| Factorization plays an important role in junior high school mathematics,which is not only the key content of“number and algebra”plate,but also an effective tool to solve the problem of fractional operation and partial higher order equation(group)descending order.However,due to the instrumental nature of factorization and the characteristics of the examination,both teachers and students pay too much attention to the calculation and practice of the content of this block,ignoring the understanding of concepts and operation principles,so they attach importance to the understanding level of the relevant content of factorization in junior high school students,and have a certain role in promoting the teaching and learning of factorization.At the same time,the mathematics curriculum standard for compulsory education has caused many disputes in the field of mathematics education after deleting the teaching content of cross multiplication method.In practical teaching,many teachers will supplement the content of this method,but because the curriculum standard is not clearly stipulated,teachers can only teach according to their own understanding,which leads to different levels of understanding of students.Therefore,the research on the teaching design of cross multiplication method can provide some reasonable suggestions for the teaching of this method and the compilation of teaching materials.The study of factorization is not a few,the difference of this study is that the cross multiplication method is also included in the content of factorization explored,and through consulting relevant literature,it is found that the undetermined coefficient method used by mathematicians in history can promote students ' understanding of cross multiplication method.Therefore,first of all,the mathematics history into the cross multiplication teaching design.Secondly,from the four levels of factorization related concepts,principles of methods,comprehensive application of methods and integration of mathematical history into teaching,this paper analyzes the students 'understanding level of factorization by means of questionnaire survey and in-depth interview,and the attitude of teachers and students towards the integration of fixed coefficient method into the classroom.Finally,explain the main factors that affect junior high school students ' understanding of factorization and give some teaching suggestions.According to the results of questionnaire survey and interview,and combined with the theory of Skemp understanding division,the main conclusions of the study are:1.Most students basically reach or reach the level of instrumental understanding of relevant concepts,principles of methods and comprehensive application of methods,rather than relational understanding level,which leads students to make mistakes when describing definitions or encountering more complex polynomials.2.Students' understanding level of factorization related concepts,principles of methods and comprehensive application of methods are different,and there is a significant correlation between the levels of understanding.Among them,the level of relational understanding of related concepts is the lowest,and only 9.7%of the related concepts basically reach and reach the level of relational understanding.3.The main factors that influence the understanding factorization of junior high school students are:the mastery of original knowledge is not firm,the limitation of thinking and the lack of self-regulation ability.4.The teaching of mathematics history into cross multiplication,most teachers think that it can promote students' understanding of the principle of cross multiplication.At the same time,without the guidance of teachers,most students express that they can understand the solution process of undetermined coefficient method,and connect with the learned cross multiplication method,and are also willing to introduce the history of mathematics into the classroom. |
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