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亠于舒 仆亠亰舒于亳亳仄舒
仆舒仆仂-仗舒从亳亠从舒 从仂仆亠亠仆亳
束舒亰舒弍仂从舒  2013損
23 - 25 仂从磡, 仂从于舒

仗 舒亰舒弍仂从亳 亳仆亠仍仍亠从舒仍仆仂亶
仂弍舒ム亠亶 亳亠仄 束仂仍亞舒損
舒舒仍亳 弌仄亳仆仂于舒
弌从舒 亟仂从仍舒亟舒
 于亠亟亠仆亳亠
 仂舒仆仂于从舒 亰舒亟舒亳 亳亰仄亠亠仆亳 仗仂亞亠舒 于
亠亠仆亳亳
 仍亞仂亳仄 Andes Physics Tutor
 仍亞仂亳仄 弌 束仂仍亞舒損
 于仂亟. 舒仍仆亠亶舒 舒弍仂舒
2
弌从舒 亟仂从仍舒亟舒

于亠亟亠仆亳亠

3
仆亠仍仍亠从舒仍仆亠 仂弍舒ム亳亠 亳亠仄

仂亢仆仂 仍亳 亟亠仍舒
亳 仄仆亠亠?
舒!

4
仆亠仍仍亠从舒仍亳亰舒亳 舒仗仂亰仆舒于舒仆亳
仂于亠舒 亟亠仆舒
弌亟亠仆 于于仂亟亳 亠亠仆亳亠 亰舒亟舒亳:

 仗仂亞舒仄仄舒  亠仄:
5
束弌仍亠亟亳亠損 亳仆亠仍仍亠从舒仍仆亠 仂弍舒ム亳亠
亳亠仄: Andes Physics Tutor
亠 弍仂仍亠亠 仗仂亟于亳仆仂亠 舒仗仂亰仆舒于舒仆亳亠 仂于亠仂于
亟亠仆仂于:

6
束弌仍亠亟亳亠損 亳仆亠仍仍亠从舒仍仆亠 仂弍舒ム亳亠
亳亠仄: 弌 束仂仍亞舒損
 仂亢亠 亟亠仍舒仍亳 束仄仆ツ 亳亠仄:

7
仆亠亠亶 于于仂亟舒 亠亠仆亳 弌 束仂仍亞舒損 亳
仗仂仍亰仂于舒亠仍亳-亞仄舒仆亳舒亳亳: 仗亳仄亠
丕仍仂于亳 亰舒亟舒亳:

弌. 于亠仄 仂弍亠仆亳 亳仆亠亠亶
(仄亳仆)

8

 亠亳仍仂:
10 亳亰 11 亠仍.,
 亳仍亳 亳仆亠亠亶:
8 亠仍.
弌. % 仆亠亰舒亳舒仆仆 亳亠仄仂亶
舒亞仂于
弌从舒 亟仂从仍舒亟舒

仂舒仆仂于从舒 亰舒亟舒亳

9
亠亟仗仂仍仂亢亠仆亳 亳 仂亞舒仆亳亠仆亳
仗仂仍亰ム 仂仍从仂
仗仂仍亰ム 仂仍从仂
仂弍仂亰仆舒亠仆亳 亳亠仄!
仂弍仂亰仆舒亠仆亳 亳亠仄!

丐仂仍从仂
丐仂仍从仂
仂亟仆仂仂仆亠
仂亟仆仂仂仆亠
仂仄仍, 弍亠亰
仂仄仍, 弍亠亰
仂弍仆亠仆亳亶!
仂弍仆亠仆亳亶!

LaTeX-仗仂亟仂弍仆亶
LaTeX-仗仂亟仂弍仆亶
亳仆舒从亳
亳仆舒从亳

10
亅舒仗 仗仂于亠从亳 舒亞舒 亠亠仆亳
亠亳亳从舒亳 舒亞舒

舒亠 仗仂亞亠舒 于
亠亠仆亳亳

弌仂仂弍亠仆亳亠 仂
舒亠 舒亞舒

?
仂仗仂 从
亟亠仆

11

弍仆仂于仍亠仆亳亠 亳仆.  
(亟仍 仗仂亟从舒亰仂从 亳 仂亠仆从亳 亰舒 亰舒亟舒)
亠亳亳从舒亳 舒亞舒: 仗亳仄亠仆亶 舒仍亞仂亳仄
 亟亠仆 于于亠仍 舒亞:
z=1+y
 舒亞 仗仂亟舒于仍ム 亳亰于亠仆亠 亳亠仄亠
亰仆舒亠仆亳 仗亠亠仄亠仆仆:
5=1+4
仂仍亠仆仆仂亠 于舒亢亠仆亳亠 仗仂舒亠 亳
舒于仆亳于舒亠  0:
if simplify(5  (1 + 4)) == 0:
//亟亠仆 于于亠仍 仗舒于亳仍仆亶 舒亞 亠亠仆亳
亠亳亳从舒亳 舒亞舒: 弍亳弍仍亳仂亠从亳
仍 仗仂亠仆亳 于舒亢亠仆亳亶 仄仂亢仆仂 亳仗仂仍亰仂于舒
弍亳弍仍亳仂亠从 SymPy:

13
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 
仆亠亳于亳舒仍仆舒 仗仂弍仍亠仄舒.
束舒亳于仆亶損 仗仂仂弍 仆亠 亞仂亟亳: 亟舒亢亠 亟仍
舒仄仂亶 仗仂仂亶 亰舒亟舒亳 亠弍亠
于仆亠亳 仍亳从仂仄 仄仆仂亞仂 仂仄仍
亠
亳 亠亠仆亳亶.

舒亞 亠亠仆亳 亟亠仆舒

14

亳 于亳仍亳亠仍仆仂 仂
仆亠 于亞仂亟仆仂

亠仆
亅
亳亠
舒仗
1
亅
1
舒
 仗2

亅
舒

仗m

Image courtesy of Keattikorn a
FreeDigitalPhotos.net
弌从舒 亟仂从仍舒亟舒

仍亞仂亳仄 亳亰仄亠亠仆亳
仗仂亞亠舒 于 亠亠仆亳亳
Andes Physics Tutor

15
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳:
仗亳仄亠
舒亟舒舒: 于亳仍亳 舒仂礌亳亠 仄亠亢亟 于亠从仂舒仄亳 a
亳b
仂亰仄仂亢仆亠 亠亠仆亳 亞亠仆亠亳ム 仆舒 仂仆仂于亠
仂仄仍:

