TO CHHl: HOAT DONG KHAM PHA TRONG OAY HOC TOAN CAO CAP
CHO SINH VIEN TRUONG CAO DANG KINH TE-Ki THUAT
PGS.TS. TRjNH T H A N H H A r - ThS, N G U Y I N THI L O A N "
Abstract: The article proposes some specific examples illustrating the designing of pedagogical situations in order lo encourage students to participate in exploration acllvilies in the process of applying Ihe 5E-teaching model lo teaching advanced mathematics to the students of College of Economics and Technology, thereby improving training quality.
Keywords: Teaching advanced mathematics, exploration actiuity; fostering thinking capacity
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pi dung Toan cao cap (TCC) duoc dira vao giang day cho sinh vien (SV)Tiifong Cao d^ng Kinh te • KT thuat (KT-KT) nham trang bi cho SV cac kien thu'c co ban ve TCC va nang luc {NL}Lfng dung kien thuc toan hgc vao cac van de ve KT- KT trong nghe nghiep. Mot trong nhung muc dich cua day hpcTCCIagop phan phattrien cho S V N L t u duysangtaovaNLgiaiquyetvande(GQVD), cuthe SV phai CO khanang phathien (PH)duac van de, lap gia thuyet, tim each lam sang to gia thuyet de kham phaduoc nhiJng trithucdoivdi ban than.
Trong pham vi bai viet, chiing toi tap trung dua ra cac v i d u minh hpa viec thuc hien ba6c 2 trong mo hinh day hpc 5E (Engage; Explore; Explain; Elaborate;
Evaluate): To chu'c cho SV tham gia cac hoat dong kham pha (HDKP) trong giang day noi dung TCC cho SV nganh KT-KT.
1.Mdhinh day hoc5E
Mo hinh day hpc 5E do Chuong trinh nghien ciiu khoa hpcSinhvat(BSCS)dexuatgan cac buoc chinh:
Kich thich; Kham pha; Giai thich; Morpng; Danh gia.
Muctieu cua mo hinh day hpc 5E la h u t ^ g toi viec SV kham phacho minh kien thucvemptvandecy the valienketkienthucmciivdi nhung kien thuc da coth anh mpthetiiong. Voi mo hinh day hpc 5E, SV luon dupc tao dieu kien hpc tap va datvao nhung co hpi thuan Ipi trong quatrinh hpc tap de kien tao trithiic mcs.
Tren ccf so plian tich dac trung cua mo hinh day hpc5E, chung toi cho ring mo hinh day hpc 5E CO tac dpng tich cue hudng den viec boi duong cho nguoi hpc cac NL quan trpng, thiet yeu nhu: NLPH va GQVD; NL kien tao; NL kham pha; NL tu duy sang tao; NL kiem tra, danh gia...
Can chuy rang, HDKP ia hoat dpng chudao, quan trpng trong bucJc 2 cua mo hinh day hpc 5E. Nhuvay
viec nghien cihj nam dupc ban chat khoa hpc, II luan ve HDKP trong day hpc segop phan van dung ttianh cong mo hinh 5E vao giang day TCC cho SV.
2. HDKP trong day hoc
Ducri goc dp tam fi hoc, co the quan niem kham pha la mpt qua trinh tu duy mang tinh sang tao cua con ngudi bao gom hoat dpng quan sat, phan tich, danh gia, phan doan, neu gia thuyet, suy luan,... de dua ra nhOng khai niem, PH nhi/ng thupc tinh mang tinh quy luat cua doi tupng; tim ra cac moi lien he ban chat giCfa cac su vat, hien tupng;... ma chu the nhan thiic chua biet truoc do.
HDKP ham chiia chinh qua trinh nhan thiic sang tao cung nhu cac qua trinh to chiic hoatdpng nhan thUc sang tao do dehinh thanh san pham tri tuekhong chi la kien thUcmacon ca phuong thiic tU duy nQa.
