VAN DUNG Li THUYET PHAT SINH NHAN THU); CUA J PIAGET VAD iflEC i o GHUi GHD SINH VIEN DAI HOG KIlN TAD TRI THDI) TDAN TS C H U TRONG THANH ThS NGUY§N N G O C BICH ThS TRUONG THj D U N G " L i thuyet p[.]
VAN DUNG Li THUYET PHAT SINH NHAN THU); CUA J PIAGET VAD iflEC io GHUi: GHD SINH VIEN DAI HOG KIlN TAD TRI THDI) TDAN TS C H U T R O N G T H A N H - ThS N G U Y § N N G O C BICH ThS L i thuyet phat sinh nhin Mc (LTPSNT) cua J Piaget la mot nhQng tiru Ion cua tam li hpc the ki XX, co tam anh hu'dng sau rong den vi^c djnh hudng nghien cuu tam li hoc, giao due hoc va li luan day hgc Dua tren ccf sd cita LTPSNT, nhieu mo hinh day hpc, PPDH dupcde mix nghien cuu va van dyng vao thi/c tien Day hpc kien t£io, day hpc kham pha, day hpc dua tren cac tinh huong la nhihig kieu day hpc dang duoc van dung rong rai hien tren the gidi va la cac vi dy minh hpa cho 81/anh hudng cua LTPSNT giao due, Xuat phat tur nhflng tu tudng chu dao LTPSNT cua J Piagetcung mo hinh day hpc kien tao, chung toide c^p van de to ehu'c cac hoat dpng tu hpc mon Toan cho sinh vien (SV) d eae trudng dai hpc Cac khai niem cong cu ciJa LTPSNT the hien day hoc tri tht/c toan d dai hoc J Piaget da xay dung LTPSNT dua tren khai niem can ban dut?c sddung nhu nhung ngon ngQcong cu de diln dat y tudng khoa hpc Dudi day, chung toi phan tich y nghTa cua eae khai niem cong cu va van dung vap day hpe mon Toan 1)Khiiniim "saddnhin thuc":J Piagetquan niem r§ng, chti the nhan thue mpt tri thi/e nao do, se hinh nen mot cau true hinh thiic luu gifl bp nao va gpi la sd nhan thu'c Qua trinh hinh sado nhan thflc tht/e hi?n theo nguyen li phan anh: nhflng gi ma eon ngfldi tiep xtjc, thao tac len mdt doi tUdng d ben ngoai se dong thdi hinh hinh anh ciia doi tupng nao Hinh anh docoxu hudng ddn gian hoa, khai quat va dupc Iflu giutrong tri nhdeiia eon ngudi Hpe tap chinh la qua trinh hinh va ciing eoeac sa nhan thflc flng vdi tri thue finh hpi ducfc Trong qua trinh day hpc m6i mon hpc, giang vien (G V) can phan tich npi dunji mon hpc cae ddn vj kien thflc, cho moi don vj kien thuc ung vdi mpt sddo nhan thflc ma ngudi hgc edthe hinh hpc tap va nghien eflu Vidu /.-Trong day hpe phan Hinh hgc cao cap, (ki2-8/2014) T R U O N G THj D U N G " khai niem muctieu afin khong gian afin /j-chleu A" se ung vdi so nhan thflc ciia SV nhu sau: Tin ggi myc tieu afin khong gian afin nchieu A"; cau true, gom mpt diem e A"ggi\a goc ciia myc tieu, mpt c o s d {ete^,-^^ e A" dupc gpi la he vectP c o s d cua muctieu; A-/'/?/eu;{0;e|ej ej hoae {0;«iU „• Co the xem bp ba yeu to: ten ggi, ci'u trucva ki hieud\ren la mot so nhan thuc flng vdi khai niem muc tieu afin trgng khong gian afin n- chieu A" Vidtj2:Qieu kien hai eai phing khong gian Oelit vuong gdc vdi nhau, flng vdi mgt cau tnic nhan thflc: Hai eai phang khong gian Oelltvuong gdc vdi neu khong gian phuang cua chung tfldng ting vuong goe vdi 2) Khii niem "ddng h6a":Theo LTPSNT cua J Piaget, nhd sy tiep XLIC vdi cac tinh