NGHIEN curu Li L U A N
Ren luyen kT nang sieu nhan thurc cho hpc vien thong qua hoat dong giai quyet van tfe trong day hoc mon Xac suat va Thong ke
U Binh Duong TruoigOai hoc Chinh tri Thach Hoa, Thgch Thffl, Hh NOi, Viel Nam Email dLiong1109@gmailcom
TOM TAT: Sieu nhan thOc va cac kl nang sidu nhan thde duoc nhi^u nha khoa hoc trong va ngoai nudc nghien cdu va van dung vao qua trinh day hoe. Viec day hoc theo hudng ren iuyen eho hoc vien mdt sd ki nang sieu nhan thdc se gdp phan phat trien tu duy cho hoc vien. Trong day hoc mdn Xac suat va Thdng ke, mdt trong nhdng hoat dong cd ^4 ren luyen kl nang sieu nhSn thdc eho hoc vidn ia hoat ddng giai quyet vSn d d , Bai vi6t tnnh bay ve sieu nhan thdc, mdt sd ki nang sieu nhan thdc, bi$n phap ren luyen ki ndng sidu nhan thdc cho hoc vien thdng qua hoat ddng giai quyet van de trong day hoc mdn Xac suSt va Thdng kd.
T Q K H O A . Sieu nh^n thil^c; ki nang siSu nh$n thiic; giai quygl v ^ n 6e.
mn bai 26/8/2018 -?• Nhan l(gl qua phan bign va chinh sira 20/9/2018 -S- Duyet flang 25/9/2018,
1. D^t vetn de
Cac hpc gia nghien cuu ve sieu nhan thtic (SNT) deu thong nhdt rang cdu true SNT duoc phan thanh hai thanh phan kien thiic va kT nang (KN) Kien thiic SNT co the dugc mo ta nhu nhung kien thiic, nhan thuc, su hieu biet sau sac han ve qua trinh nhan thiic ciia chinh minh va cac san pham. KN SNT cho phep nguoi hpc len ke hoach, kiem soat va danh gia qua trinh hpc ciia minh, hon la chi don thuan tap trung vao viec tuong tac va kiem soat dau vao cua qua trinh hoc tap hay nhan thiic [1]. Giai quyet van de (GQVD) la mot phan quan trong cua hoat dpng tri tue cua ca nhan. GQVD toan hpc dupe day cho nguoi hpc de phat trien kha nang chung trong viec giai quyet cac van de trong cupc song thuc te. KJii GQVD, dieu can quan tam kliong chi la each giai mgt bai toan nay hay bai toan khac ma con ca nhiing suy luan ciing qua trinh giai toan dong thai giai thich nhirng lap luan va qua trinh do; noi each khac, chiing ta can quan tam den khia canh SNT. Bai viet trinh bay mot so KN SNT, viec ren luyen mot s6 KN SNT thong qua hoat dong GQVD trong day hpc mon Xac suat va Thdng ke (XSTK).
2. Ndi dung nghien ciiru
2 . 1 . S i e u nhan thiiic v a k i n a n g sieu n h a n thuic
Theo Flaveil (1976), SNT la: "Su hieu biet eiia ca nhan hen quan din qua trinh nhan thiic ciia ban than, cac san pham va nhimg yeu to khac co lien quan trong do con de cap den vice theo doi tich cue, dieu chinh ket qua va sap xep cac qua trinh nay di luon huong tai muc tieu dat ra" [ 1 ].
KN SNT la "cac hoat dpng quan li lien quan den viec giai quylt cac vin di" [2]. No Uen quan den cae thanh phkn lap ki hoach, giam sat va danh gia ciia SNT No cung dupe goi la "su di6u chinh vi nhan thiic" trong do di cap den cac hoat
dpng va hanh dpng thuc hien boi ca nhan de kiem soat nhan thiic rieng eua hp.
Mot s6 KN SNT quan trpng doi vcri mon Toan gom c6:
Du doan (Prediction), lap ke hoach (Planning), giam sat (Monitoring) va danh gia (Evaluation) [3], [4], [5]. Cac KN SNT tren se dupe trinh bay chi tiet trong Bang I.
