数学教育评价的马尔科夫链模型应用

通过分析学生两次高等代数的测试成绩,应用马尔可夫链分析法考虑学生的原始状态,并在同一标准下把学生的原始成绩分成相同的等级,确定出状态空间,然后得出转移概率和转移矩阵,根据马尔可夫链模型的平稳性及遍历性求出极限向量,并进行比较判断结果表明,学生学习状态的转移概率仅与教学质量和教学条件有关,而与学生的基础无关。运用该方法对教学质量的评价说明,学生的进步情况比学生成绩本身更重要,客观地看出教师在教学方法上的优势和劣势,并使教师获取教学的反馈信息,以对自己的教学行为进行反思和调整,促进教师教学水平的提高。

Application of Markov Chain Model to Mathematics Education Evaluation

Student scores in two higher algebra tests are analyzed;any given student＇s original state is considered based on the Markov chain analysis while the students＇ original results are divided into the same class under the same standards,namely,the state space is determined,then step transfer probability and step transfer matrix are obtained,and the limit vector is achieved,at last,according to the Markov chain＇s stationary and periodicity.As a result of the process above it is seen that the transition probability of the student learning state is related only to the quality of teaching and teaching conditions and has nothing to do with student foundation.The teaching quality evaluation made with this method shows that because it is here thought that student progress is more important than his achievement both the advantages and disadvantages a teacher is possessed of in his teaching method can be more objectively seen,meanwhile,the teacher can also obtain the teaching feedback,thus helping him to reflect,readjust and improve his teaching.