A Study On The Understanding Level Of Derivatives And Their Applications In Senior Middle School Students

Calculus is one of the great achievements of the human mind, the emergence and development hailed as one of the key events of "Modern civilization, it introduces a number of extremely successful, thought to play a decisive role in the subsequent development of learning mathematics. " Again in the new round of curriculum reform, which the provisions of the calculus to choose from, derivatives and its application is one of the most important and basic part in the calculus preliminary. So necessary research sophomore students’ level of understanding of the derivative and its applications.Departure from the nature of the derivative,use the SOLO Taxomomy principle to test the sophomore students on the evaluation of the level of understanding of derivatives and its application, analysis sophomore students in the level of understanding of derivatives and its application in three dimensions(rate of change derivative meanings, derivative applications).Understanding of existing problems and their causes of sophomore students in seven knowledge in derivatives and its application, and sophomore science students, liberal arts students the differences in the level of understanding of derivatives and its application.Reflections and suggestions to help teachers and students how to solve the problems of the teaching of the derivative and its applications.Conclusion sophomore students on the level of understanding of derivatives and its application:(1)Overall, the sophomore science students and arts students in the understanding of the level of the average rate of change basically no difference, but science students was significantly higher than the average rate of change of the level of understanding on the level of understanding in further abstractions (E), liberal arts students.(2) The sophomore science students and arts students to understand there is no significant difference in the further abstraction level of understanding (E), the level of understanding of science students on the instantaneous rate of change of the instantaneous rate of change of slightly more than liberal arts students.(3) The sophomore science students to the low level of understanding of the physical meaning of the derivative, only about a quarter of science students can achieve further abstraction (E) the level of understanding, able to fully explain the physical meaning of the derivative, at the same time, nearly 10%liberal arts students at the lowest structure (D) on the level of understanding of the physical meaning of the derivative can not basically correct judgment.(4)Further abstraction level of understanding (E), sophomore science students understanding of the geometric meaning of derivative level higher than the level of understanding of the liberal arts students.(5) Sophomore science students in the use of derivative solve the function of the nature and image issues than liberal arts students even more freely, to understand more profound and thorough. On the level of correlation (R), the percentage of the sophomore science students and arts students almost no gap, but on a further level of abstraction (E), sophomore science students higher percentage in the highest level for nearly 20 percent of liberal arts students.(6) Sophomore liberal arts students to solve the problems of the derivative significance level of thinking on the overall level of less than sophomore science students, the need to The teachers further strengthen the boot liberal arts students to improve their level of thinking to solve the problem of the meaning of derivative.(7) Sophomore liberal arts students slightly above the level of correlation (R) science students, but on a further level of abstraction (E) was significantly lower than the sophomore science students, sophomore science students is only 1.96% of the students on the lowest level of structure (D),at the lowest structural level science students utilize derivative solve the optimization problem, basically did not not take advantage of the derivative to solve the optimization problem students.