16

 亟亠仆 于于亠仍 仂仄仍:
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳:
仗亳仄亠

亠于亳亟仆仂, 仂 仂仄仍舒
仆舒 仂仆仂于亠 仂仄仍 (1) 亳 (3)
丐.亠. 仗仂亞亠 亟亠仆舒 = 2/6 = 33%
17

仗仂仍亠仆舒
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于
Andes Physics Tutor

亟仆舒 亳亰
亳亠仄:
18
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于
Andes Physics Tutor: 仆亠亟仂舒从亳
亠仗仂仆仆仂, 从舒从 仂弍舒弍舒于舒 仂仄仍 
于亠从仂舒仄亳 亳 仄舒亳舒仄亳 亳仗舒
亠 亰舒亳亠仆 仂 亳仄亳舒亳亳 仗舒于亳仍仆仂
于于亠亟亠仆仆 舒亞仂于 亠亠仆亳:
于, 亟仍 仆亠亞仂 仂 仂亟仆仂 亳 仂 亢亠
仄亳舒亳亳:
19

舒于亳仍仆亶 舒亞:
弌从舒 亟仂从仍舒亟舒

仍亞仂亳仄 亳亰仄亠亠仆亳
仗仂亞亠舒 于 亠亠仆亳亳
弌 束仂仍亞舒損

20
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌
束仂仍亞舒損: 仂仆仂亠仆亳 于亳仍亳仄仂亳

21
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于
弌 束仂仍亞舒損: 亠从亳亠 仂亞舒仆亳亠仆亳
舒仄仂亳仄 仍舒亶, 从仂亞亟舒 于 仍亠于仂亶 舒亳
仂仄仍 亟亠仆舒 仂仍从仂 仂亟仆仂 仂弍仂亰仆舒亠仆亳亠:

丼亠仄 弍仂仍亠 仂弍仂亰仆舒亠仆亳亶 于 仗仂于亠磳仄仂仄 舒亞亠
亰舒仄亠仆亠仆仂 仆舒 亳仍舒, 亠仄 亟仆亠亠 仆舒亠仄
舒仍亞仂亳仄 于磦亳 亳仄亳舒亳, .:
22

仗仂仍亳 于磦亳 亳仄亳舒亳

仆亠 仗仂仍亳
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌
束仂仍亞舒損: 仆舒仂亢亟亠仆亳亠 亰舒于亳亳仄仂亠亶
 亟亠仆 于于亠仍 仂仄仍:
弍仂亰仆舒亳仄
 亳仄亠亠 舒从仂亶 亞舒
仗从舒亠仄 于 仆亠仄 仂 (c,c) 于仆亳亰,
仗仂从舒 仆亠 于仗. 仍仂于亳亠:

23

束亠从亠亠 仂仂礌亳亠損, 仗亳仂从 仂弍仂亰仆舒亠仆亳亶
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌
束仂仍亞舒損: 仆舒仂亢亟亠仆亳亠 亰舒于亳亳仄仂亠亶
 亟亠仆 于于亠仍 仂仄仍:

仂仍亳仄 亳 仗亳 

亳 于舒亢亠仆亳亠
24
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌
束仂仍亞舒損: 于磦仍亠仆亳亠 亳仄亳舒亳亶
舒从, 仂仄仍舒 亟亠仆舒:

亳 亞亠仆亠亳仂于舒仆仆仂亠 亳亠仄仂亶 于舒亢亠仆亳亠
舒仄亠仆亳仄 于 亠亞仂 仗舒于仂亶 舒亳 于亠 仂弍仂亰仆舒亠仆亳,
从仂仄亠 亠, 仂 仗亳于ム 于
, 仗仂仍亳仄:

25

从于亳于舒仍亠仆仆仂 仂仄仍亠
亟亠仆舒, 仆亠 亳仄亳舒亳
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌
束仂仍亞舒損: 于磦仍亠仆亳亠 亳仄亳舒亳亶
丼仂 弍仍仂 弍, 亠仍亳 弍 亟亠仆 于于亠仍 仂仄仍
?
 仗仂仍亳仄 于舒亢亠仆亳亠
 亠亞仂 仗舒于仂亶 舒亳 亰舒仄亠仆 仆亠亠亞仂. 弌舒于仆亳于舒亠仄
仂仄仍:
亳
26

亠 从于亳于舒仍亠仆仆, 仂 亳仄亳舒亳 仗舒于亳仍仆仂亞仂 舒亞舒
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌
束仂仍亞舒損: 于磦仍亠仆亳亠 亳仄亳舒亳亶
丼仂 弍仍仂 弍, 亠仍亳 弍 亟亠仆 于于亠仍 仂仄仍
?
 仗仂仍亳仄 于舒亢亠仆亳亠
 亠亞仂 仗舒于仂亶 舒亳 亰舒仄亠仆 仆亠亠亞仂. 弌舒于仆亳于舒亠仄
仂仄仍:
亳
亅从于亳于舒仍亠仆仆, 亳仄亳舒亳 仆亠 于磦仍磳 (仂 仂仆舒 亠)
27
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌
束仂仍亞舒損: 舒亠 仗仂亞亠舒
 亟亠仆 于于亠仍 仂仄仍:

仂仍亳仍亳 亳 仗亳:

丐.亠. 仗仂亞亠 于 亠亠仆亳亳 = 3/(3+2) 亳仍亳 4/(4+2)
28
亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌
束仂仍亞舒損: 舒于仂仄舒亳亠从仂亠 仗仂仂亠仆亳亠
亞舒舒

弌仆舒舒仍舒 仂亳仄 仂亟亠仍仆亠 亠弍舒 亞舒舒,
仗仂仂仄 仗仂仍舒亠仄 弍仂仍亠亠 仍仂亢仆 从

29
亰仄亠亠仆亳亠 仗仂亞亠舒: 仂舒仍仆亠
仍舒亳
 弌亠亟亳 仗亠仗仂亟舒于舒亠仍亠亶 仆亠 仂亞仍舒亳 仂 仂仄, 亠仄
亟仂仍亢亠仆 亰舒仆亳仄舒 亟亠仆: 于于仂亟仂仄 仂仄仍
亳仍亳 舒亳仄亠亳从仂亶
 亠亞亟舒 仆舒亶亟 仆亠仂亟亳仆舒仆亠 亟亠仆
舒亟仂 亳 仂弍舒弍舒于舒 舒亰仆亠 束仆亠
亳亟亠舒仍仆亠損 仍舒亳:
(1-3)^2+(2-4)^2=8
-4=1-5
30

x_a*x_b+y_a*y_b
=3*7+4*8

c_1*c_2=4
于仂亟

31
于仂亟
 仂于亠 舒亰于亠仆亠 亠亠仆亳 亟亠仆仂于 
于仂亰仄仂亢仆仂!
 亠仂弍仂亟亳仄仂 舒仄仂亠 亳 亟亞亳亠 从舒亶仆亳亠
仍舒亳 于亳亟仂于 于于仂亟亳仄 亟亠仆舒仄亳 仂仄仍
  亟亞亳亠 亰舒亟舒亳, 仆亠 仂仍从仂 仗仂 仍亳仆亠亶仆仂亶
舒仍亞亠弍亠
 亠 仂亳 亰舒弍于舒 仂弍 仂亞舒仆亳亠仆亳 亳
仂舒于仍 亟亠仆 于仂亰仄仂亢仆仂 亟仍 束亢舒仍仂弍損
仆舒 亳亠仄
32
仗仂仍亰仂于舒仆仆亠 亳仂仆亳从亳 亳 仗仂仍亠亰仆亠
仍从亳
弌仍舒亶亟 1
http://habrahabr.ru/post/194240/

