Collaboration 
  Learning by e-Learning
  Kazumi Yamada 
  kyamada@ed.niigata-u.ac.jp 
  Faculty of Education and Human Sciences 
  Niigata University 
  Japan
   
 
Abstract
 There 
  are many elementary schools having only small classes in small villages in Japan. 
  In the class where only 2 or 3 children are, various thoughts do not come out 
  from children, and human relations are also fixed, therefore there is a problem 
  that their learning does not deepen. In order to solve this, the student's number 
  can be increased by connecting some classrooms with a network. While exchanging 
  opinions and information by utilizing the character chat, the white board, and 
  Web Cam of messenger, they can discover that there are various views which they 
  do not notice in a small number of children, and can know each merit. I will 
  give four next examples and suggest collaboration learning in a virtual classroom 
  organized on a net and method of mathematical communication. 
  
  Example 1: the lesson of the integer that used my original “multimedia 
  animal calculator”. 
  
  Example 2: the lesson that children consider the structure of Braille while 
  they exchange with each other on a network the cads to which their name are 
  written in Braille.
  
  Example 3: the lesson that children write a book of arithmetic in collaboration 
  with each other. 
 Example 
  4: the lesson that children collect arithmetical discoveries together in the 
  virtual classroom on a network, and make an exhibition room.
  
  The summary of Example 1 is described below.
  
  I created the following “multimedia animal calculator” by myself. 
  The design of the calculator is changed into what replaced the number keys from 
  O to 9 by the keys (animal button) of different animal marks. If an animal button 
  is pushed, the cry of the animal will carry out. If "+, -,×, ÷,=" 
  are pushed, it will talk with "plus, minus, times, divided by , equal to" in 
  a child's voice, and the formula of calculation will be expressed on a display 
  with animal marks. Let’s think about a problem to infer a number of a 
  key of each which is masked in a mark of an animal by repeating calculation 
  of one column and one column with this calculator. 
  
  In the case of this problem, they will talk that it is necessary to pay attention 
  to the character of the number of abbreviation or a multiple, comparison of 
  a pattern of an expression of multiplication, the number of beams of a calculation 
  result, etc. by chats in the virtual classroom organized on a net. They will 
  consult also about solving four kinds of this problem by assigning. Furthermore, 
  the following expansive lessons are also enabled. A certain child sticks on 
  a white board the formulas used for his answer, and asks whether someone can 
  explain instead of himself why he was able to solve. It is one of the effective 
  methods of instruction of the mathematical communication for understanding the 
  others' view to guess a partner's idea.  
  
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