| Since the United States first put forward "problem-solving ability as the core of school mathematics education in the 1980s",cultivating students’ problem analysis and solving ability has become the focus of global mathematics education.As an important form of cultivating students’ problem-solving ability,application questions play an important role in developing students’ thinking ability and improving their cognitive level,and also reflect the practical value of mathematics.Mastering the knowledge related to fractions is a major sign of the leap of primary school students’ thinking,but due to subjective and objective reasons,this part of the content has become a difficult point in primary school students’ mathematics learning.High-risk areas have affected students’ enthusiasm for mathematics learning and confidence in resolving the problems.Therefore,this research takes the sixth grade primary school students of the practice school as the test and questionnaire survey objects,and the sixth grade mathematics teachers as the interview objects to carry out the investigation and research,trying to classify the types and performance of the students’ problem solving errors in answering the fraction application problems.In-depth analysis of the reasons that cause students to make mistakes in answering fractional application problems,and put forward countermeasures and suggestions that can reduce students’ problemsolving errors in fractional application problems,so as to improve teachers’ teaching and improve students’ problem-solving ability.First,the sixth grade students are tested uniformly by the test method,and the types and specific performances of the current sixth grade primary school students’ problem-solving errors are classified and analyzed.The research results show that the main types of students’ problemsolving errors are knowledge errors,strategic errors and negligence errors.Knowledge errors are manifested as vague concept of unit "1",confusion of quantity and rate,unclear examination of questions,wrong calculation of fractions,random formulas,and failure to answer;Strategic errors are manifested in the incompatibility of quantity and rate,equivalence relationship errors,and mixed use of fractional multiplication and division;Negligence errors are manifested in simple calculation errors,wrong data copying,unit errors,and wrong answering sentences.Secondly,using questionnaire survey and interview method to analyze the subjective and objective reasons of students’ problem-solving errors.Objective factors include the diversity of fraction concepts,the abstractness of unit "1",the problems with the arrangement of textbook content and teachers’ teaching-level reasons.Subjective causes can be divided into intellectual factors and non-intellectual factors.Intellectual factors include differences in problem representation strategies,insufficient working memory capacity and negative effects of mindsets.Non-intellectual factors include lack of motivation to solve problems,lack of serious learning attitude and poor learning habits.Finally,based on different types of errors,suggestions are submitted to reduce students’ problem-solving errors in fractional application problems.Countermeasures to reduce intellectual errors include strengthening the teaching of fractional concepts and improving the cognitive structure of students;skillfully combining numbers and shapes to correctly characterize problems;implementing question-checking training to clarify quantitative relationships.Countermeasures to prevent strategic errors include strengthening variant training to overcome the negative effects of fixed mindsets;emphasizing multiple solutions to one problem and cultivating model thinking.Countermeasures to avoid negligence mistakes include reducing tension and stimulating students’ motivation to resolve the problems;paying attention to problem-solving norms and cultivating good study habits. |
