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QJX\rQ WҳF Fѫ Vӣ NKRD KӑF FiFK WKӭF Wә FKӭF FNJQJ QKѭ YұQ dөQJ '++7 YjR
QTDH môn Toán. 9LӋFYұQGөQJ'++7YjR'+FKӫÿӅ³+jPV͙Yjÿ͛WK͓´FNJQJÿm
ÿѭӧFPӝWVӕtW*9WKӵFKLӋQQKѭQJFKѭDFyWiFJLҧQjRÿLVkXQJKLrQFӭXÿӅ[XҩW
FiFELӋQSKiSFөWKӇQKҵPWәFKӭF'++7FKӫÿӅQj\PDQJOҥLKLӋXTXҧFDR
9ӟLQKӳQJOtGR QrXWUrQFK~QJW{LFKӑQQJKLrQFӭXÿӅWjL '̩\ K͕F KͫS
WiFFKͯÿ͉³+jPV͙Yjÿ͛WK͓´WURQJFiFWU˱ͥQJ'E͓Ĉ̩LK͕F'kQW͡F´
20өFtiêu QJKLrQFӭX
7UrQ FѫVӣQJKLrQ FӭX Oê OXұQ Yj WKӵF WLӉQ FӫD '++7 WURQJ P{Q 7RiQ WҥL
FiF WUѭӡQJ '%Ĉ+'7 ÿӅ [XҩW SKѭѫQJ SKiS '++7 FKӫ ÿӅ ³+jP Vӕ Yj ÿӗ WKӏ´
WURQJ FiF WUѭӡQJ '%Ĉ+'7 QKҵP WtFK FӵF KyD KRҥW ÿӝQJ KӑF WұS FӫD +6 Wheo
KѭӟQJSKiWWULӇQQăQJOӵFÿӗQJWKӡLTXDÿyJySSKҫQÿәLPӟL33'+Yà nâng cao
FKҩWOѭӧQJ'+EӝP{QÿiSӭQJFiFPөFWLrXÿӅUD
3. 1KLӋPYөQJKLrQFӭX
- 1JKLrQFӭXFѫVӣOêOXұQYӅ'++7'++7WURQJP{Q7RiQ
- 1JKLrQFӭXQӝLGXQJFKѭѫQJWUuQKFKӫÿӅ³+jPVӕYjÿӗWKӏ´± KӋ'%Ĉ+'7
- 1JKLrQFӭXWKӵFWUҥQJDHHT FKӫÿӅ³+jPVӕYjÿӗWKӏ´ӣ WUѭӡQJ'%Ĉ+'7
3
- ĈӅ[XҩWELӋQ pháp '++7FKӫÿӅ³+jPVӕYjÿӗWKӏ´ YjÿѭDUDPӝWVӕJLiR
iQPLQKKӑD
- 7әFKӭF71FiFELӋQSKiSÿmÿӅ[XҩWYjÿiQKJLiNӃWTXҧTN.
4*LҧWKX\ӃWNKRDKӑF
1ӃXWKӵFKLӋQ'++7WURQJ'+FKӫÿӅ³+jPVӕYjÿӗWKӏ´WURQJFiFWUѭӡQJ
'%Ĉ+'7 PӝW FiFKOLQKKRҥW KӧSOtÿҧPEҧRFiF \rXFҫX YjQJX\rQWҳF'+WKu
NK{QJQKӳQJQkQJFDRFKҩWOѭӧQJDH PjFzQJySSKҫQUqQOX\ӋQNƭQăQJKӧSWiF
YjEӗLGѭӥQJQăQJOӵF[mKӝLFKRKӑFVLQK
5. ĈӕLWѭӧQJYjSKҥPYLQJKLrQFӭX
5.1Ĉ͙L W˱ͫQJQJKLrQ FͱX
3KѭѫQJSKiS'++7FKӫÿӅ³+jPVӕYjÿӗWKӏ´WURQJ FiFWUѭӡQJ '%Ĉ+'7.
5.23K̩PYLQJKLrQFͱX
9͉ Q͡LGXQJ &KӫÿӅ³+jPVӕYjÿӗWKӏ´± KӋ'%Ĉ+'7
9͉WKͥLJLDQ 7ӯWKiQJ8 QăP7 ÿӃQWKiQJ6 QăP8.