弌仍舒亶亟 5
1.https://moodle.org/plugins/view.php?plugin=qtype_stack
2.亠于亳仆从舒 .. 束仂亟从亳仂仆仆舒 仄仂亟亠仍 亳仆亠舒从亳于仆仂亶 从仂仄仗仂仆亠仆
仂弍舒ム亠亶 亳亠仄損. http://www.mce.su/archive/doc15643/doc.pdf
3.亠于亳仆从舒 .. 束仂仂亠仆亳亠 亳仆亠仍仍亠从舒仍仆 仂弍舒ム亳 亳亠仄 仗仂
仄舒亠仄舒亳从亠  亳仗仂仍亰仂于舒仆亳亠仄 磶从舒 Tree-Refal損 // 亠仗亠从亳于仆亠
亳仆仂仄舒亳仂仆仆亠 亠仆仂仍仂亞亳亳 亳 亳仆亠仍仍亠从舒仍仆亠 亳亠仄損. 丐. 3.  15. 2003

33
仗仂仍亰仂于舒仆仆亠 亳仂仆亳从亳 亳 仗仂仍亠亰仆亠
仍从亳
弌仍舒亶亟 5
4.S. Klai, T. Kolokolnikov, and N. Van den Bergh, Using Maple and the web to
grade mathematics tests, in Proceedings of the International Workshop on
Advanced Learning Technologies, 2000.
5.M. Mavrikis and A. Maciocia, Wallis: a web-based ILE for science and engineering
students studying mathematics, in Workshop of Advanced Technology for
Mathematics Education in the 11th International Conference on Artificial Intelligence
in Education, 2003, pp. 505512.
6.Maple T.A. http://www.maplesoft.com/products/mapleta/
7.C. J. Sangwin, Assessing Elementary Algebra with STACK, International Journal
of Mathematical Education in Science and Technology, vol. 38, no. 8, pp. 9871002,
2008.
8.C. J. Sangwin, Automating the marking of core calulus and algebra: eight years
on. http://web.mat.bham.ac.uk/C.J.Sangwin/Publications/2009-12-mmg.pdf
34
仗仂仍亰仂于舒仆仆亠 亳仂仆亳从亳 亳 仗仂仍亠亰仆亠
仍从亳
弌仍舒亶亟 5

9.Answer tests. https://
github.com/maths/moodle-qtype_stack/blob/master/doc/en/Authoring/Answer_tests.md#E
.
10.E. Melis and J. Siekmann, ActiveMath: An Intelligent Tutoring System for
Mathematics, Artificial Intelligence and Soft Computing  ICAISC 2004, vol. 3070,
pp. 91101, 2004.

弌仍舒亶亟 6

VanLehn K. (et al.) The Andes Physics Tutoring System: Lessons Learned.
International Journal of Artificial Intelligence in Education. Vol. 15.  3. 2005.
http://oli.cmu.edu/wp-oli/wpcontent/uploads/2012/05/VanLehn_2005_Andes_Physics_Tutoring_System.pdf

35
仗仂仍亰仂于舒仆仆亠 亳仂仆亳从亳 亳 仗仂仍亠亰仆亠
仍从亳
弌仍舒亶亟 13
http://sympy.org/ru/index.html

弌仍舒亶亟 16
Shapiro J.A. An Algebra SubSystem for Diagnosing Students Input in a Physics
Tutoring System. http://www.physics.rutgers.edu/~shapiro/tutor/submission3.pdf

