KHAI THAC BAI TAP HINH HOC LffP 8 NHAM BOI OITONG TUDUY SANG TAO CHO HOC SINH TRUNG HOC COSO ThS HOANG TH! THANH" I Mgtsovaidechungvehrduy sang tao (TDST) Trong hgc tgp mdn Toan, TOST la mdt dang tu d[.]
Trang 1KHAI THAC BAI TAP HINH HOC LffP 8 NHAM BOI OITONG TUDUY SANG TAO CHO HOC SINH TRUNG HOC COSO
ThS H O A N G TH! THANH"
I.Mgtsovaidechungvehrduy sang tao (TDST)
Trong hgc tgp mdn Toan, TOST la mdt dang tu
duy dgc lap nhSm tao ra y tudng mdi dgc dao, cd
hieu qua giai quyet van de cao; dd la kha nang phat
hien vain de, tim ra hudng di mdi va lao ra kel qua
mdi vdi cac giai phap la, hiem khdng quen thugc
hole duy nhat
Nhieu nghien cuu da dua ra eac eau true khac
nhau cua TOST, luy nhien cd the hieu TDST eua
HS dugc dac trung bdi ba yeu td eo ban sau: + Tinh
mem deo (ffexibility): La kha nang d l dang chuyen
ll)hogl dgng tri tue nay sang boat ddng tri tue khac;
+ Tinh nhudn nhuyen (fluency): La kha nang lim
dugc cac giai phap dudi nhieu gdc do va linh hud'ng
tim va quyet djnh phuang thuc giai quyet la hoac
duy nhat
Cac yeu tddac trung coban cua TDST khdng
lach rdi nhau ma trai lai, chung cd mdi quan he mat
khang khit vdi eac yeu td khac nhu: tinh chinh xac,
tinh hoan Ihien, tinh nhay cam van de, Tat ca
cacyd'u tddactarng nay cung gdp phan tao nen
TDST, d?nh eao nhat trong eae hoat dgng tri tue
cua con ngudi
Ngoai ra, ehung ta can quan lam ldi mdt vai yeu td
d|c trung khac ciia TDST nhu: + Tinh hoan thien
(elaboration): La kha nang lap ke hoach, phd'i hgp
giOaynghlvahanh dgng, phatlrien ytudng kiem tra
va chung minh y ludng; + Tinh nhay cam van de
(probhm'ssensibiiity):Lanang lue nhanh ehdng phat
hien ravande,sumauthuan,saitam,sulhieu logic, ;
dodd nay ra y mudn ca'u InJe lai hgp li, hai hda, tao ra
c^mdi
2.Khaithacbaitap hinh hoc lopSdeboldudng
TDST ChoHS
-VilcbdidUdngTDSTchoHS can dugc tien hanh
trgng ma quan hd huu co vd^ cac hoat dgng tri tue
Nhac nhu: phan lich, tdng hgp, so sanh, tuong tu, truu
tugng hda, die biet hda, khai quat hda, he thd'ng hda;
,.|||g do, phan tich va td'ng hgp ddng vaitrd nen tang
Cd thevan dung eac hoalddng tri tue nay de giai cac baitoan(BT)dachovadudoanketqua,timra phuong hudng giai; tudd, md rgng, dao sau va he thd'ng hda cac kie'n thde, phat hien ra van demdihoae nhin thay sulien he giua nhieu van de vdi nhau Nhd dd, HS cd the giai quyet nhung van de tong quat hon, van de tuong tu, hoae di sau vao eac truang hop dae biet
1) Khai thac, de xua't BT mdi td mpt BT da cho Tucach giai cua BT da eho, ta se lim ra cac didu
kien eo ban, yeu td khong ban ehdt de ed the suy ra cac BT tuong tu, BT din xua't Qua dd, giup HS ren
so sanh, tuong tu, truu tugng hda, dae biet hda, khai qual hda, he Ihdng hda Tu do, phal hien ra nhutig van de mdi, BT mdi va Idi giai tuang ung Day ia mdt giaiphap huu hieu de bdi dudng TDST eho HS BT/.'Cho lam giae ABC vudng tai A.Chgn A Iam dinh, theo thu tu dung ra phia ngoai tam giac ABC cac tam giac vudng can CAE va BAD Ggi P,0, Mian luollatning diem eua BD,CE,CB(/)/W/7/)
