融合内容的教学知识之课例研究

The Investigation of Knowledge of Content and Teaching of Pre-service Teachers

借鉴Kahan等的教学过程和基本要素研究框架，以情意原理、序进原理和活动原理作为解析课堂教学的框架，调查师范生融合内容的教学知识的实然水平。师范生的教学水平大致分布在三个等级上，师范生对学与教的理解有明显的缺失。如果师范生对知识的发生发展过程认识较为深刻，那么知识教学的序列安排就与知识发生的历史过程拟合得较好；如果师范生对做数学的一般机制有一定的体会，那么学生思维过程的设计就与历史上人们做数学的活动经验较为相似。数学发生发展的知识是影响师范生课堂教学水平的重要因素之一。

Drawing on Karan’s framework of teaching process and the basic teaching elements， we develop the Qingpu principles to analyze the classroom teaching. We investigate pre-service teachers’ knowledge of the content and teaching of trigonometric functions. The levels of pre-service teachers distribute three different ranks， in addition to a small number of them with high scores， most of the rest with low scores. This shows pre-service teachers lacking of understanding of learning and teaching. If the pre-service teachers have a more profound understanding of the genesis and development of mathematics knowledge， the arrangement of the sequence of knowledge teaching will fit well with the historical process. If the pre-service teachers know the general mechanisms of doing mathematics， the design of the process of students’thinking will be similar to the mathematics activities experience of the people in the history. The knowledge of the genesis and development of mathematics have important effects on the teaching level of the pre-service teachers.