Pre-Test of First Cycle

Briefly, the pre-test is aimed to know students‟ initial knowledge and ability about multiplication of fractions, especially about multiplication of a whole number by a fraction and multiplication of a fraction by a whole number. In the following, the researcher will describe some remarks got from the pre-test.

4.2.1.1 Students Initial Knowledge of Addition of Fraction and Multiplication of Fraction

Based on the answers in the worksheets, the researcher interpreted that all students could use appropriate algorithms to solve fraction addition problems, whether it had the same denominator or not. Moreover, three of them also converted improper fractions to mixed number.

Regarding to multiplication of fraction with whole number problems, the students showed various strategies. From the six students, only two students gave proper algorithm, meanwhile the other four students mixed up some algorithms.

Perhaps, the four students tried to use algorithms of multiplying fraction by

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fraction because they have already learned it. Nevertheless, they made some mistakes in using the algorithms. While two students made mistakes in converting the whole number, other two students directly multiplied the whole number by the numerator and the denominator. The following figure shows students mistakes in answering question .

Figure 4.2 Students Mistakes in Solving Multiplication of Fraction with

Whole Number

4.2.1.2 Relating Situations to Its Algorithms

From the worksheets, the researcher concluded that all students related one situation to one algorithm only. The difference lay on relating the first and the third situation, as can be seen in the Figure 4.3 below.

Figure 4.3 Students' Answers of Second Problem of Pre-test

Based on the pictures above, three students related the first situation to the second algorithm and the third situation to the first algorithm. On the other hand, the other three students related the first situation to the first algorithm and the third situation to the second algorithm. Perhaps, one of the reasons they only chose one algorithm was the tendency to make one to one correspondence. The students said that they chose the easiest algorithm for the situation.

Another possibility was because the format of questions was not clear enough for them. When the researcher asking them, one of the students realized that the first algorithm is same with the third one and after some time of discussion, all students agreed that both the first and the third situations could be related to the first and the second algorithms.

4.2.1.3 Relating Algorithms to Situations, Checking the Meaning of Fractions

After relating situations to its algorithms, the students then had to relate algorithms to the suitable situations. From their reactions, the researcher interpreted that the students did not familiar with this kind of problems. Before doing the tasks, they asked us how to answer it. From their answers, the researcher got some remarks about their understanding of fraction, addition of fractions, and multiplication of fraction with whole number.

Based on the students‟ worksheets, the researcher concluded that only one student who could give suitable situations for all questions. Below are some examples of situations given by Cici (Figure 4.4). However, the researcher interpreted that she might consider as five times, not of 5.

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Chika eats half of watermelon.

Rara eats .

Bu Selfia has many cakes.

She has 5 children Each child takes cake.

Figure 4.4 Cici Gave Suitable Situations to the Fractions

Another student, Uya, gave situations as if he got task about fraction addition and multiplication of fraction with whole number, as can be seen in Figure 4.5. Perhaps, he only knew fractions as one of subjects in his school.

When I did my homework, I found question .

I answered

Just now I got question

Because I can, I directly answered it

Because the 5 is same, I made it

Figure 4.5 Uya Related Fractions with School Task

Another one student, Iman, could give suitable situation for fraction addition problem, but when facing by multiplication of fraction with whole number problem, he directly put the question in the situations. Perhaps, he did not have idea about the meaning of multiplication of fraction with whole number. The examples of his answer can be seen in the following figure.

Mother uses sugar to make cake.

Mother wants to make two cakes.

Each cake needs kg

My mother does not like to my sister because she asked

spoons of sugar to make tea.

Figure 4.6 Different Understanding toward Addition of Fraction and Multiplication of Fraction

4.2.1.4 Strategies Used by Students to Solve Contextual Problems

Based on the worksheets, Iman wrote that half of is . Menawhile, other four students directly divided the number ( or ) by . Just after they had to explain their answer, they wrote it was because half of is . Perhaps, it was because the students did not consider a half as fraction.

The other one student, Uya, considered half of something as something times a half (for example half of is ). He said that he divided it by 2 because the denominator is 2, and it was valid also for a third. However, when the researcher changed the question to , he answered it 8, because 2 times 3 is 6 and 48 divided by 6 is 8. From the answers, the researcher interpreted that the student did not fully understand about multiplication of fraction with whole number. Perhaps, the numerator 1 in unit fractions means nothing for the students since they directly divided the whole number by the denominator. They did not

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realize that they have to multiply the whole number by the numerator before dividing it by the denominator or vice versa.