^ a) So sanh BE va CD Xac dinh gdc giua haidoan thang dd
b) Chung minh PMQ la tam giac vudng can Hudngdan:
a) Tu gia Ihiet d l dang suy/a cae diem B,A,Elh§nghang;C,
A, D thSng hang Suy
r a B E l C D vaBE =
B A + A E = D A + A C =
CD
bjTi) giai thiel suy
ra MP la dudng tmng
binhcuaABDC,dodd, B M c
MP//CDvaMP = 1/2CD(1)
Tuong tu, MQ la dudng tmng binh cua ABEC nen MQ/yBEvaMQ = 1/2BE(2).Tu(1)va(2),kethgpvdi
A M P Q vudng can tai M
* Khoa toan - Li - Tin, TnriUng Dai hoc Tay 8^c
Tap chi Gido due so 314 49
Trang 2^hai la tam giac vudng ma )a tam giae thudng, cd
A< 90° ching han Thiet lap BT tuong tu, khi do nhtJng
dieu da chung minh dugc d tren cd cdn dung khdng?
Ta thay, vdi A< 90° thi eae diem 8, A, E khdng thing
hang va C, A, D khdng thing hang; d l dang chung
minhdugcADAC = ABAE.Dodd,BE = CDvaACD =
A E B Gpi I la giao diem cua BE va CD, d l dang suy ra
el5 = 90^
Tuong lu, ta cung thu dugc kdt qua nhu cSu b)
cua BT 1 Nhu vay, vdi gia thiet A< 90", ta cd BT luang
tuBT 1 duge phat bieu nhusau:
fi7'2.'CholamgiacABC(cdA<90°).ChgnAlam
dinh, Iheo thU tu dung ra phia ngoai tam giae ABC
eae tam giae vudng can CAE vaBAD Ggi P, Q, M ian
lugt la tmng diem cua BD, CE, CB
^ a) So sanh BE va CD, Xac djnh gdc giua haidoan
thing dd
b) Tam giae PMQ vudng can
Nhan xet2:T\i nhan xet 1, ta thay d gia thiet cua
BT 1, yeu id A- 90" khdng phai la yeu tdban ehat, vdi
A< 90" van ed dugc ket qua tuong lu Tu day, GV ggi
y cho HS xet trudng hgp khi thay dieu kien A> 90° Ta
cd BT tuong tuvdi hai BT tren:
Br3;Cho'tam giacABC (cd A> 90") Chgn A lam
dinh, theo thir tu dung ra phia ngoai lam giae ABC
cac tam giae vudng can CAE va BAD Ggi P,Q, Mian
luotlatrung diem cua BD,CE,CB
^a) SosanhBEvaCD.Xaedjnhgdcgiua haidoan
thing dd
b) Tam giae PMQ vudng can
Nhan xet 3: Td ba BT tren, ta ml ra BT long
qual sau:
ST^.-Dung ra phia ngoai tam giac ABC cho tmdc
eae tam giac vudng can tai A la CAE va BAD Ggi P,
Q, M lan lugt ia trung diem cua BD,CE,CB Chdng
minh ring: a} BE = CD va BE 1 CD; b) Tam giac
PMQ vudng can
^W/!an;feM.'Tu BT4cholhay, neugglN la giao
diem cua MP va BE, L lagiao diem cua MQ vaCD, de
dang suy ra tugiae NILM la hinh chunhat Do dd, HS
cd the thay ke't luan a) va b) eua BT 3 b^ng cac cjiu
hdi khacva thu dugc BT 5
flr5;Dungra phia ngoai tam giac ABC cho tn/dc
cac tam giac vudng can tai A la CAE va BAD Ggi P,
Q,^M lan lugt la trung diem cuaBD,CE,CB; Nia giao
diem cua MP va BE, L la giao diem cua MQ va CD
Chung minh tu-giac NILM la hinh chanhat
Nhanxet5:Mo\6\eu kien coban cua BT 1 la eae
tam giac CAE, BAD vudng can tai A nhung dieu kien
501 Tap chi Gido due so 314
Mgtcachkhac'dephatbid'uBT: •^-flrff.'Dungra phia ngoaitam giac ABC cho tnrdc cachinhvudngBADGvaCAEF.GgiP.Qtheothiiti
ia lam cac hinh vudng BADG va CAEF, M la tnJj"
diem eiJa BC (hinh2) Chung minh rling: a) BE =
