Font Size: 

Covariational reasoning plays important role in mathematics education. It forms cognitive activities or thinking process which are involved in coordinating two quantities while attending to the ways in which they change in relation to each other. Fraction is one of the main concepts in studying algebra. It is the most important concept that must be understand by students. Fraction compare problem is the compare word problem involving fractions. The compare word problem of fraction may interpret as a covariational problem in an elementary level. Students must be know about fraction and compare problem. That can be made students solve the fraction the contextual problem and use the reasoning to solve compare problem about fraction. A simple covariational reasoning problem in elementary level is a fraction compare problem. But, many students assume that compare word problem are difficult. One of students 'difficulties factors in solving compare word problem is the lack of students' reasoning. The covariational reasoning is one of the reasoning behavior of students is needed to solve compare word problem especially fraction. Many reseachers have been investigated some covariational reasoning behaviors, but none had exposed covariational reasoning related to fractions in an elementary level.

 

This study was a descriptive qualitative research which employed both test and interview method. This study aimed to investigate students covariational reasoning after learning fraction word problems in the first semester on the fifth grade. The fifth grade class consisted of 12 boys and 13 girls. All students were given the fraction ability test and the fraction compare problem, which was focused on arithmetics operations (addition, subtraction, multiplication, and division). The results of fraction ability test were ranked into three levels, i.e. high, medium, and low mathematical abilities respectively. The data analysis was focused on students’ covariational reasoning, which related to five mental actions of covariational reasoning. Three students of seven students with high mathematics ability were volunteerly chosen as research subjects. All subjects, who had good communication skills, were individually participated in the interview session. The individually interview was conducted to reveal students’ reasoning while solving covariational problems.  The result of fraction ability and compare fraction tests are shown in Table 1.

 

Table 1a. Students’ Fraction Test Ressults

 

Sex

score > 80

80 ≥ score ≥70

score < 70

Boys

3

6

3

Girls

4

5

4

 

Table 1b. Students’ Compare Fraction Test Ressults

 

Sex

True

False

Boys 1

1

5

Boys 2

4

2

Girls 1

1

5

Girls 2

2

4

Girls 3

3

3

Girls 4

4

2

 

The results emphasized that the fifth grade students were nearly unable to construct the relation of the variables that change with the other variables. It cause the students faced difficulty in determining the operation of the problem solving, could not operation the fraction with different denumerator, and could not apply the concept of fractions. Our result suggest that learning fraction should be increased emphasis on coordinating two quantities changing about compare magnitude and operation of fraction of change and to improve the knowledge in fraction compare.

covariational, reasoning, compare, problem, fraction, elementary reasoning.