弌仍舒亶亟 29
https://github.com/indra-uolles/solution_tracer

36
弌仗舒亳弍仂 亰舒 于仆亳仄舒仆亳亠!
舒舒仍亳 弌仄亳仆仂于舒, 仆.. 仍舒弍. 17 丕 

smirnovanatalia2008@gmail.com

37

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X 亠亞亳仂仆舒仍仆舒 仆舒仆仂-仗舒从亳亠从舒 从仂仆亠亠仆亳
MIREA
于亟舒2012 2
于亟舒2012 2
Natalia Smirnova
亳仗仂于 .弌. 仂仆仗亠从 仍亠从亳亶 仗仂 亟亳亳仗仍亳仆亠 束亳亠仄 亳从于亠仆仆仂亞仂 亳仆亠仍仍亠从舒
亳仗仂于 .弌. 仂仆仗亠从 仍亠从亳亶 仗仂 亟亳亳仗仍亳仆亠 束亳亠仄 亳从于亠仆仆仂亞仂 亳仆亠仍仍亠从舒
Grigory Pomadchin
TMPA-2015: Expanding the Meta-Generation of Correctness Conditions by Means o...
TMPA-2015: Expanding the Meta-Generation of Correctness Conditions by Means o...
Iosif Itkin
丱舒舒从亠亳亳从舒 从亳仄仂于 仗仂 亳仆仂仄舒亳从亠 亞亳舒 2011
丱舒舒从亠亳亳从舒 从亳仄仂于 仗仂 亳仆仂仄舒亳从亠 亞亳舒 2011
从舒亠亳仆舒 亞仂于仂于舒
从仗亠仆亠 亳亠仄
从仗亠仆亠 亳亠仄
sokol_klinik
Burdtech
Burdtech
Vladimir Burdaev
Motivation and Willpower component of the student model and it's application ...
Motivation and Willpower component of the student model and it's application ...
Natalia Smirnova
亠从亳 2. 仍亞仂亳仄亳亠从亳亠 仗仂弍仍亠仄. 弌舒仆亟舒仆亠 亠仄 仗仂亞舒仄仄. 亠亟仄亠 "丐亠仂...
亠从亳 2. 仍亞仂亳仄亳亠从亳亠 仗仂弍仍亠仄. 弌舒仆亟舒仆亠 亠仄 仗仂亞舒仄仄. 亠亟仄亠 "丐亠仂...
Nikolay Grebenshikov
X 亠亞亳仂仆舒仍仆舒 仆舒仆仂-仗舒从亳亠从舒 从仂仆亠亠仆亳
X 亠亞亳仂仆舒仍仆舒 仆舒仆仂-仗舒从亳亠从舒 从仂仆亠亠仆亳
MIREA
Bionics of Intelligence Scientific Journal
Bionics of Intelligence Scientific Journal
Yafreisy Carrero
Bionics of Intelligence Scientific Journal
Bionics of Intelligence Scientific Journal
Yafreisy Carrero
仂亞舒仄仄亳仂于舒仆亳亠 亳 仗仂亠从亳仂于舒仆亳亠 (仄亠仂亟仂仍仂亞亳亠从亳亶 舒仆舒仍亳亰)
仂亞舒仄仄亳仂于舒仆亳亠 亳 仗仂亠从亳仂于舒仆亳亠 (仄亠仂亟仂仍仂亞亳亠从亳亶 舒仆舒仍亳亰)
Vadim Karastelev
20080928 structuralcomplexitytheory lecture01-02
20080928 structuralcomplexitytheory lecture01-02
Computer Science Club
Verification of 800 Automata-Based Programs Built by means of Genetic Program...
Verification of 800 Automata-Based Programs Built by means of Genetic Program...
Iosif Itkin
舒于仂仄舒亳亰亳仂于舒仆仆仂亶 仗仂于亠从亠 亠亠仆亳亶 仆亠从仂仂仂亞仂 从仍舒舒 亰舒亟舒
舒于仂仄舒亳亰亳仂于舒仆仆仂亶 仗仂于亠从亠 亠亠仆亳亶 仆亠从仂仂仂亞仂 从仍舒舒 亰舒亟舒
Natalia Smirnova
X 亠亞亳仂仆舒仍仆舒 仆舒仆仂-仗舒从亳亠从舒 从仂仆亠亠仆亳
X 亠亞亳仂仆舒仍仆舒 仆舒仆仂-仗舒从亳亠从舒 从仂仆亠亠仆亳
MIREA
亳仗仂于 .弌. 仂仆仗亠从 仍亠从亳亶 仗仂 亟亳亳仗仍亳仆亠 束亳亠仄 亳从于亠仆仆仂亞仂 亳仆亠仍仍亠从舒
亳仗仂于 .弌. 仂仆仗亠从 仍亠从亳亶 仗仂 亟亳亳仗仍亳仆亠 束亳亠仄 亳从于亠仆仆仂亞仂 亳仆亠仍仍亠从舒
Grigory Pomadchin
TMPA-2015: Expanding the Meta-Generation of Correctness Conditions by Means o...
TMPA-2015: Expanding the Meta-Generation of Correctness Conditions by Means o...
Iosif Itkin
丱舒舒从亠亳亳从舒 从亳仄仂于 仗仂 亳仆仂仄舒亳从亠 亞亳舒 2011
丱舒舒从亠亳亳从舒 从亳仄仂于 仗仂 亳仆仂仄舒亳从亠 亞亳舒 2011
从舒亠亳仆舒 亞仂于仂于舒
从仗亠仆亠 亳亠仄
从仗亠仆亠 亳亠仄
sokol_klinik
Motivation and Willpower component of the student model and it's application ...
Motivation and Willpower component of the student model and it's application ...
Natalia Smirnova
亠从亳 2. 仍亞仂亳仄亳亠从亳亠 仗仂弍仍亠仄. 弌舒仆亟舒仆亠 亠仄 仗仂亞舒仄仄. 亠亟仄亠 "丐亠仂...
亠从亳 2. 仍亞仂亳仄亳亠从亳亠 仗仂弍仍亠仄. 弌舒仆亟舒仆亠 亠仄 仗仂亞舒仄仄. 亠亟仄亠 "丐亠仂...
Nikolay Grebenshikov
X 亠亞亳仂仆舒仍仆舒 仆舒仆仂-仗舒从亳亠从舒 从仂仆亠亠仆亳
X 亠亞亳仂仆舒仍仆舒 仆舒仆仂-仗舒从亳亠从舒 从仂仆亠亠仆亳
MIREA
Bionics of Intelligence Scientific Journal
Bionics of Intelligence Scientific Journal
Yafreisy Carrero
Bionics of Intelligence Scientific Journal
Bionics of Intelligence Scientific Journal
Yafreisy Carrero
仂亞舒仄仄亳仂于舒仆亳亠 亳 仗仂亠从亳仂于舒仆亳亠 (仄亠仂亟仂仍仂亞亳亠从亳亶 舒仆舒仍亳亰)
仂亞舒仄仄亳仂于舒仆亳亠 亳 仗仂亠从亳仂于舒仆亳亠 (仄亠仂亟仂仍仂亞亳亠从亳亶 舒仆舒仍亳亰)
Vadim Karastelev
20080928 structuralcomplexitytheory lecture01-02
20080928 structuralcomplexitytheory lecture01-02
Computer Science Club
Verification of 800 Automata-Based Programs Built by means of Genetic Program...
Verification of 800 Automata-Based Programs Built by means of Genetic Program...
Iosif Itkin