Mpt diem khac vdi trong nghien cUu khoa hpc, kham pha trong hpc tap thudng khong phai la qua trinh tu phatcuanguoihpcmadupctochUc, hudng dan hoac dieu khien CO dinh hudng cua ngudi thay, ddo ngudi thay kheo teo dat ngudi hpc vao cac tinh huong covan de va giiip dd hp tu luc kien tao kien thdc. Qua trinh kham pha cua ngudi hpc la tien de va nen tang quan trong, mang tinh ren luyen hudng tdi hoatdpng nghien ciiu khoa hpc cua hp sau nay.
Trong day hpc TCC cho SV cao dang KT-KT, HDKP cua SV rat da dang, tuy thupc trinh dp nhan th lie, NL tuduy cua SV, hinh thiic to ChUc HDKP, va muc dp khd eua van de can kham pha. Giang vien (GV) CO the to ehue cho SV tham_gia HDKP thong qua viee: tra Idi cau hoi; dien vao cho trdng trong bang phy; lap bang, ve bieu do, do thi; thunghiem, de xuat
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' tnrting &ai Noc Khoa hoc - Dai hgc Tliai Nguyen
* * Tnrong Cao dang Kinli t^ - Ki tliuat - Dai hpc Thai Nguyen
Tap chi Gido due so 379 47
each giai quyet, phan tich nguyen nhan; thao luan, trao doi vemotvande, each GQVB;giai bai tap; lam bai tap Ion,chuyen de... Bieu nay cung doiholNLthiet ke'cac finh huong mang dung ysupham cda GV de thu hiit SV tham gia cac hiOKP phai 0 mgt miifc do nhatdinh.
3.Thiet ketinh huong deSV tham gia HBKP trong day hoc no! dung TCC cho SV Cao dang KT-KT
3.1. Dinh hirdng chung
Betochiic cac HBKP frong quatrinh day hpe ngi dung TCC cho SV, theo chung toi can phai dam bao eae van deco ban sau:
- B e thu hut dugc SV tham gia eac HBKP, fn/cfc hetGV can thiel l<e kich ban su pham theodinhhucmg tap tmng vao cac hoat dgng eija SV.
-Muc dp tu duy ciJa cac HBKP phai phuhc^vdimuc dich, ngi dung bai hoc vatrinh dp nhan thuc cua SV. Co nhuvay thimacducacSVcofhekhongdongdeuvekha nang nhan thuc, NLtuduy vin cothelya ehpn vatham gia nhOng HBKP phCi hpp vpi ijan than.
-Cac HBKP can duge thiet keda dang,conhiJng hoatdpng dugc thiet kede cae thanh vien trong mpt nhpm phathuy NLhgpfacdekhamphatrifhilemc*, cung can CO nhiing HBKP nham phat huy NLfuduy eua moi SV.
- Be fao dpng eg, d i n d l t va hudng d i n SV fham gia cac HBKP, doi hoi ngudi GV phai thief ke duge mpthethong cac cau hoi ggi mg.
_ Bephu hgp vdi kha nang nhan fhifc cua SV eao dSng nhom nganh KT-KT, eac HBKP dugc chung toi thiet ke'theo eac cap dp khac nhau, cu the:
Cap dSmp^ SV tai hien lai cac budc kham pha do GV dan dat. GV la nguoi datvan deva dua ra hudng giai quye't. Tuy SV khong tn/c tie'p la ngucfl PH, du doan, kham pha ra tri thuc mdi nhung thong qua qua trinh dan d§f cua GV, SV da tiep can dupe each dat van de, each tuduy va bien ketquakham pha cuaGV thanh fri thdc mdi cOa ban than.
Cap do hai SV fham gia mpt so khau trong qua frinh kham pha. G V la ngucri chu ye'u dua ra cac ggi y phari doan, eae kha nang cothe xay ra va hudng giai quyet... SV suy nghTlua chon cho minh each giaiquyet.
Trong qua trinh nay, GV thudng dua ra mpt so cau hoi ggiy de SV tuminh kham pha ra mgt vai van de ddn gian.
