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TIEP CAN NHAN CHIING HOC TRONG DIDACTIC TOAN
Nguydn Phii Loc' va Diep Van Hoang^
' Khoa Suphgm, Trudng Dgi hgc Cdn Tha
^ Ldp Cao hgc khda 19 - Chuyin ngdnh Ly lugn vd Phucmg phdp dgy hgc bg mdn Todn, Khoa Suphgm
Thong tin chung:
Ngdy nhgn: 03/05/2014
Ngdy chdp nhgn: 29/08/2014
Title:
Mathematical organizations
of sine theorem: An
investigation based on an
anthropological approach
into mathematical didactics
Tu khda:
Dfnh ly sin, dgy hgc djnh ly,
to chiec todn hgc, didactic
todn, tiip can nhdn chiing
trong Didactic todn
Keywords:
Sine theorem, theorem
teaching, mathematical
organization, mathematical
didactics, anthropological
approach into mathematical
didactics
ABSTRACT
Sine theorem in the triangle is an important theorem in geometry curriculum in secondary schools Content of this theorem indicates the relationship between the angles, edges and circumscribed circle's radius
in a Piangle Thus, in applications to sine theorem for problem solving, it
is possible to change a problem on the relationship among the sides of the triangle to the problem on the relationship among the angles and vice versa In addition, the sine theorem has many practical applications; it is
an opportunity that teachers can take advantage of to educate "realistic mathematics" for their students Sine theorem has many meanings as stated, what are mathematical organizations of the theorem in current textbooks? While solving the problems, have stiuients used this theorem as
a strategy? This paper will report the results of investigations of into textbooks and students in Phan Ngoc Hien secondary school, Bac Lieu province
Dinh ly sin trong tam gidc la mgt nhdng dinh ly quan trgng trong chuang trinh Hinh hgc a trudng trung hgc phd thdng Ngi dung dinh ly ndy^ biiu thi mdi quan hi giiia cdc gdc, cgnh vd ban kinh vdng tidn ngogi tiip ciia chuyin ddi bdi todn vi mdi liin hi giiia cdc cgnh cita tam gidc sang bdi todn biiu thi mdi lien he giiia cdc gdc vd ngugc lgi Ngodi ra, dinh ly sin
cd nhiiu ung dyng trong thuc liin; ddy la ca hdi md gido vien cd the tdn dung di gido dye tinh thuc tiin cua todn hgc cho hgc sinh Dinh ly sin cd nhieu y nghta nhu da neu, thi thi cdc "td chirc todn hgc " dinh ly sin trong sdch gido khoa hiin hdnh ra sao? Trong gidi todn vi tam gidc, hgc sinh co khuynh hudng chgn dinh ly sin nhu Id mgt chiin luge gidi hay khdng? Bdi bdo se tudng thudt kit qud khdo sdt sdch gido khoa vd khdo sdt hgc sinh d Trudng trung hgc phd thdng Phan Nggc Hien, tinh Bgc Lieu
1 CO S d L Y THUYET
Ll Tidp cdn nhSn chdng hi^c trong Didactic to^n
Tiep cdn nhan chiing hpc ttong Didactic toan
tdp trung nghidn cftu mdi quan he gifta tti thftc va
toan hpc dugc xem nhu mOt sinh vdt sdi^; do v^y,
nd cung trdi qua cac giai doan: phat sinh, tdn tgi, phdt ttidn, mat di MOt doi tugng todn hpc khdng thd "sdng" ddc lap, md nd ludn cd nhieu mdi quan
he vdi cdc ddi tugng khdc vd gan lien vdi thd chd
Trang 2ma ddi tugng nay ndm ttong Y ChevaUard (1992)
da vidt: "MOt tri tiiftc khdng tdn tgi ttong xd hOi
"rong", mgi tri thftc ddu xudt hidn d mot thdi didm
xdc dinh, trong mdt thd chd va dugc edm sau vao