Cee secr-2013-smirnova-volga

  • 1. 亠于舒 仆亠亰舒于亳亳仄舒 仆舒仆仂-仗舒从亳亠从舒 从仂仆亠亠仆亳 束舒亰舒弍仂从舒 2013損 23 - 25 仂从磡, 仂从于舒 仗 舒亰舒弍仂从亳 亳仆亠仍仍亠从舒仍仆仂亶 仂弍舒ム亠亶 亳亠仄 束仂仍亞舒損 舒舒仍亳 弌仄亳仆仂于舒
  • 2. 弌从舒 亟仂从仍舒亟舒 于亠亟亠仆亳亠 仂舒仆仂于从舒 亰舒亟舒亳 亳亰仄亠亠仆亳 仗仂亞亠舒 于 亠亠仆亳亳 仍亞仂亳仄 Andes Physics Tutor 仍亞仂亳仄 弌 束仂仍亞舒損 于仂亟. 舒仍仆亠亶舒 舒弍仂舒 2
  • 5. 仆亠仍仍亠从舒仍亳亰舒亳 舒仗仂亰仆舒于舒仆亳 仂于亠舒 亟亠仆舒 弌亟亠仆 于于仂亟亳 亠亠仆亳亠 亰舒亟舒亳: 仗仂亞舒仄仄舒 亠仄: 5
  • 6. 束弌仍亠亟亳亠損 亳仆亠仍仍亠从舒仍仆亠 仂弍舒ム亳亠 亳亠仄: Andes Physics Tutor 亠 弍仂仍亠亠 仗仂亟于亳仆仂亠 舒仗仂亰仆舒于舒仆亳亠 仂于亠仂于 亟亠仆仂于: 6
  • 7. 束弌仍亠亟亳亠損 亳仆亠仍仍亠从舒仍仆亠 仂弍舒ム亳亠 亳亠仄: 弌 束仂仍亞舒損 仂亢亠 亟亠仍舒仍亳 束仄仆ツ 亳亠仄: 7
  • 8. 仆亠亠亶 于于仂亟舒 亠亠仆亳 弌 束仂仍亞舒損 亳 仗仂仍亰仂于舒亠仍亳-亞仄舒仆亳舒亳亳: 仗亳仄亠 丕仍仂于亳 亰舒亟舒亳: 弌. 于亠仄 仂弍亠仆亳 亳仆亠亠亶 (仄亳仆) 8 亠亳仍仂: 10 亳亰 11 亠仍., 亳仍亳 亳仆亠亠亶: 8 亠仍. 弌. % 仆亠亰舒亳舒仆仆 亳亠仄仂亶 舒亞仂于
  • 10. 亠亟仗仂仍仂亢亠仆亳 亳 仂亞舒仆亳亠仆亳 仗仂仍亰ム 仂仍从仂 仗仂仍亰ム 仂仍从仂 仂弍仂亰仆舒亠仆亳 亳亠仄! 仂弍仂亰仆舒亠仆亳 亳亠仄! 丐仂仍从仂 丐仂仍从仂 仂亟仆仂仂仆亠 仂亟仆仂仂仆亠 仂仄仍, 弍亠亰 仂仄仍, 弍亠亰 仂弍仆亠仆亳亶! 仂弍仆亠仆亳亶! LaTeX-仗仂亟仂弍仆亶 LaTeX-仗仂亟仂弍仆亶 亳仆舒从亳 亳仆舒从亳 10
  • 11. 亅舒仗 仗仂于亠从亳 舒亞舒 亠亠仆亳 亠亳亳从舒亳 舒亞舒 舒亠 仗仂亞亠舒 于 亠亠仆亳亳 弌仂仂弍亠仆亳亠 仂 舒亠 舒亞舒 ? 仂仗仂 从 亟亠仆 11 弍仆仂于仍亠仆亳亠 亳仆. (亟仍 仗仂亟从舒亰仂从 亳 仂亠仆从亳 亰舒 亰舒亟舒)
  • 12. 亠亳亳从舒亳 舒亞舒: 仗亳仄亠仆亶 舒仍亞仂亳仄 亟亠仆 于于亠仍 舒亞: z=1+y 舒亞 仗仂亟舒于仍ム 亳亰于亠仆亠 亳亠仄亠 亰仆舒亠仆亳 仗亠亠仄亠仆仆: 5=1+4 仂仍亠仆仆仂亠 于舒亢亠仆亳亠 仗仂舒亠 亳 舒于仆亳于舒亠 0: if simplify(5 (1 + 4)) == 0: //亟亠仆 于于亠仍 仗舒于亳仍仆亶 舒亞 亠亠仆亳
  • 13. 亠亳亳从舒亳 舒亞舒: 弍亳弍仍亳仂亠从亳 仍 仗仂亠仆亳 于舒亢亠仆亳亶 仄仂亢仆仂 亳仗仂仍亰仂于舒 弍亳弍仍亳仂亠从 SymPy: 13
  • 14. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 仆亠亳于亳舒仍仆舒 仗仂弍仍亠仄舒. 束舒亳于仆亶損 仗仂仂弍 仆亠 亞仂亟亳: 亟舒亢亠 亟仍 舒仄仂亶 仗仂仂亶 亰舒亟舒亳 亠弍亠 于仆亠亳 仍亳从仂仄 仄仆仂亞仂 仂仄仍 亠 亳 亠亠仆亳亶. 舒亞 亠亠仆亳 亟亠仆舒 14 亳 于亳仍亳亠仍仆仂 仂 仆亠 于亞仂亟仆仂 亠仆 亅 亳亠 舒仗 1 亅 1 舒 仗2 亅 舒 仗m Image courtesy of Keattikorn a FreeDigitalPhotos.net
  • 16. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳: 仗亳仄亠 舒亟舒舒: 于亳仍亳 舒仂礌亳亠 仄亠亢亟 于亠从仂舒仄亳 a 亳b 仂亰仄仂亢仆亠 亠亠仆亳 亞亠仆亠亳ム 仆舒 仂仆仂于亠 仂仄仍: 16 亟亠仆 于于亠仍 仂仄仍:
  • 17. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳: 仗亳仄亠 亠于亳亟仆仂, 仂 仂仄仍舒 仆舒 仂仆仂于亠 仂仄仍 (1) 亳 (3) 丐.亠. 仗仂亞亠 亟亠仆舒 = 2/6 = 33% 17 仗仂仍亠仆舒
  • 18. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 Andes Physics Tutor 亟仆舒 亳亰 亳亠仄: 18
  • 19. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 Andes Physics Tutor: 仆亠亟仂舒从亳 亠仗仂仆仆仂, 从舒从 仂弍舒弍舒于舒 仂仄仍 于亠从仂舒仄亳 亳 仄舒亳舒仄亳 亳仗舒 亠 亰舒亳亠仆 仂 亳仄亳舒亳亳 仗舒于亳仍仆仂 于于亠亟亠仆仆 舒亞仂于 亠亠仆亳: 于, 亟仍 仆亠亞仂 仂 仂亟仆仂 亳 仂 亢亠 仄亳舒亳亳: 19 舒于亳仍仆亶 舒亞:
