A STUDY OF PAPER-TEST WITH OPERATIONAL ACTIVITY

对于学生K所展示的数学命题P，我们可以考虑以下三种情况。案例1)P是学生K自己构建的。案例2)P是由学生K和他的朋友构建的。案例3)P是由与学生k不同的学生构建的，但是老师不可能将这三个案例中的一个与其他案例区分开来。这就是问题所在。我们1992年研究的主要目的是为这个问题找到一个明确的答案。建立数学命题P的任务是一项需要将以下五个活动整合起来的活动。1)准备思维场（F_i） 2)准备知识和概念（C_j） 3)从（F_i）和（C_j）中获得建立p所需的信息（I_k） 4)找到（I_k）的合适组合来构造小命题（P_l）。5)找到（P_l）的合适组合来构造命题p。计算机可以记录上述每项活动的正确时间。因此，我们可以重构学生的思维过程。因此，我们能够对上述问题给出一个答案。

For a mathematical proposition P shown by student K,we may consider the following three cases. Case1) P was constructed by student K himself. Case2) P was constructed by student K and his friends. Case3) P was constructed by students different from student K.But it is impossible for the teacher to disitinguish one of these three cases from others. It is the problem. The main purpose of our research in 1992 was to find a definite answer to the problem. The task of establishing the mathematical proposition P is an activity that requires action that integrates the following five activities. 1) Prepare the thinking field (F_i) 2) Prepare the knowledge and concepts (C_j) 3) Obtain from (F_i) and (C_j) the information (I_k) needed in establishing P. 4) Find suitable combinations of (I_k) to construct mini-propositions (P_l). 5) Find a suitable combination of (P_l) to construct the proposition P.We found the following facts. It is possible for the computer to record the correct time corresponding to each activities above mentioned. Therefore, we may reconstruct the students' thinking process. Thus, we were able to give an answer to the problem above stated.