mOt trong nhidu thd chd" (ddn theo (Trdn Anh
Dung, 2013))
Do cdch nhin nhdn vd tri thftc nhu ttdn ndn cdch
tidp can nhan chftng hpc ttong Didactic todn nghien
cftu xoay quanh hai khdi nidm "tri thftc" vd "thd
chd", vd nd dugc cu thd hda thdnh ba ngi dung
nghien cuu chinh la: Ly thuydt vd chuydn ddi
didactic (Nguydn Phu Lpc, 2008), ly tiiuydt vd
quan hd thd chd vd quan hp cd nhdn (Bessot vd ctv,
2010), vd td chftc todn hpc (Bessot vd ctv., 2010;
TrdnAnh Dung, 2013))
Trong khudn khd bdi bdo nay, chftng tdi chi de
cap vd dp dyng eac lugn didm vd td chftc todn hpc
ttong Didactic todn
1.2 To chirc toan hpc
Tft quan didm xem hoat dOng toan hoc nhu mOt
hogt dpng cua con ngudi: chft thd thyc hidn mOt
Bl Kieu
nhiem vu (neu
dang toan can
xem xet)
B2 Ky thuat
(trinh bay each giai cho dang toan neu a Bl)
Cdch thuc thicc hien nhiem VM
(hoac qiiy trinh hdnh ddng di
hodn thdnh nhiem vu)
kidu nhidm vu ndo dd frong mdt tiid chd xdc dmh,
Y Chevallard (1999), tiieo (Bessot va ctv., 2010),
lap ludn rdng khi tien hanh mOt nhidm vu toan hpc, chu thd phai biet "each thftc" thyc hidn (know -how, hay praxis) vd dua ra rtiiirng ly gidi cho qud trinh hdnh ddng tten ca sd ly thuydt todn hpc lidn quan (knowledge, hay logos); vd tft dd dng da dua
ra khdi niem "td chftc todn hpc" (tidng Anb: praxeology hoac organization; tidng Ph^: praxeologie) gdm bdn thdnh phdn: kidu nhidm vy
T, ky thudt T, cdng nghd 0, ly thuydt 0 va dupe
md hinh hda nhu sau:
Md hinh nay ed y nghia Id: mdi boat dOng ciia con ngudi ddu nhdm thyc hidn nhidm vy t tiiupc
kidu nhidm vu T nao nd nhd sft dung ky thudt T,
T dugc gidi thich bdi cdng nghd 0 vd cudi cung cdng nghd d duge hpp tiiuc hda bdi IJ thuydt 0
Nhu vdy, md hinh (1) cd the didn gidi Igi nhu sau (xem Hinh 1)
B3 Cong nghe
(neu ra cac tri thuc Iam ca scr;
ly giai cho ky
thuat giai a B2)
B4 Ly thuyet
(hop thiic hoa trithucab.3; chi ro ly thuydt lam CO sor cho
tri thuc d B3)
Tri thiic vd ly thityet duac dung
ly gidi cho cdch thuc thuc hien nhiem vw
Hinh I: Sof dd dien giai "td chirc toan hpc" (praxeology) frong Didactic toan theo cdch tidp c$n nhdn
chung hpc
2 PHAT BIEU VAN DE NGHIEN CUtJ
Dinh ly sin ttong tam giac (Hinh hpc 10), mdt
dinh IJ "da ddng thftc", nd bidu thj mdi quan h?
gifta ba cgnh vdi ba gdc vd ca ban kinh vdng ttdn
ngo^ tidp efta mdt tam g i ^ Cftng vdi djnh ly
eosin, dinh ly sm ludn cd mat ttong cac sach giao
khoa ve Hinh hpc qua cdc th6i ky khac nhau eua
vide thay ddi sdch Do dinh ly sin cd vi tti quan
ttpng ttong chuong trinh HInh hpc nhu vdy, vd
Didactic toan cho phep chftng ta thyc hi^n nhftng khao cim vd td chftc toan hpc xoay quanh mdt doi tugng toan hgc mOt cdch sdu sdc Dd gdp phdn hidu quan ddn dinh Iy sin, chung tdi khdo sdt dinh ly sin vdi hai cdu hdi nghidn ctiu sau ddy:
Cdu hoi thu nhdt: Theo cdch tidp can nhdn
chftng hpc ttong Didactic toan, td chftc toan hpc ddi vdi djnh Iy sin ttong ttong hai bd sdch giao
Trang 3Cdu hdi thu hai: Sau khi hpc djnh Iy sin mdt
thai gian dai, khi giai tam gidc cd nhidu hpc sinh
dp dung dinh ly sin dd gidi hay khdng? Va thyc td
vide sft dyng djnh ly sin ttong ttinh bdy ldi gidi
todn cua cdc em hpc smh ra sao?