va BE 1 CD; b) Tam giac PMQ vudng can,
NhSn xet 6: Id
hinh ve cua BT6lai ggi y cho HS mgt each khac dd' khai thac BT Neu dung
ra phia ngoai tam giac ABC cac tam giac ABG va ACF tuong ling vudng can laiB va C Khidd, lam giac
MPQ vln la lam giac vudng can tai U Ta ed BT 7'
B7"7; Dung ra phia ngoaitam giac ABC cho trudfi'' cac tam giae BAG va CAP tuong iJTig vudng can tafB vaC, G g i P , 0 , M theo thu" tula tmng diem cuaBG; CF,BC.Chungminh ring tam giae PMQ vudng c3fi5
Hudng dan: Ta lam xual hien eac hinh vudng
BADG va CAEF vaquy BT ve BT 6 i£J
2) Nhin BTda cho dudi goc dp khac vdi BT ban dau Mdt trong cac phuong phap thudng sudwr^
de tim kiem loi giai ciJa mdt BT la thay da each ph^ b i l l
BT, thay ddi each bieu thi, cac mdi Ken quan gii?a cac
du kien cua BT Dd cung la each thay the BT da chd
bing mgt BT tuong duong vdi nd, nhung don gari
hoae quen thugc vdi HS han Mat khac, neu GV rail gdc do khac nhau se gii^ cac em tim ra nhieu each giar
eho cung mdt BT Qua dd ren luyen tu duy llnh \\o^
sanglaoehoHSkhihgctoan Cach lam trencijiggiiipf, ren luyen tinh nhuan nhuyin cua TDST cho HS
Vidu: Cho tam giac ABC vuong tai A co dudwd5
cao AH.Chung m t n h ^ = - ^ { 1 ) '.?i Hudngdan:
Cach I: (1)<=>AB.AC=AH.BC nen BT cdthe dugc phat bie'u lai nhusau: "Cho tam giac ABC vudng tai A Chiing minh ring tich haleanhgdc vuong bang tieh dudng cao nhan , ;• vi^c^nh huyen' Jd
day,!digiaiBTtrdnen hien nhien (/)/h/j 5)
Cach 2: Vide
chung minh PT (1) tuong duong vdi Chung minh AAHB Hinh 3 'tjci'Jtf
Trang 3ttieo each khac Vho tam giac ABC vudng tai A ed
dudng cao AH Chdng minh tam giic AHB dong dang
vditamgseCAB"
Cach 3;Vi|cchung minh PT (1) luong duong vdi
chung minh AAHC ddng dang vdi ABAC nen BT cd
viiong tai A, cd dudng cao AH Chdng minh tam giac
AHC dong dang vditam giac BAC
BT Chung minh hai tam giae dong dang da quen
thugc vdi HS,do doHS de dang chung minh duoc ket
quaBT
3)Lua chpn cdng cu thich hop degiaiquyet
BT Phan tieh gia thiet da eho cua BT mdt each hop
li se giup chung ta cd dugc djnh hudng dung dan
cho Idi giai BT Net khdng cd nhung phan tich, djnh
hudng dung thi nhieu khi, ta se khdng Ihu duge Idi
ren luyen tu duy logic, su linh hoal, sang tao trong
hoc lap cho HS
Nhflng BT hinh hgc so cap ndichung ludn ed nhilu
carfi giai- Vi vay, khi lam loan, HS chua nen thoa man
vdi mdt ldi giai nao dddudd la Idi giai hay ma can phan
tich dekhaiftiae dugc cac dac diem rieng cua gia thiet
kie'n thuc cu, xual hien ytudng mdi khi tim Idigiava ehu
y den sudanh gia cac Idi giai dd.Q
T&i li^u tham khao
I Ho^ng Chiang R^nluy^n khd n3ng sdng tao toan
h^c d- trtrdng ph^ thdng NXB Gido due H 1969
1 Vfl Duong Thuy {chu bidn) Thirc h i n h giai toan (giao winh d&o I90 hpc sinh irung hgc co so h? cao
dang supham) NXB Gidoduc, H 1999
2 Dang Quang Viet Ren luyCn tirduy sdng tao thOng
qua xfly dung he thflng bai tflp NXB Gido dtfc,
H 2007
SUMMARY