huong khac ma nhan thuc cua eon ngudi trd nen phong phu Qua trinh dien nhu sau; mdi tinh huong chu the gap se lam sinh mpt nhiem vu nhan thflc can giai quyet; dd, chii the se huy dpng cac so nhan thflc da co (tflc la tri thflc da hpc dflpc trudc do} degiaiquyet nhiem vy dat Dieu dupe thuc hien theo cae budc: - Budc l:so sanh, do'i chieu cac dau hieu, thugc tinh ciia cac dd'i tuong nhan thuc tinh huong (tham bien thi/c) vdi dau hieu, thupc tinh cua so nhan thflc dflpc huy dpng (tham bien hinh thflc); - Budc 2: neu cd su an khdp su so sanh diln thi ap dLing Sddo nhan thflc da huy dpng de dua ldi gial cho nhiem vu can giai quyet; neu khong ed su an khdp thi chua dua ket luan; - Budc S.'khi da dua ldi giai cho mdt nhiem vy nhan thuc, chu the can kiem tra tinh hop li ciia ldi giai; tu dd di den ket luan hoac phai tiep tyc qua trinh huy dgng, tao lap so nhan thuc mdi de giai quyet nhiem VLI dat Qua trinh huy dpng eae so nhan thflc dfla Idi giai hpp li cho mptvan de nao dugc J Piaget * Ktioa sir pham loan fioc, Tnrdng Dai figc Vinh Tap chi Gido due so 340 47 gpi la sf/'tfd/jg'/jda Nhuvay, quatrinh dien sudong hda ndi chung gom ba bfldc: 1) Nhan thdc van diva huy dgng sa dd nhan thde, 2) Gan tham bien thuc cho cae tham bien hinh thdc saddnhin thiie vi dua cau tra ldi, 3) Kiem tra suhgp licua cau tra Idi va chap nhan ldi giai Su dong hda cd vai trd quan trong hgc tap Mdi cd su dong hda la kien thflc dupc huy dgng degiai quyetvan de Do dd, dong hda la phuong ttiflc hflu hieu viec cung co kien thflc Cd nhieu tinh huong khac nhung doi chi can huy dpng cung mpt so nhan thflc de giai quyet Thong qua sudong hoa, cdthegiup ngudi hpc md rpng pham vi ap dijng cac kien thflc, ngucri hpc tflng budc ren luyen dupc cae kTnang kTxao, tich luy dan kinh nghiem, thdi gian thi/c hien cac thao tac cijng njt ng&n Trong day hgc toan, sau hinh cho SV cac khai niem, dinh li, quy tdc, thuat toan, viec cho SV luyen tgp giai toan, van dtjng kien thflc vao cae tinh huong toan hgc hay tinh huong thuc tiln g&n vd^ cac li'nh vuc nghe nghiep khac ehinh la tao ccf hpi cho cac em tht/c hien su dong hda 3) Khai niem "dieu ung": Su dieu ung diin chii the huy dpng so nhan thflc da cd de giai quyet nhiem vudat nhung khdng edng Trong tinh huong nay, chu the se phai xem xet lai cac so nhan thije cuva tai cau tnjc chung de cd si/an khdp va dua cau tra Icri hoac bo sung vao nhan thflc ciia minh so nhan thflc mdi nham giai quyet van d l Khi ndi den viec tai cau tnic nh^n thflc cua chu the la ndi den sudieu chinh each hieu cua chti the ve mpt kien thu'c nao dd Qua trinh tai cau tnjc la can thielvi nhieu trudng hcfp, cau tnic nhan thflc ung vdi kien thflc SV da hgc trfldc day edn so khai, han che Neu hethd'ng kien thflc chuong trinh hpc dupc mp rgng, nhflng cau tnjc nhan thut da cd trfldc day can xem xet lai dfla kien thflc mdi vao he thd'ng nhan thflc ciia SV Quatrinh bdsung mgt s d d o nhan thflc mdi vao nhan thflc ctia ngudi hgc dd'i vdi cae