A Study On The Understanding Of Fraction Values In The Sixth Grade Of Elementary School

Fractions are an error-prone and meaning-rich point of knowledge in elementary school.Fractions are derived from the need for real life and the closed nature of division operations,and are an important extension of the number system at the elementary level.Few studies on fractions have been conducted from the perspective of the numerical magnitude of fractions.This study focuses on the understanding of the numerical value of fractions in the sixth grade of elementary school and gives teaching suggestions and learning suggestions in relation to the problems in understanding the numerical value of fractions.This study summarizes the literature related to fractions and yields test items including comparison of fraction size,fraction maximum and minimum,fraction consistency,fraction ordering,and fraction representation.Combining Pirie-Kieren's mathematical comprehension theory,250 students from five classes of the sixth grade were tested,and their comprehension of fractions was classified into four categories: creative comprehension,flexible "constructed" comprehension,flexible procedural comprehension,and mechanical procedural comprehension.Problems:1.They are able to solve problems using pass points,but their understanding of pass points is mainly in the use of techniques.2.There is a single method for comparing the size of fractional values,and there is little sensitivity to the size of fractional values.3.Fractions are less often used to solve problems with numerical sizes of fractions.This study offers recommendations for teaching and learning:1.The identification of natural numbers and fractions through the division,combined with the line and rectangular partition representation of fractions gives teaching suggestions.2.Train fraction estimation skills to improve sensitivity to fraction values.3.Through the identification of fraction and decimal rounding characteristics,teaching suggestions for reciprocal fraction and decimalization are given along with thinking exercises.4.This article gives 5 study tips for students.