Ho Thi Mai Phuang Tap chi KHOA HOC & CONG NGHE KHAI T H A C L O I G I A I B A I T A P T O A N G O P P H A N B O I D U O N G C H O H O C S I N H \ I O T S O V E U T O C U A PII A M C H A T T R I T U F[.]
Trang 1K H A I T H A C L O I G I A I B A I T A P T O A N G O P P H A N B O I D U O N G
C H O H O C S I N H \ I O T S O V E U T O C U A PII.A.M C H A T T R I T U F
H6 Thi Mai P h u o n g '
Trucmg Dai hoc Sir pham - DH Thai \gu\ en
TOM T A ' I
Pham chat tri tuc la mot Irong nhung yeu 16 can ihiei cho hoc tap de tiep thu In ihiic ren luyen kT nang dap irng dugc nhirng yeu cau cua cuoc song Bai tap loan hoc la mot noi dung co nhieu co
giai bai tap loan neu giao vien biet each huong dan hoc sinh phan tich bai loan, biet nhm cac yeu
loan se giiip hoc smh linh hoat doc lap, tu duy duoc phat tnen phat hien van de moi tim ra huong
di moi, tao ra ket qua moi, Nhirng hoat dong nay gop phan boi duong pham chat iri tue cho hoc smh nham nang cao hieu qua cua day va hoc
Til' khoa; khai thdc ldi gtai bdi ldp todn, bdi ducrng mdl sdyeu id cua phdm chat tri tue
DAT V A N DF, cac yeu to cua PCI" I phai ttu'oc lien hanh trong Rtii d u o n s va ren luven cho HS phSm ch^t tri '^^^ ^1^'^^' '^'^^ ^^'^ trinh day hgc dac biet la trong iuc (PCTT) la mot nhiem vu c^n ihigt trong day hoc khai thac Itii giai cua bai lap lOiin, diiy hoc ttian Giai loan la hinh thuc chu yeu NHU'NG YEU T O C O BAN C U A P C T T cua hoat dong hpc loan, cac bai tap loan viia Viec bdi d u d n g cae yen to co ban cua P C l f lii muc dich la p h u o n g lien eo hieu qua va thong qua khai Ihac I61 giai bai tiip loiin ciiii khong the thay the trong viec giiip nguoi hoc dua tren nhiing tu t u o n g chu dao sau n.^m virng Ui thiic ren luyen kT nang, + Q.',^^ ^i^^ ^1,^,3,, j^,^;,^ ,|„',^ i^i „,-i,5^ ,.^1;, Day hoc loan tluic chat la day hoat dting (HD) c h u o n g trinh THCS luen iuinli
loiin hgc nham tich c u e luia I ID hoc tiip cua , j-,^^,,^ |^^-,., ,|^^^, ^,,,^1^ 1^^,,-.,^^ ^^^., ,^^^, p|^„,„^„
ht.ie smh (HS) HS la ehu tht- eua HD hoc ^ i ^ ^ ^^^^^ |,^^^ ^.^^^ ^^^^ 1^^^^ ,^^,^,, ^-^^^^ 1,^^^ ^-^^
pluil diKTc cuon luil viio n h u n e I ID hoc lap, tu , „
lue kham pha kicn thirc, Giao vien ( G V ) la
ngiroi thiet ke, tti chiic va chi dao HD hoc tap Khai thiic Itii giai biii Ifip loan plu Mtil lron^ nhiing muc dich dav hoc Toan o theo nhiing dinh hirting phiin lich, king hgp irudng pho thong la giiip HS phal trifiii niing ^iic du kit:ii e o ban trong bai toiin luc va icn luyen cac phiim chat iri lue ren + Khai tluic I61 giiii bai tap toiin phu hap voi luyt:ii III duy logic vii ngon n g u chinh \iic dtii t u o n g HS de dat d u o c nhung yeu ciiii co phiil trien kha niing suy doan va l u o n g tuong, ban vc kien thue kT nang nham htii duiing ren luyen nhu'ng IID tri tue co biin ya hinh nhimg veu tti cua P C T T
