初中数学教师HPM教学的个案研究

Case Study on HPM Instruction of Junior High School Mathematics Teachers

教师需要在教学中运用数学史，使之更有利于学生的学习．以八年级下学期“数据的代表”为具体内容，选择两位教学经验丰富但对数学史知之不多的初中数学教师，对其HPM教学进行实验研究．结果表明，HPM促进了教师教学的发展．两位教师的HPM教学分为教学准备和教学实施两个阶段，数学史与数学教学的诠释学循环经历了从分离到融合的过程．其中一位教师从数学史开始，寻求合适的角度融入教学，但过分强调数学史的面向，缺乏对学生认知和心理的关注；另一位教师则从教学内容出发，注重数学史与教材、学生认知的配合，有机地把PCK与HPM结合起来，较好地呈现了知识的自然发生过程．

Teachers use the history of mathematics in teaching and learning of mathematics to support students＇ learning. The research explored HPM instruction of two experienced mathematics teachers of junior high school who knew less the history of mathematics. The teaching content was the ＂representative of data＂ in the textbook of second semester in eighth grade. The results indicated that： Mathematics teachers＇ instruction development is promoted by HPM. After HPM involved in teaching, HPM instruction of two teachers was divided into teaching preparation and teaching implementation, and two teachers changed from single hermeneutic circle to double ones on integration of the history of mathematics. A teacher could start with the history of mathematics and integrate the history of mathematics into mathematics teaching in an appropriate method. But he overly emphasized the orientation of the history of mathematics, and couldn＇t paid attention to the cognition and mind of students. Another teacher paid attention to combine the history of mathematics with textbooks and students＇ cognition so as to present the subject in a natural way from the teaching contents.