1 Nhvng yiu tei lien quon ilin KNDCH: cau hoi CH dQtro co gay dvqc hlrng thu hQc t9P cho hQcsinh HSLco dQtdvqc myc dich dQY hQc hay khong phy thu9c vao cac y~u t6 sou: + Ml,lc ilrch:can
Trang 1ntN luyiN KI NANG OAI cAo HDIIRONG DAY . HOC . loAN
-V~c ren luy~n coc kTnang dQYhoc (KNDH)
cho sinh vien suphorn (SVSP)nol chung,
SVSPTocn noi rieng la m9t nhi~mvy quon
tronq va cOngla rnuctieudao tQOccc nha trvang
SP.Khodn2,di~u40 LUQtGi60 duendrn2005
da neu ro: «Phuonqphop dao too trinh d9 coo
d6ng, trinh d9 dQi hoc phoi coi trQng vi~c b6i
dvong y thlrc ty-giac trong hQct9P, nang
Iy-cty-hQc,ty- nghien ClrU,phat tri~ntv duy sang tQo,
remluy~n kTnang thy-chanh, tQodi~u ki~n cho
ngvai hQcthorngio nghienClrU,thy-cnghi~mlrng
dyng" KNDH thi co rat nhi~u, bai vi~t nay chi
gioi thi~u khai quatkTnang ilgt cou hoi (KNDCH)
va quy trinh rim Juy~n KNDCH trong qua trinh len
Jop cho SVSP Toan.Oay la m9t trong nhC;ngKN
co ban, quy~t d!nh chat Itlqng gia dQYcuo giao
vien (GV)
1 KTnang dat cau hoi
KTnangla kho·nangthy-chi~nthanhthQo,linh
hOQtva co k~tqua m9t hanh d9n9 nao dObang
cachv9n dyng nhC;ngtri thlrc, nhC;ngkinh nghi~m
da co d~ hanh d9n9 phu hqp voi tung di~u ki~n
cy th~ KNOCHla cach thlrC,kho nang khoi thac
thong tin cuo GV nhc5mlam sangto n9i dung van
d~ va d!nh hvong cho ngvai hQctrong qua trinh
dQYhQc
1) Nhvng yiu tei lien quon ilin KNDCH:
cau hoi (CH) dQtro co gay dvqc hlrng thu hQc
t9P cho hQcsinh (HSLco dQtdvqc myc dich dQY
hQc hay khong phy thu9c vao cac y~u t6 sou:
+ Ml,lc ilrch:can xac d!nh ro myc dich dQtCHI
myc dich khac nhou se co cac CH khac nhou;
+ Ngi dung: CH can ro rang, ngan gQn,toot ra
dvqcyd!nh can hOi,khongdvqc m9Prnad~ HS
co th~ tro lai nvoc doi; + Deii tvqng: CH phoi
phu hqp, vuo «SlrC"voi HS;+ Thai gion: can xac
d!nh thai gion tieu t6n cuo CH va quy thai gion
danh cho CH dO;+ Kit qua: CH dQt ro phoi co
dap an ro rang, chfnh xac
2) phon lo(}i CH.Dy-ovao cac y~u t6 tren co
th~ phan chio CH thanh 3 IOQisou: + CH d!nh
o DOTH!TRINH*
hvong (CH lling): Hvong HSvco suy nghTm9t n9i dungncodO,HSkhongcan tro lai hOQcchuc tro lai dvqc; + CH ki~m tro: la IOQiCH nhc5m ki~m tra ki~n thlrc cOhocc tim hi~u xem HS co hi~u m9t beoc (hay m9t chu6i) suy IU9nvuo thuc hi~n hay khong;+ CH yeu cau hanh d9n9: HS thy-chi~n ccc buoc tfnh toon, suy IU9nti~p theo oay la IOQiCH dOi hoi tv duy, do dO tfnh vuo