thiinh nhiing PCTT, T r o n g giiii lOiin, tiutSc Titih^lmh h o a i c u a t r i t u e
lien phai bicl nhin bai toiin nuil c i c h khiii
qiiiil, phiin lich ciii da eho va ciii can lim dc
ihiiy dime mtii lit:n he giua cluing Sau dti dua
vao Ciic kicui thiic dii ITnh hoi HS viui dung *) Kha niing ihiiy doi phutuig huting giai linh luiat, dgc liip de lim d u a c cac ldi giai quyel van de plui hop vtii sir ihay diii cua ciic khiic nhau cua biii loan, lim ra liri giai luiy dieu kien, biet tim ra p h u o n g luiong mtii de
nhal Siing liio nhat, Vi viiy, vice htii duting nghien ciiu va giai qiiyC-i \dn de, kluic pluic
^^^ duii dti diip kluitin llict) m.iii dnih siin, m,i\
riini li hoe clio rang, tinh Imh hoai cua Iri Uu du'oc bit}ii luen
Trang 2") Kha nang nhin nhan mgt van de mot hien
tirong duoi nhieu khia canh hay goc do quan
diem khac nhau,
*) Kha nang xac lap su phu thuoc ciia cac
kien thirc theo mgl trat tu ngugc vai each da
biet (tinh thuan nghich cua qua trinh tu' duy),
Trong qua trinh khai ihac de tim toi nhieu loi
giai cho mgl bai loan HS phai van dung cac
kien thirc von cd va tu duy linh boat de phan
tich vice giai loan doi khi con la sir mo mam
du doan tii do lim ra con duong ngan nhat, Su
tim toi khai thac tim nhieu I6"i giai cho bai
toiiii cung phan anh dugc nhung yeu to linh
hoat doc lap va sang tao ctia tu duy
linh linh hoat la pham dial can thiet doi vai
HS trong giai loan, no guip cho HS co kha
niing thay doi phuong hii'ii"ng giai quyel van
tie lim la huong di moi de dang chuyen tir boat
dting ll i tue (I IDTT) niiy sang HDTT khac,
Tinh doc lap
linh dgc lap cua tu duy the hien a kha nang
lu minh nhin tha; van dc phai giai quyet, Ur
minh lim ra loi giai dap cho van de do, Ngoai
r;i tinh dgc lap lien he mat thiet voi tinh phe
pluin eiia lu duy,
Btii dining kha nang IID tu duy dtic lap cho
IIS de ehicm lIiili kien thuc la each hicu qua
nluit dc Ciic em hieu duoc kicn thuc mot each
•liiu ^i.ic Vii cti y tluic
1 inh dpc liip cua HS con bieu bien a kha nang
titic lap suy nghT, biel each to chiic cong v iec
cua minh mtit Ciicli hap li duoi su huong dan
giiip dti'cua GV
Tinh Min<; tao
Ta thiiy linh linh boat, tinh dpc lap tinh phe
phiin cua Iri lue lii dieu kien can thiel cua tu
duy Siing lao
Tinh Siing lao cua lu duy the hien ci' kha nang
lao ra ca\ moi, phat hicn van de inai tim ra
huting di mtii tao ra kel qua moi
Ngt)iii ra tinh sang tao bat nguon tir long sav
me hoc lap, ham muon hieu biel bien no thanh
nuil nhu cau mgl iiiein vui lan ctia cugc song
Tir cho biel phan lich tim loi giai bai loan HS
ctin cd kha nang tu duy de tao ra cai moi tim
ra hirdng di mdi Boi dudng yeu to nay can khuyen khich HS tim ra nhieu Idi giai khac nhau cua mot bai toan dieu nay dua den viec cac em phai so sanh va lua chpn loi giai hay nhat dep nhat dong thdi boi dudng cho HS kha nang khai thac sang tao ra bai toan mdi MOT SO BIEN PHAP BOI D U O N G NHUNG YKU TO CUA PCTT