2 . 2 . Ren luyen k i n a n g s i e u n h $ n thiiic c h o h o c v i e n t h o n g qua h o a t d p n g g i a i q u y e t van Se b u n g d 9 y hQc mon Xac s u a t v a Thong k e
2.2.1. IVIuc dich
Hoc each GQVD trong toan hgc giiip nguoi hpc co dugc each suy nghT, thoi quen ciia su kien tri va ham hieu biet, tir tin trong nhiing tinh huong khong quen thupc. GQVD co vai tro quan trpng trong viec ren luyen tu duy va cac KN toan hoc cho hgc vien, giiip cho hpc vien ren luyen duae cac KN can thiet nhu kha nang tim hieu, nhan biet van de, lap ke hoach, kiem tra, danh gia va dieu chinh...
2 . 2 . 2 . C Q S 6 khoa hgc
Viec Sli dung cac quy trinh SNT ho tra nguoi hpc GQVD trong qua trinh giai quyet va cai thien kha nang ciia hp de dat dupe muc tieu [6]. Swanson [7] khang dinh, eang ki^m soat va giam sat cac chien luoc hp sir dung nhieu hon thi kha nang GQVD eang t6t. Schoenfeld [8] cho rang su thanh cong hay that bai cua viec GQVD ciia mot nguoi dua tren su ka hgp ciia b6n y&u t6 chinh la Ngu6n (co so tri thiic), chiSn luge heuristic (GQVD), kilm soat (giam sal va tu digu chinh cac khia canh ciia SNT) va niem tin. That bai trong viec GQVD noi chung la k^t qua ciia that bai trong viec lua chon phuong phap hieu qua nhkt, t6 chiie eac hoat dpng toan hoc, hiSu dupe vkn di, phan tich, giam sat va kiem soat eac hoat dgng
62 TAP CHI KHOA HOC GIAO DUC VIETNAM
Le Binh Duong
Bang 1 : Mgt S6'KN SNT
Dij doan Du doan co the' dugc mo ta nhu nhOng KN cho phep suy nghT v6 nhong muc tieu hoc tap, dSc diem hoc tap thi'cti hdp va thcJi gian co the
Ngoai ra, du doan con lien ket cac van d'e nhat dmh vdi cac van d'e khac, phat trien true giac ve nhong dfeu ki^n tien quygt
^ de'thuc hien mot nhiem vu, phan biet ro rang va thuc te nhQng kho khan trong GQVD toan hoc [5], U p kg hoach U p ke' hoach la mOt hoat dong co chu y nham thiet lap cac muc tieu phu de theo doi su tham gia mflt nhiem vu.
KN lap kg hoach la suy nghi trudc phai hanh dong nhu the nao, khi nao va tai sao dg dat duoc muc dich thfing qua mgt c h u o i c a c m u c t i e u p h u d S n d g n c a c m u c t i e u c h i n h c i j a v a n d ' e [ 4 ] ,
Giam sat KN giam sat cd the dugc md ta nhu su kiem soat, t u dfeu chinh cac K!\l nhan thUc duoc SLI dung trong viec thuc hien thuc tg, de xac dmh cac van d'e va sila ddi ke hoach [3]
Giam sat dg lua chon cac KN thich hop va dieu chinh hanh vl khi yeu c'au ntiiem vu thay ddi, biet sd dung cac h i l u biet v'e kjgn thitc da cd va chgn each hgc tap thich hgp [4]
Oanh gia (va Danh gia, cd thg dugc dmh nghia la nhOng phan anh duoc thuc hien sau khi mdt su kien da xay ra [3], tU dd nh'in vao dieu chinh) nhOng gi da lam cd dan den mgt ket qua mong muon hay khdng.
Cu the danh gia phan anh v'e kgt qua va su hie'u bigt ve cac van de va su phU hop c^a ke' hoach, thuc hien cac phuong phap giai cQng nhu v'e tinh day du cua cac cau tra Idi trong bdi canh cua van d'e [4].
dugc thuc hien [9]. Trong viec GQVD, cac khung duac tao ra de mo hinh tung buoc qua trinh. Hau het cac cong thiic ciia mgt khung GQVD deu cho thay mot so moi quan he vai cac buac GQVD ciia G. Polya, G. Polya [10] cho rang qua trinh GQVD bon giai doan khong the tach roi la: 1. Tim hieu va nhan biet van de; 2. Tim giai phap; 3 Thuc hien giai phap; 4 Nhin lai. Tuy nhien, GQVD khong dan gian la thue hien thu tu bon giai doan, ta co the chuyen qua cac giai doan neu thich hpp.