«SlrC"can dvqc coi trQng
3) Quy trinh thlfc hi~n mgt CH:GV neu CH
~ HS suynghT(cotfnh thai gion) ~ GV gQi 1 HS tra lai ~ HS tra Ioi ~ M9t s6 HS khac nh9n xet, b6 sung~ GV danh gia va k~tIU9n.Khithy-chi~n CHI GV can xac d!nh dQngCHI xac d!nh khoang thai gion phu hqp cho m6i cong dOQntrong qua trlnh (k~ ca thai gion HS dlrng len ng6i xu6ng);
CH khi giang bai phai dvqc tfnh bc5nggiay
4) H~ theing CH:O~ xay dy-ngh~ th6ng CH cho m9t bai dQY,GV can quon tam d~n cac di~u ki~n: thong qua CH d~ chuy~ntai n9i dung bai dQY;h~ th6ng CH phai phat tri~ntvduy cuo HS cang nhi~u cang t6t, phu hqp voi n9i dung hOi, voi HS va thai gion cho phep
o~ xac d!nh s6 Ivqng CH cuo m9t phan bai dQYcan thy-chi~n cac bvoc sou: - Xac d!nh cac bvoc di cuo phan bai dQY;- Xac d!nh CH cho m6i bvoc; - Tfnh thai gion tieu t6n cuo m6i CH
va tfnh tang cac CH r6i d6i chi~u voi thai gion cuo bai hQcd~ di~u chinh
5) Thoi gion ddnh cho cac cou hoi (TGDCCH) cuo phon boi dqy thuang iluqc tinh nhu sou: TGDCCH = TGQD - (TGGB + TGDG + TGV + TGM);trong dO:TGoo la thai gion quy d!nh cho m9t phan dQY(do GV quy d!nh trong quy thai gion 45'/ti~tL TGGB la thai gion ghi bai cuo HS,TGDGla thai gion dien giang cuo
GV, TGVla thai gion ve hlnh hOQcd6 thi (ch6ng hQn, ve m9t porabol: 1'30", ve m9t tam giac:
22",ve m9t tlr giac: 43" .L TGMla thai gian sli
*Truong B~ihqcSU'ph~m - B~ihqcThai Nguyen
~) T_~~P_C_h_iG_i_aO dU C so_~_2_5_3 (k_i_1_-_1/_2_01~1)
Trang 2dl,lng mo hlnh (tuy thuqc vco mO.hlnh, eMdung
cu th~ vo phlJang phap sudl,lng c1etfnh thai gian)
2 Quy trinh ren luy~n KNDCH t~ong dqy
hoc Toon cho SV: Gicmg viencung cap coso If
lu¢n v~ KNOCH ~ Giang vien c1lJara nqi dung,
yeu cau svxoc c1jnhrnuc c1ichva xay dvng h~
th6ng CH phu hop vai nqi dung ~ GQi SV trinh
bay phan chuan bj, nhung SV khac b6 sung y
ki€in, c1anh gia, thao IU9n ~ Giang vien chfnh
sua, nh9n xet va k€itlu9n
Vf dlJ:Remluy{m KNOCH cho SV khoa T06n
thong qua bai dQy«DfnhIfCosin"(Hinh hQc 10):
Bvoc 1: Xac clfnhmlJcclfchDH, tfnh cheftcuo
nqi dung boi dc;Jy,Xac c1jnhc1ay10bai d9Y mqt
c1jnhIf, CH se dung vai mvc c1fchgQ'imo c1~HStv
phat hi~n c1lJQ'ccong thllC a2 =b2 + c2- 2bccosA
lam co sO c1~chfnh xac h6a nqi dung c1jnhIf Cosin
Bvoc 2: phon tfch nqi dung boi hqc.Xac c1lnh
nqi dung trQng tam 10Djnh If Cosin phon chia
nqi dung bai d9Y theo tlrng c1anvj nho g6m: on
