Research On Learning Trajectory Of Understanding The Concept Of Fraction From The Perspective Of Quantity

As the most abstract and complex concept in primary school,the meaning of fractions is hierarchical and diversified,and students' correct understanding of the multiple meanings of fractions is not achieved at the same time.In primary school,fractions can represent both “quantity”(amount)and “rate”(relationship),which makes it difficult for students to understand and make clear the meaning of fractions which has also been troubling the majority of frontline teachers.Combining the development history of fractions with the experience and laws of understanding and mastering natural numbers,as we can see,the meaning of fractional “quantity” is fundamo hard for students to understand and master the meaning of fractional “quantity” well.“The roots are deep and the leaves are luxe”.It is crucial to lay a solid foundation for any new concept.Although in recent years,so many scholars at home and abroad have conducted heavy researches on “fractions”,they still fail to consolidate students' understanding of the meaning of fractional“quantity”.This research attempts to solve thiental.However,a large number of studies have shown that it's tos problem.The general question of this research is: What is the learning trajectory conducive to students' understanding of the meaning of fractional “quantity”? More specifically,this research mainly explore the following two problem:(1)What is the optimized and perfect learning trajectory? How to get the trajectory?(2)How can we test that the learning trajectory has been optimized and improved?Follow these steps,the research team conduct the empirical research.Firstly,by analyzing the textbooks and relevant literature,the hypothetical learning trajectory were designed to understand the meaning of fractional “quantity” through the models of “pieces”,“meters” and “hours” respectively.Students of intermediate level were selected from parallel classes to carry out small exploratory teaching experiments to improve the imaginary learning trajectory and get the revised learning trajectory.Secondly,Teacher T carries out teaching in Class A according to the revised learning trajectory,and conducts post-test and individual interview for students after class.The research team carried out discussion based on students' classroom performance,post-test and interview.After optimizing the learning trajectory,the teaching was implemented in Class B,and post-test and individual interview were also conducted after class.The performance of class A and class B in class,post-test and interview was compared to verify the optimization of learning trajectory.Thirdly,the research team carried out research,reflection,improve the learning trajectory.Finally,after teaching all content about the meaning of fractional “quantity”,two weeks later,the“experimental class” and “control class” were organized to carry out comprehensive tests.On the one hand,the effectiveness of the learning trajectory designed in this study was verified by comparing the immediate post-test with the delayed post-test.On the other hand,by comparing the comprehensive test results of “experimental class” and “control class”,explores that comparing with the learning trajectory from PEP textbooks,if the learning trajectory that designed by this research more helpful for students to understand the meaning of fractional“quantity”?Through this research,we can draw the following conclusions:(1)The comparison of fractions should go hand in hand with the recognition of fractions.In everyday life,saying “a small piece of the Pizza” is more common than saying “one-third of a Pizza”,and failing to accurately describe “half a Pizza”does not highlight the need for fractions.However,the comparison between “such a block and such a block” cannot be made accurately,which highlights the necessity of introducing fractional representation.Therefore,in the process of understanding fractions,the “comparison” of fractions should run through the whole process.(2)The perceptual experience of students is irreplaceable,so students should try their best to experience the meaning of fractional “quantity” through hands-on operation.In addition to paying more attention to students' hands-on operations,attention should also be paid to improving students' thinking in the class.Therefore,the task design should not only enhance the activity and operability of the task,but also improve the thinking content of the task.(3)It takes at least two periods for students to truly understand the meaning of of fractional “quantity”.In the first period,students have a preliminary understanding of the meaning of fractional “quantity” through the “pieces” model,and in the second period,students consolidate the meaning of fractional “quantity” through the “meters”and “hours” model.Refer to the above research,the following suggestions are made:(1)When curriculum is written and edited,the study of fractional knowledge can be introduced from the meaning of fractional “quantity”;Select “quantity” which is close to students' daily life and convenient for students to operate,and add activities.(2)When teaching and arranging the tasks,teachers should not only pay attention to the activity of the task,but also pay attention to the improvement of students' thinking level.The “cognition” and “comparison” of fractions should go hand in hand,regardless of you and me;Pay attention to the classroom presentation standards,to avoid causing students misunderstanding.