9͉NKiFKWK͋NK̫RViW .KҧRViWWKӵFWUҥQJ WҥLWUѭӡQJ'%Ĉ+'76ҫP6ѫQ±
7KDQK+yDYjWUѭӡQJ'ӵEӏĈҥLKӑF'kQWӝF7UXQJѭѫQJ ± 9LӋW7Uu TәFKӭFTN
ÿѭӧFWKӵFKLӋQWҥLWUѭӡQJ'ӵEӏĈҥLKӑF'kQWӝF7UXQJѭѫQJ ± 9LӋW7Uu.
63KѭѫQJSKiSQJKLrQFӭX
6.1. 3K˱˯QJSKiSQJKLrQFͱXOtOX̵Q:
- Nghiên FӭXFѫVӣOêOXұQ'++7
- 1JKLrQ FӭX FiF WjL OLӋX YӅ ÿһF ÿLӇP +6 GkQ WӝF WKLӇX Vӕ YӅ WUѭӡQJ
'%Ĉ+'7YӅSKѭѫQJSKiS'++7WURQJP{Q7RiQWҥLFiFWUѭӡQJ'%Ĉ+'7.
- 1JKLrQFӭXQӝLGXQJFҩXWU~FFKӫÿӅ³+jPVӕYjÿӗWKӏ´± KӋ'%Ĉ+'7.
6.2. 3K˱˯QJSKiSÿL͉XWUD- NK̫RViW:
- 6ӱ GөQJ EҧQJ KӓL ÿӕL YӟL *9 Yj +6 ÿӇ NKҧR ViW WKӵF WUҥQJ YұQ GөQJ
DHHT trong DH FKӫÿӅ³+jPVӕYjÿӗWKӏ´WҥLFiFWUѭӡQJ'%Ĉ+'7.
4
- ĈһW FkX KӓL Yj WUDR ÿәL YӟL *9 Yj +6FiF WUѭӡQJ'%Ĉ+'7 ÿӇ WuP KLӇX
QKұQWKӭFWKiLÿӝFӫDKӑYӅQKӳQJYҩQÿӅFyOLrQTXDQÿӃQÿӅWjLQJKLrQFӭX
- 1JKLrQFӭXJLiRiQOrQOӟSFӫD*9YӣYLӃWYjVҧQSKҭPKӑFWұSFӫD+6ÿӇFy
WKrPWK{QJWLQÿiQKJLiFKtQK[iFNKiFKTXDQWKӵFWUҥQJ FNJQJQKѭNӃWTXҧWәFKӭFTN
YұQGөQJ'++7WURQJDH FKӫÿӅ³+jPVӕYjÿӗWKӏ´ WҥLWUѭӡQg '%Ĉ+'7
63K˱˯QJSKiSTXDQViW
- QXDQ ViW Yj JKL FKpS ÿҫ\ ÿӫ KRҥW ÿӝQJ DH FӫD GV và +6 ӣWUrQ OӟSYj
WURQJJLӡWӵKӑFÿӇWKXWKұSWK{QJWLQYӅKjQKÿӝQJWKiLÿӝêWKӭFKӧSWiF FӫD+6
6.4. 3K˱˯QJSKiSWKFQJKL͏P V˱SK̩P
7LӃQKjQKTN DHHT trong trong DH FKӫ³+jPVӕYjÿӗWKӏ´WҥLFiFWUѭӡQJ
'%Ĉ+'7 QKҵPNKҷQJÿӏQKWtQKNKҧWKLYjKLӋXTXҧFӫDÿӅWjL
7. 1KӳQJÿyQJJySPӟLFӫDOXұQYăQ
79͉OêOX̵Q
- +ӋWKӕQJKyDFѫVӣOêOXұQYӅ'++7TX\WUuQK'++7WURQJP{Q7RiQWҥL
FiFWUѭӡQJ'%Ĉ+'7
- Trên FѫVӣOjPU}ÿһFÿLӇPQKjWUѭӡQJYjÿһFÿLӇPWkPOtFӫDKӑFVLQKFiF
WUѭӡQJ'%Ĉ+'7 ÿӇ Wӯ ÿy ÿѭD UD KѭӟQJ YұQ GөQJ KLӋX TXҧ SKѭѫQJ SKiS '++7
