毕业论文 基于马氏链的教学质量评估的数学模型.doc
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毕业论文 基于马氏链的教学质量评估的数学模型,摘要本文通过建立数学模型对教学质量进行评估，应用马尔科夫链分析法考虑学生的原始状态，在同一标准下把 、 教师学生的初始成绩分成五个等级，确定出状态空间，然后根据施教后的成绩，求出一步转移概率，建立一步转移概率矩阵，最后根据马尔科夫链的遍历性求出极限分布 ．对每一等级赋予分数，对教学效果的定量指标加权平均，由所得的数学期...
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摘 要
本文通过建立数学模型对教学质量进行评估，应用马尔科夫链分析法考虑学生的原始状态，在同一标准下把 、 教师学生的初始成绩分成五个等级，确定出状态空间，然后根据施教后的成绩，求出一步转移概率，建立一步转移概率矩阵，最后根据马尔科夫链的遍历性求出极限分布 ．对每一等级赋予分数，对教学效果的定量指标加权平均，由所得的数学期望来评价教师的教学质量，这种方法克服了学生原有基础存在差异的问题.转移概率矩阵 集中反映了教学质量、教学条件、学风及社会环境等等因素的影响， 的极限状态说明，这些因素稳定时，教学效果在这些条件的影响下可能达到的程度，且这一可能达到的程度与学生原有的基础无关．由极限分布 可以对极限状态下各等级人数进行预测，通过分析使教师获取教学的反馈信息，以对自己的教学方式进行反思和调整，促进教学水平的提高．
对马氏链模型进行改进，在求得一步转移概率矩阵后，定义学生成绩“进步度”，即学生进步的程度（退步时进步度为负值），把握学生成绩的整体进步、退步情况，同时也消除了基础差异的因素．通过计算进步矩阵和效率值又能对教学效果进行评价，且与马氏链模型所得的结论一致，同时还能得到一些很有参考价值的教学反馈信息．
关键词：马尔科夫链；转移概率矩阵；遍历性；教学质量评估；极限分布
ABSTRACT
In this thesis, we study a mathematical model which can eva luate the quality of teaching. We analysis the original state of the student by Markov chain, In the same standard, we divided the students who tought by teacher A and teacher B respectively into five levels by initial achievement, then determine the state space. We calculate the one step Transition probability matrix according to the student’s achievement that after teaching, and obtain the Limit distribution by Markov chain Ergodicity. The quantitative index of teaching weighted average by given every level scores, so we can eva luate the teaching quality according to the mathematical expectation. This method overcome the problem of student’s basis difference, therefore, Transition probability matrix reflects the quality of teaching, teaching conditions, style of study and social environment, and so on. Limit distribution shows teaching effectiveness may reach when these factors are stable, and it have nothing to do with the students’ basis difference. By analyzing the feedback information, teachers can adjust their teaching style, and improve the teaching quality.
To improve the Markov chain model, we define ‘progress degree’,which is the extent of the student progress (the progress degree is negative when regress). From the progress degree we can learn the overall progress of students achievement, and it also eliminates the factor of basis difference. We can eva luate the teaching quality by calculate the progress matrix and the value of efficiency, and it’s conclusion is similar to the model of Markov chain, we can also get some valuable feedback information.
Keywords: Markov chain; Transition probability matrix; Ergodicity; Teaching eva luation; Limit distribution
目 录
前 言 1页
第一章 马氏链基本理论 2页
1.1马尔科夫过程及其概率分布 2页
1.1.1马尔科夫性及其马尔科夫过程 2页
1.1.2马儿科夫链及转移概率 2页
1.1.3转移概率矩阵 3页
1.2遍历性 3页
第二章 问题的分析 5页
第三章 模型的建立与求解 6页
3.1模型的建立 6页
3.2实例求解 8页
3.3成绩的分析及结论 9页
3.4模型的改进 11页
第四章 模型的评价 13页
参考文献 14页
附 录 15页
致 谢 17页
本文通过建立数学模型对教学质量进行评估，应用马尔科夫链分析法考虑学生的原始状态，在同一标准下把 、 教师学生的初始成绩分成五个等级，确定出状态空间，然后根据施教后的成绩，求出一步转移概率，建立一步转移概率矩阵，最后根据马尔科夫链的遍历性求出极限分布 ．对每一等级赋予分数，对教学效果的定量指标加权平均，由所得的数学期望来评价教师的教学质量，这种方法克服了学生原有基础存在差异的问题.转移概率矩阵 集中反映了教学质量、教学条件、学风及社会环境等等因素的影响， 的极限状态说明，这些因素稳定时，教学效果在这些条件的影响下可能达到的程度，且这一可能达到的程度与学生原有的基础无关．由极限分布 可以对极限状态下各等级人数进行预测，通过分析使教师获取教学的反馈信息，以对自己的教学方式进行反思和调整，促进教学水平的提高．
对马氏链模型进行改进，在求得一步转移概率矩阵后，定义学生成绩“进步度”，即学生进步的程度（退步时进步度为负值），把握学生成绩的整体进步、退步情况，同时也消除了基础差异的因素．通过计算进步矩阵和效率值又能对教学效果进行评价，且与马氏链模型所得的结论一致，同时还能得到一些很有参考价值的教学反馈信息．
关键词：马尔科夫链；转移概率矩阵；遍历性；教学质量评估；极限分布
ABSTRACT
In this thesis, we study a mathematical model which can eva luate the quality of teaching. We analysis the original state of the student by Markov chain, In the same standard, we divided the students who tought by teacher A and teacher B respectively into five levels by initial achievement, then determine the state space. We calculate the one step Transition probability matrix according to the student’s achievement that after teaching, and obtain the Limit distribution by Markov chain Ergodicity. The quantitative index of teaching weighted average by given every level scores, so we can eva luate the teaching quality according to the mathematical expectation. This method overcome the problem of student’s basis difference, therefore, Transition probability matrix reflects the quality of teaching, teaching conditions, style of study and social environment, and so on. Limit distribution shows teaching effectiveness may reach when these factors are stable, and it have nothing to do with the students’ basis difference. By analyzing the feedback information, teachers can adjust their teaching style, and improve the teaching quality.
To improve the Markov chain model, we define ‘progress degree’,which is the extent of the student progress (the progress degree is negative when regress). From the progress degree we can learn the overall progress of students achievement, and it also eliminates the factor of basis difference. We can eva luate the teaching quality by calculate the progress matrix and the value of efficiency, and it’s conclusion is similar to the model of Markov chain, we can also get some valuable feedback information.
Keywords: Markov chain; Transition probability matrix; Ergodicity; Teaching eva luation; Limit distribution
目 录
前 言 1页
第一章 马氏链基本理论 2页
1.1马尔科夫过程及其概率分布 2页
1.1.1马尔科夫性及其马尔科夫过程 2页
1.1.2马儿科夫链及转移概率 2页
1.1.3转移概率矩阵 3页
1.2遍历性 3页
第二章 问题的分析 5页
第三章 模型的建立与求解 6页
3.1模型的建立 6页
3.2实例求解 8页
3.3成绩的分析及结论 9页
3.4模型的改进 11页
第四章 模型的评价 13页
参考文献 14页
附 录 15页
致 谢 17页
