The Investigation Of Students' Mathematical Abstraction In Fraction Situation

Mathematical abstraction,as the core of mathematics core literacy,has always attracted the attention of scholars.How to improve students' mathematical abstraction ability has been a topic of discussion in the field of mathematics education.Because the development of abilities is a gradual process,and the knowledge of mathematics in middle school is smaller,it is more abstract.Therefore,we cannot wait until middle school to pay attention to the development of students 'mathematical abstraction ability.We should focus on training students' mathematical abstraction ability from elementary school.In Shanghai's elementary school,the fifth grade is a graduation class,and investigating the level of mathematics abstraction in Shanghai's fifth grade primary school students can also help the pre-primary teachers understand the academic situation.Research on students' mathematical abstraction ability needs to be implemented in specific mathematical content.Scores are the most important and difficult point of mathematics learning in elementary school.When solving the problem of applying grades,students often have the problem of "solving this problem,not solving this type of problem".The reason is that students do not abstract a class of score problems.This paper uses literature method,test method and interview method for research.First,through extensive and in-depth review of relevant literature,to understand the research status of mathematical abstraction ability and the application of fractions,combined with the syllabus and the Shanghai teaching version of mathematics textbooks,the research content of mathematical abstraction ability is divided into four dimensions Part,difference ratio condition to find part,multiple ratio condition to find whole,difference ratio condition to find whole,according to the RBC model,students' performance in four types of score problems is divided into three levels,and quantitative analysis of large samples shows that students in each The overall level distribution in a class score problem.Considering the difficulty of the four types of score problems,based on the dynamic RBC model,the author constructs an evaluation framework of students' mathematical abstraction level in the four types of score problems,and analyzes the performance of individual students in the four types of score problems and generates difficulties through interviews.s reason.This article selects all fifth gradestudents from a primary school in Shanghai as the research object.The main research conclusions are as follows:(1)The current situation of students' scores in the multiplier condition: 1.More than half of the students reach level three;2.Students who have not reached level three have similar difficulties in level one and level two.The main reasons for not reaching level three: the concept of scores is not clear,and the basic knowledge is not strong.(2)The current situation of students' scores in the part of the difference condition: 1.Compared with the part of the condition of double ratio,the proportion of students who have reached level three has decreased;2.The students who have not reached level three are mainly at level one.Difficulties arose.The main reasons for failing to reach level three: difficult translation of key sentences and weak reasoning ability;calculation errors and insufficient training.(3)The current situation of students in the overall score problem of multiple ratio condition: 1.Compared with the partial condition condition,the proportion of students who reach level three is greatly reduced;2.The students who do not reach level three are at level one and Level 2 is about the same level of difficulty.The main reasons for not reaching level three: insufficient computing power and immersion in abstraction.(4)The current situation of students in the overall score problem of the difference ratio condition: 1.Compared with the difference ratio condition calculation part,the proportion of students reaching the level three in the difference ratio condition overall is significantly reduced;Of students encountered great difficulties mainly at level one.The main reasons for failing to reach the third level: frustrated problem solving and lack of exploration spirit;limited to intuitive operation,weak analysis and generalization ability.Based on the research results and educational psychology theories and related literature,the author puts forward five points of teaching suggestions to cultivate pupils' mathematical abstraction ability:(1)focus on conceptual teaching and feel mathematical abstraction;(2)focus on other accomplishments and develop mathematical abstraction;(3)Appropriate variant exercises,reflection to form abstraction;(4)help to understand abstraction through intuitive operation;(5)enhance mathematical confidence and dare to deal with abstraction.