phan mon Toan can chij y de'n tinh chat suy diln ciia toan hgc de tranh st/ ngp nhgn Do dd, qua Uinh dieu ung hgc tap mdn Toan xay khd khan hdn so vdi cac mdn Inge khac Nhflvay,dieuflnglasutaicautnJccacsod6nhan thflc da cd hay bd' sung them vao stJ nhan thflc mdi, giup chil the vupt qua cac nhiem vu nhan thflc dat mpt tinh huong nao dd Sudieu ung la cP sdehoviectiepthu kien thflc mdi (bd'sungso nhan thflc mdi) hay nhin nhan kien thflc da hpe bang mdt 481 Tap chi Giao due so 340 each nhin mdiva lam tang hieu lyc ap dung cua kien thflc (cai to', cau tnic lai so nhgn thflc da cd) Vidu 3:0 tn/dng tnjng hoc phdthdng, hpc sinh da hgc khai niem hai dudng th§ng vudng gdc, dudng t h i n ^ vudng gdc vdi mat p h l n g bac dai hpc, hpe vequan he vudng gdc gifla hai cai phang, G V cd the dua cac tinh hudng thyc tien dan den viec mo ta mdi c|uan he b^ng phuong cua eae eai phang vdi sd chieu nhieu hon hai nham giup SV hinli soddnhan thflc mdi, ijng vdi khai niem mdi (quan he vudng gdc gifla hai eai phSng) thdng qua st/cautnjc lai sddd nhan thflc da CO (sddd nhan thflc ung^va khai niem hai dfldng th5ng vudng gdc, dfldng thang vudng qdc vol mat phlng) 4^/f/?a7n/em"ca/i/)an5".-J Piaget dung thu^t ngfl''can bang" de chi cac tinh hudng ma nhiem vij nhan thflc dat ra, do, chiJ the cd the huy ddng so dd nhan ttiflc da cd degiai quyet van de Nhu vay, sucan b i n g edthe hieu la can bang gifla nhan thflc ciia ehu the (yeu tdben trong) vdi tinh hudng tao nhiem VLI nhan thflc (yeu td ben ngoai) Trong day hpe, can ciing cdkidn thflc hay ren luyen kTnang nao dd cho SV, GV can tao cac tinh hudng cd sy can b i n g 5) Khii niim "thich ngr/i/".Thich nghi dflpc hieu la kha nang tai lap Igi st/ can bang ciia chu the nhiem VLI dat vuot qua vd'n hie'u biet ciia chij thd Viec tao lap lai sucan b i n g dupc thue hien thdng qua qua trinh dieu flng Day la ca che cua qua trinh hoc tap Hpc la Sfl phdi hgp gifla ddng hda (cung cdsodd nhan Wiflc da cd) va dieu ung (phat trien sa mdi) nham tao su can b^ng cang cao (su can b i n g quatrinh phattrien) Theo (1; tr 36}, tac gia da phan chia sflthich nghi ba cap dp: - Cap I: Thuan dong hoa cap nay, nhiem vu nhgn thflc dgt ludn phii hpp vdi kien thflc da hgc, khdng can den sflbien doi, thay doi cac chitiet so dd nhan thut da cd cung cd the giai quydt dflpc van de Dd'ivdingudihgc, neu chi dap flng st/thich nghid cap dp thi dd la bieu hien ciia su hpc tap can ban, tai tao, chfla cd bieu hien ciia st/sang tao - Cap rfd2;Phdi hgp giua ddng hda vadieu ung dd hinh sado nhan thflcmdi ung vdi cac tri thflc st/ vgt, tflc la tri thflc ve ddi U/ong nghien cuu Day la cap dpchiiyeu lam cPsdchoquatrinhdgyhpc Bidu hien eiia cap la ngudi hpc biet each bien dd'i cac chi liei sodd nhan thflc flng vdi cac kien thflc da hpc dd cd dupc so mdi (nhin nhan kien thflc da hpc (ki2-8/2014) dudi mdt gdc nhin khac); biet de xuat, kiem tra du doan, hinh gia thuydt va xac lap s y dting din ciia cac gia thuyet Neu ngudi hoc