TAP CHi KHOA HQC DHSP TPHCM Le Trung Tin
/VAN DUNG Li THUYET SIEU NIL^N THU'C
TRONG DAY HQC MON TOAN 6 TRU'DNG TRUNG HOC PHO T H 6 N G L^ TRUNG TiN' TOM TAT
Thugt ngd "Sidu nhan thue" dugc su dung tic cudi nhimg ndm 70 cua thi kiXXdi cap din qud trinh tu duy eua mdi cd nhdn vi tu duy cua chinh minh. Nhimg ndi dung cua li thuyit sieu nhgn thirc dd mang din mgt quan diim dgy hgc hieu qud, phdt huy tdi da vai tro cua ngudi hQC, gdp phdn quan trong vdo qud trinh chimin ddn tic ddo tgo sang tu ddo tgo trong gido due. Trong bdi bdo ndy, tdc gid di xudt mdt sd bien phdp van dung li thuyit sieu nhgn thue trong dgy hoc mdn Todn d trudng trung hoe phd thdng.
Tit khda: Sidu nhgn thdc, mdn Toan, hgc sinh trung hgc phd thdng.
ABSTRACT
Applying metacognitive theory in teaching mathematics at high schools The terminology "Metacognitive" has been in use since the 70s to discuss the cognitive process of each individual about their own cognition. The contents of metacognitive theory have brought about an effective teaching approach which maximizes learners' role, playing an important role in shifting from the educating paradigm to a self - educating paradigm. In this article, the author proposes some measures for applying metacognitive theory in teaching mathematics at high schools.
Keywords: metacognitive, mathematics, high school students.
1. Dat van de
Tri thdc cua thd gidi ngay nay dang gia tang theo tde dg luy thua ddi hdi giao due can phai ddi mdi theo hudng chu trgng den vide day cho hgc sinh each hgc, each tu duy. Ndi each khac: giao due khdng chi quan tam ddn kdt qua nhan thuc ma quan trgng ban can quan tam ddn qua trinh tu duy dd ed dugc kdt qua dd. Li thuydt Sidu nhgn thdc xuat hien td cudi nhiing nam 70 eua thd ki XX da mang den mdt quan didm dgy hgc hidu qua, phat huy tdi da vai trd eua ngudl hgc, gdp phan quan trgng vao qua trinh chuyen dan tu dao tao sang ty dao tgo trong giao due.
2. Khai niem Sieu nhan thi^e Sidu nhan thdc da dugc dd cgp ddn trong mdt sd nghien euu eua cae tae gia trong va ngoai nude nhu: J.H. Flavell, A.
Brown, Tobias va Everson, H. M.
Wellman, J. Wilson, Vu Diing, Nguydn van Thanh...
"Sieu nhgn thuc la sy hidu bidt ca nhan lidn quan ddn qua trinh nhan thde cua ban than, cac san pham va nhiing ydu td khac cd lidn quan trong do cdn d^ c4p ddn vide theo ddi tich cyc, didu chinh kdt qua va sip xdp cac qua trinh nay dd ludn hudng tdi myc tieu dat ra" (J.H. Flavell, 1976) [2].
"Sieu nhgn thuc la mgt hinh thuc
* ThS, Trudng THPT chuyfen Nguyen Hu$, Ha NOi; Email. [email protected]
TAP CHi KHOA HQC DHSP TPHCM Sd 4(82) ndm 2016
cua nhgn thue, la qua trinh tu duy bgc hai hay cip do tu duy eao han, nd lidn quan ddn boat dgng dieu khien bdn ngoai qua trinh nhgn thue. Sidu nhan thue cimg cd thd dugc hidu la tu duy vd tu duy hay nhgn thuc vd nhan thdc cua mdi ngudi"
(H.M. Wellman, 1985) [6].
"Sieu nhgn thuc la su linh boat vd kidn thuc va sy didu khidn qua trinh nhgn thde cua ban than"(A. Brown, 1987) [1].
