化学学历案促进深度学习的发生——化学平衡移动复习课

学历案是关于学习经历或过程的方案，利用学历案构建一个“以学为主、以教促学”的教学模式，改变了教师的主导地位，凸显了学生的主体地位。笔者尝试借助学历案，以花青素为载体，通过生活化的化学实验，将化学平衡常数K作为分析工具，进行证据推理，以外界条件使花青素溶液颜色变化，到花青素的工业合成为明线；以化学平衡移动的本质到化学平衡移动原理的应用为暗线，双线结合，学生自主建构“化学平衡移动”的认知模型，从而促进深度学习的发生。     

Constructive strong regularity and the extension property of a compactification

In contexts in which the principle of dependent choice may not be available, as toposes or Constructive Set Theory, standard locale theoretic results related to complete regularity may fail to hold. To resolve this difficulty, B. Banaschewski and A. Pultr introduced strongly regular locales. Unfortunately, Banaschewski and Pultr's notion relies on non-constructive set existence principles that hinder its use in Constructive Set Theory. In this article, a fully constructive formulation of strong regularity for locales is introduced by replacing non-constructive set existence with coinductive set definitions, and exploiting the Relation Reflection Scheme. As an application, every strongly regular locale L is proved to have a compact regular compactification. The construction of this compactification is then used to derive the main result of this article: a characterization of locale compactifications (and thus, classically, of the compactifications of a space) in terms of their ability of extending continuous functions with compact regular codomains. Finally, an open problem related to the existence of the compact regular reflection of a locale is presented.