dap ijng dupc cap dp thich nghi se la dieu kien td't cho viee hgc tap cd ket qua, bieu hien budc dau eua susang tao - Cap dd3:C6 day dii bieu hien dea'p dp 2, ngoai ra, cdn cd kha nang thay doi each thflc tac ddng vao ddi tupng nhan thflc (bien ddi ddi tugng), tao tri thu^ mdi ve phuang phap nhan thflc Neu ngudi hpc dap flng duoc cap dp la bieu hien cua sysang tgo cao, khdng chi cd kha nang dua dflpc tri thflc su vgt mdi ma cdn sang tao phuang phap nhgn thflc mdi Si/ sang tao dac biet can thidt ddi vdi ngudi nghien eu'u khoa hpc canh dd, ta dugc sau dudng thing tao nen mdt hinh luc giae Chung minh cac dudng cheo cua hinh luc giae dong quy tai m dt diim" Khi giai BT nay, viee true tiep ddng hda cac kidn thuc da cho gia thiet khdng d l dang mang lai ketqua Neu tai cau tnJe cae sa nhan thue ung vdi kien thflc da biet cung khd nhgn (chflng minh dudng thang thfl ba di qua giao diem ciia hai dudng thing cdn Igi) Tat ca eae kho khan ddi hdi ngudi giaiphai ddng thcri su'dung nhieu thii phap tuduy, bien ddi cac yeu tdciia BT Neu SV tim Idi giai, cac em se kidn tgo dugc eae so 66 nhan thflc flng vdi thii phap dd Tn/dng hgp edthe xem n h f l S V d a t d e n c a p d g thich nghi thfl Ldi giai tdm tat BT: cac "yeu to afin" BT Ba cap dp ciia su thich nghi a tren cd the md ta tren; khai niem "tam giae", "ti sd don", "trpng tam bang sado Be minh hga cho cac cap dp cua st/ cua tam giae", nen day la BT afin Chgn tap thich nghi day hpc mdn Toan bac dgi hpc, xet hop cae tam giae tuang duang afin vdi tam giae ABC mdtsdvidLisau: mgt tam giae deuA'B'C Trong hinh hgc Oelit, tam Vidu 4: Sau hpe ve thuat toan lap phuang glac deu la tn/dng hgp dae biet so vdi eae tam giae trinh tham sdcua mdt cai phang, GV yeu cau SVJap bat ki; nhung vdi hinh hgc afin, tam giae deu tupng phuang trinh tham sdcua mgt cai phing cu the; ehing dupng afin vdi mpi tam glac bat ki khac Tflc la tdn han phupng trinh tham sdcua 3-phing phep afin /'trong E^sao eho: /i',4;=/i;/fS;=s;/(^^C'.Tren cac canh er,C'>4', Cilng c6 k i ^ thte, C^pdpl md rpng ph^m vi ap A'B', lan IflOt cd cac diem chia la A,, A^ 6,, B^; C,, C^ , Hogt d^ng dyng Tin luy^n kT dong hoa cho: B'A,= A,Ag nang, hinh Ih^nh kT dem thuan = AgC-=C-B, = B,Bg xilo, tich IGy l(mh nghi|m =BlA'=A'C,=C,Cg= Tinh C a p d $ : C^S'.Tacd luc giae huong Dieu img h^cl^p DLFGHI {hinh 1) cap thap Can chflng minh D,G n i m tren dudng Tn thirc sir viit mcri Capd$3: tnjng tn/e ctia canh Tri thiJc phuong ph^p Dieu ling cap fi'C'va dudng trung , cao(c6su bicn doi doi tn/c di qua dinh tuqmg) A' Tuang tu, hai dinh L, Wnim tren dudng taing tn/c Scfdo I Cac cap thich nghi ciia canh CA'; cac dinh F, / n i m tren dudng tmng tn/c SV thyc hien viec xac djnh phfldng ciia cai phang ciia canh A'B' Cac dudng trung trt/c eiia tam giae deu cd Cd sd la mgt h^ gdm vecta (he vecta dgc >4 B ' C ddng quy nen cac dudng cheo cua lyc giae lap tuyen tinh) Sau dd, SV viet phuang trinh tham DLFGHIdonQ quy Tinh chat ddng quy v i n