3 PHU'CfNG PHAP NGHIEN CUtJ VA
D 6 I TU*ONG KHAO SAT
- Phan tich npi dung (Nguydn Phu LOc,
2014); Phan ti'ch nOi dung todn hgc lidn quan
ddn dinh IJ sin ttong Chung tdi phdn tieh cdc sdch
sau ddy:
Mi; Ei; Gi ldn lugt la Hinh hoc 10 - ndng
cao (Vdn Nhu Cuong va ctv., 2006a), Bai tap Hinh
hpc 10 - nang cao (Vdn Nhu Cuang vd ctv.,
2006b), Hinh hpc 10 nang cao -Sach giao vidn
(Vdn Nhu Cuong va ctv., 2006c)
Mi; E2; G2 ldn lugt la Hinb hpc 10 (Trdn Van
Hao vd ctv., 2006a), Bdi tdp Hinh hpc 10 (Trdn
Vdn Hao vd ctv., 2006b), Hinh hgc 10 - Sdch giao
vidn (Trdn Vdn Hgo vd ctv., 2006c)
~ Thd nghi$m su ph^m: Xay dyng mdt tmh
hudng thft nghidm Id mpt bai todn gidi tam gidc vdi
nhidu dft kidn cho phdp gidi bdng mdt sd cdch khdc
nliau, ttong dd cd cdch dp dyng dinli IJ sin nhdm
kidm nghipm xem hgc sinh uu tidn ehpn each van
dyng dinh IJ sin vdo gidi todn, hay khdng vd tiiuc
tidn ap dung dinh IJ sin trong Idi gidi ra sao Vdi
myc dich kidm nghidm ndu trdn, bdi todn dugc dua
ra thft nghiem se cd cdc bidn tinh hudng sau day:
VI: Cho cdc ydu td xdc djnli mOt tam gidc Tinh
cdc ydu td cdn lai
VI nhgn ba gid tri:
VI.1: Bidt hai canh vd-mpt-gdcikep-gijia.—
Tinh canh thft ba
VI.2: Bidt hai gdc, mOt cgnh kep gifta
ho|c bdn kinh vdng trdn ngogi tidp Tinh hai
canh cdn lai
V1.3: Bidt ba canh Tinh cac gdc
V2: Cho bidt didn tich eua tam gidc Tinh mdt
canh hoac mOt gdc eua tam gidc
V2 nhdn ba gid tri:
V2.1 Bidt dipn tich, mpt gdc va mOt cgnh
kd Tinh cgnh kd cdn lai
V2.2 Bidt di?n tich, hai cgnh Tinh gdc kep
gifta
V2.3 Bidt dien tfch, hai canh vd bdn kinh
Tu phdn tich ndu tten ve VI, V2 vd V3, ttong tinh hudng thu nghidm ma chung tdi dua ra se cd hai bidn VI, V2 , vd cdc gia tti dugc chgn Id: VI.1
vd V1.2 va V2.1 V2.3 Cu tiid nhu sau:
"Cho tam gidc ABC, bidt AB= c=3, AC=b=2,
- ^/^
^ = 60 , smB = , ban kinh dudng ttdn ngoai
7
^121 Syji
tiep R va dien ti'ch S
3 • 2 Tinh dO dai canh BC (= a)?"