  • 21. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌 束仂仍亞舒損: 仂仆仂亠仆亳 于亳仍亳仄仂亳 21
  • 22. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌 束仂仍亞舒損: 亠从亳亠 仂亞舒仆亳亠仆亳 舒仄仂亳仄 仍舒亶, 从仂亞亟舒 于 仍亠于仂亶 舒亳 仂仄仍 亟亠仆舒 仂仍从仂 仂亟仆仂 仂弍仂亰仆舒亠仆亳亠: 丼亠仄 弍仂仍亠 仂弍仂亰仆舒亠仆亳亶 于 仗仂于亠磳仄仂仄 舒亞亠 亰舒仄亠仆亠仆仂 仆舒 亳仍舒, 亠仄 亟仆亠亠 仆舒亠仄 舒仍亞仂亳仄 于磦亳 亳仄亳舒亳, .: 22 仗仂仍亳 于磦亳 亳仄亳舒亳 仆亠 仗仂仍亳
  • 23. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌 束仂仍亞舒損: 仆舒仂亢亟亠仆亳亠 亰舒于亳亳仄仂亠亶 亟亠仆 于于亠仍 仂仄仍: 弍仂亰仆舒亳仄 亳仄亠亠 舒从仂亶 亞舒 仗从舒亠仄 于 仆亠仄 仂 (c,c) 于仆亳亰, 仗仂从舒 仆亠 于仗. 仍仂于亳亠: 23 束亠从亠亠 仂仂礌亳亠損, 仗亳仂从 仂弍仂亰仆舒亠仆亳亶
  • 24. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌 束仂仍亞舒損: 仆舒仂亢亟亠仆亳亠 亰舒于亳亳仄仂亠亶 亟亠仆 于于亠仍 仂仄仍: 仂仍亳仄 亳 仗亳 亳 于舒亢亠仆亳亠 24
  • 25. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌 束仂仍亞舒損: 于磦仍亠仆亳亠 亳仄亳舒亳亶 舒从, 仂仄仍舒 亟亠仆舒: 亳 亞亠仆亠亳仂于舒仆仆仂亠 亳亠仄仂亶 于舒亢亠仆亳亠 舒仄亠仆亳仄 于 亠亞仂 仗舒于仂亶 舒亳 于亠 仂弍仂亰仆舒亠仆亳, 从仂仄亠 亠, 仂 仗亳于ム 于 , 仗仂仍亳仄: 25 从于亳于舒仍亠仆仆仂 仂仄仍亠 亟亠仆舒, 仆亠 亳仄亳舒亳
  • 26. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌 束仂仍亞舒損: 于磦仍亠仆亳亠 亳仄亳舒亳亶 丼仂 弍仍仂 弍, 亠仍亳 弍 亟亠仆 于于亠仍 仂仄仍 ? 仗仂仍亳仄 于舒亢亠仆亳亠 亠亞仂 仗舒于仂亶 舒亳 亰舒仄亠仆 仆亠亠亞仂. 弌舒于仆亳于舒亠仄 仂仄仍: 亳 26 亠 从于亳于舒仍亠仆仆, 仂 亳仄亳舒亳 仗舒于亳仍仆仂亞仂 舒亞舒
  • 27. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌 束仂仍亞舒損: 于磦仍亠仆亳亠 亳仄亳舒亳亶 丼仂 弍仍仂 弍, 亠仍亳 弍 亟亠仆 于于亠仍 仂仄仍 ? 仗仂仍亳仄 于舒亢亠仆亳亠 亠亞仂 仗舒于仂亶 舒亳 亰舒仄亠仆 仆亠亠亞仂. 弌舒于仆亳于舒亠仄 仂仄仍: 亳 亅从于亳于舒仍亠仆仆, 亳仄亳舒亳 仆亠 于磦仍磳 (仂 仂仆舒 亠) 27
  • 28. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌 束仂仍亞舒損: 舒亠 仗仂亞亠舒 亟亠仆 于于亠仍 仂仄仍: 仂仍亳仍亳 亳 仗亳: 丐.亠. 仗仂亞亠 于 亠亠仆亳亳 = 3/(3+2) 亳仍亳 4/(4+2) 28
  • 29. 亰仄亠亠仆亳亠 仗仂亞亠舒 于 亠亠仆亳亳 于 弌 束仂仍亞舒損: 舒于仂仄舒亳亠从仂亠 仗仂仂亠仆亳亠 亞舒舒 弌仆舒舒仍舒 仂亳仄 仂亟亠仍仆亠 亠弍舒 亞舒舒, 仗仂仂仄 仗仂仍舒亠仄 弍仂仍亠亠 仍仂亢仆 从 29
  • 30. 亰仄亠亠仆亳亠 仗仂亞亠舒: 仂舒仍仆亠 仍舒亳 弌亠亟亳 仗亠仗仂亟舒于舒亠仍亠亶 仆亠 仂亞仍舒亳 仂 仂仄, 亠仄 亟仂仍亢亠仆 亰舒仆亳仄舒 亟亠仆: 于于仂亟仂仄 仂仄仍 亳仍亳 舒亳仄亠亳从仂亶 亠亞亟舒 仆舒亶亟 仆亠仂亟亳仆舒仆亠 亟亠仆 舒亟仂 亳 仂弍舒弍舒于舒 舒亰仆亠 束仆亠 亳亟亠舒仍仆亠損 仍舒亳: (1-3)^2+(2-4)^2=8 -4=1-5 30 x_a*x_b+y_a*y_b =3*7+4*8 c_1*c_2=4
  • 32. 于仂亟 仂于亠 舒亰于亠仆亠 亠亠仆亳 亟亠仆仂于 于仂亰仄仂亢仆仂! 亠仂弍仂亟亳仄仂 舒仄仂亠 亳 亟亞亳亠 从舒亶仆亳亠 仍舒亳 于亳亟仂于 于于仂亟亳仄 亟亠仆舒仄亳 仂仄仍 亟亞亳亠 亰舒亟舒亳, 仆亠 仂仍从仂 仗仂 仍亳仆亠亶仆仂亶 舒仍亞亠弍亠 亠 仂亳 亰舒弍于舒 仂弍 仂亞舒仆亳亠仆亳 亳 仂舒于仍 亟亠仆 于仂亰仄仂亢仆仂 亟仍 束亢舒仍仂弍損 仆舒 亳亠仄 32
