【作者】 于福群；

【导师】 秦德生；

【作者基本信息】 东北师范大学 ， 教育， 2008， 硕士

【摘要】 数学理解已经成为继“问题解决”之后国际数学教育界关心的又一中心话题,是数学教育研究与实践的焦点。导数在世界各地都已成为高中课程的教学内容,大多数国家都将其作为高中选修课程,这也是世界性的方向。本文通过问卷调查和访谈等方法,研究以下几个问题:(1)高三数学“导数”学完后,学生是如何理解导数概念的?(2)学生导数概念理解中常见问题有哪些?(3)学生导数概念学习困难的主要原因。本研究结果表明:学生的导数概念表象主要是曲线切线的斜率,物理运动方程中的瞬时速度。很少有学生的导数概念表象是标准的瞬时变化率。学生对于导数的理解是机械的静态的,不能从动态的无限趋近的角度去理解。不能在不同的情境中对导数赋予正确的意义。学生的协变推理能力整体来看水平不高。高中学生对函数概念理解的常见问题有:1.概念意象的片面或错误;2.对变化率、平均变化率、导数三个概念没有清晰的认识,不清楚三者之间的关系;3.对导数的理解受到情境的影响显著;4.对导数定义式的内涵没有清晰的理解;5.对导数概念的理解停留在静态上和常量数学阶段。更多还原

【Abstract】 Mathematical understanding has become another central topic the mathematical educators concerned about after "problem solving" in the world, and it’s also become the concern that international education research and practice is focused on. As a field of study and practice direction, mathematical understanding of learning and teaching has recently attracted public attention in the field of education ,and also has achieved much results. Derivatives has become the courses of high school around the world.This paper studies the following questions through questionnaire survey and interview:(1) After“derivative”study in high school, how about the students’understanding of the derivative concept?(2) What kind of questions they will meet about derivative concept?(3)What’s the main cause on learning the derivative concept? These findings indicated that: student’s derivative concept representation is mainly the curve tangent slope and the instantaneous speed in physics equation of motion. The students’understanding of the derivative is just static, not dynamic. They cannot entrust with the correct significance in the different situation to the derivative. Overall, the students’ covariational reasoning faculty level is not high.The high school students’questions about understanding of the function concept are following:1.The concept image wrong;2. They have not clear understanding about the rate of change, average rate of change and derivative;3. The influence on the understanding receives the situation to the derivative are remarkable;4. They have no clear understanding on derivative definition-like connotation;5. They just stay on the stage about the derivative concept’s understanding in static and the constant mathematics.更多还原