trong DH FKӫÿӅ³+jPVӕYjÿӗWKӏ´WҥLFiFWUѭӡQJ'%Ĉ+'7
79͉WKFWL͍Q
- ĈiQKJLiÿѭӧFWKӵFWUҥQJQKұQWKӭFFNJQJQKѭYLӋFVӱGөQJSKѭѫQJSKiS
DHHT trong quá trình DH P{Q7RiQWҥLWUѭӡQJ'%Ĉ+'7QKӳQJWKXұQOӧLYjNKy
NKăQFӫD*9Yj+6
- 7KLӃWNӃPӝWVӕJLiRiQWuQKKXӕQJ'++7FyKLӋXTXҧWURQJ DH FKӫÿӅ
³+jPVӕYjÿӗWKӏ´FKRKӑFVLQKFiFWUѭӡQJ'%Ĉ+'7
- .ӃWTXҧ QJKLrQFӭXOjWjLOLӋXWKDPNKҧRKӳXtFKGjQKFKR*9Yj+6WURQJ
TXiWUuQKGҥ\YjKӑFP{Q7RiQWҥLFiFWUѭӡQJ'%Ĉ+'7
5
&KѭѫQJ&Ѫ6Ӣ/Ë/8Ұ19¬7+Ӵ&7,ӈ1
1.1.KiLTXiWYӅGҥ\KӑF KӧSWiF
1.14XDQQL͏PY͉'++7
Theo QJKLrQFӭXFӫDcác WiFJLҧ([17], [ @ FK~QJW{LKRjQWRjQWKӕQJQKҩW
TXDQQLӋPYӅ'++7
+ͫS WiF 7KHR 7ӯ ÿLӇQ 7LӃQJ 9LӋW KӧS WiF Oj FQJ FKXQJ VӭF JL~S ÿӥ OүQ
QKDXWURQJPӝWF{QJYLӋFPӝWQKLӋPYөQjRÿyQKҵPPӝWPөFÿtFKFKXQJ
Nhóm: Theo TӯÿLӇQ7LӃQJ9LӋW, QKyPQJKƭDOjQKLӅXQJѭӡL cùng tham gia
YjRPӝWKjQKÿӝQJFKXQJQjRÿy.
Theo 7UҫQ %i +RjQK QKyP Oj PӝW WұS WKӇ QKӓ ÿѭӧF KuQK WKjQK ÿӇ WKӵF
KLӋQPӝWQKLӋPYөQKҩWÿӏQKWURQJPӝWWKӡLJLDQQKҩWÿӏQK. [14, tr.55]
1Kѭ Yұ\ FK~QJ W{L TXDQ QLӋP QKyP Oj PӝW WұS KӧS QKӳQJ Fi QKkQ Fy ít
QKҩWWӯhai QJѭӡLWUӣOrQÿѭӧFOLrQNӃWYӟLQKDXWURQJPӝWKRҥWÿӝQJFKXQJQKҵP
WKӵFKLӋQPӝWPөFWLrXFKXQJJLӳDKӑWӗQWҥLQKӳQJJLiWUӏFKXQJYjFiFQJX\rQWҳF
QKҩWÿӏQKFҫQWXkQWKӫ.
Nhóm HTHT: ³Nhóm HTHT OjPӝWÿѫQYӏFҩXWKjQKFӫDWұSWKӇOӟSKӑFEDR
JӗPPӝWWұSKӧSQKӳQJFiQKkQ+6ÿѭӧFOLrQNӃWYӟLQKDXWURQJPӝWKRҥWÿӝQJFKXQJ
QKҵPWKӵFKLӋQQKӳQJQKLӋPYөKӑFWұSFKXQJÿӗQJWKӡLWURQJTXiWUuQKOLrQNӃWÿyVӁ
KuQKWKjQKYjWtFKKӧSFiFTXDQKӋWuQKFҧPFiFFKXҭQPӵFYjTX\WҳFQKyP´ +Rjng
Công Kiên, 2014).
