International Education Studies; Vol. 9, No. 7; 2016 ISSN 1913-9020 E-ISSN 1913-9039

Published by Canadian Center of Science and Education

145

Limited Intervention at Sub Concept of Fractions in the Object Conversion into Fractions

Henry Kurniawan1,2, Toto Nusantara2, Subanji2, Susiswo2, Iwan Setiawan3, Akbar Sutawidjaja2, Abdur Rahman As’ari2 & Makbul Muksar2

1 Politeknik Negeri Lampung, Indonesia 2 Universitas Negeri Malang, Indonesia 3 SMA Negeri 2 Martapura OKU Timur Sumatera Selatan, Indonesia

Correspondence: Henry Kurniawan, Program Studi Manajemen Informatika Jurusan Ekonomi dan Bisnis, Politeknik Negeri Lampung, Indonesia. E-mail: henry_stk@polinela.ac.id

Received: December 18, 2015 Accepted: January 23, 2016 Online Published: June 28, 2016

doi:10.5539/ies.v9n7p145 URL: http://dx.doi.org/10.5539/ies.v9n7p145

Abstract This research is an exploratory study with a qualitative approach, which is based on interviews with a task-based the purpose of this study is to describe the understanding of elementary school students in interpreting sub concept fractions in changing of the object is given to fractions with limit intervention. While intervention on problems solving mathematical in a fraction of this is an attempt to change behavior, thoughts and feelings of a person to develop the students’ knowledge in achieving the objectives of the fractions learning experience.

Keywords: interpretation, fractions, object, limit intervention

1. Introduction This article discusses the learning of mathematics in elementary school (elementary school) about the basic concepts of fractions by using media/props are believed to provide pleasure and understanding to students. Learning by using media/props greatly assist the creation of learning in accordance with the demands of the curriculum in 2013, namely: fun, contextual and meaningful through the steps of learning to observe, ask, experimental/discovery, process the information and summarizing the results which were consistent with the objectives.

Learning activities to recognize the concept of ordinary fractions will be more meaningful when it is preceded by a story about the use of real objects e.g. eggs, apples, tomatoes, tofu, pancakes, followed by fractional block or shaded paper. To avoid misunderstanding in assessing the concept of fractions and arithmetic operations on these numbers we will need to pay close attention to sub concept of fractions. Sub concept is useful to guide the understanding and give command of the facts, operations and principles of the fractions as an integral part of mathematical objects.

According to Psychology Bruner (1966) learning will be more meaningful and more quickly achieve the goal if it starts from the stage of concrete (enactive) that uses the real object, then semi-concrete (econic) the object that replaced the image, and the last is abstract (symbolic) the grain which is only in the form of emblem/symbol that only in the form of letters, or numbers only. According to Bruner if students are experienced math learning for each topic with treatment by the third stage, the students will be able to develop knowledge far beyond what they received from the teacher.

In the process of teaching the fifth grade students of SDN 2 Merjosari, teachers beginned by fractions ½ using paper one sheet is cut into two equal parts, and they told his students “a piece of paper divided into two parts, then the result is ½”, herein if No students ask “why ½?, why not the paper into two pieces?” On learning activity it is seened that some of students do not understand the concept of fractions ½.

Then the learning continue after students acquired basic knowledge of the fractions concept, the teacher wanted to measure students’ reasoning and the ability to apply the basic concepts of fractions. Those students were asked to determine the fractional value as congruent parts of a whole based on the colors red, yellow and white as in the Figure 1 below:

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149

name), to indicate a relationship “many parts of the whole part of the same” (a part-to-whole relationship).

If p and q are numbers chopped and q ≠ 0, then the fraction or p/q, showed p dividing by q equal parts

(equivalent), p is called the numerator (numerator) and q is called the denominator (the denominator).

