| For many years,it has been an idea in the design of senior high school entrance examination to "rely on the syllabus and textbooks" and "originate from textbooks and be higher than textbooks".Textbooks are the blueprint of teachers’ teaching.It is one of the current tasks for teachers to think deeply about the design intention of textbooks,the knowledge points and mathematical thinking methods contained in them.The pedagogy of variation of textbook examples and exercises can promote students’ comprehensive understanding of knowledge and deepen their understanding of mathematical knowledge.In this paper,141 junior high school students from a public school in a district of Shanghai were investigated.A questionnaire survey was conducted on 32 mathematics teachers in two junior middle schools in a district of Shanghai and a test for 57 students in Grade 7 in a public school in a district of Shanghai on their mastery of sector area was carried out;Based on the theory of the pedagogy of variation,variable teaching design is carried out for the section of sector area,and a one-week variable teaching experiment is carried out.Through the changes of the math scores before and after the test of the experimental class and the control class,The main conclusions are as follows:(1)According to the statistical analysis of the mathematics test questions in Shanghai senior high school entrance examination in recent five years(2014 ~ 2018),the average number of questions derived from textbook example exercises is about 13,accounting for 53.6% of the total number of questions,accounting for about 43.07%of the total score on average.(2)According to the questionnaire survey of students,most of them are satisfied with the example exercises in the textbook,and more than 80% of them agree with the role of variant exercises,and think that the example exercises and their variants are helpful to improve their problem-solving ability.(3)Based on the questionnaire survey and interview of junior middle school mathematics teachers,most of them are quite satisfied with the textbook example exercises and can explain more than 80% of the textbook examples.The most frequently used cases of textbook examples and exercises are analysis,explanation and variant expansion.The main reason why it is not analyzed and explained andvariant expansion is that the class time is limited.Most teachers are full of expectations for variant teaching and believe that they will study it in mathematics teaching.(4)According to the pretest paper about the learning of the sector,the concept of "central Angle corresponding to arc length" has not been strengthened for the three elements of sector concept.For the two calculation formulas of sector area,most students have a more profound memory of formula 1.As for the application of the formula of sector area,students are weak in the ability to calculate the area of the shaded part by using the cut-and-fill method and solve practical problems by using the formula of the sector area.(5)After the variable teaching experiment on the sector area,through the post-test paper,it was found that students in the experimental class had a deeper understanding of the concept of sector and the formula of sector area,and had a higher accuracy in the calculation and application of sector area.The effect of variable teaching is better in concept teaching and formula teaching.(6)The strategies for variable teaching of textbook examples include: Using non-standard variations to deepen students’ understanding of concepts;For mathematical formula,using progressive variable problem group to make it increasingly difficult;Deeply excavating the teaching material examples and exercises,,making changes based on basic figures and one math problem. |
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