Research On The Teaching Of Preliminary Understanding Of Multiplication Based On Multivariate Representation And Transformatio

Multiplication is not only one of the key contents of mathematics learning in primary school by itself,but also the basis for students to learn division.Students begin to learn multiplication in the second grade of primary school.The focus of multiplication learning includes understanding the meaning of multiplication,mastering multiplication tables,and being able to use multiplication to solve mathematical problems.When students learn multiplication at the beginning,they will face the multiple representations and transformations of them.What are the learning effects of students under different transformation methods of representations? What are the problems in the transformations of multiple representations? What strategies can teachers use in multiplication teaching? To solve these questions,after analyzing the current teaching situation firstly from the three-dimensional perspectives of students,teachers and teaching materials based on the theory of multiple representation,the author found that students can not understand the more complex quantitative relationship deeply in the two-step operations compared with one-step addition(subtraction)operations;teachers and students had a preference for the use of representations and transformations in teaching,they preferred representations of image and symbol,but less representation of oral language.In addition,it was found that all versions of teaching materials paid attention to the application of real situation,multiple representations and transformations of them through comparing various versions of teaching materials,they also highlighted the significance of multiplication in the content of "preliminary understanding of multiplication" and the hierarchy and presentation order of multiple representations,which are in line with the development law of students’ thinking.Compared with the textbook of People’s Education Press(PEP),some other textbooks paid more attention to the teaching of many-to-one relationship and the application of rectangular models.Based on the analysis of the current teaching situation,the author put forward the teaching strategy of "preliminary understanding of multiplication" which includes choosing a reasonable multi-representations and transformations of them,designing rich learning activities and highlighting the value of multiplication compared with addition.Then the author selected 10 common transformation methods of multiple representations,compiled the corresponding 10 questions into the test paper,and organized students’ tests before and after teaching implementation.Finally,the author analyzed students’ learning effects and problems existing under various transformation methods of representations on the basis of statistics of students’ answers in the post-test papers and interviews with students,and put forward corresponding teaching suggestions.According to the statistical analysis of the test paper and the interview with students,the main conclusions of this study are as follows:Firstly,the ten transformation methods of multiple representations can be divided into three levels for the students.Level one includes the transformations from concrete representations to abstract representations,such as the transformations of images or real situations into oral language or multiplication formulas.Level two involves the transformations between abstract representations,which is the transformation between formulas of addition and multiplication.Level three includes the transformation methods from abstract representations to concrete representations,such as the transformations of multiplication formulas into image,oral language and real situation.Secondly,the principal question faced by students in the transformations of representations is the lack of experience with equivalent groups model or rectangular model.It is easy for students to characterize multiplicands and multiplicators as addends,and characterize the multiplication as addition.Thirdly,teachers should make full use of equivalent groups model or rectangular model when teaching multiplication,design corresponding teaching links,guide the students through rich learning activities and transformation of multiple representations to enhance their experience of many-to-one relationship in concrete models.That can cultivate students’ sense of number and promote students’ understanding of multiplication as preparation for further multiplication learning.