Research On Learning Trajectory Of Elementary Understanding Of Fraction Concept

The concept of fraction is a mathematical concept with multiple meanings.It is also the most abstract and complex concept in elementary school,which makes it difficult for students to understand.Although scholars at home and abroad have made some researches on the concept of fraction,there is a lack of researches on learning trajectories that are conducive to students' understanding and grasping of the concept of fraction.This research attempts to solve this problem.Specifically,this research focuses on the following three issues:(1)How is the learning trajectory for the concept of fractions in existing textbooks designed?(2)What is the optimized and perfect learning trajectory,and why is it so designed?(3)How to verify that the learning trajectory has been optimized and improved?This research utilized the following steps to conduct action research.First of all,teacher T carried out teaching in class A according to the hypothetical learning trajectories of fraction concept.After class,the students were tested and interviewed.Secondly,we discussed the teaching and learning performance in the class A with the research team after class,optimized the learning trajectories and taught in class B.A fter class,we tested and interviewed the students.Then,comparing the post test results of class A and class B with the students' classroom performance,we could verify the optimization of the learning trajectories,and improved the learning trajectories again through discussion and reflection.Finally,the "experimental groups" and the "control groups" were organized to conduct a comprehensive test.According to the test results,the effectiveness of the learning trajectories designed in this research was verified.Based on the above researches,the following conclusions were reached:(1)The teaching of the concept of fractions should be introduced from the meaning of "quantity"(the number of objects).We used the continuous quantity model to carry out tasks around the three “quantities” of “pieces”,“meters” and “hours”.First,understand unit fractions and clarified the meaning of each part of the fractions(denominator,fraction line,numerator).Second,recognize non-unit fraction.Finally,the size of the same denominator fraction and unit fraction were compared,and the laws were summarized.(2)Then the fractions as the "rate"(the relationship between two quantities)should be recognized.We took "one object","one unit","one figure"(using the continuous model above),and "one whole"(using the discrete model)as the scenarios to build the students' complete understanding of the meaning of "part-whole".By showing the animation from continuous model to discrete model,the transition from continuous quantity to discrete quantity was realized,and thus the administration from perceptual concrete to perceptual general was realized.(3)The last was to realize the integration of "quantity" and "rate".To understand the meaning of "quantity" and "rate",we must be able to distinguish "quantity" and "rate".First,three tasks were set up to distinguish between "quantity" and "rate".Then we asked students to create a fraction and explain its meaning with intuitive and abstract representations,including the meanings of "quantity" and "part-whole".This task not only pulled through the meanings of fractions,but also penetrated the different representation models and representation methods of fraction,thus realizing the abstraction from perceptual general to rational concrete.The research made the following recommendations:(1)When curriculum is written and edited,the study of fractional knowledge can be introduced from the meaning of fractional “quantity”;tasks should convenient for students to operate,and establish a fixed point of “quantity” to the teaching.(2)When teaching and arranging the tasks,teachers should consider the cognitive development of students and pay attention to the transition of students' thinking levels;pay attention to the standardization of classroom language,weak the application situation of fraction,and grasp the core essence of fraction.(3)When studying,students should communicate the relationship between fraction-related knowledge with the teacher and improve the mathematical knowledge system;pay attention to the connection between fraction and life,and actively use fraction knowledge to solve problems in the daily life.