Garofalo & Lester [11] da de xuat khung nhan thiic, SNT de thuc hien nhiem vu trong toan hgc gom bon thanh phan:
1. Dinh huong; 2. To chtic; 3. Thuc hien; 4. Kiem tra. Bon thanh phan nay tuong ung vai bon buac cua G. Polya trong GQVD, Nhu vay, co the khang dinh, GQVD va SNT co quan he chat che vcri nhau. Thong qua hoat dpng GQVD eo the ren luyen dupe eac KN SNT va hoe vien khi co KN SNT se giiip cho viec GQVD t6t han.
2.2.3. Cach thiJc thuc hien
a. Hudng ddn hoc vien thuc hien hoot dong tim hieu vd nhdn biet van de
Trong day GQVD, co the ren luyen dugc cac KN SNT thong qua thuc hien hoat dpng GQVD Truoc tien, giang vien tap luyen cho hge vien thuc hien hoat dpng tim hieu va nhan biet van de, nham phan tieh lam ro y nghTa quan trgng cua viec hieu cac thong tm voi viec tim ra each giai. DS hinh thanh cho hpc vien KN SNT du doan trong hoat dong tun hiem va nhan biet van de, giang vien can chuyen hoa thanh cac cau hoi. Cu the nhu sau:
• Da hiiu thdu ddo bdi todn chua? Yeu cdu cua bdi todn la gi^ Nhirng thong tm quan trong da cho Id gi? Thong tin con thiiudiGQVDldgi?
De CO the tim dugc giai phap GQVD, yeu can dau tien voi hpc vien la phai hieu va nhan biet dupe van de, Giai phap khong the dua ra dupe neu nguoi GQVD khong hieu va nhan biet van de. DSy la giai doan nhan dang va phat bieu van de.
Giai doan nay phai di sau phan tich van de de lam ro, hieu ro cac thong tin da cho va thong tin can tim.
• Co the mo td cdc thong tin cdn thiet tren mot hinh ve khong?
Day la giai doan xac dinh va giai thich thong tin; la mpt giai doan cau noi de co the hen ket cae thong tm va cac kien thiic da biet de tim phuang huong phu hpp GQVD. Xac dinh va giai thich thong tin co the sii dung cac hinh anh true quan, CO the tao ra nhung tinh hudng cu the don gian hon de hieu dugc nhiing thong tin phiic tap.
• Dd bao gid gidi GQVD nhu the nay tru&c day? De gidi quyit bdi todn thi vdn de kho khan Idgl? Khd ndng gidi quyet duoc khong?
Giai doan nay ckn kit n6i vkn dS voi Id^n thiie da co va dua ra nhiing du doan so luge ban dau ve van de can giai quyet,
b. Huong ddn hoc vien thuc hien hoat dong tim gidi phap Bi hinh thanh cho hgc vien KN SNT lap ke hoach trong hoat dong tim giai phap, giang vien ckn chuyen hoa thanh cac ciu hoi. Cu the nhu sau:
• Muc dich cua bdi todn Id gi? Tren co so xac dinh ro muc dich ciia bai toan dat ra se dinh huong cac giai phap can thuc hien.
• Dd timg gap vdn de tuong tu vd each GQVD do nhu the nao? Trong giai doan nay, hgc vien cin nghT ra cae quy tac, cac thuat toan, cac dinh li, cac vkn de, cac bai toan nao do ho da timg bigt se rat hiiu ich trong viec GQVD.
• Di gidi quyk duoc hdi todn can gidi quyet cdc nhiem vti nhd nao? Khi giai quyfit mpt vkn di phiic tap can tach van de khoi diim thanh nhiiu van di (giai doan, buoc) nho quy tu
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NGHIEN c a u LI LUAN
vao no va dkn dat den ch6 tim ra dieu ckn hiit De tun dupe phuang an hieu qua giai quyet mot tinh hu6ng nhan thirc phiic tap, hgc vien can biet phan nho cac ySu t6 ciia vin d^.
• De gidi bdi todn nay cdn sd dung nhimg kien thuc, khdi niem, tinh chdt, dinh Ii, quy tdc nao? Hgc vien thirc hien cac hoat dpng lien tuong den cae kien thiic lien quan, huy dpng cac kien thiic da biet, chuyen doi ngon ngii, bien doi doi tugmg, phan tich moi lien he giiia cac thong tin, ket noi kien thiic de tim giai phap.