'++7EDRKjPFҧYӅ33Gҥ\FӫDWKҫ\Yj33KӑFFӫDWUz1ӃX[pWWӯJyFÿӝ
*9YӟL+Ĉ'+QJѭӡLWDWKѭӡQJQyL'++7FzQQӃX[pWWӯJyFÿӝQJѭӡLKӑFVӁOj
KӑFKӧSWiF7K{QJ WKѭӡQJFiFWjLOLӋXOtOXұQ'+SKѭѫQJ7k\ GR[XҩWSKiWWӯ
quan ÿLӇP'+Oҩ\QJѭӡLKӑFYӟLKRҥWÿӝQJKӑFOjWUXQJWkPWKuNKiLQLӋPKӑFKӧS
WiFÿѭӧFGQJNKiSKәELӃQ[13, tr.27]
Ӣ9LӋW1DPWURQJOtOXұQ'+'++7ÿѭӧFQJKLrQFӭXWLӃSFұQWӯQKLӅXJyF
ÿӝNKiFQKDX
6
'++7OjP͡W+77& .KLÿӅFұSWӟL'++7QKѭOjPӝW+TTC DHWӭFOjÿm
[HPQyQKѭPӝWFiFKWKӭFWәFKӭFWLӃQKjQK+Ĉ'+FKRSKKӧSYӟLPөFÿtFKQӝL
GXQJFӫDEjLKӑF
&iFK WLӃS FұQ DHHT QKyP YӟL Wѭ FiFK Oj PӝW HTTC DH ÿѭӧF FiF QKj Ot
OXұQ '+ QKѭ ĈһQJ 9NJ +RҥW 1JX\ӉQ 1JӑF 4XDQJ /r .KiQK %ҵQJ... WKӯD
QKұQTác gLҧ 1JX\ӉQ 1JӑF %ҧR WURQJ FXӕQ +R̩W ÿ͡QJ DH ͧ WU˱ͥQJ 7+&6, cho
UҵQJ ³'+QKyPWҥLOӟSOjPӝWKuQKWKӭF'+FyVӵNӃWKӧSWtQKWұSWKӇYjWtQKFi
QKkQPjWURQJÿy+6GѭӟLVӵFKӍÿҥRFӫD*9WUDRÿәLQKӳQJêWѭӣQJQJXӗQNLӃQ
WKӭFJL~SÿӥKӧSWiFYӟLQKDXWURQJYLӋFOƭQKKӝLWULWKӭFKuQKWKjQKNƭ QăQJYjNƭ
[ҧR7ӯQJWKjQKYLrQNK{QJFKӍFyWUiFKQKLӋPYӟLYLӋFKӑFWұSFӫDPuQKPjFzQ
FyWUiFKQKLӋPTXDQWkPÿӃQYLӋFKӑFWұSFӫDEҥQNKiFWURQJQKyP´ (1JX\ӉQ1JӑF
%ҧR, 2000).