(Thdi gian ldm bai 10 phut) Can cu vao the chd vd cdc td chftc toan hpc ddi vdi dinh ly sin, chiing tdi tidn dodn bdi toan ttdn cd the dugc hgc sinh giai bang eac chidn luge sau day:
Chiin luac SI (VI, V1.2): Sft dyng dinh IJ sin:
- ^ = 2R
sin^
Theo dinh li sin ta cd:
, , V2T,
= 2R.sin A = 2.^^^^.sin 60" = -Jl
sin A 3
CUen luge S2 (VI, VI.2)- S i dyng dinli ly sin;
a b
sin A sin 5
a b S.sinA 2.sin60°
- = x/7
— — ' W ^ =
-smA s i n 5 s i n 5 v 2 I Chidn luge S3 (VI, Vl.l): Sft dyng djnh li cosin
Theo dinh li cosin ta cd:
a^ =b^ -\-c^ - 2bc cos A
= 2 ^ + 3 ^ - 2 2 3 0 0 8 60" = 7
^a = ^
Chiin lugrc S4 (V2, V2.1, V2.3): Sft dyng cdng
thftc didn tich tam giac
Theo cdng thuc tinh didn tich tam gidc, ta cd:
1
S -—6csmA
2
Trang 4Hoac
^/21 3^/3
=> a =
4R be
Nhan dinh ban dau:
4.-= v/7
Chidn luge SI, S2 vd S3 cd tiie dugc nhidu
hpc sinh ehpn lya vi dp dung UTTC tidp dinh IJ sin
va cosin
Chidn luge S4 sd ed it hpc sinh lua ehpn vi
phdi su dyng cdng thftc tinh didn tich tam giac
1 abc
S=—be sm A (3) hoac S = (4) Hai cdng
2 4i?
thftc (3) vd (4) khdng tidn dyng cho bdi toan
ndu ttdn
- Phdng van gido viin (hinh thdc ddm dqo):
Phdng vdn ndm gido vidn cua trudng THPT Phan
Ngpc Hidn vd tiiyc td gidng day dinh IJ sin
- Boi tuang hgc sink dugtc khao sat: Hpc
sinli hai ldp flCI (N=38) vd 12Ci (N=36) thuOc
Trudng trung hpc phd thdng Phan Ngpc Hidn, tinh
Bgc Lieu Chiing tdi ehpn hpc sinh ldp 11 vd 12 vi
cdc em ndy da hpc xong dinh IJ sin trudc dd it nhdt
mOt nam Khao sat xem sau khi hpc dinh Iy mdt
thdi gian ddi, ttong gidi tam gidc cdc em thudng
ehpn lya cdng thftc ndo, cd van dung dinh IJ sin dt
gidi hay khdng?
4 KET QUA VA BAN LU^N
4.1 Td chftc todn hpc doi vdi dinh IJ sin
4.1.1 Kit qud
Qua phdn tich cac sach Mi; Ei; M2; E2, chung
tdi thu dugc kdt qud Id ed sau kidu nhidm vu xoay
quanh dinh IJ sin, cy the Id:
Tl: Tim dO dai canh efta tam gidc
T2: Tim sd do gdc cua tam giac
T3: Tim bdn kinh dudng ttdn ngogi tidp cua
tam gidc
T4: Gidi tam gidc
T5: Chiing minh ddng thftc
Te: LTng dyng tiiyc td
Kiiu nhidm vy Ti: Tim dO ddi canh khi bidt
trudc mdt cgnh vd hai gdc
Ky thugt T^: Ky thugt gidi quydt kidu nhi$m vu
gdm cdc budc sau:
Budc I: Tinh gdc cdn lai (ndu cgnh cdn tinh va cgnh dd bidt ldn lugt Id canh ddi eiia hai gdc thi bo qua budc 1)
a b 6.sinA
Budc 2: = ^ a = (gia sir
sin A sin S sin B
cdn tim cgnh a)
Cong nghe Or Sft dung dinh IJ sin
Ly thiQ>it &}• He thftc lugng ttong tam gidc
Vidu (7];r|):Xemvidu5,M2,ttang61 Kidu nhidm vu Ti: Tim sd do gdc cua tam gidc khi bidt hai canh vd mOt gdc
KJ thudt giai quydt Tj : Budc 1: Tim cgnh cdn lgi ddi didn vdi gdc dd eho (ndu tdn tfu mOt cap cgnh - gdc ddi didn till
bd qua budc 1)
Budc 2: a _ b _ > sin 5 = 6 sin A sin A sinB
(gid sft cdn tun gdc B)
Budc 3: Suy ra gid tti gdc B
Cong nghe Qf Sft dyng dinh ly sin
Ly thuyit &r He tiiuc lugi^ ttong tam gidc
