vận dụng quan điểm hoạt động trong dạy học đại số và giải tích 11 thpt

i
L


u ca riêng tôi.
Các s liu, kt qu nêu trong lu c ai
công b trong bt k công trình nào khác.









ii

Lu

              chuyên
 h
 

Sh
  h      
    Thái Bình) 








10 












iii



GV

HS

NXB

PPDH

SGK

Sách giáo khoa
THPT

TH







iv

 1

           
 4
1.1. C 4
1.1.1 4
1.1.2 25
 26
 26

 29
 32

 34
2  34
2.1.1.   34
  36

  38
  41
  43
  45
  47
 49
tính  51
 53
 56
 58
 60
 61
 63

v
   66
 70
2.4.  71
 72
2.4.2. -  75
2.4.3.  80
 85
2.4.5.  91
 97
 98
  98
  98
  98
  98
 99

 100
 101
 102



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








        
 



- 
duy sáng t


- 


giáo viên 


- . L




2



- 

  
tích 11


“Vận dụng quan điểm hoạt động
trong dạy học Đại số và Giải tích 11 THPT”.


 
 


a. 
Toán.
b. 


c.  
.
d. 



vào 





3




 















môn Toán




4




MÔN

1.1. C
1.1.1. Các thành tố cơ sở của hoạt động dạy học Toán


a) Phát hiện những hoạt động tương thích với nội dung


á Kim [10, Tr.129], GV   
 
- Nhận dạng và thể hiện;
- Những hoạt động Toán học phức hợp;
- Những hoạt động trí tuệ phổ biến trong môn Toán;
- Những hoạt động trí tuệ chung;
- Những hoạt động ngôn ngữ.
* Hoạt động nhận dạng và thể hiện có 



- 

  
 [10, Tr. 97]
.1: 




5



1.2: 



- Theo t

 [10, Tr. 98]
 1.3: Đạo hàm của hàm hợp 


1
3
2
100
3
21

(2 1)
(2 1)
yx
yx
yx





1; 2
yy


3
y
. V
21xu


-  

 
 [ 10, Tr. 99]
.4:  
3
yx


1.5: 


3
yx


* Những hoạt động Toán học phức hợp ,
             
Khi HS

6



       giúp      
Toán , 
1.6: 
(sinx)' cosx


2
1
(tanx)'
cos x


* Hoạt động trí tuệ phổ biến trong Toán học: 

- Lật ngược vấn đề:  
()fx
và

()gx

K.
0
lim ( )
xx
f x L


và
0
lim ( )
xx
g x M


(
0M 

0
()
lim
()
xx
f x L
g x M


. N
0

()
lim
()
xx
f x L
g x M


(
0M 
)     
0
lim ( )
xx
f x L


và
0
lim ( )
xx
g x M


hay
không?
*Những hoạt động trí tuệ chung 




.7: 
()fx
K và
0
xK
.

()fx

0
x

thành 
 K 
0
x

0
()fx

+
0
lim ( )
xx
f x a




+

0
lim ( )
xx
f x b





0
()a b f x

*Hoạt động ngôn ngữ
 



7



.8: 

b) Phân tích hoạt động thành những hoạt động thành phần
Trong quá trình h
        

 






c) Lựa chọn hoạt động dựa vào mục đích
            
 





[10, Tr.130]
d) Tập trung vào những hoạt động Toán học




           nhận dạng và thể hiện
những khái niệm, định lý và phương pháp Toán họchoạt động Toán học
phức hợp  

8



          


a) Thế nào là gợi động cơ cho hoạt động




Hoạt động được đặc trưng bởi tính đối tượng
của nó. Do vậy điều chủ yếu để phân biệt hoạt động này với hoạt động khác là ở
chỗ đối tượng của chúng khác nhau. Quả vậy, chính đối tượng của hoạt động làm
cho hoạt động có một hướng nhất định
Đối tượng của hoạt động là động cơ thực sự của hoạt động”,
“Khái niệm hoạt động gắn liền một cách tất yếu với khái niệm động cơ. Không có
hoạt động nào không có động cơ; hoạt động “không động cơ” không phải là hoạt
động thiếu động cơ mà là hoạt động với một động cơ ẩn dấu về mặt chủ quan và về
mặt khách quan














9












 


 







                 
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b) Các cách thường dùng để gợi động cơ
i) Gợi động cơ mở đầu


Đạo hàm, GV 
 
         


10

Vật lí, Hoá học 
õ 
 Hàm số lượng giác.


- 

 

     
 






 



-  

- 

- 



 

11










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ti

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.9: 
0
 0  a  
0

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
0

. 