Cip dgba: SV la ngUiM kham pha. Tinh huong co van d l cothe do GV hoae chinh SV dua ra. Tie'p theo SV la ngudi chii dpng tukham pha vaGQVB. Trong mpf vai truong hgp, GV c o t h e t i ^ tuc djnh hudng de
48 Tap chi Giao due so 379
SVtim toi, xem xetvan detheo hucmg mdrpng hoac tie'p can van detheo cac gdc dp khac nhau deSVfi^
tuc kham pha them nhflng van de mdi.
3.2. Vidu minh hga
Vdi muc tieu: Thong qua viec tham gia eac HDKP, SV kham pha va tu PH ra cac finh chaf co ban cua dinhfh lie vavan dung Chung vao giai bai tap eh ungtoi da thief ke'cac hoatdpng cufhesau:
Hoat dpng 1 : Cung eo khai niem, each finh dinli fhiie theo dinh nghTa. GV chia Idp thanh 4 nhom va yeu cau tinli cac dinh thuc sau:
(2 -, i-i p -2 n N h 6 m 1 : A = - - ' " ' ; N h o m 2 : B = - ' " -J
Nh6m3:C = ; N h d m 4 : D = i
Kef thuc hoat dgng 1, eac nhom cho kef qua:
det(A)= 14;def{B)= 14,def (C) = -14;def(D)=0 Hoatdpng 2: Kham pha finh chat: det(A)=det(A).
GV: Nhic lai djnh nghTa ma tran chuyen vj vaco nhan xet givevj fri gifla cac hang vacac cot cua ma tranAvaB? ^
SV: Chuyen hang thanh cot eiia matranAtadit^
ma tran B hay ma tran B chinh la ma tran chuyen vj ciia ma tran A.
GV: Can cfl ketqua tinh dinh thflc (Hoatdpng 1), cc nhan xet give dinh thue eua ma tran A va ma Iran chuyen vl ciia nd?
SV: def(A) = d e f ( A |
Hoatdpng 3: Kham pha tinh chatSjnh Ihuc ilS da'u khita doi chohai hang (hoac hai cot) euamatran chp nhau.
GV:C6 nhan xetgivevj tri gifla cac hang ciiama Iran A va C?
_ SV: Ma tran C thu dugc tOl ma tran A bang each dpi cho hai hang 2 va3 cho nhau.
GV:Can cfl ke't quatinh dinh thflc (Hoat dpngi), CO nhan xetgive gia tri cua djnh thflc khita del chohai hang eho nhau?
^SV: Khita ddi c h i hai hang cho nhau fhidinhlhite doi dau.
GV: Hay tao matranE b l n g each doi c h i halc?t bat ky ciia ma tran A eho nhau. Tinh djnh thul; ma tran Eva eho nhan xet.
SV:Tafhudugcke'tquadef(E) = -14.Va;e!nh thflc ddi da'u khi fa ddi chd hai hang (hpac hai cot) cua ma tran cho nhau.
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Hoat dgng 4: Kham phatinhchat:Djnhfhflcse b l n g khong tie'u CO hai harig (hoac hai cot) ti le.
- GV: NhSc lai finh chat 6 va he qua ciia no (bai trude)vatinh nhanh def(D)?
- SV: PH fhay hang 4 co thua s d chung la 2, va dua ra ngoai da'u djnh thflc.
- GV: NhSc lai va van dung dugc tinh chat 3 vao tinh budc tie'p thep eua def(C) va cho biet nhan xet ctiaminh?
- SV: Vi hang 1 va hang 4 ciia dinh thflc b l n g nhau neri det(B) = 0 va nhuvay, djnli thflc se b l n g khong neu co hai hang (hoac hai cot) ti le.
Hoat dong 5: Kham pha tinh chat: Ne'u fa nhan mpf hang (hpac mgt cot) ciia djnh thflc vdi ciing mpt sdthuc k thi ta thu dugc djnh thflc mdi b l n g k nhan vol dinh thflc ban dau.
GV: Yeu cau tinh 2 dinh thflc va cho nhan xetve mflcddkho?
