A Survey On The Level Of Understanding Of Decimal Multiplication Among Fifth-grade Primary School Student

Decimal multiplication is an important knowledge content in primary school and an important part of the multiplication system.As the transition stage between integer multiplication and multiple decimal multiplication,it is very important to understand the students’ understanding of multiplying one decimal by one decimal,and to study the students’ understanding status,existing understanding problems and their influencing factors.This study used a combination of test questionnaires and interviews to analyze the current situation of students’ understanding of multiplying one decimal by one decimal.The test paper is divided into two parts,namely,understanding the meaning of decimal multiplication and understanding of decimal multiplication operations.Tested data shows:In the fractional multiplication meaning section,the translation of written symbolic representations into realistic situational representations has a good understanding level,but the types of errors in this representation are mainly divided into four types,namely,problem checking error type,multiplication meaning understanding error type,confusion between multiplication and division type,and careless type;The translation of written symbolic representation into oral language representation has a good understanding level,but there are two main types of errors in this representation:fuzzy memory of multiplication concepts and confusion of multiplication and division itself;The translation of realistic situational representations into written symbolic representations has a good understanding level,but the main reasons for errors in this representation are students’ careless copying of numbers and missing decimal points;The level of understanding in translating realistic situation representations into verbal language representations is average,but there are mainly three types of errors in this representation:mixing the meaning of division into the meaning type of multiplication,and interpreting the meaning of integer multiplication into the meaning type of decimal multiplication,that is,finding the sum of several identical addends and being unable to understand the meaning type of the topic;The mastery of converting verbal language representation into realistic situation representation is slightly better,but there are two main types of errors in this representation:lack of good learning habits and confusion of division;The conversion of verbal language representations into written symbols indicates that students’ understanding level is good.The types of errors in this representation are mainly due to careless copying of numbers and reading of questions by students.In the fractional multiplication operation section,students have a good understanding of the synthesis and decomposition of numbers,but there are four main types of errors in this dimension:confusion in the understanding of the topic,confusion in integer multiplication and fractional multiplication,unclear rules in multiplication operation,and carelessness;The understanding level of operational law is slightly better,but there are two main types of errors in this dimension:confusion between integer multiplication and decimal multiplication,and ignoring the "0" in the vertical form;The level of understanding of the concept of bit value system is average,but there are two main types of errors in this dimension:the type of problem understanding error,and the type of bit value system understanding limited to integer types;The understanding level of the decimal point dimension is slightly better,but there are three main types of errors in this dimension,namely,basic knowledge point incomprehension type,mathematical concept ambiguity type,and mechanical memory method typeIn response to the problems of this study,corresponding suggestions are proposed:(1)Suggestions for teaching.1.Pay attention to teaching the internal arithmetic of decimal multiplication and go deep into it layer by layer;2.Properly expand the history of decimal multiplication knowledge and enrich classroom content;3.Teaching should make good use of blackboard writing to present the calculation process clearly and clearly.(2)Suggestions for teaching materials.1.Situational stories focus on arousing learning interest and enhancing the sense of familiarity with the content;2.Pay attention to guiding students’ mathematical thinking,and do not mechanically present it.