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

在我国，语言和听力障碍专科学校的数学教材和方法与非专科学校相同。我们的研究表明，学校为有特殊需要的学生使用的材料不适合这些学生。在接下来的过程中，我们开发了适用于普通学校和聋哑学校的新的数学教材和教学方法。设M_1， M_2和M_3为“三个我”，定义如下。M_1: M_1收集“外部对象”信息。M_2: M_2收集“内部对象”的信息。M_3: M_3结合了M_2给出的信息和M_3给出的信息。（其中“外物”是每个人都能通过五感确认的注意对象，“内物”是形象。）(1)结合M_1、M_2、M_3的活动，建立了与学生数学思维活动相对应的信息加工模型。(2)在(1)给出的信息加工模型的基础上，构建与M_1、M_2、M_3活动相对应的“思维框架”。(3)用(2)给出的思维框架来表征M_1、M_2、M_3的活动。(4)思维框架对学生思维的表征可以看作是“有思维的学生的表征”。此外，我们还为以思维框架为代表的学生准备了教材和讲解，以培养他们的思维能力。然后，我们发现了以下事实。如果聋哑学校和普通学校的学生能根据需要把M_1、M_2和M_3的活动结合起来，他们的思维肯定能得到发展。这一事实对于提高数学教育的教与学过程具有十分重要的意义。

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.