  • 33. 仗仂仍亰仂于舒仆仆亠 亳仂仆亳从亳 亳 仗仂仍亠亰仆亠 仍从亳 弌仍舒亶亟 1 http://habrahabr.ru/post/194240/ 弌仍舒亶亟 5 1.https://moodle.org/plugins/view.php?plugin=qtype_stack 2.亠于亳仆从舒 .. 束仂亟从亳仂仆仆舒 仄仂亟亠仍 亳仆亠舒从亳于仆仂亶 从仂仄仗仂仆亠仆 仂弍舒ム亠亶 亳亠仄損. http://www.mce.su/archive/doc15643/doc.pdf 3.亠于亳仆从舒 .. 束仂仂亠仆亳亠 亳仆亠仍仍亠从舒仍仆 仂弍舒ム亳 亳亠仄 仗仂 仄舒亠仄舒亳从亠 亳仗仂仍亰仂于舒仆亳亠仄 磶从舒 Tree-Refal損 // 亠仗亠从亳于仆亠 亳仆仂仄舒亳仂仆仆亠 亠仆仂仍仂亞亳亳 亳 亳仆亠仍仍亠从舒仍仆亠 亳亠仄損. 丐. 3. 15. 2003 33
  • 34. 仗仂仍亰仂于舒仆仆亠 亳仂仆亳从亳 亳 仗仂仍亠亰仆亠 仍从亳 弌仍舒亶亟 5 4.S. Klai, T. Kolokolnikov, and N. Van den Bergh, Using Maple and the web to grade mathematics tests, in Proceedings of the International Workshop on Advanced Learning Technologies, 2000. 5.M. Mavrikis and A. Maciocia, Wallis: a web-based ILE for science and engineering students studying mathematics, in Workshop of Advanced Technology for Mathematics Education in the 11th International Conference on Artificial Intelligence in Education, 2003, pp. 505512. 6.Maple T.A. http://www.maplesoft.com/products/mapleta/ 7.C. J. Sangwin, Assessing Elementary Algebra with STACK, International Journal of Mathematical Education in Science and Technology, vol. 38, no. 8, pp. 9871002, 2008. 8.C. J. Sangwin, Automating the marking of core calulus and algebra: eight years on. http://web.mat.bham.ac.uk/C.J.Sangwin/Publications/2009-12-mmg.pdf 34
  • 35. 仗仂仍亰仂于舒仆仆亠 亳仂仆亳从亳 亳 仗仂仍亠亰仆亠 仍从亳 弌仍舒亶亟 5 9.Answer tests. https:// github.com/maths/moodle-qtype_stack/blob/master/doc/en/Authoring/Answer_tests.md#E . 10.E. Melis and J. Siekmann, ActiveMath: An Intelligent Tutoring System for Mathematics, Artificial Intelligence and Soft Computing ICAISC 2004, vol. 3070, pp. 91101, 2004. 弌仍舒亶亟 6 VanLehn K. (et al.) The Andes Physics Tutoring System: Lessons Learned. International Journal of Artificial Intelligence in Education. Vol. 15. 3. 2005. http://oli.cmu.edu/wp-oli/wpcontent/uploads/2012/05/VanLehn_2005_Andes_Physics_Tutoring_System.pdf 35
  • 36. 仗仂仍亰仂于舒仆仆亠 亳仂仆亳从亳 亳 仗仂仍亠亰仆亠 仍从亳 弌仍舒亶亟 13 http://sympy.org/ru/index.html 弌仍舒亶亟 16 Shapiro J.A. An Algebra SubSystem for Diagnosing Students Input in a Physics Tutoring System. http://www.physics.rutgers.edu/~shapiro/tutor/submission3.pdf 弌仍舒亶亟 29 https://github.com/indra-uolles/solution_tracer 36
  • 37. 弌仗舒亳弍仂 亰舒 于仆亳仄舒仆亳亠! 舒舒仍亳 弌仄亳仆仂于舒, 仆.. 仍舒弍. 17 丕 smirnovanatalia2008@gmail.com 37

