Practical Research to Unite Class Teaching Based on Education Method of Mathematical Course with Actual School Classes

数学教育陷入了一个不可避免的恶性循环，典型的死板数学课增加了不喜欢数学的学生数量。这些学生成年了，他们成为了家长和老师，拥有典型的僵化的数学概念。当这样的家长和老师教学生数学时，这些学生又会不喜欢数学。因此，恶性循环永远不会停止增加不喜欢数学的学生的数量。培养具有极大灵活性的数学观念和课堂教学观念的好教师，是走出恶性循环的有效具体措施。作为这一目标的一步，努力开发教材，将基于数学课程教育方法的课堂教学与学校实际课堂相结合。研究结果如下：1.教师应具备丰富的数学知识和教学技巧，灵活地进行课堂教学，实现数学活动自由开展的课堂；2.教师或有志成为教师的学生可以通过滚动式学习有效而具体的课堂教学情景。他们应该多次体验实际的数学课，像一个解决未知问题的学生一样玩弄木桶。对情景的实际体验自然会引发对学习心理、教学方法、课程和数学背景下的发展性研究的动机。学生和教师的共同努力取得了成效。结果取决于所选的教材。在这些努力中，可以开发出新的好教材。特别是以下是吸引人的实质性问题：-支付120日元的方法有多少？-开放式方法的课堂发展初等几何(带故事的问题结构)复习-草图的数学背景

Math education has fallen in an inescapable vicious cycle, Typical rigid math classes increase the number of students who dislike math. Those students become adult, and they become parents and teachers with typical rigid mathematical concept. When such parents and teachers teach math to students, again, these students will dislike math. So, the vicious cycle never stops increasing the number of students who dislike math. To nurture good teachers with great flexible mathematical concept and class teaching concept is an effective concrete measure to escape from the vicious cycle. As a step for the purpose, efforts to develop teaching materials were made by uniting class teaching based on education method of mathematical course with actual school classes. Findings are as follows :1. Teachers should have great knowledge on math and teaching technique to conduct a class flexibly, for realizing a class where mathematical activities freely develop,2. Teachers or students who want to be teachers can study effective and concrete class teaching scenes through roll playing. They should experience actual math classes many times, by playing the pail of a student who tackles with unknown problems.3. Actualexperience of the scenes naturally triggers motivations toward developmental study on psychology of learning, teaching method, curriculum and mathematics in the background.4. Joint efforts by students and schoolteachers produce effects.5. Results depend on chosen teaching materials. New good teaching materials could be developed in the efforts. Especially, followings were attractive and substantial problems :- How many ways for paying 120 yen?- Class development on open-ended approach Review on elementary geometry (Problem structure with a story) - Mathematical background of sketchmap