DEVELOPMENT OF TEACHING MATERIALS AND TEACHING METHODS OF MATHEMATICS VALID BOTH IN ORDINARY SCHOOL AND DEAF-AND-DUMB SCHOOL.

在我国，语言和听力残疾人专门学校的数学教材和教学方法与普通学校相同。我们的研究表明，特教学校的教材对这些学生来说是不合适的，我们开发了新的数学教材和教学方法，这些教材和教学方法既适用于普通学校，也适用于聋哑学校。M_1：M_1收集“外部对象”的信息。M_2：M_2收集“内部对象”的信息。M_3：M_3将M_2给出的信息与M_3给出的信息结合起来。（这里的“外物”是每个人都能通过五官确认的注意对象，“内物”是意象。）(1)考虑到M_1、M_2和M_3的活动，我们建立了一个与学生数学思维活动相对应的信息加工模型。(2)我们在（1）给出的信息加工模型的基础上，建立了与M_1、M_2、M_3活动相对应的“思维框架”。(3)我们用（2）给出的框架表示M_1，M_2，M_3的活动。(4)我们可以把思维框架对学生思维的再现看作是“有思维的学生的再现”，并为思维框架所代表的学生准备了教材和讲解，以发展他们的思维。我们发现，如果聋哑学校和普通学校的学生能根据需要把M_1、M_2、M_3的活动联合收割机结合起来，肯定能发展他们的思维，这对改进数学教育中的教与学过程是非常重要的。

In our country, teaching materials and methods used for mathematics in specialized schools for the speech-and hearing-impaired are the same as those used in non-specalized schools. Our research suggests that materials used in schools for those with special needs are inappropriate for these students.We have developed new teaching materials and teaching methods of mathematics valid both in ordinary school and deaf-and-dumb school in the followin procedure.Let M_1, M_2 and M_3 be "three myself" defined by the following. M_1 : M_1 collects information of "outer object". M_2 : M_2 collects information of "inner object". M_3 : M_3 combines information given by M_2 with information given by M_3. (where "outer object" is the object of attention which everyone can confirm it by five sense, and "inner object" is the image.)(1) Considering the activities of M_1, M_2 and M_3, we make a information processing model corresponding to the students' mathematical thinking activities.(2) We make "thinking frame" corresponding to the activities of M_1, M_2 and M_3 on the basis of information processing model given by (1).(3) We represent the activities of M_1, M_2 and M_3 by means of the tinking frame given by (2).(4) We can regard representation of a student's thinking by the thinking frame as "a representation of the thinking student".Further, we have prepared teaching materials and explanations for the students represented by the thinking frame in order to develop their tinking. Then, we have found the following fact.If the students in deaf-and-dumb school and ordinary school can combine the activities of M_1, M_2 and M_3 as occasion demands, surely they are able to develop their thinking.The fact is very important for the improvement teaching learning process in mathematics education.