- '++7OjP͡W33'+ ĈӅFұSWӟL'++7QKyPYӟLWѭFiFKOjPӝW33'+WӭF
OjÿӅFұSWӟLQyQKѭPӝWFiFKWKӭFPӝWFRQÿѭӡQJÿӇÿҥWÿѭӧFPөFÿtFKFӫD'+
&iFKWLӃSFұQ'++7QKѭOjPӝW33'+ÿѭӧFFiFQKjOtOXұQ'+WKӯDQKұQ
YjÿѭӧFJӑLFKXQJOj 33'++77URQJFXӕQ ³6ӵSKiWWULӇQQKұQWKӭF KӑFWұSYj
JLҧQJ Gҥ\´ ) ( :HLQHUW ÿm YLӃW ³*Lӡ KӑF QKyP +6 Wӵ OjP YLӋF WURQJ Wә WKҧR
OXұQWұSWKӇYjJLҧQJGҥ\OүQQKDXÿyOjPӝWVӕÿӏQKGҥQJGQJÿӇFKӍPӝWNLӇX'+
YjFKӍGүQWKӇKLӋQWtQK[mKӝLWURQJÿyWӯQJQKyPFiQKkQKӑFYӟLQKDXYjKӑF
KӓL OүQ QKDX´ 4XDQ ÿLӇP Qj\ FNJQJ ÿѭӧF PӝW Vӕ QKj Ot OXұQ '+ 9LӋW 1DP QKѭ
1JX\ӉQ.Ǥ7UҫQ%i+RjQK7KiL'X\7X\rQWKӯDQKұQ7iFJLҧ1JX\ӉQ.Ǥÿm
FKRUҵQJ'++7QKyPOjPӝWWUѭӡQJKӧSFӫD33'+
Trong [24 WU@ WiF JLҧ +RjQJ /r 0LQK ÿm ÿѭD UD TXDQ QLӋP '++7 Oj
33'+WURQJÿyPӛL+6ÿѭӧFKӑFWұSWURQJPӝWQKyPFyVӵFӝQJWiFJLӳDFiFWKjQK
YLrQWURQJQKyPÿӇÿҥWÿѭӧFPөFÿtFKFKXQJ
- DHHT OjVJLDRWKRDJLͷDPPDH và HTTC DH
7URQJ47'+FyQKӳQJORҥLF{QJYLӋFYӯDÿyQJYDLWUzOj33YӯDÿyQJYDi
WUzOjPӝW+77&DH;XҩWSKiWWӯTXDQQLӋPQj\PӝWVӕWiFJLҧYtGөQKѭ1JX\ӉQ
7
1Kѭ$QWURQJFXӕQ ³33JLҧQJGҥ\*LiRGөFKӑF´ÿmFKRUҵQJ'++7QҵPJLDRWKRD
JLӳDKDLSKҥPWUFѫEҧQFӫDOtOXұQ'+ 3KҥPWU33'+YjSKҥPWU+77&DH, nó
YӯDPDQJQKӳQJÿһFÿLӇPFӫD33'+YӯDPDQJQKӳQJÿһFÿLӇPFӫD+77&DH.
33 WKѭӡQJ ÿѭӧF KLӇX Oj FRQ ÿѭӡQJ FiFK WKӭF ÿӇ ÿҥW WӟL PөF ÿtFK QKҩW ÿӏQK
33'+OLrQKӋYӟL47'+WURQJÿyYLӋFGҥ\ÿLӅXNKLӇQYLӋFKӑF33'+OjFiFKWKӭF
KRҥWÿӝQJYjJLDROѭXFӫDWKҫ\Jk\QrQQKӳQJ KRҥWÿӝQJYjJLDROѭXFӫDWUzQKҵPÿҥW
ÿѭӧFFiF PөFWLrX'+[18, tr.102]. 7URQJ47'+33'+FKӏXWiFGөQJÿӏQKKѭӟQJ
FӫDPөFÿtFKQKLӋPYө'+0һWNKiF33'+JySSKҫQKRjQWKjQKFiFQKLӋPYө'+
SKKӧSYӟLPөFÿtFK'+ĈӗQJWKӡL33'+ÿѭӧFTX\ÿӏQKEӣLQӝLGXQJ'+6RQJ
QKӡFyVӵOӵDFKӑQYjYұQGөQJKӧSOtFiF33'+PjQӝLGXQJ'+VӁGҫQWUӣWKjQKYӕQ
NLQKQJKLӋPFӫD+61KѭYұ\FyWKӇ[HP33'+FKtQKOjFiFKWKӭFKRҥWÿӝQJFӫD*9
Yj+6WURQJWѭѫQJWiFWәFKӭFÿLӅXNKLӇQKӑFFӫDWKҫ\YjWӵKӑFFӫDWUz
7ӯNKiLQLӋPYӅ33'+TXDQQLӋP'++7WӯNӃWTXҧQJKLrQFӭXQKӳQJÿһF
WUѭQJFӫDQKyPHTHTFK~QJW{LTXDQQLӋPUҵQJ ³'++7OjP͡W33'+WURQJÿy
P͟L+6ÿ˱ͫFK͕FW̵SWURQJP͡WKD\QKL͉XQKyPFyVKͫSWiFJLͷDFiFWKjQKYLrQ
JLͷD FiF QKyP Yj YͣL V W˱˯QJ WiF FͯD *9 ÿ͋ ÿ̩W P͡W PͭF ÿtFK FKXQJ´ (Hoàng
Công Kiên, 2014).
