Developmental Study for Teeching and Assessment on Variation of School Mathematics

教师有如下共识：（a）在保持教学与评价平衡的前提下，让学生按照自己的方式创造数学是可能的;（B）教师可以通过教学和评价活动引导学生进行更高层次的数学活动。在课题组的研究过程中，我们有机会与参与者就如何提高“奥菲本”教学与评价分进行了交流，通过这些活动，我们发现：（1）为了提高“奥菲本”教学与评价分，数学课堂上使用的问题需要在其数学内容中包含发展性特征。我们一直在争论发展这些问题的重要性，注意到“方法和内容，是开放的人类和数学”。(2)教师应该通过每天使用这些问题来发展他们的课堂活动。我们提出的教学和评估方法，使教师能够总结学生的各种思维从数学的角度来看，并引导学生的思维方式，提高他们的兴趣。这一方法将有助于各年级数学课堂活动的开展和推广，这两点正是本研究所取得的成果，也是本研究的特点。

Teacher has a consensus as follows ;(a) it is possible for students to create mathematics on their own way with keeping a balance between teaching and assessing aspects,(b) it is possible teachers lead students to higher level mathematical activities through teaching and assessing their activities. Throughout our research working group, we had opportunities to meet with participants how to enhance "Aufheben" teaching and assessing points.Thgrough these activities, the following points were found ;(1) For the purpose of promorting "Aufheben" teaching and assessing points, problems used in the mathematics class need to contain developmental features in its mathematical content. We have been arguing on the importance of developing these problems by noting the words "method and content that are open to both human being and mathematics".(2) Teachers should develop their class activities by using these problems on a everyday basis. We propose teaching and assessment methods that enable teachers to summare students' variety of thinking from a mathematical perspective and to lead students to the ways of thinking that enhance their interests. This method will serve for developing and generalizing mathematics activities in the classroom across all grades.These two points had exactly what our study has accomplished and constituted characteristics of our study.