Q V : C h o m a t r a n A = P ' M . I ' 0 tt) 1) Hay thuc hien phep toan nhan ma tran vdi 2.
2) Hay tinh phep nhan sd2 vdi djnh thflc cua ma Iran A.
SV: Vdi nhiem vu (1), hau het SV lam dung:
2 2 5 3=4 1 0
Vdi nhiem vu (2): Tinh gia tri: I = 2 Nhieu SV lam sai vi thitc hien phep nhan sd2 vdi tat cacac phan tucija dinh fhuc,saud6mgi tinh gia trj dinh thflc.
GV: Hay n h i c lai cdng thflc trien khai tinh dinh thflc b l n g each frien khai theo hang (i).
SV: det(/4) = (-f )•' [a„def(/M„) - a^det(/WJ + ...i a^det(WJl
GV: Khi I = 1 (hay noi each khae tinh djnh thflc thep hang 1), hay eho biet kef qua nhan 2 vdi djnh thflc cda ma fran A, tfldd cho nhan xet?
SV:Taed
I = 2.(-1)'*' [a„def(/W„) - a,;def(/W„) + ...x a„det(M,Jl = 2.def(A). ^
Vay: Khinhan cae phan filciia mgthang (hay mpt cot) cOa djnh thilc vdi cung mpt sdthuckthidfldc mgt dinh thflc mdi bang djnh thuc cu nhan vdi k.
Hoatddng 6: Kham pha tinh chatBjnhthuc khong thay doi ne'u fa cgng vao mpf hang (hay mptcpf) mpf fd hgp tuyen finh cae hang (hoac cac cot) khae ciia dinh thflc.
2 1 3 4 5 7 6 1 5
; A ' = 2 0 0
1 3 - 2
3 1 - 4
SV: Tinh duge: A = - 2 0 , A' = - 2 0 . Viee finh djnh thflc A' ddn gian hgn vi cot thfl nhat ehi co mpf gia frj khackhpng.
GV: Hay thuc hien phep bien ddi sau ddi vcri dinh thuc A: Lay (-2) nhan vdi hang 1, rdi edng vdi thfl hang 2 va tinh gia trj cua djnh thfle mdi.
SV: Ta fhu duoc dinh thflc A'
4+ (-2)2 5 * (-2)1 7H
vaA* = -20
GV: Tie'p tuc nhan hang 1 vdi (-3) rdi cpng vdi hang 3, sau dd khong tinh cu the nhung co the biet dugc giatrj eua djnh thflc b l n g bao nhieu khdng?
SV: Ta thu duoc dinh thflc A "
3 (-2)3
5
.
2 1 3 0 3 1 6 1 5
3 1 (-3)3
.
2 0 01 3 - 2
3 6 + (-3)2 l + (-3)l 5-1 - 4
v a t a c d A ' * chinh la A'nen A** = - 2 0 . GVjCd nhan xet gi sau khita thuc hien cac phep bien doi tren?
SV: Ta coiDjnh thut khong thay doi neu la cgng vao mot hang (hay mpt cot) mpt to hgp tuyen tinh cac hang {lioac cac cot) khac cua djnh thu'c.
Qua vi du minh hpa cu the tren cho thay dich cua cac HDKP cung rat phong phu: SV kham pha ra mpt khai niem m6i,mpttinh chatmdi.each giaiquyetmptbai t£phoachieusau hon vempt khai niem,mpttinh chat, bosung them nhOng each giai mdi cho mptbai tap...
D e d i n h hudng giiip SV dat duoc muc tieu khi tham giacac HDKP thi viec thiet ke'cac tinh huong su pham, chuan bj cac cau hoi mang tinh goi md la het sue quan trpng trong viec tao dpng co de SV tich cue, chu dpng tham gia vao HDKP vdi cac cap dokhaenhau. •
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Tai lieu tham khao
1. NguySn Ba Kim. Phuwng phap d^y hoc mon Todn, NXB Dai hgc Supham, H. 2009.
2. BOi Van Nghj. Van dung liluan v^o thuc ti&n d£iy (Xem tiep trang 33)
