The Study On The Errors In Solving The Word-Problems On Multiplication And Division Of Fractions Of The Sixth Grade Students In Township Schools

As an important part of mathematics education in primary schools in China,“problem solving” takes on the task of cultivating pupils' thinking ability and developing pupils' intelligence.Among them,the word-problems on multiplication and division of fractions are the focus and difficulties of the "problem solving" part of primary school mathematics,and it is also an important hub connecting mathematics and life.However,affected by objective factors such as the non-concrete and complex computing characteristics of fractions,inequality of educational resources across regions,and students' family education concepts,the mathematics level of the sixth grade students in township schools is relatively low,there are frequent errors in solving the word-problems on multiplication and division of fractions,and the learning effect is not good,which seriously affects the enthusiasm of learningof elementary school teaching.Therefore,it is necessary for us to deepen our understanding of students' various problem-solving errors,find the subjective causes of errors reasonably and effectively,and seek to circumvent and correct the teaching strategies of students' problem-solving errors,so as to improve the “problem solving”of students in township schools.This article uses questionnaire to understand the level of solving word-problems on multiplication and division of fractions for students;through the analysis of the test paper,the error types and error rates of the students on solving word-problems on multiplication and division of fractions are presented;combine with follow-up interviews to understand the thinking process of students' problem solving,analyze the causes of errors,and find strategies that can correct students' problem solving errors and improve teaching effects.The results of the study show that:(1)The sixth grade students in township schools have a lower level of problem solving word-problems on multiplication and division of fractions,there are many errors,and students lack motivation to solve problems.(2)Corresponding to the processing of word-problems on multiplication and division of fractions,the strategy selection of problem solving has the highest error rate,followed by relationship representation errors,semantic representation errors and problem solving operation errors.Typical error types are: quantitative relationship errors,unanswered,non-logical errors,multiplication and division errors,not answered as required,conceptual errors,calculation errors,incorrect problem solving format,transcription errors,etc.(3)The analysis found that semanticrepresentation errors are mainly caused by students' weak awareness of problem-solving procedures,imprecise perception and unclear concepts;relational representation errors stem from students' lack of awareness and representational methods to sort out quantitative relationship;errors in strategy selection are mainly caused by weak student foundation,poor motivation to solve problems,and find unit“1” unsuccessfully;problem-solving manipulation errors are mainly affected by limited working memory capacity,unfamiliar calculation rules,and lack of problem-solving habits.(4)Based on the above analysis,put forward corresponding teaching suggestions:consolidate the basic knowledge,strengthen the problem-solving process awareness,increase the means of intensive reading questions;cultivate the meaning and ability to analyze the quantitative relationship;stimulate learning motivation,scientific understanding unit “1”;cultivate good problem-solving habits,improve computing skills and reflection awareness,guide pay attention to problem-solving standards,etc.