试论数学教育中模式与模型构建的思维方式

On the Way of Thinking of Pattern and Model Construction in Mathematics Education

在大数据时代背景下,模式与模型成为数学教育讨论的热点问题之一。对于模式与模型的概念、二者间的关联以及如何构建模式与模型的思维范式等问题的探讨对推进数学建模研究至关重要。模式是构建数学模型的本原,模型是用数学的语言讲述现实世界的故事。数学概念经历了现实的和逻辑的两次抽象,命题模式构建需要经历“三阶段”,数学模型的构建需要“三化”的思维范式。简约和想象是数学模型构建的核心思维特征。简约是基于现实与逻辑的抽象;想象是实践经验与思维经验的复合。

In the era of big data,pattern and model have become a hot issue in mathematics education.It is very important to discuss the concepts of pattern and model,their relationship and how to construct their thinking paradigm.Pattern is the origin of mathematical model and model tells the story of the real world in mathematical language.Mathematical concepts have experienced two abstractions of reality and logic,the construction of propositional pattern needs to go through three stages,and the construction of mathematical model needs“three⁃orientation”thinking paradigm.Simplicity and imagination are the core thinking characteristics of mathematical model construction.Simplicity is abstraction based on reality and logic while magination is the combination of practical and thinking experience。