"Sidu nhan thuc la thuat ngu chi hanh dgng suy nghT vd tu duy hoac nhgn thuc vd nhan thuc. Dd la kha nang dd bgn kidm soat suy nghT eiia bgn" (Vu Dimg, 2008) [5].
Trong nghien euu nay ehung tdi quan niem: Sieu nhdn thuc Id qud trinh tu duy cda bdn thdn vi tu duy cua chinh minh bao gdm: Su hiiu biit vi vdn kiin thuc vd tu duy cua chinh mlnh; theo doi, ddnh gid qud trinh nhdn thuc cua bdn thdn; nd lue dieu chinh qud trinh nhdn thuc khi cdn thiit nhdm gidi quyit vdn dl
3. Cae chiic nang co ban cua Sieu nhan thuc
Theo J. Wilson (1998), Sidu nhgn thuc cd ba chuc nang co ban: Chuc nang nhan bidt (awareness fiinction), chuc nang danh gia (evaluation fiinction) va chuc nang didu chmh (regulation fimction) [7]:
Chuc nang nhgn biet dd cap ddn kha nang hieu biet cua mdi ngudi vd cac qua trinh nhan thue, nhiing chidn luge hgc tap va nhung kidn thue vdn cd; y thue cua ban than vd kha nang nhan thuc ciia chmh mmh. Theo Halter (2005), ehuc nang nhan bidt cua Sidu nhan thuc bao
gdm: Y thuc duge minh bidt nhiing gi;
xac dinh muc tieu hgc tgp; xem xet cac ngudn Iyc, cae didu kien hgc tap; tu duy vd nhiing gi nhiem vu dgt ra; tim ra each thue dd danh gia vide thuc hidn; nhan thiy nhiing thugn Igi va khd khan trong qua trinh hgc.
Chuc nang danh gia cua Sidu nhan thdc de cap den su theo ddi eac qua trinh tu duy va danh gia didm mgnh, didm yeu trong qua trinh tu duy eiia mdt ngudi 6 nhdng tinh hudng ey the. Trong dd moi ngudi cd thd dua ra nhan xet cua minh v6 hidu qua tu duy va vide lya ehgn cac chien luge. Qua cae tidu chf danh gia, ngudi hgc nhin Iai qua trinh hgc tap cua mmh va biet muc do hoan thanh nhiem vy nhgn thue da duge dat ra. Chue nang nay cd nhiem vy theo ddi, kidm tra tinh hidu qua cua kd hogch va nhiing ehien luge da su dyng. Reid (2005) da dua ra mdt sd cau hdi giup thuc diy qua trinh danh gia nhu: Trudc do tdi da timg thuc hien nhiem vu tuong ty nhidm vy nay chua? Tdi da thyc hien nhidm vu dd bang each nao? Tgi sao tdi lai thiy nhidm vu do de hay khd? Tdi da hgc dugc nhiing gi? Tdi phai lam gi dd hoan thanh nhiem vy? Tdi ndn thyc hidn nd bang each nao?
Tdi cd ndn thyc hien theo each gidng nhu tdi da Iam trudc do khdng?...
Chuc nang didu chinh ciia Sieu nhgn thuc didn ra khi cac ea nhan dieu chinh qua trinh tu duy cua minh. Hg sir dyng cac ki nang Sidu nhgn thuc dd didu khidn kien thuc va tu duy. Ddng thai hg suy ngam ve qua trinh tu duy va vdn kidn thuc cua ban than va dua ra nhdng thay ddi cin thiet. Schraw (1998) da dua ra he
TAP CHl KHOA HQC OHSP TPHCM Le Trung Tin
thdng cau hdi nham thue diy qua trinh didu chinh: Ban chit nhidm vy la gi?
