国外数学理解研究的进展与展望

The Pro gress and Prospect of Foreign Mathematical Understanding Research

数学理解是国际数学教育的重要研究主题。目前，西方数学理解研究已经逐渐成熟，研究者多年来一直从多个方面进行理论和教学实践的探索。研究内容包括数学理解的涵义、模式和水平、教学实践、评价等方面。虽然西方研究者都在强调要重视数学理解的作用，但对什么是数学理解学者们的看法又不尽相同。斯根普的两种数学理解模型和皮瑞———基伦超回归的理解水平影响深远，需要我们必须深入地了解它们。国内数学理解研究应从细化数学理解层级、做好数学课例研究、关注教师和学生两类视角等方面努力。

Mathematical understanding is an important research topic in international mathematics education .Nowadays，western mathematical research has gradually become mature . Researchers have been exploring theories and teaching practices from multiple aspects over many years. The research contents include the meaning，model and level，teaching practice and evaluation of mathematical understanding. Although western researchers have been emphasizing the importance of mathematical understanding，scholars have different views on what mathematical understanding is. The mathematical understanding model of Skemp and Pirie-Kieran?s mathematical understanding transcendent Recursive Model have profound effect， and sowe need to understand them in depth. The study of China'mathematical understanding should be done from the following aspects： to refine mathematical understanding levels， to conduct high-quality research on math lessons， and to pay attention to both teachers’ and students’ perspectives etc.