Research On The Differentiation Point Of High School Students' Mathematics Learning

There will always be learning mathematics knowledge, easy to cause the students in the learning process of differentiation, we call it "differentiation". Differentiation point content of master degree, directly affects the student's academic record, it is also an important factor lead to polarization. From the point of mathematics teaching process, the emergence of the poor student can be traced back to one specific differentiation point of study. Although a part of teacher has been to higher mathematics differentiation point to explore research, but according to the chapter discuss mostly, less comprehensive summary and classified analysis; Most of the research focuses on the differentiation of external performance, involves the specific content, cause analysis, especially less psychological reason analysis.At first, this paper adopts the method of literature research, combined with personal understanding of the concept of differentiation point for the definition:in the process of teaching, the characteristics of knowledge itself and the influence of students' psychological characteristics, overlooked by teachers of the teaching content; Or is due to inadequate teaching obsolete concept makes the problem solving learning difficulties caused by the difficult point of content; Or is caused by a massive landslide in math, influence students' subsequent knowledge of knowledge learning and finally the college entrance examination, are referred to as "differentiation".On this basis, in view of the higher mathematics required a and required the knowledge content of four, for the teachers and students, teacher interview and the questionnaire survey to the students at brdinary times assignments and test investigation. Through the statistical analysis, this paper get high student mathematics study (compulsory and required four) in differentiation, differentiation from its own characteristics, cognitive characteristics of students, teachers' teaching situation three aspects analyzes the differentiation point of origin, and put forward the breakthrough differentiation point of general teaching strategies and teaching strategies of different types of differentiation points. Finally choose two classes students as the research sample, such as group to experiment on.Through questionnaire investigation, cause analysis and strategy research, the way such as experiments, this study mainly from the following basic conclusion:(1) concluded that high student mathematics study (a compulsory one and required 4) point of differentiationA questionnaire by the teachers and students, students' assignments and test statistics at ordinary times, concluded that high student mathematics study (compulsory and required four)' point of differentiation, concrete is:subset, the complete complement, intersection, and the concept of set, the function and image, function, simple nature, the concept of mapping, score index power, exponential function and logarithmic function function of zero, the equation solved by dichotomy of approximate solution, function model and its application, arbitrary Angle trigonometric functions, with the Angle of the triangle function relation, induced formula of trigonometric functions, trigonometric functions, function of the image, the image and nature of the basic theorem of plane vector, the vector number by two Angle, the application of the vector, and with bad of sine and cosine trigonometric function of double Angle.(2) the characteristics of itself from the split point, the students' cognitive characteristics, teachers' teaching situation analysis of the cause of the high student mathematics study differentiation pointsFound in this study, from the point of differentiation point itself, in the point of differentiation of the knowledge content collection, functions, trigonometric functions for peace; Look from the cognitive characteristics of students, there is a high student's cognitive structure is not perfect enough, the minds of students there are contradiction between development and academic thinking, developing students' affective and cognitive development is not enough coordination and ability of learning ability and the factors of self consciousness is not strong; Analysis from the teachers' teaching situation, there is "role differentiation", "empirical" light, heavy result light process, knowledge method, etc.(3) in this paper, according to the statement sexual differentiation, differentiation of procedural point, procedural points breakthrough differentiation some teaching strategies are put forwardThrough to the high student mathematics study differentiation point investigation, cause analysis, put forward the teaching strategies, specific tips for declarative differentiation:promote students to present sexual differentiation point content organization and processing, and promote the formation of students' "schemata"; For procedural differentiation points:promoting the construction of student production system, and promote the cultivation of students' self-monitoring ability; Process for sexual differentiation point hope teacher can provide students with the proper situation, make them experience the constructing process of knowledge.(4) in combination with the concept of "function and image" differentiation point research paradigm is given, and experimental research on the effectiveness of teaching strategies and other groupBased on the concept of "function and image" differentiation point of investigation and analysis, put forward the teaching link of three stages:acquisition stage, concept, application stage, the concept phase of ascension. And groups such as experimental study, the author found out that if properly of differentiation point of analysis, teaching strategy properly, the students' learning interest and learning achievement improves, breakthrough has positive influence on differentiation points.