教学效率数学模型建构的教育原理及意义

Principles and Significance of Mathematical Modeling for Instructional Efficiency

如何提高教学效率,是各层次各类教学研究的重要问题。在教学理论和实践基础上首次提出的"教学效率的数学模型",可以直观地理解教学效率的三个限制性原理,即在学校教育中不能仅仅强调学生自主学习,不能仅仅强调教师单向传授知识,教与学是相互"耦合"的。其原理表明三个不可能:只要求学生自主学习,不可能高效;只要求教师灌输,不可能高效;不将教师的教学转化为学生的自学,不可能高效。以此模型推论,对于不同学科、不同水平的教师和学生,两条"学历-效率"曲线的交点O是不同的。这就为因材施教地研究教学效率提供了新思路。在系统研究教学模型基础上建构的"教学模型的数学模型",是"模式的模式",即元模式。元模式的研究具有方法论价值,为教师在教学中选择合适的教学模型提供了实用的模式"网络结构"。这些数学模型之于远程教育的意义是:远程教学十分需要新的突破。

How to improve the efficiency of instruction is an important issue for all kinds and levels of educational research. Based on instructional theory and practice, the author suggested for the first time the Mathematical Model for Instructional Efficiency, which reveals intuitively the three restrictive principles of instructional efficiency, i.e., in school education, students＂ autonomous learning cannot be overemphasized, neither can teachers＂ impartation of knowledge, and teaching and learning are closely interrelated. The principles indicate that efficiency is impossible with learningJs autonomous learning alone, or with teachers＂ one-way impartation alone, or without the transfer from teachersj impartation to learners~ autonomous learning. It is deducted from the model that for teachers and students of different disciplines and levels, the intersection point O of two ＂degree-efficiency＂ curves is different, which provides a new thought on studying instructional efficiency according to learnersj aptitude. Based on a systematic study of instructional modes, the author constructed the Mathematical Models for instruction models, which are models of models, i.e., meta-models. The meta-model research is of methodological value, providing practical network structure of models for teachers to choose from in their teaching. The significance of these mathematical models for distance education is that new breakthroughs are in urgent need in distance instruction.