基于动态系统的教育创新模型

Modeling educational innovation using a dynamic system

为了定量描述教育创新这个动态系统的变化规律、增长演变过程,利用微分方程的理论与方法,在考虑教育与环境之间的相互关系的条件下,对具有代表性的单一创新型建立了微分方程模型,对教育互补型、教育竞争型、教育替代型分别建立了微分方程组模型,并得到了模型的稳定点、非稳定点及稳定性条件.通过对模型的分析,得到了教育创新系统是一个稳定系统的结论,以及教育与环境之间的最佳协调条件.这些模型可为模拟与预测新旧教育更替、结果演变过程及构建研究型大学提供一定的理论依据.

Innovation in education is necessarily dynamic.To quantitatively evaluate degrees of innovation and understand the evolutionary processes that are involved,it was found necessary to apply the theory and methods of differential equations.The relationship between educational outcomes and the learning environment was considered,and based on this a simple differential equation model was built to represent a single innovation type.Further differential equations were built to increase the types of education modeled,including complementary,competitive and alternative.Based on this,stationary points,non-stationary points and the conditions for stability of the model were derived.Through analysis of the model,it was concluded that educational innovation is a stationary system with optimal conforming conditions between education and the environment.These models can provide a degree of scientific certainty,with simulations providing insight into the results of substitutions of new forms of education for old ones.They can show probable results in terms of the evolution of educational structures and the means needed to construct an ideal research university.