ti le 5 3 C i c h ehia n h u t h i n i y eung khdng d i m b i o dUoe tfnh edng b i n g vdi hai doi ehdri neu t r d choi t i e p tue thi eo h d i t h i n g cuoc eua dpi m6lse cao hOn D o d o HS tiep c i n p h u o n g an t i l p theo d l ^
quyet van de ehia t i l n t h u d n g
- Phaang dn 3: Co t h l chia tien t h u d n g theo ti \i 1:1
hoae ehia theo t l ie sd v i n t h i n g eua hai ngudi, tuy nhlfti
la ehia theo c d hpi t h i n g cuge cua t d n g d d i , N l u trd chof
ddl chien t h i n g Ba v i n choi tao t h i n h 8 n g i u nhl^n,
t r o n g d d ehi ed m d t ngau n h i ^ n l i m eho ddi thdhal
t r d t h i n h doi ehien t h i n g c h u n g cude, Vi v i y ehia tifc
t h u d n g cho hai d p i t h e o t l le l i 7:1, dpi t h d n h i t di/^ic
bao duoe t i n h eong b i n g vdi hai d o i ehoi
5 K^t q u i
D d lieu t h u t h i p duoe tU nghien cdu nay eho thiy bai t o i n k i t t h u c m d m a n g den eo hoi d l HS t i l n hSnh
sat Idp hoe cho thay hau h i t HS da t h o i t khdi suy nghl
duoe t i li thuan vdi so v o n dau t u ban d i u cua hai ngi/fli
c i e n h d m HS khi kham p h i bai t o i n nay ddoc md t i cy
t h l n h u sau:
- Lap k4hogch: HS phan tich g i i t h i l t cda b i l toin,
d i t ra m o t sd h u d n g khae nhau d l k h i m p h i tinh hufing
deu s d t i l n b i n hang cho hai ngUdI hoae ehia theo til?
g d p von ban dau eua hai n g u d i ,
- Lifa chgn chien luac: Hau h i t HS d i u sd dyng
k i l n thde v l eae dai fuong ti le t h u i n d l dUa ra phdOTig
an chia t i l n t h u duoc, C i e HS 6 n h d m 2 da dda ra ba
p h u o n g i n ehia t i l n t h u duoc: chia theo it 1^ 1:1 t r i 1^
theo t l le 1:1, ehia sd t i l n t h u duoe theo ti le gdp von ban daueCia hai n g u d i
- Ddnh gid viec hgc: D d lieu t h u thap duoe tiJ
viee quan sat Idp hoe eho thay c i e em h i i ldng vdl cic
p h u o n g i n ehia den t h u dugc m i b i n t h i n d i dua ra
- Theo ddi hiiu biit: K i l n thde m i HS c i n sd dgnS
d l g i i l q u y l t van d e chia t i l n b i n h i n g t h u ddpc trong
Trang 4Ns
Niitm 2._
- -PhJOnriii :J.t„.,ii,,i„„i^^^
, - —Uehj {SK ces ^Si
J k r i , „ , T^-J^_.ii_l^Tg^J,-,;
"iKi-So' Jui, a t t i i fc £16,., a„
^ ,ioo£ one iTri^ _
X -^ /y=" - t ,LM 1£ a ,:j, liL.zl( -tiK^,
V , ;,^ , > - l « ^
' ' •^TSilt.lf —
-^Hf' i ' i i J i | '<'.-?.-.i-t^lilij
P ^ - ; \ -InU:'-rinr :lusiS_
- i ' J-t'_.-aiiS
-l>ii.-tUj-Hinh 2 Bdi Idm cua nhdm 2
11 u l ^ * " ' ''"f "'>' " " ' ' " * " * ' " *?' IKdng ti le thuan
Nhdng kien thde niy nim trong mien hieu bift toin cua
•' cic em td eap Trung hoc eosd
'"'""•'""••Vdlbiitoinl.hSuhftHSdeutriiqua
hoat dong kham phi toin vdi ba cho trlnh khep kin
"bdng tang dan yeu cau v i mdc dd nhan thdc nhSm tim
'• ra phUdng i n tdl uu de' giii quyft va'n de ma bii toin
i dat ra
; Sau khi lim quen vdl viee kham phi bil toin diu
tien, HS tiep tuc tien hanh hoat ddng SNT khi tim kie'm
phUdng i n tdi uu de giii quyft vin de trong bai toin thd
2 Cung gidng nhu khi kham phi bii toin 1, hau hft HS
- deu cho ring cd thS ehia sd bi d i eUdc theo tl le 1 1 hoic
