单项选择题

Mathematics Education of Japan Generally speaking, people emphasize that elementary school children should be taught just basic mathematic fundamentals and knowledge, such as basic calculation or understanding the names and the properties of simple diagrams. In such lessons, teachers teach mathematics lessons in a way that children do not think deeply about mathematical maters, that is, children just learn the procedures of calculation, the properties of diagrams, etc. I am sure that children should learn basic and fundamental skills and knowledge, however, such lessons do not promote interest and appreciation of mathematical learning. I think that children do need to think for themselves and act for themselves through mathematics lessons in addition to mathematic fundamentals. Then, how can we foster children’’s abilities to think and express themselves mathematically I will present my fundamental ideas and an actual record of lessons. Add Advanced Learning in Mathematics Curriculum or Develop the Curriculum Curriculum standards show explicitly minimum essentials that children have to learn in school. Japanese textbooks are written based on the curriculum standards and it has no extension because of limitation. It is a teacher’’s responsibility to lead his/her lesson to develop children’’s thinking beyond the restrictions of the textbook. Furthermore, we need to plan advanced learning in our mathematics curriculum within limited teaching hours. This means that we should intersperse the curriculum standards with expanded content. Changing from "Knowledge Pouring-type Lessons" to "Knowledge Creating-type Lessons" Next, we teachers need to change our views of elementary mathematics lessons. We should try to change from traditional "Knowledge Pouring-type Lessons" to "Knowledge Creating-type Lessons". Knowledge pouring-type lesson means a traditional and conventional style where teachers give children ready-made mathematics knowledge and concepts in a one-side way. On the contrary, knowledge creating-type lesson means that children create mathematics knowledge and concepts themselves. This change is needed for children as well as for teachers. It is important that children feel that learning mathematics is to create new mathematics thinking, while talking about mathematical maters together. The Way of Thinking About "Knowledge Creating-type Lessons" The necessary condition to approve "Knowledge Creating-type Lessons" is the thought that elementary mathematics lessons consist of children’’s constructive activities (the view of constructive learning). Constructive learning is done through children’’s collaborative and interactive learning about each thought. Therefore, teachers do not explicitly teach children their knowledge and skill but children grasp a problem themselves, pursue, and solve the problem. Thus, they create new knowledge themselves through the learning of problem solving, (but, I do not agree to what is called "New-New Math", overemphasizing constructive learning without basic drills. Until now it has been said that such learning is only for advanced children; however, this method could be used to deepen mathematical understanding in low-level children also. The situation where the class includes various types of children all thinking together in mathematics lessons makes it possible to practice knowledge creating-type lessons. That is, in normal classrooms of mixed abilities, we can make use of children’’s thoughts, developing their learning and creating new knowledge. Because of this we do not need to group children specially. The Role of Teacher is to Draw Out Children’’s Thoughts What is the way to be able to make use of low-level children’’s thoughts as 1 stated in the above chapter It means that children’’s simple and natural questions and thoughts could be important elements of mathematics lessons. That is, children’’s expressions, words, attitudes, and responses could be elements that are integrated into mathematics lessons. Sometimes, children’’s murmuring and mistakes can be important cues. The teacher needs the ability to draw out children’’s expressions and to teach children how to express their thoughts. The teacher has to draw out children’’s thoughts, listen to them, and let children discuss them together, and by doing so expanding their thoughts. In other words, a teacher would act as a chair presiding over a lesson or as the coordinator of it. When to Advance Children’’s Mathematical Thinking and Expression Abilities Although we might say we can do it in every lesson stage, it is first clear that we can encourage children when to ask questions. Children discover new problems when facing various mathematical teaching materials that the teacher presents in, a lesson. When discovering new problems, they have to think about it in many ways and express their thoughts. Next, their abilities can be developed at the stage where they pursue their problem cooperatively. Then, they have to think out and express their thoughts and solutions. Moreover, to analyze the expression presented also can become a mater to think about together. Therefore, It is important that we teachers lead children to discover other new problems after they solve the previous problem. That is, knowledge creating-type lessons show continuous problem solving from problem to problem. Such lessons make it possible to draw out and encourage children’’s thinking and expressions. The point is that we let children think about and discuss mathematical matters, which can be a method to foster children’’s mathematical thinking and expressions ability. Recently, it has been said loudly that we should reform our mathematics education. But frankly speaking, we cannot say it has been very fruitful. Various proposals have been made about how to teach mathematics lessons, however, I have not heard mathematics classroom in school has been actually reformed. The reason why lesson reform has been less successful may be that teachers have not considered much of children’’s thoughts and feelings in mathematics lessons until now. Therefore, we need to accept and consider children’’s thinking and expression much more. In other words, we need to reform our lessons into continuous problem solving lessons that foster children’’s mathematical thinking and expression abilities. Through continuous practicing lessons that make children think and expression themselves mathematically, children acquire basic skills and knowledge. It is not too much to say that basic mathematic fundamentals can be acquired through advanced learning and developing curriculum standards. Moreover, teachers also need to develop new teaching materials in order to create lessons fostering children’’s mathematical thinking and expression abilities. It is important that teachers study the subject of mathematics themselves and teach children mathematics creatively. The author prefers "Knowledge Pouring-type Lessons" to "Knowledge Creating-type Lessons" in the teaching of mathematics.