Nhidm vy cua tdi la gi? Tdi can su dyng loai thdng tin va chidn luge nao? Tdi se can bao nhidu thdi gian? Tdi cd hidu nhidm vy dd ro rang khdng? Tdi ed ein thay ddi didu gi khdng? Tdi da dgt duge myc tidu chua? Tdi dS Iam dugc gi va chua iam dugc gi? Tdi se Iam gi khac trong Ian sau?...
Nhu vay, cae ehuc nang cua Sidu nhan thuc giup mdi ca nhan y thuc dugc vd nhan thuc cua ban than, vd nhidm vy, tidn trinh thyc hidn nhidm vu, danh gia va didu chinh dd thyc hidn nhidm vy hidu qua hon.
4. Van dyng li thuyet Sieu nhan thu-c trong dgy hge mon Toan d tnrdng THPT
De tap luydn eho HS kha nang ty lap kd hoach hgc tap, tu theo doi, danh gia, didu chinh qua trinh nhgn thde va qua trinh hgc cda ban than, trong cac gid hgc toan GV cd thd su dung phdi hgp cae bidn phap, cac kT thuat sau:
Ldm mdu vd gidi thich cho HS cdch thuc theo ddi, diiu chinh, ddnh gid qud trinh tu duy cua chinh minh: Trudc khi yeu cau HS giai quydt mdt van dd, GV co thd ddng vai tro ngudl ddng hanh cung HS giai quydt m^t van de tuong ty. GV se eung HS: Tim hidu xem kidn thuc nen giup gi cho vide thuc hidn nhidm vu; thao Iuan de lap kd hogch giai quydt van de.
GV chia sd vdi HS: Cach tim kidm va lidn ket cac thdng tin quan trgng; each nhin ra didm khdi diu va nhirng khau then chdt dd giai bai toan; each dua ra nhdng dy doan; each phat trien cac gia
thuyet; each didu chinh chuyen hudng khi gap khd khan.
Sic dung cdc cdu hoi yeu cdu HS phdi suy nghi, xem xit ve vdn kiin thuc, kinh nghiim cua bdn thdn tic do dua ra lira chgn phuang hudng gidi quyet vdn di: DQ giai bai toan nay can su dyng nhiing kien thuc, khai niem, tinh chat, dinh Ii, quy tic nao?
Sic dung edc cdu hdi yeu cdu HS phdi xdc dfnh muc tieu, lap ki hogch cho hogt dgng hgc tap: Em hay ndu cae budc can tidn hanh dd giai bai toan?
Su dung cdc cdu hdi yeu cdu HS phdi theo doi, diiu chinh qud trinh nhdn thuc cua bdn thdn: Trong cac budc da neu de giai bai toan, budc nao la khd khan nhit? Tai sao? Khi thye hien budc nay em gap phai khd khan gi? Cd nhiing each nao dd giai quydt khd khan nay? Em chgn each giai quyet nao? Tgi sao em Igi chgn each giai quydt nay? Tai sao dinh li, quy tac... khdng ap dung dugc cho bai toan nay. Ta cd the didu ehinh, thay ddi, bd sung, cai tidn... nhu the nao de cd the ap dyng vao bai toan nay?
Sic dung cdc cdu hdi yeu cdu HS phdi ddnh gid qud trinh nhgn thuc, qud trinh hgc tap vd kit qud dgt dugc so vdi mi^c tiiu, ki hogch di ra: Trong gid hge em da lam dugc nhiing vide gi? Chua iam dugc vide gi? Hay lap ke hoach giai quydt nhdng vide cdn tdn dgng
Khuyin khich HS tham gia vdo cdc cuoc thdo ludn: Trong cac cudc thao luan dd ydu eau HS phai ndu dugc rd rang, mgch lac y dd thyc hien giai quydt van dd cua minh dd cac HS khac nhgn xet, danh gia. Qua dd HS ty xem xet, danh gia.
TAP CHi KHOA HQC OHSP TPHCM SS 4(82) ndm 2016
dieu chinh Iai nhiing suy nghT eua minh.