t9P ki€in thllC cO (c1jnh If Pitago, phon tfch mqt
vecta thanh hi~u cua hai veda, cong thllC tfch vo
hlJang cua hai vecta); cac phlJang phap chllng
minh mqtc1jnh If (t6ng hQ'pva vecta); c1jnh If va
cong thllC bi~u di~n c1jnhIf
Bv6c 3: Xac clfnhcla;lur;mgDH:HS ph6 thong,
di~n c19itra
Bvoc 4: Xac clfnh nqi dung cld clgt CH.Nqi
dung se c1QtCH10:ki€inthllc cOlien quan c1€inbai
d9Y, phat bi~u va cach chllng minh c1jnhIf, cong
thllC bi~u di~n, ap dyng vao giai bai t9P cy th~
Bvoc5: Nqi dung cac CHclgtro Giang vien
gQi 1 SV len bang trinh bay h~ th6ng CH c1a
chuan bj len bang c1~ca lap thee dOi, thao IU9n,
b6 sung Sau c1ay10nqi dung h~ th6ng CH cua
SV c1Qttheo mau giang vien yeu cau:
- Chuo c1Qtc1lJQ'cCH (chi€im f I~ tha'p)
- CH c1Qtra con qua chung chung hOQcqua kho c16ivai HS, chuo co sv gQ'i mo giup HS tim
ra ccch giai quy€it bai toon, ch6ng hen: «Hay chvng minh clfnh If?".D~ giup HS d~ hi~u han, d~ xcc djnh dlJQ'ChlJang giai quy€it, GV co th~ gQ'iythem bang coc CH khac: «Mqtemhay neu gia thiit vo kit lugn cua clfnhIf?"(nham mvc c1fch ki~m tro, c16i tlJQ'ngki~m tra 10 HS trung binh);
«Hay neu hvong chvng minh clfnh If?"(t90 ca
hqi cho HS thoai mai dlJa rayki€in, suy nghTcua minh, gay c1vQ'ckhong khr hllng thu hQc t9P);
«a, b, cclvqc bidu thf boi cac vecta noo? phon tfch vecta BCthonh nhiJng vecta noo?"(CH khi€in
HS lung tung khong c1jnhhvang c1lJQ'cnen phon tfch theo 2 hay 3veda, thee t6ng hay hi~u cua 2 vecta ) GV cOng co th~ c1QtCH 10 «Phon tfch veda Be thonh hi~ucua 2 veetanoo?"(nham myc c1fchbi€in c16i,c16itllQ'ng HS kha)
- Cau hoi con mang Hnh ap c1QtHS thee cach
«dat tay chi vi~c" nhlJ: «Hay chvng minh bang phvang phap vecta?".D~ tranh c1i~unay, GV co th~ c1QtCH:«Ngooi cach chvng minh clfnhIfbang phvang phap t6ng hqp, cac em con co cach chvng minh noo khac khong?"(CH gQ'iy: «Li~u
cothd sv dlJngphvang phap veda cldchUngminh clfnh If khong?). Hay «Tv clang thu-c vecta
BC =AC - AB ,hay binh phoong hai vi cldclvqc kit qua moi?".GV co th~ thay bang CH: «Hay chuydn hoa tv clang thvc clqdoi thonh clang thvc vecta cldtimro cach chvng minh ?".Ta tha'y cach c1QtCH sau c10ihoi HS phat huy cao han Hnh tfch
cvc, chu c1qngso vai yeu cau cua CHtnrac.
- ChlJa sap x€ip cac CH hQ'p logic, khong
co c1Qgan k€it giua nQi dung toan hQc voi
cach di~n c19t tlr thlJCt€i.