1.1.2. %̫QFK̭WFͯD'++7
&K~QJW{LKRjQKRjQQKҩWWUtYӟLTXDQÿLӇPFӫDWiFJLҧ>@YӅEҧQFKҩWFӫD
DHHT.
³'++7EDRJӗPFiFWKjQKWӕ*9+6YjQӝLGXQJ'+%DWKjQKWӕWUrQYӯD
WӗQ WҥL ÿӝF OұS YӯD WiF ÿӝQJ TXD OҥL YӟL QKDX WURQJ P{L WUѭӡQJ QKyP 1Kѭ Yұ\
'++7YӅEҧQFKҩWOjTXiWUuQKWәFKӭFYjÿLӅXNKLӇQPӕLTXDQKӋJLӳDFiFWKjQKWӕ
GV - 1KyP+6QKҵPWKӵFKLӋQQӝLGXQJEjLKӑF.
- HS /jWUXQJWkPYjOjFKӫWKӇWtFKFӵFFӫDKRҥWÿӝQJKӑFWӵPunh tìm ra
NLӃQWKӭFEҵQJFKtQKKjQKÿӝQJFӫDPuQKEҵQJVӵKӧSWiFYӟLEҥQYӟLWKҫ\
8
- Nhóm 0{L WUѭӡQJ [m KӝL Fѫ Vӣ QѫL GLӉQ UD TXi WUuQK KӧS WiF Yj JLDR OѭX
JLӳDFiF+6WURQJPӝWQKyPYjJLӳD+6YӟL*9OjPFKRFiFWULWKӭFÿmFiQKkQKyD
ÿѭӧF[mKӝLKoá. ĈӗQJWKӡLQyFzQOjPӝWFKӫWKӇWtFKFӵFFӫDKRҥWÿӝQJKӑFWұS
- GV 1JѭӡLKѭӟQJGүQWәFKӭFÿLӅXNKLӇQKRҥWÿӝQJWӵKӑFFӫDQKyP+6
JL~S+6WӵOӵFWuPUDWULWKӭFWK{QJTXDFiFTXiWUuQKFiQKkQhóa[mKӝLhóa.
- 7ULWKͱF 'RWUzWӵWuPUDWURQJ VӵKӧSWiFYӟLEҥQYjYӟLWKҫ\
&iFWKjQKWӕWUrQOX{QOX{QWiFÿӝQJWѭѫQJKӛYӟLQKDXWKHRPӝWWUұWWӵQKҩW
ÿӏQKWҥRQrQVӵWKӕQJQKҩWWRjQYҽQFӫDTXiWUuQKYұQGөQJ'++7YjOjPFKRQy
YұQ ÿӝQJ ÿӇ WҥR UD PӝW FKҩW OѭӧQJ PӟL Ĉy Oj QKӳQJ WUL WKӭF Nƭ QăQJ Yj WKiL ÿӝ
ÿѭӧFKuQKWKjQKӣ+6YjVӵWUѭӣQJWKjQKFӫDFKtQKQKyPKӑFWұS
7ӯ QKӳQJ OұS OXұQ WUrQ FK~QJ W{L FKR UҵQJ 9̵Q GͭQJ '++7 Oj TXi WUuQK
WKFKL͏QQKͷQJEL͏QSKiSFyF˯VͧNKRDK͕Fÿ͋W͝FKͱFYjÿL͉XNKL͋QP͙LTXDQ
K͏JLͷDFiFWKjQKW͙ *9QKyP+6YjWULWKͱFOjPFKRFK~QJY̵Qÿ͡QJYjSKiW
WUL͋Q WKHR P͡W WU̵W W QK̭W ÿ͓QK QK̹P WKF KL͏Q FiF QKL͏P Yͭ DH. ´ (Hoàng
Công Kiên, 2014)
1.1.3˰XÿL͋PYjQK˱ͫFÿL͋PFͯD'++7
1.1.3.1. ˰XÿL͋P
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