文章导读 如果说医生的真功夫体现在临床上，那么教师的真功夫体现在课堂上。[1]由于教师这一职业的复杂性，因此对于教师该具备哪些知识才能更好地进行课堂教学，成为学界近来重要的研究议题。[2-7]教师真功夫集中表现为教师能有效地转化课程内容并使之适合学生的学习，从而实施高质量的课堂教学。内容是把数学课程与其他学科课程区别开来的决定因素，因此对内容及其变化的研究应该成为数学课堂教学研究不容忽视的一个方面。[8]在转化过程中起底层支持作用的是融合内容的教学知识（Knowledge of Content and Teaching, KCT）。KCT是面向教学的数学知识(Mathematical Knowledge for Teaching, MKT)的一个组成部分。融合内容的教学知识，是指为了达到教学目的和教学目标，教师根据学情的知识，而采取的合适地表征内容的教学手段和策略的知识，主要表现为教师能在课堂教学中有效地实施情意原理、序进原理和活动原理。[9]本研究以三角函数为抓手，建立体现内容底层支撑作用的分析框架，以此分析课例中师范生融合内容的教学知识的实然水平，并从数学发生发展的角度对师范生融合内容的教学知识实然水平进行归因。
Abstract：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.
徐章韬. 融合内容的教学知识之课例研究[J]. 基础教育, 2014, 11(4): 48-56.
XU Zhang-Tao. The Investigation of Knowledge of Content and Teaching of Pre-service Teachers. JSS, 2014, 11(4): 48-56.
2014, Vol. 11 