.- Thai gian dv c1inh cho m6i cau hili chi mang Hnh
lJac c10an, trong qua trinh thvc hanh
se dan c1i~u chinh cho phu hQ'p nQi dung bai d9Y
TT N(ii dung CH Ml,Ic dich f)6i Hlnh Thai lOlliCH
tll9'ng thuc oian
1 Hay philt bi~u dinh Ii? Ki~m tra TB Tai ch6 30" Ki~m tra
2 Hay chUng minh dinh Ii? SUy luan Kha Tlli ch6 1' Yeu c;\u himh dong
3 Hay su dl,lng phuong philp vecta
Suy lu~n Khii 30" Ki~m tra
4 Phan tich BCthilnh nhCrnovecta nao? Biiln d6i Khii nt 1'45" Yeu c;\u himh dong
5 AD dl,lng tich vo htJ6'ngclla hai vecta Biilnd6i Kha nt 1'30" Yeu c;\u hanh d(ing
6 ChUng minh a'=b' + c' - 2bccosA? Biilnd6i Kha nt 1'30" Yeu c;\u himh d(ing
7 Gec A b~nQ 90 do? Biilnd6i TB nt 30" Ki~mtra
8 Ap dl,lng giai vi du 1? Ap dung TB nt 30" Ki~mtra
Thong qua phan trinh bay cua SV tren bang,
c16ngthai ki~m tra phan chuan bj cua mqts6 SV
khac, chung toi nh9n tha'y nhCingsai lam SV gQP
phai 10:
***
Renluy~n KNDH noi chung, KNOCH noi rieng
10 mqtdoi hoi ca'p thi€it, c1ap ling yeu cau cua
(Xem tiip trang 20)
~T~~p~C~h~i~Gi~a~O~d~~c~s6~2~5~3~(~k~i1~._1~/~20~1~1)~ ~
Trang 3
-hQi Myc dich xlrng dang phai 10 rnuc dkh
mol hooc chuo dot ducc trong xo hQi, hooc
ccc phuonq ti~n d~ dQtrnucdkh phdl mol
Myc dkh dQt ra phai cu th~, khong chung
chung, tnru tlJqng, khong qua hep, khong
phai 10nhungcni vun VQt;mucdkh c6 th~
tro thonh hocl boocuecacuocdoL Muc dkh
ST c6 th~ gQP nll ro, kho~g dlJqc ~hung
nglJai xung quanh ti6p nhqn D~ tro thonh
mQt nhan cach ST, cac co nhan phai donh
thai gian d~ xac d!nh dlJqc myc dkh xlrng
dang, n6 10di~u ki~n cua SY'ST
- Giao dl/c tre bidt cachxdydlfng chl.lOng
trinh, ke hogch hogt dgng phI) hqp vai mvc
dich.D6 10thi6t k6 mQtk6 hOQchhonh dQng
h~tSlrCcuth~va kha thi thlJChi€mmucdkh K~
hOQchc6n m~mdeo, linh'dQnS,phu hqp voi
tinh hinh thY'ct~va phai t1nhd~n cac di~u ki~n
he trq, thai gian hqp Ii
- Rim luy~n khd nang lam vi~ccoo,d61a
khd nang lam vi~cc6hi~uqud, hvng thu,say
me trong mgt thai gian doi. Con nglJai luon
lao dQngtrong trQngthai tY'nguy~n,tY'giac,
vui ve Kha nang lam vi~c coo con th~ hi~n co
nhanc6 th€ lamvi~cday hlrng thu trong nhung
di~u ki~n kh6 khan, thi~u cac di~u ki~n can
thi~t N6i cach khac, d6 10nhung nglJai bi~t
VlJqtlen mQi kh6 khan d~ dQt myc dkh, c6
kha nang duy tri wang dQ lao dQng " mlrC
coo trong khoang thai gian doL
- Hueinluy~n h<;>c sinh biet cach gidi quydt
nhvng vein de ggp phdi trencondr.rOngthlfc
hi~n mvc drch.SY'STcong Ian thi con doong
di d6n ST cong nhi~u chong gai, thli thach
