Developmental Study for Teeching and Assessment on Variation of School Mathematics

教师有如下共识；(a)学生有可能在保持教学和评估之间的平衡的情况下以自己的方式创造数学；(b)教师有可能通过教学和评估学生的活动来引导学生进行更高水平的数学活动。在我们的研究工作小组中，我们有机会与参与者会面，了解如何提高“Aufheben”教学和评估点。通过这些活动，发现了以下几点：(1)为了促进“完美”教学和评点，数学课堂中使用的问题需要在数学内容上包含发展性特征。我们一直在讨论开发这些问题的重要性，并指出“对人类和数学开放的方法和内容”。(2)教师应该在日常生活中运用这些问题来开展课堂活动。我们提出的教学和评估方法，使教师能够从数学的角度总结学生的各种思维，并引导学生的思维方式，提高他们的兴趣。这种方法将有助于在所有年级的课堂上发展和推广数学活动。这两点正是我们的研究已经完成的，也是我们研究的特点。

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.