Creative thinking is the most fundamental re-source of individuals, the essence of personal crea-tivity and the basic purpose of education.Fostering creative thinklngin students needs carryingout in organic relationta other intellectual activities and reality teaching geometry faces many difficulties, teachers have not yet paid enough attention io en-courage students' creative thinking, and many are confused about choosing contents and practical methods.This article summarizes some critical is-sues in creative thinking, thus, proposing the use
of 8'" - grade geometric problems for fostering the conjunction with other intellectual activities: some solutions suggested hythe author include: Develop and promote new problems from previous ones or from solutions of previous ones, approach given problems in different ways, choose adequate meansfor solving problems
Nhirng yeu to cv ban
•- ' (Tiep Iheo trang 28)
trong lao dgng ndng nghiep phai gdp phan hinh thanh
sunang ddng trong nghe nghiep, linh kien tri trong hgc
t£^3, tinh flian doan kel, hda ddng vdi SV eae DT khae
3 Ngoai nhihg yeu tdehu quan va khaeh quan cd
anh hudng tich cue, edn cd mdtsd yeu id anh hucng
tieu cue den tinh each cua SVDTDao.Dieu kien dia Ii,
lac hau vln Ion tai, tinh bao thu trong quan diem sdng,
qua coi trgng cac gia In tmyen thd'ng, qua de cao linh
cdket cgng ddng ma chua manh dan tham gia cac
hoEfldgng xahgi, da khien SVDT Dao phan nao cham
thich ung vdi cac dieu kien sdng mdi Trong giao tie'p,
SVDT Dao ngai chd ddng ngudi va thudng thieu tinh
ch&dgng nen tn/dc Idp, tn/dc dam ddng hothudng njt
re.Trong hoc lap, hgehua the hien rdtinh can eu, chju
kho,cham thich ung Irong viec phdihgg hoalddng hgc
tap, thudng trdng chd vao suhudng dan, kich thich iCf
phia giang vien Nhung han che nay anh hudng ration
d^tich each cua SVDT Dao Do dd,nhatnrong, cac Id'
chuttrongnhatnrdng.giang vien can chu ytd'ehuc eac
hoat ddng phong phii va da dang nh&m kich thich tinh manh dan, tich cue trong giao tiep, tinh can cii, chju khd trong hgc tap cua SVDT Dao.Q
Tai li^u tham khao
1 VQ DQng Tamil h(jc dan toe NXB TCr diin bdeh Ichoa H 2009
2 Q6 Vigt Ddng - NguySn Kh^c Tung - NOng Trung •
hpc xa hdi, a 1971
3 Do Huy LSI s6'ng dSn toe va hien dai - may vAn di
U lufln vi thirc ti^n NXB Vdn hOa thdng tin H 2007
SUMMARY
There are many factors affecting the character of the Dao ethnic minority students, including subjec-tive factors and objecsubjec-tive factors Subjecsubjec-tive factors Including knowledge capital self-culUvaUon Objective factors including: family education: school education; Dao ethnic culture: the interference ofthe traditional culture ofthe Dao ethnic with the values of modem culture: the process of exchange: the intention with other ethnic groups and industry practices Theseare the basic elements that have the most influence on the formation ofthe character ofthe Dao ethnic mi-nority students
Tap chi Giao due so 314 51