• Cdc bu&c cdn Uen hanh de gidi bdi todn Id gi? Cd gidi phap de gidi quyet bdi todn khong? Day la giai doan xac dinh each thiic GQVD, hoc vien ket noi cac kien thirc va cac thong tin VOI nhau de ehpn lua giai phap phu hop. Viec tim toi each thiic suy nghT giai quyet tinh huong cu the duoc tao ra se lam tien di giiip hgc vien du doan, dinh huong va dua den each thiic GQVD tong quat dat ra.
c. Huang ddn hoc vien ihuc hien hoat dong thirc hien gidi phdp
Sau khi hieu van de, tim giai phap la den buoc thuc hien giai phap. Thuc hien giai phap !a giai doan bien ke hoach thanh hanh dgng. Day la giai doan nhan ra lieu ke hoach ma ta da dua ra co tien hanh duoc khong. Neu ke hoach ta da dua ra khong tien hanh duac thi co the xem lai giai doan tim hieu van de va tim giai phap, Giai doan trinh bay giai phap la giai doan thuc hien eac buoc da lap a giai doan xay dung ki hoach, trong qua trinh thuc hien phai ra soat, sua ch&a va dieu chinh giai phap trong truong hgp can thiet.
d Hirong ddn hoc vien nhin lai gidi phdp Giai doan nhin lai van de ia each tu danh gia tot nhat can day cho hoe vien; boi no khong chi danh gia tinh hop li cua van de ma con danh gia hoat dgng tu duy ciia chinh
nguoi hpc. Danh gia giai phap GQVD va ma rpng van de la giai doan quan trpng ciia GQVD, do chinh la cac hoat dpng cung cip CO hpi phat trifin nang luc phat hien va GQVD, nang luc sang tao cho hgc vien. DS hinh thanh cho hoc vien KN danh gia va tir diSu chinh trong giai doan nhin lai van de, giang vien ehuygn hoa thanh cac cau hoi khi danh gia, giup hpc vien lam quen voi cac cau hoi do khi danh gia mpt lui giai Cu thi:
Ddnh gid ve hoat dong tim hiiu vdn de. tim gidi phdp:
+ Cach xac djnh va giai thich thong tin da phii hgp chua?
+ Viec xac dinh muc tieu va chia nho nhiem vu da hgp li chua? Viec phan chia cae truong hpp da day du chua? Co each chia nho khac khong?
+ Cach GQVD da ehinh xac ehua'? Co phuong phap giai quyet khac tot hem khong?
Ddnh gid ve hoat dong thuc hien gidi phdp.
+ Ket qua co diing khong? Cae buoc tinh toan co chinh xac khong? Cac buac bien doi co diing khong?
+ Lai giai da xet day dii cac truong hpp chua? Lap luan chat che chua'' Trinh bay da khoa hpc, hop li chua?
2 . 2 . 4 . V i d u v ^ n dung
Vi du: Theo trmh sat tran dia cua ta nhan djnh m6t chiec may bay tiem kich cua dich eo the tin cong tran dia phdng ngu ciia ta tit hai huong, huong I vol xac suat la 0,6, hudng 2 voi xac suat la 0,4. Tran dia phong ngu co 4 khau phao duoc bo tri de tren timg huong deu co. Biet xac suat diet may bay ciia moi khau phao la 0,7 va cac khau phao hoal dpng dgc lap voi nhau. Tinh xac suat diet may bay dich cua cac phuang an b6 tri 4 khau phao tren cac huang. Cach van dung dupe trinh bay chi tiet trong Bang 2.
Bang 2: Cac ho^t dgng tie'n hanh khi GQVD
Giai doan Cau hoi ajnh hudng Cdu M idi mong doi Tim hie'u van Oa hie'u can ke bai toan
dg chua? Nhiing thdng tin quan irong da cho la g i ' ' Yeu c'au cua bai loan la gl?
NhOng bign cd can md ta trong bai toan la gi?
NhQng bien cd nao xac suat d a ^ e ' l ? _ NhOng bign c d cd xac suat con thieu de GQVD \^^
Dang cua van de la gi?
Tim giai Muc tieu ciia bai toan la gi?
phap _ _ ._ _ _ .
May bay cd the' ian cdng tran dia phdng ngu tU hai hudng, hudng 1 vdi xac suSt la 0,6, hudng 2 vdi xac suat la 0,4.