Vi du vd (r2;r2) '• Xem bdi t§p 3, M| ttang 59
Kilu nhidm T3: Tim ban kinh dudng tton ngoai tidp cua tam giac
K? tiiudt 73:
Budc 1: Fim mgt cap gdc vd canh ddi dipn v<S nhau (ndu tdn tai mpt cap cgnh - gdc doi didn till bd qua budc I)
Budc 2:
2R-sin A 2 2R-sin A
Cdng nghi O3: Su dung dinh IJ sin
Ly thuyit Q3: He thftc lugng ttoi^ tam gidc
Vidu (r3;i-3):Xemhoatddng6,Mi, ti^g52 Kidu nhidm vy T4: Gidi tam gidc
- Kidu nhiem vy Tt^ Gidi tam giac khi biet
gdc A vd B va canh e
Trang 5Biroc 1: Tfnh goe C= 180°-(A+B)
Bttoc2:Tinhcanha:
a c
sin A sin C
Budc 3: Tinh cgnh b:
b c
sin B sin C
=>a =
=>b =
csinA sinC
csinS sinC
Budc3: TinhA=I80"-(B+C):
Cdng nghi O^c: Sft dung dinh IJ sin va tdng ba
gdc ttong efta mdt tam giac bdng 180°
Ly thuyet ©4c: He thuc lupng ttong tam giac
Vi du ( 2 ^ ; r ^ ) : Xem bai tap 34c, M2, ttang 66 Kidu nhi^m vu T5: Chung minh ddng tiiftc ttong tam gidc
Cdng nghi 04a: Sft dung dinh Iy sin vd tdng ba
gdc ttong cua mdt tam giac bdng 180"
Ly thuyit 04a: He thftc lugng ttong tam gidc
Vi du(2^;r4^): Xem bai tdp 33a, M2, ttang 66
Kidu nhiem vy T4b: Gidi tam gidc khi bidt gdc
A, gdc C vd cgnh c
Ky thugt T^l^:
Budc 1: Tinh gdc B= 180" - (A+C)
Budc 2: Tinh canh a:
a _ c _ csinA
sin A sin C sin C
Budc 3: TInli canh b:
b e
sin B sin C
cs'mB
sinC
Cdng nghi 04b: Sft dung dinh IJ sin vd tdng ba
gdc trong cua mdt tam gidc bdng 180"
Ly thuyit 04i,: He thuc lugng ttong tam gidc
Vl dy (^;r^j): Xem bdi tap 33c, M2, trang 66
Kidu nhiem vu Tjc: Giai tam giac khi bidt gdc
C, cgnh a vd b
Ky thugt T, : Theo thft ty cdc budc sau:
Budc 1: Tinh cgnh theo djnh li cosin:
r^ =a^+b^-2ab.cosC
Budc 2: Tinh gdc B:
b c „ 6sinC
sin 5 sinC c
Ky tiiudt giai T^ : Theo tiiu ty cdc budc sau:
Budc 1: Xac dinh hudng (chidn luge) chiing minh:
- Bidn ddi vd trdi thdnh ve phdi (hodc nguac
¥)
Chftng minh "Vd trai - Vd phai = 0" _ _ Chiing minh vd phdi vd ve trdi ciing bdng C Budc 2: LTi^ dung dinh li sin vd kidn thftc lidn quan dd bidn ddi suy ra dieu phdi chftng minh
Cdng nghi O5: Sft dyng dinh IJ sin vd cdc cdch
gidi mdt ddng thftc
Ly thuyet 0^: Hd thftc lugng trong tam gidc,
cdc tinh chat dang thuc vd quy tdc dien djch
Vi dy (T^;TA '• Xem vi du 4, M2, trang 5
Kidu nhidm vu Te: Gidi bdi toan thyc td
Ky tiiugt giai T^ : Theo thft ty cdc budc sau:
Budc 1: Chuydn bdi todn thyc td vd bai todn gidi tam gidc
Budc 2:Tun each gidi bai toanxtam^giac- phdt_ bidu ttong Budc I -,-v—w- ™r,,
Cdng nghe 06: Dinh li sin vd cdc ky thugt
ndu tten
Ly thuyit 0c: He thuc lugng ttong tam gidc
Vi du (r^; r^): Vi du 3, M2, trang 56:
Tit vi tri AvdB cua mdt tda nhd, ngudi ta quan sdt dinh C cua mdt nggn niii Biit rdng dg cao AB
Id 70 m, phuong nhin AC tgo vdi phuang ndm ngang gdc 30", phucmg nhin BC tgo vdi phuang nam ngang goe 15°30' Hoi nggn nui do cao bao nhiiu met so vai mat ddt?
