Study On High School Students' Understanding Of The Concept Of Derivative

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.