I r a n dia phong ngu cd 4 khau phao. Xac suat diet may bay cua mdi khau phao ia 0,7. _ _ Tinh xac suat diet may bay dich cua cac phuong an bd t r i 4 kha'u phao tren cac hudng.
Bien cd A="May bay xuat hien d hudng 1 " ; B^ "May bay xuat hien 6 hudng 2 " ;
H^ "May bay b| tigu diet" _ _^
p(A)=0,6. p{B)^0,4
Xac suat diet may bay ciia mdi kha'u phao p = 0.7_. _ Bign cd H CO xac suat cdn ihieu
Bien cd H phu thudc vao bien cd A xay ra hoacjiien cd B^cay ra va cac phijong an bd tri.
Bai toan tinh xac suat cua bien cd H phu thudc^ien c o A ya B. ^ Can tim: P(H)
64 TAP CHI KHOA HOC G!A0 DUC VIETNAM
Lg Binh Duong
Cac phuong an bd tri cua bai + Phuong an 1:3 khau phao dat tgi hudng 1,1 khau phao dat tai hudng 2.
toan la gi? + Phuong an 2 : 2 kha'u phao dat tai hudng 1,2 khau phao dat tai hudng 2.
+ Phuong an 3 : 1 kha'u phao dat tai hudng 1,3 khau phao d ^ * * ' ' ' ' ^ " " " " ' ^
Nhin 1^
phap
j i hudng 2, Oe' giai quyet dugc bai toan M6i phuong an cd 2 tinh hudng: May bay xuat hien d hudng thu nhat va hudng thu hai can giai quyet cac nhi^m vg + Can tinh duoc xac suat ciia bign cd: "May bay bi tieu diet khi xuat hien 5 hudng thu nhat"
nhd nao? + C5n tmh dugc xac suat cOa bign cd: "May bay bi tieu diet khi xuat hien d hudng ihU hai".
Oe giai bai toan nay can su Bien cd H phu thudc vao bign cd A xay ra hoac bien cd B xay ra va tUng phuong an bd t n , Day dung nhung kig'n thUc, khai la he 2 bien cd d'ay dti nen can sii dung cdng thUc xac suat day du
mem, tinh chat, dinh li, quy tac nao"?
Cac budc can tign hanh fl giai bai loan la gi*^
Ttiuc hien Cach thiJc GQVD theo giai phap phuong an 1 la gi"?
Cach thtic GQVD theo phuong an 2 la gi?
Cach thUc GQVD theo phuong an 3 la gi?
giai Cd nhan xet gi ve cac phuong an?
Theo cdng thdc xac suat dSy Qii: P(H) = P(A}P(H/A) + P(B}P(H/B), de'tinh dugc P(H) can tmh dugc P(H/A) va P(H/B).
P/ji/mg a/7/.• 3 kha'u phao dat t a i h u d n g l . l kha'u phao dat tai hudng 2.
+ Budc 1; Tinh P(H/A)
Bign cd {H/A) = "May bay bi tieu diet khi xuat hien d hudng 1 " .
Hudng 1 cd 3 kha'u phao, nSn bien cd (H/A) tuong duong vdi bien cd "Cd it nhat 1 kha'u phao diet dugc may bay"
Do dd p(H!A) = p3(k > 1) = 1 - O.S^ ^ 0.973.
+ B u d c 2 : T i n h P ( H / B )
Bien od (H/B) = "May bay bi tieu diet khi xuat hien d hudng 2 "
Hudng 2 chi cd 1 kha'u phao, nen bien cd (H/B) tuong duong vdi bien cd "Cd 1 kha'u phao diet duoc may bay".
D o d d p ( B / B ) = p , ( k - 1 ) - 0 . 7 . + B u d c 3 : T i n h P ( H )
Theo cdng thdc xac sua't day du: p(H) = p(A)p(H|A) + p(B)p(H|B) - 0.6 x 0.973 + 0.4 x 0.7 = 0,8638
Phuong an 2:2 khia phao dat tai hudng 1,2 kha'u phao dat tai hudng 2 + Budc 1: Tinh P(H/A)
Bien cd (H/A) = "May bay bi lieu diet khi xuat hien d hudng 1 " , Hudng 1 cd 2 kha'u phao, nen: p(H|A) = P2(k > 1) - 1 - 0.3^ = 0 91 + B u d c 2 T i n h P ( H / B )
Bign cd (H/B) = "May bay bi tieu diet khi xuat hign 6 hudng 2".
