A Study Of Seventh-year Students' Understanding Of Real Obstacles

Seventh-grade students have many problems with understanding real numbers.The first lesson introduced by the concept of real numbers appeared in the seventh grade.Therefore,students' understanding of real numbers becomes the main research issue of this article.In order not to repeat previous work,this article adds a historical perspective to the analysis of students' real numbers based on the duality theory of mathematical concepts.This paper sorts out the history of real numbers and the definition of real numbers in more than 30 early Western textbooks.On the basis of literature research and teacher testing,a set of test questions was compiled for students' real numbers.Questionnaire surveys and interviews were conducted with two junior high school students in Shanghai.Then analyze the concept,representation,classification,calculation,nature,and application of real numbers.The following conclusions are drawn: From a whole,the seventh grade students have a more comprehensive understanding of real knowledge,and boys and girls do not have obvious differences in understanding.From each specific point of view,students have different obstacles to mastering each aspect.Finally,some teaching suggestions are put forward in light of the above conclusions:(1)Strengthen the relationship between numbers and real numbers;(2)Strengthen the application of mathematical classification in real numbers;(3)Strengthen analogy;transformation;4)Try to avoid negative transfer of real numbers and rational numbers(5)Active guidance,avoid passive acceptance of learning(6)Avoid learning without seeking solutions,and flow into the use of a calculator.With a view to the real number of teaching has a certain reference value.