• chia theo tl l i so van thing eua hai ngddi chdL Cac pha
trong hoat ddng SNT eua HS khi kham phi bai toin niy
augc md t i cu the nhu sau
- Ldp kihodch: HS phan tich gii thift eua bil toin
dit ra mdt sd hudng khic nhau de khim phi tlnh hudng
ban dad Do inh hddng td each giii quyft va'n de khi
khim pha bai toin mdt nen ta't ea cie nhdm HS diu lin
ke hoach chia deu sd bi d i dat cuoc eho hai ngudi hoac
chia theo ti i i thing code cua hai ngudi
- Laa chgn chiin luac: HauhftHSdeusddungklen
thde ve eae dai Iddng d le thuin de dua ra phUdng an
chia so bl dat cudc luc diu khi khim phi bai toan hai
Tat ci cie HS dda ra phuong i n thd nhft l i chia sd bi dat
cuoc theo ti le 1 -1 luc dd mdl ngudi chdi se nhan dudc
li_12 yien bi Tiep tuc vin dung phddng i n giii quyft
van de d bai toan 1, tft ci cie HS deu eho ring chia sd
bl toi uu nha't Chi cd 20% HS trong Idp nhin ra ring cd
thi tiep can bai toin 2 theo hudng khac khi gia sd trd
Choi van tiep tuc de tim kiem cd hoi thing cude cua mdi
ngudi VI neu trd choi vin tiip toc thl ehi can tdl da 2
van nua tro Choi se kft thdc Hai van ehdl tao nin 4 ngiu
nhien mi chi cd mdt ngau nhiin khi Hii thing ei ha
van moi thuan loi cho Hil nghla li loc dd Hii l i ngdft
Hlnh 3- Bdi tdm cuo nhdm 4
8 vien bi
- Bdnh gid vlec hpc: Dd lieu thu thap dude td viic
quan sit Idp hdc eho tha'y HS thao luin can than ve cic xua't duoc phUdng i n toi du de chia so bi ban diu Dd ehoi van tiep tuc
- Theo ddl hiiu biit: Mdt trong nhdng kien thdc
ma HS can sd dung di" giai quyft van de dat ra trong bii toan nay l i dai luong ti l i thuan Tuy nhien, cie kien thde
ve dai luong B le thuin lai khdng du de mang den cho cac em phUdng i n tdi du de giii quyft van de Do dd, HS IJhii buy ddng kien thdc d cip do eao hon la xie suft khi tim kiemjjhuong i n tdi uu de giii quyft van de
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bm kiem eho minh phuong i n Idi uu de giii quyft van
de ban dau Nhdng kien thdc ve xic suft d i duoc van toi uu nhat Tddng tu nhd bai toin thd hai, hau hft HS deu gii su trd ehoi van tiep tuc de tim ra co hdl thing cuoc cua moi nguft Sau dd cae em Ida chon phuong i n ehia tien thUdng theo ti le xic sua't thing cudc cua mol can toi da 3 van nda mdi xic dinh dudc ddl chie'n Ihing
W ba van ehd, tao thanh 8 ngau nhien, trong dd chi eo mot ngau nhien lam eho ddl thd hai trd thinh dni ehie'n thang ehung cudc nen xie sua't de' ddi thd hai ehie'n
I - ^ —^ — • - " ^ ="•" uc uui tnu nai chiin Ch,.n thing Nhdviy Hi, ehi cd i cd hdi chie'n thing thing trong trudng hop nay l i I Xic suft d ddl thd cdn Nam cd den —
theo tl le 3 1 lue do Nam duoc 16
^ CO hdi ehiln thing nen chia sdbi nhatthingcupetrong trdehoi nayla :
W vay chia tiln
n bl cdn Hil ddde thdfttg cho hai ddi theo ti le l i 7:1 nen ddl thd nha't
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duoe 875.000 dong v i ddi thU 2 duoc 125.000 dong nhU
eaeh tiep can van de cua eae HS d nhom 7:
Hinb 4- Bdi Idm cua nhdm 7
Thdng ke sd lieu ve cie phuong an khim phi ba bai