Hudng 2 cung cd 2 khau phao, nen: p(H|B) = p^lk > 1) - 1 - 0.3^ = 0.91 + B u d c 3 : T i n h P ( H )
Theo cdng thdc xac suat day du:
p(H) ^ p(A)p(H|A) + p{B)p(H|B) = 0.6 x 0.91 + 0 ^ X 0.91 = 0.91 Phuongan3:^ khau phao dat tai h u d n g 1 , 3 k h a u phao dat tai hudng 2.
Budc 1: Tinh P(H/A)
Bien cd (H/A) = "May bay bi tieu diet khi xuat hien d hudng 1 " . Hudng 1 chi cd 1 khau phao, nen: p(H]A) ^ pi(k ^ 1) = 0.7, B u d c 2 : T i n h P ( H / B )
Bign cd (H/B) = "May bay bi tieu diet khi xuat hien d hudng 2".
Hudng 2 cd 3 kha'u phao, nen:
p(H|B) = P3(k>1) = 1 - 0 , 3 3 ^ 0 . 9 7 3 . + Budc 3- Tmh P(H) Theo cdng thdc xac suat day du:
p(H) = p(A)p{H|A) + p(B)p(H|B) = 0.6 x 0.7 + 0.4 x 0,973 = 0 8Q92 + cac phuong an bd tri cd xac suat diet may bay d'eu tren 80%.
+ Phuong an 2 cd xac suai Idn nhat Cho nen dudi gdc nhin xac suat viec bd tri theo phuong an 2 tdt hon phuong an 1 va phuong an 3.
+ Do phuong an 2 la lot nhat nen trong trudng hop, khac phuong an bd tri chia deu luc iuong cac hudng nen dugc lua chgn, _ _
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NGHIENCUTULILUAN
Phugng an bd tri khac la gi? + Phuong an 4 : 4 khau phao dat tai hudng 1 0 khau phao dat tai hudng 2 Hieu qua cua chdng ra sao? Tuong tu cd the tinh duoc: p{H) = 0.59514
+ Phuong an 5- 0 khau phao dat tai hudng 1,4 khau phao dat tai hudng 2, Tuong t u cd the tinh duoc. p(H) = 0.39676
.. N ] m a y ^ e m a t _ x a c ^ t c d t h g t h a y h i e u q u a c u a 2 p h u o n g a n n a y k h d n g c a o . _ Khi giai xong can lien hanh danh gia va nhin lai qua trinh giai de xem xet tinh chinh xac cua phuong phap giai, tinh chinh xac cua cac budc giai, su chinh xac cua tinh loan, cac kien thUc da dugc sQ dung. Ne'u sai can di'gu chinh nhu thg nao cho hgp li? _ _
3 . Ket ludn t6t co thi nghT v^ mot vkn di hoac ti^p can mpt nhiem vu Day hge GQVD la ca hoi tot de ren luyen mot so KN hgc tap, chon chi6n luge phu hpp va dua ra quyet dinh ve SNT gop phan nang cao chat lugng day hpc, dac biet la phat mot qua trinh hanh dgng dl giai quySt cac van de hoac thuc trien tu duy cho hpc vien. Hoc vien co KN SNT phat tnen hien nhiem vu thanh cong.
T^i Ueu tham khao
[1] Flaveil - I. H., (1976), Metacognilive aspects of problem solving.
In L. B. Resnick (Ed.), The nature of intelligence (pp. 231-235).
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TRAINING METACOGNITIVE SKILLS FOR STUDENTS THROUGH PROBLEM-SOLVING ACTIVITIES IN TEACHING PROBABILITY AND STATISTICS
Le Binh Duong
Political University ABSTRACT: Metacognilion and metacognilive skills are researched by numerous domestic Thacti Hoa, Thacli Thai, Hanoi, Vielnam g ^ i j foreign scientists and applied in the teaching process. Metacognilive skiiis-based Email djong11G9@gmailcom . . • , . , ^ . ^ ^ ,...,.• ,
teaching will contnbute to the development of students thinking. In teaching probability and statistics, problem-solving activities are used to train metacognilive skills for students.
This paper presents about metacognilion, metacognilive skills, and some solutions to develop metacognilive skills for students through problem-solving activities in teaching probability and statistics.
KEYWORDS' Metacognilion; metacognilive skills; problem-solving.
66 TAP CHI KHOA HOC GIAO DUC VIETNAM
