C. Khai quat hoa, trim tugng hoa, dac biet hoa trong day hoc giai toan
t f MH •&g; f^ &g;
3.1.4. Gidp hgc sinh nhan ra cdi hay, cdi dep cdi thu vi cda todn hgc ciing
nhirng irng dung thuc tien cua nd
Trong cupc sdng hdng ngay, khdp nai mpi ebon, chiing ta diu thdy dau
' f f
vet ciia todn bpc bdi todn hoc Id cdng eu thiet yeu giiip eon ngudi boat ddng
cd hieu qud trong mpi linh virc. Dieu ndy da timg dupe CdcMdc (K.Marx)
nhdn manh: "Mgt khoa hgc chi thuc su phdt triin niu nd su dung duac cdc
kien thirc vd phuang phdp cda todn Ape". [2] Chdng han, xdc suat thong ke
todn hpc la mdt ngdnh todn dupe cdc nhd khoa hpc ndng nghiep van dung de
f
tao ra cdc cay, eon gidng phuc vu ndng, ldm, ngu nghiep. Cdc nhd y hpc diing nd de chuan dodn benh vd phuc vu cdng tdc dich te. Cdc chuyen gia kinh te
dimg nd de du bdo vd dieu chinh nhimg thay ddi ve kinh te eiia ddnh nude; cdc nhd xa hpi hpc dimg nd de nghien eiiu dan sd vd ke hoaeh hod gia dinh cimg sac thdi tam ly cua cdng ddng dan cu. Todn hpc rdi rac dupe sir dung vdo ITnh
vuc tin hpc vd vien thdng. Co bpc ly thuyet vd dac biet Id co hpc siic ben vat lieu dupe dimg trong xay dung cdu, dudng, cdc khdch san, cdc chung cu cao tdng, ehi tao vd d td, tau thuy, ten lira vd cdc loai vii khi. Ly thuyet Graph va
mang dupe cdc nhd qudn ly giao thdng sir dung de lap he thdng giao thdng dd
thi vd giao thdng todn qude..,
Kiln thiie vd phuang phdp todn hpc quan trpng vd gan gui cupc sdng Id
nhu vay, nhumg thue tl hpc sinh d phd thdng dau cd hieu het dupe dieu dd, Cdc em thudng eho viee hpc todn Id khd bdi todn hpc toan la nhimg cdng thire
khd Cling, hinh ve rdi ram, con sd vd hon nen cdc em da khdng yeu thich, say
me hoe todn nira, Nguyen nhdn dan den each hieu sai lam tren eiia hpc sinh
phdi kl din mdt phan do phuang phdp gidng day ciia ngudi thay.
Trude nhimg bat cap kl tren, dl nang cao hieu qua day hpc mdn todn ddp
img yeu cdu cap bach vl viec ddi mdi phuang phdp day hpc trong nhd trudng
hpc toan ngdy nay khdng cdn dan thuan chi cung cap kien thiie todn hpc cho hpc sinh ma phai gdp phan ddo tao cdc tri thire khoa hpc, nang ddng sdng tao, linh boat trong viee van dung tri thire da hpc de thich img vdi mpi sir thay ddi, nhiing con ngudi biet tu hpc sudt ddi, tu ren luyen vuom len de khang dinh
/ f
minh trong the gidi hien dai. Mudn dat dMoz muc tieu dd, ngudi gido vien
ludn phdi tim tdi ede bien phdp giiip hpc sinh tu minh khdm phd cdi hay cdi dep, cdi thii vi ciia todn hpc ciing nhumg iing dung thuc tien ciia nd qua nghe
thuat day hpc gidi todn ciia gido vien nhu Id:
a. Tdng cuang cho hgc sinh gidi cdc bdi todn thuc tien, hoac gidi thich cdc vdn de thuc tien bdng kien thue cda todn hgc.
Vidu:
^ f
Bdi todn 1:" Cd hai vuomg qude d hai bd cua mdt con sdng, ngudi ta mudn
f \ r 1 r '
xdy dung mdt chiee cdu bac qua sdng de ndi hai vuong qude vdi nhau sao eho
f r t f \
dudng giao luu giira hai vuong qudc la ngan nhat, biet rang hai bd song song
song vdi nhau va cau xay dung vuong gdc vdi bd song".