Editor's Notes

  • #3: 弌亠亶舒 仗仂仗仍仆舒 亠仄舒 仂仆仍舒亶仆-仂弍舒亰仂于舒仆亳: 于亠 仍舒仍亳 仗仂 Coursera, Udacity, EdX. 亅仂 仂仍亳仆亠 仂弍舒亰仂于舒亠仍仆亠 仗仍舒仂仄, 仂亟亠亢舒亳亠 仄仆仂亞仂 仗仂仍亠亰仆 从仂于. 仂 仄仂亢仆仂 仍亳 亳 亟亠仍舒 弍仂仍亠亠 亳仆亠仍仍亠从舒仍仆仄亳? 仂仂弍亠 亳仍亠亟仂于舒仆亳 仗仂 亳仆亠仍仍亠从舒仍仆仄 仂弍舒ム亳仄 亳亠仄舒仄 (intelligent tutoring systems) 于亠亟 亟舒于仆仂 亳 亠仆 亠 仂 仗亠亟仍仂亢亳 仗仂亞舒仄仄亳舒仄-仗舒从亳从舒仄. 仂亶 舒亠 于 仆舒仆仂-仗仂仗仍仆仂亶 仂仄亠 舒仄舒亳于舒ム瓿亠亰仍舒 亳 于于仂亟, 仗仂仍亠仆仆亠 仆舒仆仄 仂仂弍亠于仂仄, 仗仂 仗仂仂亠仆亳 从仂仆从亠仆仂亞仂 于亳亟舒 亳仆亠仍仍亠从舒仍仆 仂弍舒ム亳 亳亠仄.油
  • #4: 弌亠亶舒 仗仂仗仍仆舒 亠仄舒 仂仆仍舒亶仆-仂弍舒亰仂于舒仆亳: 于亠 仍舒仍亳 仗仂 Coursera, Udacity, EdX. 亅仂 仂仍亳仆亠 仂弍舒亰仂于舒亠仍仆亠 仗仍舒仂仄, 仂亟亠亢舒亳亠 仄仆仂亞仂 仗仂仍亠亰仆 从仂于. 仂 仄仂亢仆仂 仍亳 亳 亟亠仍舒 弍仂仍亠亠 亳仆亠仍仍亠从舒仍仆仄亳? 仂仂弍亠 亳仍亠亟仂于舒仆亳 仗仂 亳仆亠仍仍亠从舒仍仆仄 仂弍舒ム亳仄 亳亠仄舒仄 (intelligent tutoring systems) 于亠亟 亟舒于仆仂 亳 亠仆 亠 仂 仗亠亟仍仂亢亳 仗仂亞舒仄仄亳舒仄-仗舒从亳从舒仄. 仂亶 舒亠 于 仆舒仆仂-仗仂仗仍仆仂亶 仂仄亠 舒仄舒亳于舒ム瓿亠亰仍舒 亳 于于仂亟, 仗仂仍亠仆仆亠 仆舒仆仄 仂仂弍亠于仂仄, 仗仂 仗仂仂亠仆亳 从仂仆从亠仆仂亞仂 于亳亟舒 亳仆亠仍仍亠从舒仍仆 仂弍舒ム亳 亳亠仄.油
  • #5: 弌亠亶舒 仗仂仗仍仆舒 亠仄舒 仂仆仍舒亶仆-仂弍舒亰仂于舒仆亳: 于亠 仍舒仍亳 仗仂 Coursera, Udacity, EdX. 亅仂 仂仍亳仆亠 仂弍舒亰仂于舒亠仍仆亠 仗仍舒仂仄, 仂亟亠亢舒亳亠 仄仆仂亞仂 仗仂仍亠亰仆 从仂于. 仂 仄仂亢仆仂 仍亳 亳 亟亠仍舒 弍仂仍亠亠 亳仆亠仍仍亠从舒仍仆仄亳? 仂仂弍亠 亳仍亠亟仂于舒仆亳 仗仂 亳仆亠仍仍亠从舒仍仆仄 仂弍舒ム亳仄 亳亠仄舒仄 (intelligent tutoring systems) 于亠亟 亟舒于仆仂 亳 亠仆 亠 仂 仗亠亟仍仂亢亳 仗仂亞舒仄仄亳舒仄-仗舒从亳从舒仄. 仂亶 舒亠 于 仆舒仆仂-仗仂仗仍仆仂亶 仂仄亠 舒仄舒亳于舒ム瓿亠亰仍舒 亳 于于仂亟, 仗仂仍亠仆仆亠 仆舒仆仄 仂仂弍亠于仂仄, 仗仂 仗仂仂亠仆亳 从仂仆从亠仆仂亞仂 于亳亟舒 亳仆亠仍仍亠从舒仍仆 仂弍舒ム亳 亳亠仄.油
  • #6: https://moodle.org/plugins/view.php?plugin=qtype_stack
  • #7: https://moodle.org/plugins/view.php?plugin=qtype_stack
  • #8: https://moodle.org/plugins/view.php?plugin=qtype_stack
  • #9: 5f7 15 仄亳仆 亠亳仍 2a5 5 仄亳仆 仆亠 亠亳仍 亠仄 仂弍亠仆亳 仗仂从舒亰舒仆仂 仂仍从仂 亠 从仂 仗仂 亠仆仂从 于亠 亟亠仍舒仍
  • #10: 弌亠亶舒 仗仂仗仍仆舒 亠仄舒 仂仆仍舒亶仆-仂弍舒亰仂于舒仆亳: 于亠 仍舒仍亳 仗仂 Coursera, Udacity, EdX. 亅仂 仂仍亳仆亠 仂弍舒亰仂于舒亠仍仆亠 仗仍舒仂仄, 仂亟亠亢舒亳亠 仄仆仂亞仂 仗仂仍亠亰仆 从仂于. 仂 仄仂亢仆仂 仍亳 亳 亟亠仍舒 弍仂仍亠亠 亳仆亠仍仍亠从舒仍仆仄亳? 仂仂弍亠 亳仍亠亟仂于舒仆亳 仗仂 亳仆亠仍仍亠从舒仍仆仄 仂弍舒ム亳仄 亳亠仄舒仄 (intelligent tutoring systems) 于亠亟 亟舒于仆仂 亳 亠仆 亠 仂 仗亠亟仍仂亢亳 仗仂亞舒仄仄亳舒仄-仗舒从亳从舒仄. 仂亶 舒亠 于 仆舒仆仂-仗仂仗仍仆仂亶 仂仄亠 舒仄舒亳于舒ム瓿亠亰仍舒 亳 于于仂亟, 仗仂仍亠仆仆亠 仆舒仆仄 仂仂弍亠于仂仄, 仗仂 仗仂仂亠仆亳 从仂仆从亠仆仂亞仂 于亳亟舒 亳仆亠仍仍亠从舒仍仆 仂弍舒ム亳 亳亠仄.油
  • #11: 5f7 15 仄亳仆 亠亳仍 2a5 5 仄亳仆 仆亠 亠亳仍 亠仄 仂弍亠仆亳 仗仂从舒亰舒仆仂 仂仍从仂 亠 从仂 仗仂 亠仆仂从 于亠 亟亠仍舒仍
  • #12: https://moodle.org/plugins/view.php?plugin=qtype_stack
  • #13: https://moodle.org/plugins/view.php?plugin=qtype_stack
  • #15: Image courtesy of Keattikorn at油FreeDigitalPhotos.net
  • #16: 弌亠亶舒 仗仂仗仍仆舒 亠仄舒 仂仆仍舒亶仆-仂弍舒亰仂于舒仆亳: 于亠 仍舒仍亳 仗仂 Coursera, Udacity, EdX. 亅仂 仂仍亳仆亠 仂弍舒亰仂于舒亠仍仆亠 仗仍舒仂仄, 仂亟亠亢舒亳亠 仄仆仂亞仂 仗仂仍亠亰仆 从仂于. 仂 仄仂亢仆仂 仍亳 亳 亟亠仍舒 弍仂仍亠亠 亳仆亠仍仍亠从舒仍仆仄亳? 仂仂弍亠 亳仍亠亟仂于舒仆亳 仗仂 亳仆亠仍仍亠从舒仍仆仄 仂弍舒ム亳仄 亳亠仄舒仄 (intelligent tutoring systems) 于亠亟 亟舒于仆仂 亳 亠仆 亠 仂 仗亠亟仍仂亢亳 仗仂亞舒仄仄亳舒仄-仗舒从亳从舒仄. 仂亶 舒亠 于 仆舒仆仂-仗仂仗仍仆仂亶 仂仄亠 舒仄舒亳于舒ム瓿亠亰仍舒 亳 于于仂亟, 仗仂仍亠仆仆亠 仆舒仆仄 仂仂弍亠于仂仄, 仗仂 仗仂仂亠仆亳 从仂仆从亠仆仂亞仂 于亳亟舒 亳仆亠仍仍亠从舒仍仆 仂弍舒ム亳 亳亠仄.油
  • #21: 弌亠亶舒 仗仂仗仍仆舒 亠仄舒 仂仆仍舒亶仆-仂弍舒亰仂于舒仆亳: 于亠 仍舒仍亳 仗仂 Coursera, Udacity, EdX. 亅仂 仂仍亳仆亠 仂弍舒亰仂于舒亠仍仆亠 仗仍舒仂仄, 仂亟亠亢舒亳亠 仄仆仂亞仂 仗仂仍亠亰仆 从仂于. 仂 仄仂亢仆仂 仍亳 亳 亟亠仍舒 弍仂仍亠亠 亳仆亠仍仍亠从舒仍仆仄亳? 仂仂弍亠 亳仍亠亟仂于舒仆亳 仗仂 亳仆亠仍仍亠从舒仍仆仄 仂弍舒ム亳仄 亳亠仄舒仄 (intelligent tutoring systems) 于亠亟 亟舒于仆仂 亳 亠仆 亠 仂 仗亠亟仍仂亢亳 仗仂亞舒仄仄亳舒仄-仗舒从亳从舒仄. 仂亶 舒亠 于 仆舒仆仂-仗仂仗仍仆仂亶 仂仄亠 舒仄舒亳于舒ム瓿亠亰仍舒 亳 于于仂亟, 仗仂仍亠仆仆亠 仆舒仆仄 仂仂弍亠于仂仄, 仗仂 仗仂仂亠仆亳 从仂仆从亠仆仂亞仂 于亳亟舒 亳仆亠仍仍亠从舒仍仆 仂弍舒ム亳 亳亠仄.油