A Study On Learning Trajectory For Adding And Subtracting Rational Numbers

The adding and subtracting rational numbers are the starting points and difficulties of operation of rational numbers,although scholars at home and abroad have done a lot of research on operation of rational numbers,but there is less research on the learning trajectory that is easy for students to understand the algorithm and rules.Therefore,it is necessary to study the learning trajectory for adding and subtracting rational numbers.This study focuses on the following four problems:(1)how to design the learning trajectory of adding and subtracting rational numbers in the textbook;(2)what is the learning trajectory of the optimized adding and subtracting rational numbers;(3)how to verify the learning trajectory of adding and subtracting rational numbers is optimized.(4)what is the understanding of the adding and subtracting rational numbers in the junior middle school of different grades.Carry out the action research according to the following process.First of all,by studying different versions of the mathematics textbook,we put forward the hypothesis of learning trajectory for adding and subtracting rational numbers,then the classroom teaching will be carried out.Secondly,based on the students' post test and after class discussion,then optimize the learning trajectory to teach again.Thirdly,the optimization of the learning trajectory is verified by using the post test and the students' classroom response,and through the discussion and reflection to improve the learning trajectory.Finally,three months after the end of teaching,two classes of grade seven were tested postponement,and the same survey test for students in grade eight and nine.Based on the above study,the conclusions are drawn:(1)The optimized learning trajectory of adding rational numbers starts from the real situation,to spoken symbols,then to pictures,and then list the formulas and summarize the rules,the internal unity of theory and rule is achieved.With a goal difference for the real situation,using the model of the circle offset to explore the rule of adding rational numbers.Taking the problem of travel as a realistic situation,theaxis model to consolidate the rule,help students break through difficulties on sums of different signs,and summarizes the key factors of the adding rational numbers' rule is the sign by the absolute value of the big decisions.(2)The optimized learning trajectory of subtracting rational numbers is concerned with the unification of addition and subtraction.With temperature for the real situation,characterized by visual axis,then make the students set the real situation to express the positive number minus the positive numbers' result is negative numbers,guide students to conjectures and verifies rules,thus making algorithm infer to rules more smooth.(3)The post test comparison based on the two teaching,according to the optimized the learning trajectory of adding and subtracting rational numbers to teach,it is more conducive for students to understand the algorithm and rules,and the effect of delayed post test is better.(4)With the increase of grade,junior middle school students forgot the algorithm and rules of adding and subtracting rational numbers,but the procedural understanding changed little.As for the intuitive understanding and abstract understanding,the grade seven students are obviously more correct than the eight or nine grade.But when they summarize the rules,they have the same characteristics of thinking.First,consider the determination of symbols,this is basically the same as the key points extracted from the optimized learning trajectory.The following suggestions are put forward:(1)When the textbook is written,we should choose the proper real life situation of adding and subtracting rational numbers,which is convenient for students to understand the algorithm and rules,so as to realize the unity of the algorithm and rules.(2)Teachers should fully understand the importance of algorithm understanding in teaching,pay attention to the linkage of multiple symbols,grasp the key tasks of learning trajectory,and make the students explore independently.(3)When students are learning adding and subtracting rational numbers,students can't just use the rules to calculate,and the skills should be formed on the basis ofunderstanding the algorithm.