0
= 720
0
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 



*Hướng tới sự hoàn chỉnh, hệ thống
.10: 







lim( 1)
n
n  




12

*Lật ngược vấn đề







()y f x


0
x
nh lí này có

||yx
liên

* Xét tương tự

 
.11: 
1 3 2
2x x x


*Khái quát hóa
Khái quát hóa là chuyển từ việc nghiên cứu một tập hợp đối
tượng đã cho đến việc nghiên cứu một tập hợp lớn hơn bao gồm cả tập hợp ban
đầu

ông gian. [2,
Tr.22]
.12: 

 
()s f t

00
0
( ) ( )
lim
t
f t t f t
t

  



0
t


13




()y f x
, ta hãy nghiên


00
( ) ( )f x t f t
t
  

khi
t

 .13:
22
2sin .cos sin2 , 2 sin .cos .cos2 sin2x x x x x x x
ta khái
quát
1
2 sin .cos .cos2 cos2 sin2
n n n
x x x x x


.
*Xét sự liên hệ và phụ thuộc
.14: 

sin cos a x b x c
.

 



 




ii) Gợi động cơ trung gian



38]

* Hướng đích


 


14





 


 





.15: 
n
A cosx.cos2x cos2 x



2sinxcosx sin2x
.
*) Quy lạ về quen



.16: 
2
asin sinx 0 ( 0)x b c a   


2
0 , 0at bt c a   

sinx t
.
*) Xét tương tự
.17: 



.18: nh công



*) Khái quát hóa

15



.19: 
 

.20: 

2'
32
10 ' 9
( ) ( ) 2
( ) '( ) 3
( ) ( ) 10
f x x f x x
f x x f x x
f x x f x x
  
  
  


1
( ) '( ) ( 1, )
nn
f x x f x nx n n N


    

xR

*) Xét sự biến thiên và phụ thuộc
.21: 
2
2 cosx
x




2
2
x




iii) Gợi động cơ kết thúc





.22: 
2
2

x

        





16




 

2
2
x


2 sinx cos 1 0xx   








4i) Phối hợp nhiều cách gợi động cơ tập trung vào ngưỡng trọng điểm




                 
h


  

- 
- 
- 


               



17




                

- Tri thức sự vật



[15, Tr.31]

- Tri thức phương pháp


Tr.31]
- Tri thức chuẩn

0
lim ( ) lim ( )
o
x x x x
f x f x L




0
x
.
- Tri thức giá trịToán
học có vai trò quan trọng trong khoa học kỹ thuật cũng như trong đời sống”, “Thực
tiễn là nền tảng của nhận thức, là tiêu chuẩn của chân lý”, “Khái quát hóa là một
thao tác trí tuệ cần thiết cho mọi người [15, Tr.31]



           


pháp cho HS :
a) Trang bị cho HS một cách tường minh các tri thức phương pháp được quy

định trong chương trình
Ví .23: 

x

0
x
, tính

18




( ) ( ).
oo
y f x x f x    


y
x


.

0
lim .
x
y
x





b) Thông báo tri thức trong quá trình tiến hành một hoạt động
.24: 

sin x
và
cosx
.

22
asin cos ( 0)x b x c a b   

- 
- 
sinx cos 2 os( )
4
x c x

  
?
- 

22
asin cos sin( )x b x a b x

   


22
0ab
(*)
- 
22
2 2 2 2
1
ab
a b a b
   

   

   
?

2 2 2 2
os ;sin
ab
c
a b a b




- 

c) Tập luyện cho HS các hoạt động tương thích với các tri thức phương pháp
không có trong nội dung sách giáo khoa (Các phương pháp tìm tòi lời giải)
  .25:      

32
3 1 ( ).y x x C  
 

( 1;3)M 
.

0 0 0
'( )( ).y y f x x x  


         

( 1;3)M 


19




( 1) 3y k x  
(d).


32
2
3 1 ( 1) 3 (1)
3 6 (2)
x x k x

x x k

    






Thay (2) vào (1) ta có
3 2 2
3 1 (3 6 )( 1) 3 1x x x x x x        
thay
1x 


3k 

3yx
.









 



 
này. [10, Tr.150]

a) Sự phức tạp của đối tượng hoạt động :

 
.26: 
sinx sina
, GV

 :

20




2
sin(3 ) osx
3
xc


 

sinx sina
.
.27: -

 
( 1)
n
x 

2
(2 )
n
xy
.
b) Sự trừu tượng, khái quát của đối tượng
        


.28: 
1 2 1
lim
n
xo
x
x





n 2,3, n 3;nN  


c) Nội dung hoạt động


 

.29: 

 :
 
sinxy 
;

3
sin 2yx
.
d) Sự phức hợp của hoạt động:
             

.30: 
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
