A Research On Methods Taken By Primary And Middle School Students To Rewrite Fraction Line Into Sign Of Division

The part of number and algebra plays an important role in the mathematics course of compulsory education.And the transition from arithmetic to algebra requires students to change the reflections on logarithm to the understanding of symbols,which means the structural understanding of formulas is the premise of correct use of symbols for algebraic operations.With the research objects of the students in sixth,seventh,and eighth grades from some public schools in Jiangsu Province,who were asked to take a written examination to test their methods to rewrite the fraction line in the fractional numbers and fractions into the sign of division.The following conclusions were reached when the reasons for taking such methods to rewrite the fraction line were analyzed so as to find out the factors influencing the methods taken by students to rewrite the fraction line:There are seven different methods to rewrite the fraction line into the sign of division taken by those students,four of which were correct and other three were wrong.To verify the use of "useless" brackets and "psychological" brackets,it turned out be that students would use redundant brackets to express their emphasis on the structure,and no use of brackets doesn’t necessarily mean their lack of structural understanding.If a student adopted a certain method in a fractional number,it is very likely that he would continue to use the same method in fractions with similar structures.The consistency of methods adopted by students in the arithmetic and algebra indicated their recognition of the structure of formulas.A majority of the students in the seventh and eighth grades were able to recognize the basic structure of formulas and those students who can recognize the basic structures could also select the right methods to deal with the problems no matter whether this method meets the task requirement.However,there is a difference in the grasp and understanding of different structures,and the different forms of the same structural expression would exert certain influence on the students when selecting methods.Students who failed to recognize the structures would flexibly select the proper methods according to various forms of the formulas.When the basic structure of an expression was simple,the accuracy rate of students was relatively higher,but as the formulas become more complicated in the structure,the accuracy rate would decline by a certain degree.With the increase of grade,students tend to ignore the requirements of the questionnaire tasks.Most of the eighth graders can still recognize the structure of the formula,but they show a stronger consistency in the fractions with the same structure and are more flexible than the seventh graders when it comes to processing of fractions.And they tend to adopt the strategy of step-by-step calculation and fractional operation.In addition,some formula structures may trigger the use of specific methods by students.Different types of structures can trigger different kinds of methods,and students will change their preferred methods with the increase of grade.