Analysis Of Derivative Test Questions,errors In Solving Problems And Teaching Countermeasures In Senior High School Mathematics

The derivative is an important content in the mathematics of the college entrance examination,and its score is also quite high.However,because derivative has the characteristics of rich question types,diverse solutions,high difficulty of thinking,and large amount of calculation,and often appears as the finale question,it is a major difficulty in teaching.Therefore,it is very necessary to conduct research on how to carry out teaching in the derivative chapter.However,the current teaching research on derivatives either focuses on the basic concepts and conventional question types,or only puts forward theoretical teaching strategies,studies the final questions of the derivative and proposes the solution and teaching plan of the literature is very scarce.Therefore,this article will take the whole chapter content of the derivative(including the finale)as the research object,and the main body is divided into four parts.The first part is the analysis of the test questions.First,on the basis of the "College Entrance Examination Evaluation System" and part of the research,an analysis framework for the test questions is designed.Then the 2013-2020 National New Curriculum Liberal Arts Papers were analyzed respectively,and the knowledge of the derivatives of the college entrance examination was summarized into nine main lines,and each main line was analyzed and summarized in the secondary main line.Finally,the score statistics and difficulty comparison of each main line are carried out,and the key and difficult points of the research are determined as: the zero point of the function,the proof of the inequality,and the constant hold and the solvable problem.The second part is the analysis of problem-solving errors.First of all,on the basis of the previous chapter,designed the "Senior Third Derivative Special Analysis Volume",which comprehensively covers the main lines of knowledge and thinking methods.Then a control group was set up to test,and the test paper was analyzed as a whole and item by item,showing the students' typical misunderstandings and wonderful solutions.Then I designed the "Questionnaire on Derivative Learning of Senior High School Students",which investigated the learning situation and learning needs of students from a subjective perspective.Finally,combining the test and the questionnaire,the following conclusions are obtained: the two classes are of the same level and the research is feasible;the students do not perform well on the above three main lines;the students need to summarize the question types,summarize the methods,and form a problem-solving module;students are easy to fall into three categories Errors:calculation errors,detailed errors,logical errors.The third part is teaching strategies and teaching examples.First,on the basis of the first two chapters,five teaching strategies are proposed from a theoretical perspective.Then the teaching mode of "multiple questions and one solution" was adopted to carry out the teaching of "The Zero Point of Function",and the "upstream proposition system" and "equivalent proposition system" were generated.Then,using the teaching mode of "one question with multiple solutions",the teaching of "Proving Inequalities" was carried out,and the "downstream proposition system" was constructed,and the commonly used proof methods of the three downstream branches were summarized.Finally,the "mind map" teaching mode was adopted to carry out the teaching of "Constantly Established and Solved Problems",and the problem-solving module was constructed to standardize the thinking order of the problem: the natural zero point method,the necessary sufficient method,the parameter separation method,Including the discussion method,prompting the scaling method.The fourth part is teaching feedback.Through the post-test: review papers,questionnaires,interviews,the students' learning situation is investigated from an objective and subjective perspective,and compared with the pre-test.The results show that this teaching practice enables students to have a better Great progress,more in-depth mastery of problem types and problem-solving methods,and clearer ideas for problem-solving.Through the research of this article,not only provides teachers with theoretical teaching strategies,but also provides specific problem-solving schemes for students' learning,and also provides detailed teaching cases for teachers' teaching.