Several studies have been conducted to investigate the difficulties in understanding and learning the material fractions. Vale (2007) found that students will be more likely to make mistakes on a fractional operation if only a fraction of learning material focuses on memorizing formulas and procedures for operating without sufficient attention to the meaning of fractions. Part-whole relationship as a sub identifies key ideas and overall understanding of fractions which will be interpretation in fractions (Kieren, 1988). In addition, the complexity of the characteristics and stages of understanding the concept of fractions requires that made it can not be understood in a relatively short period (Yusof and Malone, 2003). Further research conducted Clarke, et al. (2007) found that the methods and learning strategies that are less precise can also contribute to the misconceptions students.

According to Bell, Castello, and Kucheman (1983) the concept of fractions can be interpreted into seven ways, namely:

a. Part group congruent part

Fractions as part group congruent part. Fraction is interpreted as an area divided into b congruent parts and

pay attention to a part.

b. Part group non congruent part

Fractions as part group non congruent part. Fraction is interpreted as an area divided into sections that are not

congruent b and pay attention to a part. c. Part whole congruent part

Fractions as part whole congruent part. Fraction is interpreted as a set consisting of b objects are congruent

and noticed an object d. Part whole non congruent part

Fractions as part whole not congruent part. Fraction is interpreted as a set consisting of b objects that are not

congruent and noticed a object. e. Part group comparison

Fraction as part group comparison. Fraction is interpreted as a relative comparison of two areas A and B. The

number of areas that are congruent to A is A, while the B as b. f. Part whole comparison

Fraction as part whole comparison. Fraction is interpreted as the ratio of the bunch is the comparison of the

relative number of objects in a set A with a lot of objects in a set B g. Number line

Fractions as the number line. Fraction is interpreted as a point on the number line. In this case, a unit on the

number line is divided into b equal parts, then point to note-a

The ability of representation is one of the standard math learning process should be developed and owned by the students. These process standards should not be submitted separately to the mathematical material. Unfortunately,

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Diagram 7. Interpretation of the results of interviews S4

In the diagram 7 visible S4 interprets many parts of the whole 6 (N) with a fractional value of the orange (O) to black (Bk) is 2/4 indicated by the flow arrows in blue and fractional value of the black to orange is 4/2 indicated by a green arrow groove.

Because S4 wrong answer is not in accordance with the fractional value corresponding to the color, the researchers conducted interviews with intervention Limited to the following S4

Researcher : What is the sum of that images a collection?

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Researcher : Exactly. Then how many images are in black? And how many pictures are orange?

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Researcher : great.

Interventions conducted by researchers to S4 shown in the diagram below 8:

Diagram 8. The results of interviews S4 with limited intervention

From the results of the Limited interventions conducted by researchers of the S4 at no 4 on the diagram 8, it appears that the S4 begin to understand the value of fractions as part whole non congruent part to black is 4/6 and orange is 2/6.

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159

Researcher : True or with other words the ratio is of = comparisons.

And what if the fractional value based on the ratio? (Limited intervention)

S3 : Oh yes, sir. 3/4 of is the value

Researcher : You are very smart!

Interventions conducted by researchers to S3 shown in the diagram 12 below:

Diagram 12. The results of interviews S3 with limited intervention

From the results of the limited interventions conducted by researchers of the S3 in question no 6 on the diagram 12, it appears that the S3 began to understand the value of a fraction as the part whole comparition based on the green to purple is 3/4.

The last picture interpret fractions as the number line shown in the students’ answers below:

Fractional as the number line

Figures 7 and 8 above error interprets the fractional value of the primary colors (first/previous) is above as the basis for determining the value of the fraction. Whereas in Figure 9 and 10 above error interprets the fractional value of the second color as the basis for determining the value of such fractions by looking at other parts. Later Figures 11 and 12 above interprets the fractional value in the second color as the basis for determining the value of a fraction without seeing the whole.

5. Conclusions Completion of the process of student answers appeared that students cannot understand fractions as ratios and parts are congruent and incongruent of the whole or a set of objects which was given, it is seen from the inability of students to write answers to a fractional value of the three categories in the discussion. Students interpreted the fractional value soch as

1) The dominant colors are located on top of the other colors to see part of the overall

2) Colors are asked as part of other colors regardless of the whole.

3) The combination of No. 1 and 2.

After the intervention of the settlement of the problem of students, then the problem can be solved with the desired questions.

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