An Exploratory Study On The Knowledge Of The Multiplication And Division Of Fractions By Mathematics Teachers In Junior High Schools

Operation is the most basic skill and quality of mathematics.It plays an important role in the study of mathematics.Some people even call operation and thinking “the essence of mathematics”.Fractions and the operation of fractions are the key content of mathematics learning in the whole primary school and even junior high school.Because fractions and operations integrate all the contents of the four operations,it is of great significance for mathematics learning to master the knowledge of fractions.Traditional mathematics teaching only fouces on getting the correct result,and makes students remember the rule through a large number of calculation exercises,but ignores student's understanding of calculation.However,the study of algorithm has a profound influence on the development of students' mathematical ability.Teachers play an important role in the process of student learning,so for teachers,we not only ask teachers to know what to do,but also to know why.Therefore,this paper mainly focuses on the “calculation theory” of fraction operation to explore the understanding degree of in-service mathematics teachers on fraction operation.In the first chapter,the background,significance,problems are introduced;in the second,the related literatures are reviewed in more detail;in the third,the theoretical basis of the research is explained;in the fourth,the research methods,research objects are discussed;in the fifth,the four dimensions of the DTMR test questions are used to analyze the teacher's interviews;in the sixth,the conclusions and suggestions of this research are presented.The research finds that the teacher selects the reference unit,judges the score multiplication formula or the fractional division formula in the problem situation,and equally divides these aspects.There is a certain degree of mastery,but there is a slight lack of division and inclusion of the two models for division.Through the interview analysis,it is found that teachers' knowledge is mainly divided into three levels of understanding.The first is to grasp both algebraic ideas and concepts;the second is to understand concepts based on algebraic ideas;the third one is just algebra.Among the three levels of understanding,the second level has the most teachers.Therefore,we need to strengthen teachers' understanding of the concept of fraction,so as to better understand the operation of fraction.