Trang 6c
Thong ki kiiu nhiim vu
Trong Bdng 1 dudi day, chung tdi thdng kd sd
bai tgp thupc mdi td chftc todn hpc dd dugc chi rd d
ttdn Bang tiidng kd ndy bao gdm 136 bdi toan dugc
phan thanh 06 kieu nhidm vy cau hdi, trong do:
B a n g 1: T h d u g kd theo bai t d p theo kidu nhidm vu
Cd 2 0 cdu Id nhiing vi dy vd boat dOog co mat ttong phdn IJ thuydt efta M j , M2
Cd 116 cdu d u g c d e nghj ttong phdn bai iSp
ciia M l , M2 vd El,
£2-K i l u nhi£m vu
T,
Tim do dai canh cua
tam gidc
• ' • 2
Tim so do goe ciia
tam gidc
Ts
Tim ban kinh duong
tron ngoai tiep tam
fiiac
T
Giai tam gidc
Tj
Chijmg minh ddng
thijc trong tam gidc
T6
LTng dung th\TC te
TSne cans
Ky
thuat
n
2"2
T
h
^5
^6
6
Vidu
- Hoat dong
3
2
4
5
2
4
20
Bai Trong tap
Ml
4
2
5
3
2
16
Bai trong tap
!Vl!
7
4
4
8
3
3
29
Bai t a p troDg E l
9
7
7
7
3
33
Bai t a p Tong so
t r o n g E l bai tSp
4
5
8
10
6
5
38
24
18
24
28
9
13 13<
4.1.2 Bdn lugn
Td chftc todn hpc ddi vdi djnh IJ sin ttong hai
sach dugc khdo sdt nhin chung Id t u a n g ddng nhau
Hai sdch deu d u a ra 6 kidu nhidm vu (dang todn)
eho dinh ly sin Cd hai sdch ddu cd quan tdm d u a ra
ftng dung efta dinh ly sin Nhin chung, cac tdc gid
sach gido khoa qudn ttidt tinh thdn ddi mdi giao
dye Cdc kieu nhidm vu d m u c dO van dung cdp
tiiap, khdng "sa ldy" vdo cdc dgng bai t§p phuc tap
vd qud khd
4.2 K d t q u a k h a o sdt viec v a n d u n g d i n h li sin ciia hpc sinh
4.2.1 Kit qud khdo sdt
Kdt qud lam bai eua h p c sinh ddi vdi bdi todn
md chung tdi d u a ra t h u nghiem hpc sinh (dk bai d
m u c 3) d u g c tdng kdt n h u sau (xem Bang 2):
Trang 7^^Pg 2: Bang thdng ke ve chien luge giai
Ldp SI sd Dinh Ii sin
sin A sin B
y5m.A )
Dinh li cosin Cdng thirc didn tich tam giac
(0,0%)
(0,0%)
4.2.2 Bdn ludn
Dya vao kdt qua thu dugc (Bang 2) vd vide xem
xet bdi ldm efta bpc sinh, chftng tdi cd mOt sd y
kien ban ludn sau ddy
- Tdt cd hoc sinh (74 em) ddu lam bdi: 58 hpc
sinh ehpn chidn luge dinh Ii cosin nhimg ttong tinh
Trong khi dd, chl cd 16 hpc sinh ehpn chidn luge
dinh li sin: 11 em sft dyng ddng thftc:
= 2R trong djnh Ii sin dd gidi bdi toan vd 05
sin A
hpc sinh cdn lai thi chgn ddng thftc:
a b
= ; cd 16 Idi gidi dung vd cho kdt qua
sin A sin B
chinh xde
- Hpc sinh cd Idiuynh hudng su dung dinh ly
cosin de gidi tam gidc han Id dp dyng dinh IJ sin:
73% d Idp 1 ICi vd 83% d Idp 12C,
De IJ gidi thyc tidn neu tren, chiing tdi da ttao
doi vdi mdt so giao vien eua trudng ndy dd timg
dgy ldp 10, vd J kidn eua cac tiidy vd cd nhu sau:
- Khi ldn ldp, chl ddnh khoang 15 phut eho
gidng gidi nOi dung djnh Ii sin (theo J kidn cda thdy
L.T.LvdcdV.T.X.M)
- Dinh li sin ngdn gpn; ndn vide tiep can
