Difficulties Of Curves And Their Equations Concept In Senior High School And Design Research On Teaching

The curve and their equation as a difficulty concept in analytic geometry,plays an important role in middle school mathematics. Investigation shows that the concept of curve and equation is one of the top ten most difficult mathematical concepts in the mind of both teachers and students.The purpose of this study is to find the cause and difficulty analysis of curve and equation which is a difficult concept, then research on classroom instructional design in concept teaching, and puts forward teaching strategy may improve the difficult concept.The research of the formation process of the concept use logic analysis, methods of analysis and thought processes. And employed a students' and teachers' questionnaire and interview to study the causes of the difficult concept. In the classroom instructional design, use pretest and aftertest to experiment and improve instructional design.The results of the study as an improvement of the curve and equation concept teaching evidence.The author use the method of investigation and the form of questionnaire and interview.Chose 32 first-line teachers as investigator for concept and teaching strategy. Summary teaching and learning difficulties of Curves and Their Equations concept, as well as the core of the concept of the word. From two school four class's and grade's among 145 students was conducted, through the questionnaire analysis, provide the basis of teaching design research.On this basis, the author and the study of teachers'cooperation, on the basis of APOS theory from the concept of learning at different stages in the first round of the teaching design research, and teaching design class. Through group discussion reflections on the first round of the teaching design research, through to the students after the data statistics and analysis of the questionnaire, and interviews students to form the final perfect teaching design. And through the student questionnaire data statistics and analysis verify the scientific nature and effectiveness of teaching design.Through the author's research, finally get the following conclusions: understanding of the concepts of curve and equation; Curve and the equation of the concept of discrimination; The understanding of why you need to test; Argument is that the points on the curve equation solution of equation solution for the coordinates of points on the curve; For the number form combining ideas understanding barriers.According to the author's investigation questionnaire and interviews to teachers, teachers summarize curve and their equation concept of teachers teaching difficult points:definition of the concept of curve and equation; Curve is the curve of the equation, the equation of curve equation;Understanding of the equation. Curve and the equation of the concept of completeness.Through to the teachers' questionnaire investigation and study, and to meet the requirements of curriculum standard, summarizes the core of the concept of curve and equation of words are:"one to one correspondence", "equation of the curve, the curve equation"," the points on the curve equation of the solution ", "a collection of equal".Summarizes teaching and students' learning difficulties and obstacles of Curve and equation, as well as the core words, put forward the corresponding teaching strategies. Including the coordinates of points on the curve equations with "one a corresponding" teaching strategy; Curve, the curve equation of "equation" teaching strategy.Conclused creative design and teaching effect in difficulties of Curves and Their Equations concept:primary and high contrast plane analytic geometry research methods; Adopt the method of collection and pictorial, promote students understanding of the concepts of curve and equation and deepening; analysis the concept of Curve and equation, function and image.