Font Size: 

Fraction is important not only in mathematics but also other subjects. Understanding of fraction is the gateway to understand the higher concept in mathematics. Besides that, mathematical fraction magnitude knowledge is referred to student mathematics achievement or support each other. Poor mathematics can be affected by learning problems. Two type of learning problems can be distinguished into a learning disability which is addressed in the child’s own cognitive, while learning difficulty is situated outside the child.

 

In elementary schools, students’ knowledge of fraction magnitude may predict their mathematics achievement. Student mathematics achievement is influenced by student mathematics difficulties. Take this into account, mathematics difficulty in fraction becomes special attention.

 

This study exposes students representation in estimating fractions to indicate students’ fraction magnitude knowledge. This research is conducted on a class of the 4^th grade of elementary students in Surabaya It consists of 8 girls and 20 boys, and had chosen purposively from 3 available classes. All students had to answer two tests, namely the diagnostic test and the fraction magnitude knowledge test. The diagnostic test investigates student mathematics difficulty gradually. It examine from the easiest to the hardest concept of fraction magnitude. The fraction magnitude test is focuses on the ability to estimate fraction through representation. Two volunteer students were selected as research subject which have mathematics difficulty in fraction and take into consideration of students’ document scores test results. Semi-structured interview were conducted to all subjects to reveal students’ thinking process when solving diagnostic and fractions magnitude tests.

Result of the diagnostic test showed 92% of students have mathematics difficulty in understanding fractions. Most of them did not know how to compare and represent non unit fractions. Meanwhile in the fraction magnitude test, 95% of students with mathematics difficulty were not able to represent and to estimate fractions, for example in estimating 3/4, they did not know the relationship between numerator and denominator. They considered numerator and denominator as an independent number. Here, students’ scores of diagnostic test, fraction magnitude knowledge test, and score document (semester final test score).

 

Figure 1. Students test results

 

This study underlined that the students with mathematics difficulties were not able to represent fractions with different denominators and estimate them. Here, examples of student fractions representation in estimating fractions.

 

Figure 2. Student fractions representation and estimation.

 

The student with mathematics difficulties represent numerator and denominator as an independent number, for instance ½ is represented as a bar which is devided into 3 equally parts and one part is in shaded. He considered 1 and 2 (in the number ½) as independent numbers. Therefore he concluded that 1/5 is the greatest fraction. This error is influenced by he had difficulty in fraction magnitude.

Fraction magnitude knowledge, mathematics difficulty, representation.