dung sdflng vdi vide thay tpa dp cua cac vecta ed s d lan vdi tam giae ABCbaX ki tuang duang afin vdi tam giae Iflot vao cac cgttham sdva tpa dp cot ctia mpt diem ABU Quy trinh day hpc trl thuc toan theo quan thupc cai p h i n g dd vao cot he sd tt/ dp Qua trjnh giai bai toan (BT) nhuvay tioan toan chi cd su ddng diem kien tao LTPSNT cua J Piaget la ea sd tam li cua nhieu li hda xay Trudng hop chi d i l n suthich nghi thuyet dgy hgc Trong do, li thuyet kien tao la mdt dea'p d p i , , l'/rfi/5;Khihgcve cac batbien afin, batbien dang nhflng li thuyet day hpc dang dugc quan tam Cfl, h/ong dfldng afin, GV cho SV giai BT: Vho tam nghien eflu va ap dung rdng rai d nhieu nudc Quan giae ABC, mdi canh eua nd duac ehia thinh ba phan diem day hpc kien tao sudtjng cac khai niem cdng ctJ bing Noi eae diem chia vdi dmh ddidign cua ciia LTPSNT nhfl: sP dd nhan thflc, su ddng hda, (ki 2-8/2014) Tap chi Gido due so 340 49 dieu ung va thich nghi de trinh bay li lugn, thiet ke ke hoach dgy hpc Nhieu tac gia da dua quy trinh chung khithue hien quatrinh day hpc Iheo quan diem kien tao Theo (2), (3), (4), cac tae gia da phan tich va dua so dd dgy tipe kidn tao ap dung eho qua trinh dgy hpe mdn ToanaphoXhong nhusau (xem sad62): » *, rs:=n E-i 9\ '5S, u i S cac dang toan, ), G V can chu y ttS vS'n de tao co hdi va khuyen khich ngudi hpc kidn tgo tri thflc phuang phap (cap thich nghi 3}; - Yeu tdti/hpc ciia SV (tfl kien tgo kien thflc, kT nang, thai do} cd vai trd quan trgng, anh hudng den chat lugng day hpc bge dai hpc, dli ap dung PPDH nao di chang nfla thi hogt ddng ty hpc cua SV cung khdng the thieu Tuy nhien, neu van dyng quan diem kien tao vao day hpc, kha nang tu hgc ciia S V se cang dugc nang cao Suv So Tien trinh day hoc kien tao kiin thiic toin Trong day hpc toan theo quan diem kidn tao lay LTPSNT lam cd sd tam li, G V can n i m ducfc mgt sd luan diem sau ve day hpe toan theo quan diem kidn tao: - Day hgc mdi tri thflc toan (mgt khai niem, dinh li, mdt thuSt loan, ) la qua trinh to chflc, tao dieu kien cho ngfldi hge hinh cau true nhan thflc tuong flng vdi kien thflc dd; - Tri thflc dflgc SV hinh theo quy trinh sado {hoac mgt bidn the nao cua nd) Trong sado 2, eae khau then chdt gdm: mdi trudng GV thiet lap phai tuong tac dupc vdi SV; tri thflc, kinh nghiem da cd giup SV nhgn nhiem vu nhan thflc, bj cudn hut vao nhiem vu nhan thflc va de xua't cac dfl doan, gia thuye't Viec kiem nghiem cac gia thuyet chicd tac dung loai bo, dieu chinh lai (neu cho ketqua sai} hogc ciing cd niem tin vao di/ doan, gia thuyet (neu cho ket qua dung) chfl chfla phai la tri thflc can hinh T f l viec Cling cdniem tin vaogia thuyet, GV can giup SV xua't hien nhu cau suy dien, dua djnh nghla (neu day khai niem) hoae thiet igp phep chflng minh (neu day djnh li), sau dd xac nlian cac tri thflc SV da kien tao nen; - Can ehu y den viec phdi hop gifla hoat ddng kien tgo mang tinh chat ca nhan (kien tao ca ban) va hoat dgng kien tao mang