Ddu mdi budi hgc GV ghi lin bdng nhimg kiin thii-c cdn hgc, cudi mdi buoi hgc GV tdng kit lgi trin bdng nhimg kien thirc HS dd duge hgc kem theo viic gidi thich y nghia khi HS hgc duge nhiing kiin thue ndy: Vide lam nay se cung cip eho HS h? thdng kien thuc can thidt va ehuan b} nhung didu kidn can va du cho tien trinh hgc t ^ sap tdi. GV can giai thich myc dich, y nghia cua vi?c hgc kidn thde dd gdm ca myc dich mang tinh Ii thuyet va tinh thye td. HS ehi ed the hge tap va tu duy hidu qua khi thyc su cd nhu ciu nhgn thue va thay kidn thue dd hiiu ieh cho vide hgc tgp va cugc sdng eua cac em.
Yeu cdu HS ghi "nhdt ki hgc tap ":
HS ghi vao "nhgt ki hgc tap" tit ea nhiing gi da hgc dugc sau mdi budi hgc ca vd mgt kidn thuc va nhgn thue; ghi Iai nhiing vi?c da iam duge va ehua iam duge so vdi muc tidu kl hogch da dd ra. Hang thang, GV va HS se eung xem Iai "nhat ki hgc tap" de danh gia su tidn bd cua ban thanHS.
Vi dll minh hpa:
Sau khi hgc xong gid hgc Ii thuydt bai hge "Hai mat phing vudng gde", trong gid bai tap GV ed thd tap luydn cho HS kha nang tu theo doi, danh gia, didu chinh qua trinh nhan thuc eiia ban than thdng qua day hgc bai tap sau:
Cho lang try dung ABC.A'B'C cd day ABC la tam giac can dmh C, mat bdn ABB'A' la hmh vudng cgnh a. Ggi M, N, P lin lugt la trung didm cua BB\ C C , BC va Q la m§t didm trdn cgnh AB sao
cho BQ - 4 (MAC)±(NPQ).
Chung minh rang
Hoat dgng (HD) 1. GV ydu eau HS trinh bay 2 phucmg phap chung minh hai mat phang vudng gdc
Y dd td chuc HD: Giup HS huy dgng nhgn thuc cua ban than vd phuong phap ehung minh hai mat phang vudng gdc va kidm tra, didu ehinh Iai nhgn thdc (didu chmh lin 1). HD cua HS: HS se phai nhd Igi khai niem gde giiia 2 mSt phang, khai niem 2 mat phing vudng gde, dinh Ii didu kien can va du de luu mat phang vudng gde td dd rut ra 2 phucmg phap ehung minh sau day:
Phucmg phap 1: Dd chimg minh hai mat phing vudng gdc hay chimg mmh mgt trong hai mat phang chua mgt dudng thang vudng gdc vdi mat phing kia;
Phuang phap 2: De chung minh luu mat phang vudng gdc hay tim gdc giiia hai mat phing dd thiy gdc bing 90°.
HD2. GV yeu ciu HS lya chon phuong phap chiing minh
(MAC) -L (NPQ) va vidt ra cac budc cin phai tidn hanh dd giai bai toan
YdS td ehuc HD: Tap luyen cho HS xae dinh muc tieu, ty lap kd hoach eho hogt ddng hgc tap eua ban than.
TAP CHi KHOA HQC DHSP TPHCM Le Trung Tin
HD cua HS: HS sd phai ap dung phucmg phap chung minh ma minh lua ehgn cho trudng hgp cy thd va vgeh ra cac biidc can thye hidn dd giai bai toan.