D I giai dugc bai toan tren viec trude tien la hgc sinh phai sir dung cac thao tac tu duy: phan tich, so sanh, tuang tu hoa cimg vdi tri tudng tugng
khdng gian dl bilt chuyin bai toan thuc tien vl bai toan toan hgc nhu sau:
" Cd hai dudng thing di va ^i song song vdi nhau. Hai diem A, B nam ve
hai phia cua hai dudng thing (hinh ve dudi). Tim vi tri cua M va N tren
dudng thing d, va dj dl AM +MN +NB dat gia tri nho nhit, bilt ring MN
vudng gdc vdi hai dudng thing". Khi chuyin xong, hgc sinh phai biet sir
dung phep tinh tiln va phep ddi ximg true ciing cac kien thirc toan hgc khac de
d2
N
B
Bdi 2: Cd 3 nha thdng thai ( NTT ), mgt thing hi va 5 chile mu (3 mu den, 2
mil trang ). Thang he bat cdc NTT quay mat di rdi nd giau di 2 mii trang, sau dd dpi vdo ddu 3 NTT 3 mii den. Ldm xong, nd gpi ede NTT quay mat lai vd dd : Dd ede anh dodn dupe tren ddu minh dpi mu mdu gi ?
Mdt NTT da xung phong trd ldi ludn, hdi nhd thdng thdi suy nghi nhu
f
the ndo ma trd ldi dimg dugcl {lien he v&i gidi vd bien luan phuang trinh)
(J bdi todn 2 cdc em phdi du dodn nhieu khd nang xdy ra, trong mdi khd
nang dd lai ed trudmg hgp cu the horn. Sir phiie tap ndy cung gidng nhu khi cae em gidi bien luan phuong trinh: Ta phdi chia tham sd thdnh cdc trudmg
hop dae biet khde nhau rdi gidi, trong mdi trudng hpp dd cd the cdn dupe
r
L&i
Ldi giai bai toan thuc te
- Gpi ten 3 NTT Id A, B , C
- Gia Sli NTT A cd cau trd ldi: Vay dng ta cd each nghi nhu sau:
+ Neu minh dpi mii trang thi thdng B nd se nghT rang: Nd md dpi mu trang
thi thang C se dodn dupe ludn, C khdng dodn thi nd se dodn dupe minh.
+ Cd B vd C khdng dodn chiing td minh dpi mii den.
r
Ket ludn: A dodn minh dpi mu den
giai
Cac bu-dc thu-c hien bai toan toan hoc
• • «
f 1
- Qud trinh bien ddi dua phuang trinh hay he phuang trinh ve dang quen thupc - Chia tham sd thdnh cdc khodng khde
nhau
- Gidi phuang trinh hay he theo tham sd
-Ket luan nghiem ciia phuong trinh hay he
Bdi 3: Bd bdn hdng ngay that ( Ung dung BDT Cosi a lap 10)
Ndi dung bdi todn: Mdt bd bdn hdng ngay that ed mdt cdi can hai dTa. Bd khdng tin vdo can eiia minh, Bd nghT neu can dieu eho ngudi mua Id cd tdi cdn can thilu cho minh thi bd khdng mudn. Bd nghT ra cdch can nhu sau: Cdn sd hdng ciia ngudi mua ldm hai ldn nhu nhau: Lan thir nhat dat qud can ben nay
vd lugng hang ben kia. Lan thir hai bd lam ngugc lai ldn mot. Hdi bd ldm nhu
the bd cd lgi hay thiet
Bdi 4: Cdt tam tdn HCN cd ede kieh thude sau ddy(d=16, r=9; d=100, r=16;
f t '
(j=49^ r=4) lam thanh lap be hinh vudng cd ciing dien tich.iphep bien hinh)
Bdi 5: Chia thira rudng HCN va cai ao hinh tron thanh hai phan cd dien tich
bing nhau ma trong tay chi cd hai cai egc va sgi day {cung cd cdng thuc lien
quan den HCN vd hinh trdn)
Bdi 6: Giai thich cau ndi sau day bing kiln thirc cua toan hgc
" Oil ai ndi nga ndi nghien; Ldng ta van giir nhu kieng ba chan" {lien quan
Vdi viec cho hgc sinh gidi cdc bdi todn thuc tien d tren khdng chi ren luyen cac thao tdc tri tue, ciing co khde sdu kiln thiic todn bpc md cdn gdn kit giira ly luan vd thue tien, giiip cdc em y thiie dupe gid tri cua viec hpc tap todn ddng thdi ciing xod di trong cdc em sir khd ciing eua Todn hpc.
