一个通用的学生考试成绩分布的数学模型研究

学生考试成绩分布是教学研究的一个重要课题,可以从多个角度开展研究,如讨论成绩分布的基本规律、分析成绩分布的基本决定因素、研究如何获得准确合理的成绩分布、探讨根据成绩分布如何改进教学活动等.目前人们基本上是以定性研究为主,很少见到定量的学生成绩分布的研究.为了促进该领域研究的进一步开展,提出了一个定量的研究学生成绩分布的数学模型,该模型中唯一的假设是学生考试成绩取决于学习时间和学习效率.利用学生人数随着学习时间和学习效率分布的两个基本规律,获得了学生人数随考试成绩分布的基本规律.实践中两个基本规律可以通过问卷、测试、谈话或者借助于一定的理论分析等多种方式获得.基于分子运动论和高斯模型,获得了一种学生人数随着学习时间和学习效率分布的两个特殊规律,分析了其中参数的意义和影响,给出了一些很有意义的结论.该模型可以预测学生考试成绩的分布规律,获得学生学习状况的许多信息,有助于改进教学活动和提高学生学习积极性.这是一个非常初步的定量化研究,希望在未来的研究中不断改进和丰富.

A General Mathematical Modeling Formulation of Grade Distribution

Grade distribution (GD) is an important source to investigate the state of student studying a course. There are many research topics regarding GD: how to obtain the basic function of GD, what fundamental factors would determine GD, how to improve teaching activities according to GD, et al. At present, the researches in this field are mainly qualitative, and few quantitative researches could be found. In order to improve the research in this field, a general quantitative mathematical model is put forward, which could be very helpful in studying GD. The only hypothesis in the model is that the grade depends upon the studying efficiency and the studying time length. Making use of the distribution of student studying efficiency and the distribution of student studying time length, we establish a general mathematical formulation regarding GD. Two distributions could be acquired by means of investigations,questionnaire, informal talk and testing or theoretical analysis. Based on molecular kinematics, we acquire a specific formulation, and find many interesting and helpful conclusions by analyzing the role of parameters and their influence on the GD. This general formulation could predict GD, and provide useful information about student studying a course, so it would be very helpful in improving teaching activities, even though it is a very preliminary quantitative model.