- Ren luyen cho HS kha nang nhin nhan phan tich danh gia mgt hien tuong dirdi nhieu khia canh goc do quan diem khac nhau, kha nang thay doi phuo'ng huong giai quyel van de phii hpp VOI su thay doi ciia cac dii kien, biet tim
ra huong mdi, de dang chuyen lii HDTT nay sang HDT"r khac, khac phuc sir dap khuan may moc, suy nghT theo duong mon,
- Khuyen khich lim nhicu Idi giai khac nhau cua mot bai loan, doi hoi HS chuyen tir phuong phap (PP) nay sang PP khac, tir thao lac tri tue nay sang thao tac tri luc khac boi duong cho HS kha nang di chuyen nhanli chong lir tu duy thuan sang tu duy nghjch
- Tap dugl cho IIS bict du doan suy luan co
li de tu minh phat hien van dc du doan duoc ket qua, tim dugc ldi giai bai loan Lua chon bai loan khting mau muc, Ren luyen cho HS co thoi quen khdng tim ldi giai san
BOI DUONG PCTT CHO I IS QUA DAY 1 IOC KHAI THAC L6I GIAI BAI TAP TOAN Trong pham vi cua bai bao nay, khai ihac Icri giai bai tap toan de giiip hgc sinh nghien ci'ru cac du kien de phan lich bien doi bai loan nham tim dutTC nlueu Idi giai khac nhau hoac
de \uat bai loan mdi, Muon Viiy irudc hcl MS can nam duoc cac kicn llu'rc eg ban trong bai loan do, dong thdi phiii co cai nhin linh hoat biel long hgp npi dung bai loan dutVi nhirng goe do va tinh huong cu llie, Viec khai thac Idi giai bai tap loan vdi nhirng dung y khac nhau va co nhieu y ngliTa
O day ta di sau vao viec day IIS khai thac ldi giai bai lap loan vdi dung y boi dudng cho HS tinh linh hoat dgc lap sang tao nhirng yeu to col loi ciia PCTl
Trang 3Co the tha\ \ icc boi dircmg PCTT cho HS j j n g pT ,Jf{x) = g(x) trong do f'(\) i i ( \ | la
qua da> hoc cacli khai thac tim loi giai bai tap ^ ^ j ^ , „,.,^ (,5^ „l,5, „|,^, ^ j ^ ,^ ^^ ^ ^ 1 , ^ j ^ ,
I " * " sau; khac nhu sau:
Giai phuong trinh
Ta CO V^ X' - 2x - X' -t- 2.V ^ 3
73-{-v'+2.V) =.v'+2.V + 3 (2)
\'3 - V" - 2.V - X' + 2.V + 3
PhAn tich
Ta nhan tlia\ bai loan co dang " " ' -^" + '' = ' 'a co
) fix) = ^ ' ( - \ ' ) nen ta nghT toi viec tint dieu ( - )
kien de -) f ix) co nghTa binli phuong hai \ e ^^ J l ^ T T = / ^ ~, <= J ' ^ ' ^ "
dc khir can thuc dua bai toan ve phirong trinh j.", - f ^ (/ ^ 3)
CO ban da biet each giai
N'lui \ay ta co the giai bai loan nhu sau
I a CO \/3 - - -v" - 2.V = -Y" + 2.V + 3
/ > - 3
r + 7/ + 6 = C
:2i-*3>(l
r 2r-(v i2\-i.f
=> v" + 2.V -3-|,r+2i)4\-+2i| -l^(.r+2tJ4i; (nghiem kep)
Va> phuong trinh dii
«= (-V + 1)" = 0 o V ^ - 1
) mot nuhieni la
j V v e / f
| ( v ' - l 2 v ) ' + 7 ( v - + 2 v ) + 6=;() (11
Vc trai ciia ( I ) \uat hien nlian tu chung
.•'+2.V
Dal X +2\ = t thi phuong trinii (1) do
Ihanh phuong trinll bac 2 an t
c ^ - 1 Ciing \ 6 i huong phan tfch nhu lien, neu nhin nhiin linh hoat hicu (hue duoi d^ii can l;T lam Ihuc bac : IIS co ihO lach
v ' + 2 Y - 3 = (3 V 2 v ) + 6 de CO loi giai khiTc cho bai tt^aii
I a CO 73-.V 2.V .V +2.v( 3