tinh xa hgi, tinh tap the (kien tao xa hdi); phdi hap giua cac hoat dgng kien tgo tting kien thflc dan le (kien tao vi md} vdi hoat dgng kien tgo nhflng ngi dung phflc hgp (kien tao vT md) Kien tao vi md ludn ludn can hudng tdi kien tgo vT md De kien tao vT md dupc td't, GV can thuc hien cac hogt ddng kien tao yi mo cdehat lupng Kidn tgp mdi kien thflc vflng c h i c la gdp phan xay dyng duac nen tang tam li, nhan thflc de qua trinh kien tao vi md tiep theo va kien tao vT mo cd hieu qua; • Song sorig vdi viec tgo mdi trfldng de ngudi hgc kien tao kidn thflc toan (cac khai niem, dinh II, 50 Tap chi Gido due so 340 Cae khai niem edng cu LTPSNT ciia J Piaget va md hinh dgy hgc kien tao cho phep phSn tich edu tme eiia qua trinh dgy hgc cac tri thflc toan mot each rd rang Viec van dung cac hinh thflc, cac cdp 6q day hpe kidn tao (the hien qua cac cap dp ciia sy thich nghi) n h i m tflng budc nang cao hoatdpng tuhgc, ty kidn tao kien thflc ciia SV Day hpc tri thflc tcan &ieo quan diem kien tgp hoan toan phu hpp vd^ phuang thflc dao tao theo hpc che tin chi • (1) D6 Van Cuong BSi dird-ng cho hgc sinh ndng l^cc thich nghi tri tu^ nhdm ndng cao hi^u qud dt^y hQC hinh hoc khdng gian & truang trung hoc phd Ihdng Luan an tiifn sT Gido dye hpc, Truflfng D^i hpc Vinh, 2011 (2) NgO T& Ho9t Ndng cao hiiu qud d^y hQC xdc sudt thd'ng ki it tru&ng dai hoc supham kt thu^t theo hu&ng phdt hiin vd bdi du&ng mdt sd thdnh tSndng life kien f^o cho sinh viin LuSn an ti^n si Gi&o due hoc, Truang D£ii hpc Vinh, 2011 (3) Bi^i van Nghj VSn dung Ii lu^n vao thuc ti§n day hpc mdn Todn & trirong phd thdng NXB D^i hqc su pham, H 2008 (4) Dao Tam - Le Hi^n Dirong Tiep cSn cdc phinmg phdp day hpc khdng truyln thd'ng d^y hpc toan o- tnrdng d^i hpc vd tnrong phd thdng NXB Dai hqc supham, H 2008 Tai lieu tham khdo Nguygn MOng Hy Hinh hoc cao cSfp NXB Gido due H 2003 Nguyen Ba Kim Phuvng phdp d^y hpc mdn Todn NXB Dai hoc suphgm, H 2006 Phan Trpng Ngp - NguySn Due Huong Cdc Uthuy(ft phat trien tkm li ngud^ I ^ B Dai hgc su pham, H.2008 SUMMARY In this paper we Investigate the following problems: - The performance of tool concepts of cognitive development theory In teaching mathematical knowledge in universities: - Constructivlst teaching model and levels of adaptation and application to teaching mathematical knowdedge in universities (ki2-8/2014) ... thuat toan, viec cho SV luyen tgp giai toan, van dtjng kien thflc vao cae tinh huong toan hgc hay tinh huong thuc tiln g&n vd^ cac li''nh vuc nghe nghiep khac ehinh la tao ccf hpi cho cac em tht/c... vi ap dijng cac kien thflc, ngucri hpc tflng budc ren luyen dupc cae kTnang kTxao, tich luy dan kinh nghiem, thdi gian thi/c hien cac thao tac cijng njt ng&n Trong day hgc toan, sau hinh cho SV... du&ng mdt sd thdnh tSndng life kien f^o cho sinh viin LuSn an ti^ n si Gi&o due hoc, Truang D£ii hpc Vinh, 2011 (3) Bi^i van Nghj VSn dung Ii lu^n vao thuc ti? ?n day hpc mdn Todn & trirong phd thdng