HS ed thd ndu 1 trong 3 cau tra Idi sau:
cac budc giai BT bing each I: Tim trong (MAC) (hoSc (NPQ)) mgt dudng thang a; Chdng minh rang a vudng gdc vdi 2 dudng cat nhau trong (NPQ) (hoac (MAC));
Cac budc giai BT bang each 2: Tim hai dudng thang ISn lugt vudng gde vdi (MAC), (NPQ); Tim gdc giiia hai dudng thang ay;
cac budc giai BT bang each 3: Tim giao tuydn a eua (MAC) va (NPQ); Chgn didm O trdn a, tu O Ian lugt dung cac dudng thang b, c Ian lugt nim trong trong (MAC), (NPQ) va cimg vudng gde vdi a;
Tim gdc giiia b va c.
HD3, GV chia eac HS chgn eung mdt each giai vao cung mgt nhdm dd thao Iuan, trao ddi y kidn xoay quanh vide tra Idi cau hdi: Trong cac budc da ndu dd giai bai toan, budc nao la khd khan nhat?
Tai sao? Em cd tim ra each nao dd giai quydt kho khan nay khdng?
Y dd HD: giup HS cd eo hdi trinh bay rd rang tu duy cua minh; xem xet, danh gia suy nghT cua ngudi khac va chinh minh.
HD cua HS: HS se tham gia thao lugn va ed thd ed nhidu y kidn khae nhau.
GV tdng hgp lgi thanh 3 y chinh sau day:
Ndu giai bai toan theo each 1 thi vide khd khan nhat la phai tim trong (MAC) (hoac (NPQ)) mdt dudng thing a vudng gdc vdi mat phang con lgi;
Ndu giai bai toan theo each 2 thl
vide khd khan nhat la phai tim ra hai dudng thing lin lugt vudng gdc vdi (MAC), (NPQ);
Ndu giai bai toan theo each 3 thi vide khd khan nhat la phai dyng dugc cae dudng thang b, c lan lugt nSm trong trong (MAC), (NPQ) va ciing vudng gdc vdi a tgi mgt didm.
HD4. GV chi ra cho HS: Vide giai quydt bai toan theo ca 3 hudng ma HS da neu gap khd khan la do mgt phang (NPQ) nam d mdt "vi tri" khdng thugn Igi cho vide chung minh vudng gde. Dd giai bai toan ta cin dyng mgt mgt phing song song vdi (NPQ) nhung d vi tri thuan Igi cho vide chung minh vudng gdc vdi mp(MAC). GV hudng dan HS thao lugn theo cac nhdm dd tim ra mat phang nay vdi.
Y dd HD: Tap luydn cho HS kiem tra, danh gia, nhan ra didm khidm khuydt, ehua hgp Ii trong tu duy cua ban thdn. Tu do cd nhOng sy chuydn hudng, dilu chinh khi can thidt (didu chinh Ian 2)
HD cua HS: HS se phai huy ddng tri thuc phuang phap vd chdng minh song song va ap dung cho hoan canh cy thd. Ndu HS vin gap khd khan GV ed the ggi y: Ggi I, K la trung diem A'B', AB thi ^^''^'^ \^{NPQ)II{C'B1)
PQIlCKilC'l]
HD5. GV ydu cau HS su dung cac each ehung minh hai m^t phang vudng gdc da ndu d HD 1 dd chung minh {MAC) 1 {CBI) va trinh bay Idi giai ehi tidt cho bai toan
Ydd HD: Giup HS eung cd lgi nhan thiic vd eac phuang phap ehung minh hai
TAP CHI KHOA HOC DHSP TPHCM S6 4(82) nam 2016
mat phang da biet va bo sung them nhan thuc mdi.
HD ciia HS: HS trinh bay loi giai:
MBM = ABB'I(c-g-c) suy ra AUB^BW
AMB+B'Bl Mat C ' / I A A ' ] C ' / 1 A ' 5 '
suy
= 90° =s AM ± BI (*)
•=>C71(AA'B'B)=>
ra
khac
• C l a.AM(**)
Tu (*) va (**) ta ed AML{C'B1)^ {MAC)± {CBI) (2)
Td (I) va (2) suy ra (MAC) ± (NPQ) (dpcm)
HD6. GV yeu eau HS ghi bd sung them mdt each chung minh hai m^t phang vudng goc vao "nhgt ki hgc tap"
va ghi tdm tit 3 each chiing minh hai mat phing vudng gdc.