o i Y - x - 2 Y - - - ( 3 I -2.VI + 6 (."ll
Dill v " 3 - v 2 v = / 1 / > 0 | thi phuong trinh (3) tro Ihanlr
<>l +11+ h- 0 <
Vni / = - ! : : : >
v't2v=-lt>.i-'+2v+l=0o(.v+l)"- ()< >.v=-l
(nghicin kep)
\ o i / = - 6 - >
\ - ' i l v ^ - 6 » r - i 2 v 4 6 ( I < > ( T - I | 4 5 = 0
(\o nghiem)
Nen phirong trinh d.a cho co nghiein la
V ^ • 1
\ e i i hep tiic nhin nhan cac \ c i i to o hai \ e cua
I ' I IIS phan lich \i\ nhan thav bieu lliuc
h - x ' - l x - - ^J•'3- ( V - + 2 v ) Khi do hai ^ -\
\e Ciia phirong trinh co chung bicu dure \ i^.^- nhin nhan ^.i, du kien clio iroin.; bai
/ - -C + 6 c^r +t- 6 = l)c >-^
< o ( v + l ) " = ( 1 < > V - 1 m g h i c m k c p l
\',i> pluioiie Innh da cho co moi iiglucni
Trang 4irinh da cho vc dang x ' + 2 x + l = 0 hudng
HS den viee phan tich hai vc ciia PT de cung
xuat hien bieu thuc chung (x + l)" de tiiu ra
each tliai khac
I a co;
V3 - -V - 2.V - x~ + 2.V + 3
> v / 4 ^ x + \)- =(.v + l)- + 2 (4)
Dat (.v + l ) - = / { / > 0 ) thi phirtTng uinh
( 4 ) t r a thanh
Voi I 0 =-,^(A-+I)' =0<i^_v = - ]
(iigliic;m kep)
Viiy phuang trinh di"! eho cti mtit nghiem la
.V = - 1
Vdi Ciich giai nay ta co phuong irinh
/" + 5/ = 0 (/ > 0 ) , day la phirong trinh cti
iighicm duy nhal, goi y HS di chirng minh (4)
CO nghiem duv nhal vii do cimg la nghieni duv
nhiil ciia phutTiig Irinh ban dau biing ciich
nhiim nghiem
Cdch 5 Bicn titii Iun ve lam \ual luen {,\ i ! ]
, diii iin phu de qui vt; PT co ban ytii iin phu
Ta CO Vr - X - 2x = x" + 2.V + 3
c ^ 7 4 - ( A " + ] ) - =(.v + l)-' + 2 (4)
Dal Cv+I)- = / (/ > ( ) ) Ihi (4)
<r> V'4 - / = / 1-2 (5)
DiCnikien: 0 < / < 4
ra Ihiiy 1 = 0 hi nghitjni cua phuang trinli (5)
I [ T - ^.fJ^t < 2
\rp - / + 2 > 2
phutmg trinh (5) vti nghiem tren mien
0 < / < 4
\ay 1 0 lit nghiem duy nhal cua phuong
irinh (5)
Vdi 0 < / < 4
<=^x+l)'=0<=:>Y=-l
Vay phirting trinh da cho c6 mgt nghiem Y - - I ~
Nhu vay bang viec dat an phu tuang tir ta dira dugc PT ve he phuong trinh hai an biet each giai
v 3 - v " -2.V = II
[x~ + 2.V + 3 = V
do ta CO he phuong irinh"
ft.=v | t , = v [Li Av=6[ir +11-6^0
(vi I/.V>0)
Voi u == y =2 la co:
j3'-.v -2v=4 Jx'+2x+l=0
l.r+Zv+3=2 ^ r i 2 v + l = 0 (nghiem kt:p)
Vay phuong irinh dii cho co mtil nghiem la V = - I ,
Vay dirng irutic mtil bai toiin doi hoi HS phai biet phan lich bai lOiiii nhin bai loan dudi nhieu khia canh de tim ra nhieu Idi giai khac nhau cho mot bai toiin Vice tim loi phan lich cac dicu kien bai loan theo cac hudng khac nhau gliip htic sinh tim ra dugc Idi giai hay ngan gon mang tinh sang liio Qua do sir linh hoat, su doc lap trong suy ngliT duac ren luyen boi dirdng vii phat trien, Khi HS hnh hoat trong khai thac lim nhicu Idi giai bai toan giiip HS nam chac kien llu'rc ca ban dong thcri bdi dirong eho HS each viin dung kicn thirc mgl each mem deo hnh hoat suy luan hgp 16 gic de phan lieh bien doi bai loiin lim ra hudng giai quyet cung nhu c6 nhirng ldi giai hay, dong thdi de ,\ual dirac nhung bai loan mdi Vdi each nhin nhan suy nghT nhu Iren