b. Khuyen khich ngu&i hgc tlm nhiiu l&i gidi cho mat bdi todn c. Tap cho hgc sinh sdng tdc cdc bdi todn thuc tiin
3.1.5. Su dung cong nghe thdng tin hd tra viec dgy hgc gidi todn
Cdch day gan 3000 nam nhd todn hpc ndi tieng eua Hylap Id Pithagor da
f * f \ t f \ , f
du bdo rang: cdc con sd se dieu khien the gidi. Ve sau, mai den the ky XX nhieu nhd khoa hpc vdn cdn hodi nghi du bdo ndy. Nhung tir khi Viet Nam ra
f f f
ket ndi mang Internet eho den nay thi cdng ngdy viee sir dung cdng nghe thdng tin hd trp trong day hpc ndi chung va day hpc todn ndi rieng lai trd
y •\ r r f r i
thdnh nhu cdu cdn thiet vd cdp thiet cua xu the ddi mdi phuang phdp day hpc d cae trudng phd thdng hien nay . Nhd khai thdc sii dung cdng nghe thdng tin
•\ t t
chung ta cd dieu kien thuan Ipi de thuc hien viec ddi mdi phuang phdp day
hpc truyin thong sang phuang phdp day hpc " lay nguai hgc ldm trung tdm".
Day hpc gidi todn Id mdt trong nhimg ndi dung quan trpng cua day hpc
todn vdi nhilu bdi todn phong phu vd da dang ve cd dp khd ldn kieu loai.
Chinh vi thi trong day hpc gidi todn, neu ngudi gido vien biet khai thdc hieu
qua mdt so phdn min todn hpc se ed tdc dung kich thich khd nang tu duy ciia bpc sinh tren eon dudng khdm phd, tim tdi ldi gidi bdi todn cung nhu qud trinh
sdng tdc ede bdi todn mdi bdi nhd cd cdng nghe thdng tin hpc sinh de ddng
thiy dugc moi lien he giira cac dir kien da cho trong bai toan vdi an so can
tim; tilp kiem dugc thdi gian ve hinh va tinh toan ... Vi du:
- Viec sir dung phin min Powerpoint giup giao vien he thong hda cac
r
hong kien thiic ciia hpc sinh bang he thdng bdi tap trdc nghiem ngay tren lap
' * f t r
de rdi giup hoc sinh ciing ed khac sdu cdc kien thirc dd mot cdch nhanh chdng hieu qua.
- Hai phan min Geometer's sketchpad vd Cabri Id nhiing phdn min hinh hoc cd chiic nang dae biet ho trp cho gidi cdc bdi todn hinh hpc. Vdi cabri gido
vien ed thi thue hien cdc thao tdc "keo", "thd", "an", "hien" dk thue hien hinh
ve d nhieu gdc dp khde nhau giiip cho hpc sinh phdt hien nhimg thude tinh lien quan den ldi gidi cua bdi todn md bpc sinh rat khd phdt hien d mdt vdi hinh ve tren bdng den. Bdi todn sau ddy minh hpa cho dilu dd
Bdi todn 1: Tam gidc ABC ed hai dinh B, C cd dinh vd dilm A chay tren
dudng trdn. Tim quy tieh trpng tdm G cua cua tam gidc ABC.
De de ddng tim ra ldi gidi bdi todn, gido vien ed the sir dung phdn men binh hpc cho hpc sinh quan sdt vet di eua G khi A di ddng tren dudng trdn. Nhd dd bpc sinh da phdt hien vet cua G tao ra mot dudng trdn vd AG ludn di qua trung diem I cd dinh cua doan BC da cho. Tir dd cdc em tim ra quy luat lien he
giua G vd A nhu sau: [Q^-14 tire G Id dnh ciia A qua phep vi tu y~^,
Bdi 2: Cho tam gidc ABC vd dilm M tiiy y ciia mat phdng. M] Id mot diem
ddi xiing vdi M qua A, M2 Id dilm ddi ximg vdi Mi qua B, M3 Id diem ddi
xiing vdi M2 qua C. Chiing minh rdng MM3 ludn di qua mdt diem ed djnh
Vdi phdn min hinh hpc gido vien de ddng dung dupe cdc diem Mj, M2,
M3 Sau dd eho M di ddng dk hpc sinh quan sat vet eua MM3;tir dd hpc sinh ed
thi du dodn dilm co dinh md dudng thdng MM3 di qua rdi tim cdch chimg
minh dieu minh du dodn.
Rd rdng, trong day hpc gidi todn neu ngudi gido vien biet kheo leo ket
hop cdng nghe thdng tin cimg ede phuang tien day hpc khde nhau se tao nen