Y dd HD: Giup HS hgp thuc hda kidn thuc va dieu chinh lai nhgn thuc vd phuong phap chung minh hai mat phing vudng gdc ddng thdi theo ddi duge sy tien bg vd tu duy eiia ban than so vdi nhdng gid hgc dudc.
HD cua HS: HS ghi nhd thdm mdt phuong phap chdng minh hai mat phing vudng goc: Dd chimg minh (P)-L(Q) cd did chung minh (P) vudng gdc vdi mdt mp(R) song song vdi mp (Q).
5. Ket Iuan
Nghidn cuu eua R. J. Marzano (1998) vd 4000 phuang thuc can thiep trong giao dye da cho thay: "Phuong thuc cd hidu qua nhit ddi vdi vide cai thien qua trinh hgc tap va tu duy cua hgc sinh la tap trung vao each thue hgc sinh suy nghT vd qua trinh tu duy ciia minh va each thuc hgc sinh cam nhan vd ban than vdi vai trd la ngudi hgc" [3].
Chung tdi da tien hanh van dyng li thuydt Sidu nhan thuc trong dgy hgc mdn Toan tai 05 trudng THPT trdn dia ban cac tinh, thanh phd: Ha Ngi, Thanh Hda, Bic Giang mdi trudng 01 ldp thyc nghidm va 01 Idp ddi chimg. Kdt qua thye nghidm eho thay van dyng li thuyet Sidu nhan thuc trong day hgc da giup HS:
Dinh hudng va lap kd hoach hgc tap mdt each khoa hge va ro rang hon;
Theo ddi, ty danh gia va didu chinh dugc mdt sd budc, mdt sd khia canh ciia qua trinh hgc;
Phat tridn tu duy bae cao nhu tu duy phd phan, tu duy sang tgo;
Phat tridn tinh dde lap. thich nghi tdt hon vdi trang thai mat can bing giua chu thd vdi mdi trudng.
Van dyng Ii thuydt Sidu nhgn thiic trong dgy hgc se gdp phan tich cyc hoa, phat huy tinh ehu ddng sang tgo eua' ngudi hge, bien qua trinh dao tao thanh ty dao tgo, ren luyen cho HS kha nang tu hoc sudt ddi.
TAP CHi KHOA HOC DHSP TPHCM Le Trung Tin
TAI LIEU THAM KHAO
1. v a Dung (2008), Tir diin tdm li hgc, Nxb Tir didn Bach khoa. Ha Ndi.
2. Nguydn Van Thanh(2012), "Ren luydn kT nang sidu nhdn thuc cho HS Idp 7 trong day hgc toan ti Id thuc", Tgp chi Gido due, 290, tr. 26-28.
3. Brown A. (1987), Metacognition, excutive control, self-regulation and other more musterious mechanisms. In Metacognition, Motivation and Understanding, Erlbaum, NJ, USA.
4. Flavell J. H. (1976), Metacognitive aspects of problem solving. The Nature of Intelligence, USA.
5. Mari^ano R. J. (1998), A theory based meta analysis of research on instruction, www.mcrel.org/ PDF/ Instruction/ 5982RR InstructionMeta Analysis.pdf
6. Wellman H. M. (1985), Origins of Metacognition , In Metacognition, Cognition and human performance, Orlando, Florida, USA.
7. Wilson J. (1998), The Nature of Metacognition: What do primary school problem solvers do?. National AREA conference, Melbourne University, Australia.
(Ngay Tda soan nh$n 6ugc bai: 23-7-2015; ng^yph^n bi§n ddnh gid: 08-12-2015;
ngdy chip nh§n dSng: 24-4-2016)