HS giai duac cac bai loan urang ur nhu sau: Giai phuong trinh
2.V- + 3x + sJ2x- + 3.Y + 9 = 33
Trang 5Kcl luan Tinh linh hoat tinh dtic lap tinh
phe phan cua Iri liie la yeu to quan trgng giiip
HS tim ra nhieu ldi giai bai loan BSng nhii"ng
each nhin linh hoat va sang t a o phan tich kT
cac diJ kien bai loan HS se khai thac lim d u o e
nhieu Idi giai qua d o cac kien thuc kT nang
dutic cung CO va nang c a o Tir cho HS biel
each phan tich tim ra nhieu Idi giai bai toan
HS eiing CO kha nang phat trien l u duy tao ra
eai mdi, phat hien van de nidi, lim ra h u d n g
dl mdi tao ra kel qua mdi diic riit kinh
nghiem trong giai loan, qua d o nhirng dire
tinh: linh boat, doc lap sang lao d u g c boi
d u d n g va phat trien
Boi d u o n g ren luyen cho HS nhirng yeu td
eua PCTT la khau quan trpng va vo cimg can
thiel trong xu the day hpc hien nay Doi vdi
ngu'di giao vien day loan ngoai nhiem vu
cung cap cho HS nhiing kien thiie va kT nang
CO ban dieu qun Irong can chii trgng khau
nay day la mgt trong nhiing dmh huong can
t h u c hien thirdng xuyen hen tuc trong qua trinh day hpc noi c h u n g va day hgc giai bai lap toan noi rieng gop phan doi mdi phirong phap day hgc bdi d u d n g cho HS kha nang lu hoc, tir nghien ciru nham nang cao chat lirong gianii day tronii nha trtrom: hien nay
IAI U l E U T H A M K H A O
1, Hoang Chung Phuong phap day hpc loan hoc a trudng pho thong trung hoc co so - Nxb Giao
duc-1 9 9 7 '
2, Pham (Ua Due Bui I kiy Ngoc, Pham Dire Quang PPDH ciic npi dung mtin loan
- Nxb DHSP, 2007
3 Nguyen Thai Hoe Ren luyen tu duy qua viec giai bai tap toan N \ b Giao due
4 Le Thong Nhai Ren luyen kT nang giai loan o THCS Nxb Giiio due
5 Tran Thiic Trinh Tir duy v a hoat dong loan hoc
Ha ngi2003
6 SGK SBT Toan THCS Nxb Giao dye 200.S,
S U M M A R Y
MINI^G MATH SOLUTION MFTTINt TRAININ(,
FOR STUDl'N IS SO.MI-: I I I M T N T S OF INTKIJ.Ff I I \ l Q l \i.l l\
Ho Thi MaiPhuonji
>l!ei.y t,l I Jnumon - l \ l
hilellecUial quahlics is one of the essentials I learning, acquiring knowledge iraimng skills meel ihc demands of hie Hxercise is a matheniiilical conlcni lo loslcr opporiunilics for sludci
students to analy/e problems, look at die factois that have die diffcieni relationship, said ma
developed to detecl new problems, liuding new diieciion^ cicale new rcsulls lliesc acUvili conliibute to Ihe inielieclual qualily training for sludenls in order in improve the effectiveness leaching and ledtning in schools lodiiy
Key yyord: To esploil die answers of malhemalical exeicises the irainin-e, some elements iiilcllecluat quality
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Plum hiin kluui hoc: IS Bin lln Hanh ldm Tnrdng Dai hoc Supham - Dll lhai \^i