A Study On The Learning Strategies Of "Derivatives And Their Applications" Of Senior High School Students

Derivative, as a hub and bridge, delicately connects the mathematical knowledge between senior high school and universities. It plays an essential role in the process of the knowledge structure building of students and paves a solid foundation for their future learning in the realm of the advanced mathematics. Derivative is one of the core concepts of Calculus and has a wide application in many fields. It provides a more effective and easier method in terms of solving the maxima and minima questions of functions as well as in studying the monotonicity of functions and the trend of graph variations. Functions and Derivative are important parts in the college entrance examination (CEE) and appear usually in the question and answer group of the CEE on mathematics. However, the derivative consists of a certain extent of abstraction. Students tend to feel difficult in learning this part and thus the scoring rate has been low in the CEE. In view of this, it is significant to conduct research on the learning strategies of the "derivative and its application" module for the senior high school students as well as to table a teaching proposal towards resolving the problem.This dissertation focuses on the usage of learning strategies of the senior high school students for the "derivative and its application" module, using the testing methodology to conclude the problems that occur during the learning process and through questionnaires to analyze the cause of selections of their learning strategies, in order to propose concrete measures in consolidating the students’capacity in the usage of their learning strategies. On the basis of the above mentioned learning strategies for mathematics, combining the teaching characteristics of senior high school mathematics, following the chronological order of the math studies of students, this dissertation focuses on the tripartite research dividing the learning of derivative into before class, during class and after class. Furthermore, it is based on the McKeachie learning strategies classification including the strategy in each learning period consisting of the cognitive strategies, meta-cognitive strategies and resource management.This dissertation adopts the empirical research methodology through questionnaires and statistical analyses using SPSS. It surveys the learning strategy selection of the students in before, during and after class on learning "derivative and its application". The results have been analyzed and the question existing in these three learning periods have been identified. Teaching suggestions towards the different learning period has been raised in order to facilitate the effective selection of learning strategies of the students and to promote the effective learning on the derivative module.Through the analyses of the testing and questionnaire, this study has concluded the following in relation to the derivative learning strategies:1. Students mainly strategize their "derivative and its application" learning during and after class. Learning strategies were seldom used at the before class period.2. During the three learning periods, students mainly applied the cognitive strategies, while they tend to be weak in the meta-cognitive and resource management.3. There have been obvious differences in the selection of learning strategies during and after class between different subject directions. In comparison with the humanity students, science students appeared to focus more on the learning strategies during these two periods. Even though there has been difference in choosing the strategies before class, the difference was not obvious.4. There have been differences in selecting strategies before and after class between the genders. And the female students score more than the male students on average, meaning female students applies more strategies before and after class than the male students to consolidate their knowledge on this part, in order to enhance their learning.Based on the results analyses, following the learning periods, the following summaries a teaching proposal on helping students reasonably using learning strategies:1. During the before class period, teachers should focus on the usage of the meta-cognitive learning strategies, and leave elastic learning time for students; help them adjust their psychological attitude and mental preparedness as well as guide them on setting their learning goals, and cultivate their learning attitudes. They should guide students with different subject directions effectively use cognitive strategies, e.g. help humanity students form their learning habits and learning methods and encourage the science students to conduct pre-learning before class to enhance their knowledge network and form their cognitive structure.2. At the during the class period, teachers should guide students effectively using meta-cognitive strategies and resource management to increase their learning efficiency in class. They should pay attention to achieving the results when designing the teaching activities:increase the students’experiences, and have students be the principal part of the class; provide opportunities to students to speak in the classes and give them chances to repeat; enhance the monitoring and self-adjusting of students; and encourage students to think independently and work in teams.3. During the after class period, teachers should focus on guiding students to use the cognitive, meta-cognitive and resource management strategies in the revision, e.g. guiding students to self-think and summarize, encouraging them to self-evaluate; the homework design should be useful to the construction of the cognitive structure of students; guiding students on the cultivation of proper imputation methods and help them increase their time management abilities.