toin ma cac nhdm HS dua ra daac trinh biy d bang sau:
Bdng 1 Phaang dn gidi quyet vdn de cua cdc nhdm HS
Bii toin
Bai toin 1
Bil toan 2
Bil toan 3
Phuong an
Phuong in 1
Phuong an 2
Phuang an 3
Phuang in 1
Phuong an 2
Phuong an 3
Phuong an 1
Phuong an 2
Phuong an 3
S o n h d m H S
10
9
9
10
10
2
10
10
5
So lieu thu duoc td nghien cdu eho thay, kiln thde
da cd eua HS v l cac dai luong ti le thuin d i anh hudng
den each giii quylt van de cua HS khi eae em lam viee
vdl eie bii toan thd hai v i thu ba Nhdng kien thde nay
uu d l giil quyet van de, Oiy la chudng ngai nay sinh
cap do cao hon, la ehudng ngai mang tinh tn thdc iuin
Do do khi ehuyen t d viec khim p h i b i l toan mdt sam
bai toan hai, chl eo hai trong tong s6 mUcri nhdmHS nhien, so luong nhom HS dUa ra dupe phUemg an toi
d l giil quyet van d i c i n g t i n g khi cic em quen dan vfi hoatddng sleu thdc trong no lue kham p h i eac bil toin
k i t thuc md, Cu t h l , da eo nam trong so mudi nhdm HS
d i d l xuat duoe phuang i n tdi Uude kham p h i bil toin bai t o i n thdba
6 Ket luan
Ket q u i thu dUoe tCf nghien cdu niy eho thiy, rf^ ti'eh hop eic b i i t o i n k i t thue mdvao eae thue hinh dm
hpe toan da mang d i n eo hoi de HS tien hanh hoat Sfyn
do, viee t i l n hanh eie hoat dgng SNT trude, trong vi sau khi khim p h i cic b i i t o i n k i t thue md nhu lap klhojdi
v i lUa chon ehiln luoe eiing cic hoat ddng mang tfi*
d i l u hanh nhU dinh g i i viee hoe, theo doi hieu biltvS kiem soit i n h hudng d i n k h i nang giii quylt thSnh cdng bai toan k i t thuc md ban d i u , Chlnh hoat ding khic nhau d l glii quyet van de va d l xuat duoe phudng
md Do do, cd the thay vide tich hop eic b i l toin kit thik ren luyen v i phit triln ki nang SNT eho HS
T A I L I $ U T H A M K H A O
[1], Nguyen Thl Duyln, ^20^ 4), Nghiin cdu bdi hgc eua gido viin tdp trung vao khdm phd todn cua hoc siiA trong day hgc mdn todn d tradng trung hoc phS thdng,
Luin an Tien si, Trudng Dai hpc Supham HaNdi,
[2], Kapa, E., [2001], A metacognltive suppat during the process of problem solving in a computerisd environment Educational Studies In Mathematics,47(3),
317-336
[3j, Schneider, W/,, & Artelt, C, (2010), fvletacognltlon and mathematics education, ZDM, 42(2), 149-161 E4] Tobias, S & Everson, H T, (2002), Knowing what you know and what you don't Further research « metacognltiveknov/ledgemonitoring.Technical Reports,
The College Board Research Report
METACOGNITIVE ACTIVITY IN PROCESS TO EXPLORE OPEN-ENDED MATHS EXERCISE
NguyenThiHuong LM
Tan Trao OnivtriUf
Email: nguyenlancdtq@gmaU.OM
was "h'^'r'o'le"olm'J^r""T' ' " " " " S " ' " " " ""' "fueled the attention of Maths educators One afihe interesllnglm oc2„'heoZesToZ7 '° '""' "'"'"-'""I -''"Ity- The paper focuses on understanding metacogiiHK'
Z eZdeZ^s\L7°y ""r'"""'"""'' " ""'" <X' " " ™ « ofmetacogniilan ,o successful sd-sZlgabZ """"" ""'""'"'""""•" O ™ " " •"etacognltlveoclivilles andsludetH Keyvrords: Metocognioon; exploration, open-ended Maths exercise