hai klid, trim tugng (theo J kien cua thdy N.N.P),
vi vdy chi ydu cdu hpc sinh thira nhdn dinh Ii vd
bidt cdch dp dung, khdng cdn chiing minh (vi nd
rudm ra)
Dinh Ii sin khdng duge su dyng rtiiidu ttong
chuang ttinh Todn 10 va cdc ldp kd tidp (theo J
kidn cua ed P.A.T.H) Vi the khi gidng dgy, nd it
dugc quan tdm, mang tinh ddi phd eho du chuang
trinh
- Nhittig djnh Ii mang ti'nh chdt "da ddng
thftc" nhu djnh li sin thi HS thudng gap khd khdn
ttong van dyng gidi bdi tgp, vi thd ttong kidm tra 1
tiet hay thi hpc Id thudng bgn che cho bdi tap ed lidn quan ddn dinh li sin (theo J kidn cua thdy T.T.H), do vay dinh li sin dang bi xem nhe vd ting dung ciia nd dang bi "thu hep" ddn
Ket qud khdo sat va vdi cac J kien efta gido vidn, dinh IJ sin khdng phdi la nOi dung ttpng tdm cua chuang ttinh toan hpc phd thdng Gido vien khdng danh nhidu thdi gian luydn tap cho hpc sinh Tuy vay, ttong thyc td khao sdt vdn cd 16/74 (21, 62%) em sft dung dinh IJ sin vao gidi todn va tdt cd deu ttinh bdy Idi giai chinh xdc Didu ndy ndi ldn rang dinh ly sin khdng phdi la ndi dung khd nhd vd kho van dung so vdi dinh Iy cosin
5 KET LUAN Qua ket qua nghien cftu thu dugc ddi vdi dinh
IJ sin - mdt ddi tugng toan hpc- nhu da tudng thudt sat cac td chuc toan hoc doi vdi mdt ddi tugng todn hpc ttong mOt thd chd xdc djnh theo hudng tiep cdn nhan chiing hpc ttong Didactic todn sd cho giao vidn toan thay mgt cdch toan didn cae kieu nhidm
vy tuong ling vdi ddi tugng todn hpc dd Vd sy van dung dinh Iy sin, dft cd it hpc sinh uu tien vdn dyng dinh ly sin ttong gidi todn nhung nhiing em vdn dyng dinh IJ sin vdo gidi todn ddu cho ldi gidi dftng Do vdy, gido vidn cdn cd cdc chien luge day hpc sao cho hgc sinh quan tam hon vide van dyng cao chdt lugng vide day hgc todn efta minh
TAI LIEU THAM KHAO
I Bessot, A., Comiti, C , Le Thi Hoai Chdu,
Ld Van Tien, 2010 Nhftng ydu td ca ban ciia Didactic toan NXB Dai hpc qudc gia
TP Hd Chi Minh
^ Van Nhu Cuong & cfv, 2006a Hinh hpc
10 ndng cao NXB Gido due Ha NOi
3 VanNhuCuang&cft', 2006b Bdi tdp hinh hpc 10 nang eao NXB Gido due Hd Npi
Trang 84 Van Nhu Cuong & c/v, 2006c Hinh hpc
10 ndng cao - Sach gido vidn NXB Giao
due Ha NOi
5 Trdn Anh Dung, 2013 Day hpc khai nidm
ham sd Udn tuc d trudng trung hpc phd
thdng Ludn dn tidn sT, Tnrdng Dai hpc su
phgm TP Hd Chi Minh
6 Trdn van Hao &C/V, 2006a-Hinh hpc 10
NXB Gido due HaNoi
7 Trdn VdnHao&c/v, 2006b Bdi tap Hinh hgc 10 NXB Giao dye Hd Ndi
8 Trdn Vdn Hao &C/V, 2006c Hmh hpc 10-Sdch gido vien NXB Gido dye Ha
NOi-9 Nguydn Phu Lpc, 2008 Gido trinh joi hudng dsQ' hoc khdng truydn tiidng.Trudng Dai hpc can Tha
10 Nguydn Phft Lpc, 2014 Phuong phap nghien cftu ttong Giao due NXB Dai hpc can Tha