Con nglJai can c6 y chi va ngh! h,c, bang
nhung hi€u bi6t va kinh nghi~m tkh loy d~
giai quy6t nhung vuong mac; can hQccach
binh finh, IQcquan, tim ra nguyen nhan dkh
thY'ccua mei kh6 khan d~ tim cachgiai quy6t
- Rim luy~n khd nang suy doan cho h<;>c
sinh.Kha nang nay giup hQcsinh nhqn thlrc
van d~ nhanh ch6ng va hi~u qua han Day
cOng10kha nang giup cho con nglJai hOQt
dQngST
***
ST10qua trinh tQOra cai mOi,cai dQcdao
c6 kh cho xo h9i Du moi hay dQcdao d6n
dau, sanph6m STcOngphai bat ngu6n tV thY'c
ti~n Mo hinh cai mOiSTra boo gia cOngdlJqc
xay dY'ng til c,acmo hinh tam I.ben trong
Gloo due ST10mQtcong vi~c h~t SlrCphlrc tQPvo
kh6 khan,Vl-vqy,hi€u ro co ch6tamIIcuo qua trlnh ST,dQc bi~t 10nhung dQc di€m co bancuo nhan
ccch STse giup cho nho giao due ti6n honh giao
due hoc sinhcue minh tro thonh nhung nhanccch
STc6 hi~Uqua 0
Tai li~u tham khao
1 Phan Dung.Phmmg pbap lu~n sang tl;lokhoa hQc-ki
thu~t ghii quyet van de va ra quyet djnh.NXBTP Hb Chi Minh, 1998.
2, Jack Foster Biquyet sang t~o.NXB Tre, TP He, Chi
Minh 2005
3 Huynh Van Scm.TamIihQcsang t~o.NXBCiao dt,tc.
H 2009
4 Nguyen Canh Toan - Nguyen VanLe -Chau An Khoi
dl}ytiem nang sang t~o.NXBCiao d~tc, H 2004.
5 Nguyen Minh Trie't.Danh thli'c tiem nang sang t~o
NXB Tre, TP He, Chi Minh 2007.
6 Nguyen Huy Ttl.De cmmg bai giang tamIihQcsang t~o.Vi~n Khoa h9C giao dl,lc,H 2000
7 Nguyen Huy Ttl.Tai nang - quan ni~m,nMn d~ng va dao t~o.NXBCiao d~tC, H 2004.
Ren luyvn ki nang
(Tidptheo trang 53)
chu6n ngh~ nghi~p va d6i moi n9i dung, chlJong trinh, phlJong phap dQYhQc" ph6 thong D~ c6 KNDCH va vqn dyng tat trong thY'cti~n DH Toan
o ph6 thong can mQtqua trlnh rEmluy~n thlJang xuyen thong qua cac 10Qiboi hQckhac nhau, voi cac dai tlJqng khac nhau va tv d6 tY'di~u chinh cho phu hqp 0
T:Hli~u tham khao
1 Bui Hien Nguyen Van Giao Nguyen Huu Quynh
-Vu Van Tao Til'dien Giao d'QchQc.NXBT£'r dien bach
khoa, H 2001.
2 Nguyen Ba Kim Phmmg phap d~y hQcmon Toan
NXB Ciao d~tc, H 2003.
3 Tran Ng9c Lan "Sl'rdl,lngki thu~t d~t cau hoi trang d~y h9Ctoanatieu h9Cnh~m tich CI,lCh6a ho~t dOngh9C~p cua h9Csinh".T(lp chi Ciao dt,tc, kl 1 thang 9/2006.
4 Bui Van Nghj.GiaotrinhphU01lgpbapd~yhQc nhiing nQi dung C'Qthe mon Toan NXB DQi h(>c su ph(l.n1.
H.2008
5 Petr6pxki A.V.Tam IihQchratu6i va tam IihQcSlf
ph~m.NXBCiao dltC, H 1982.
6 Dinh Xuan Scm - Nguyen Anh Tuan NghifP V~t su ph(lnl. Giao trinh danh cho sinh vien khoa Toan Truerng D~i h9C su ph~m - D\li h9C Thai Nguyen, 2003