Study On Learning Trajectory Of Fractional Division Based On Deductive Reasoning

Fractional division is an important part of primary school arithmetic teaching,and it is also a difficult point for students to learn and teachers to teach.Students often just remember the "reverse multiplication" algorithm,but do not understand why it is done.How to design a learning trajectory that is conducive to students' understanding of the calculating principle of fraction division is a hot topic of current research.Professor Shi Ningzhong proposed the teaching of fractional division based on deductive reasoning,essentially deducing the calculating principle of fractional division based on the basic properties of equations.At present,there are few studies on the teaching of fractional division of deductive reasoning.This study attempts to explore this learning traj ectory.This study will focus on the following two questions:(1)What is the learning trajectory of fractional division based on deductive reasoning?(2)Is the fractional division learning trajectory based on deductive reasoning feasible?The research team carried out the research according to the following steps:First,the research team sorted out the prerequisite knowledge that students needed to carry out this study,and taught them in Class A and Class B as a pre-class,and pretested them to determine the learning progression and drew up the hypothetical learning trajectory.Secondly,invite expert teams to improve the traj ectory,then took a lesson in Class A by using the optimized learning trajectory,conducted post-test and interview.After that,discuss and improve the trajectory to get the perfect learning trajectory and taught in Class B,conducted post-test and interview.Finally,Compared with the "comparison class" learning according to PEP textbooks to verify whether the learning trajectory of this study is more conducive to students' understanding.Two weeks after the end of the teaching,delayed test was conducted for Class A and Class B to verify the effectiveness of the learning traj ectory in this study..Based on the above research,the following conclusions are drawn:(1)The learning trajectory of "fraction divided by integer" revolves around the equal division task of “dividing the cake”.Task 1 to 4 are:(?).The initial understanding of arithmetic was based on the visual representation.With the appearance of letters,the difficulty of the visual representation increased,leading to the formal representation.In this process,students gradually realize the superiority of deductive reasoning.(2)The learning trajectory of "dividing a number by a fraction" revolves around the inclusive division task of dividing milk".Task 1 to 4 are:2÷2/5?3/4÷2/5?a/b÷c/d?a÷b.When the divisor is changed into fractions,the superiority of formal representation is highlighted.Finally,students deduct the division calculating principle from fractions to rational numbers,and realize the integration of calculating principle.(3)In general,the fractional division learning trajectory based on deductive reasoning is more conducive to students' understanding of arithmetic and is feasible.The study made the following recommendations:(1)When compiling the textbooks,the fractional division by deductive reasoning should be clarified;The accomplishment of logical reasoning and symbol consciousness should be Implemented;Visual representation is paralleled with formal representation when representing computation;The integration of fraction and integer calculating principle should be emphasized.(2)In teachers' teaching,the importance of arithmetic should be recognized in fractional division teaching;The cognitive order of students should be followed;The requirement of deductive reasoning norm should be handled.