A.Harpeni D.

Analysis of Student’ Way of Thinking in Solving Percentage Problems

in grade VA MIN 2 Model Palembang

This activity was carried out on Saturday, September 5, 2013, about 8.45 am.

This activity took about 30 minutes involving 2 students of grade VA as a subject of observation, namely Kartika Buana and Athia Zainun Faqiha S. who were randomly selected by Miss Eva, mathematics teacher in grade VA.

One student was interviewed by one observer. A.Harpeni Dewantara interviewed Athia while RatihAyu Apsari interviewed Kartika.

There are three questions given to students in this activity, those are:

3/10 dari sepeda yang diperiksa ternyata rusak.Berapa persen kah sepeda yang rusak tersebut?

1

Berapa persentase dari siswa kelas 5 yang merupakan anggotaekskul sepak bola?

Hasil dari pendaftaran ekskul kelas 5

Apakah kamu anggota ekskul sepak bola?

YA :

TIDAK :

2

Jika harga sebuah sepeda Rp 600.000,- dan kamumendapatkan diskon 15% maka berapa uang yang haruskamu bayar jika ingin membelinya?

3

Student was allowed to use any strategy to solve those problems.

From interview with Athia, we found that generally she has been able to solve the percentage problems well. Though in some parts she still needed the observer’s guidance.

Result of interviews and analysis of student’s answer.

As we addressed, in the first question, student was asked to convert fraction to percent. Athia could understand the question easily. In addition, from interview, it seemed that her understanding about concept of percent is quite good. Referring to her understanding that percent means per hundred, then she surely said that to convert the fraction to percent, both numerator and denominator of such fraction should be multiplied by a certain number, so that the denominator would be 100.

3/10 dari sepeda yang diperiksa ternyata rusak.Berapa persen kah sepeda yang rusak tersebut?

1

Strategy she used was by multiplying 3/10 to 10/10. In other words, Athia multiplied each numerator and denominator by 10to obtain a fraction whose denominator is 100, since percent means per hundred.

A further, Athia also explained that each of the numerator and denominator must be multiplied by the same number, for example, if 10 as the denominator in 10/10 multiplied by 10, then 3 as numerator must be also multiplied by 10. Although she did not why it so.

Berapa persentase dari siswa kelas 5 yang merupakan anggotaekskul sepak bola?

Hasil dari pendaftaran ekskul kelas 5

Apakah kamu anggota ekskul sepak bola?

YA :

TIDAK :

2

Findings

Athia found difficulty in understanding the problem and determining the strategy that will be used to solve it. It’s because she read the information

partially, that she missed some information

Using the same strategy as used in the first problem, by multiplying each numerator and denominator of the fraction by a certain number to

obtain fraction whose denominator is 100.

She was able to find another strategy to solve the problem after guided by observer

Concluding that students who attended soccer extracurricular is as much as 75%,

Multiplying 20 (the numerator fractions 15/20 and 5/20) by 5 to obtain fractions whose denominators are 100.

Because the numerator is multiplied by 5, then the numerator must also be multiplied by 5. So Athia gained 15/20 = 75% and 5/20 = 25%.

Converting both 15/20 and 5/20 to percent

Notating the fraction representing the number of students who enrolled (15/20) and didn’t enrolled (5/20) the soccer extracurricular.

Finding the number of students who enrolled and didn’t enrolled the soccer extracurricular.

Steps;

Another Strategy :

By using visual representation

strategy

Steps;

Firstly she drew a rectangle and then divide it into 20 equal parts. To represent 15/20, she shaded 15 of the 20 parts, as in the picture below.

Furthermore, to convert the fraction 15/20 into percent, Athia subdivided each part in the previous picture. Referring to the idea that percent is per hundred, she decided that each part must be

divided by 5 to obtain 100 parts of a whole.

After dividing each part into 5 smaller parts, Athiah counted the number

of shaded parts. At first she tried to count one by one, ie, by calculating

the 5 +5 +5, and so forth until she eventually realized that it was a

repeated addition.

So she found that the number of the shaded area is 5 x 15 = 75 parts, and

the number of parts as a whole is 5 x 20 = 100 parts.

From these findings, she was able to explain well that each of the

numerator and denominator of the fraction 15/20 should be multiplied by

5, to obtain the final answer is 15/20 = 75/100 or 75%.

Athia was able to solve problems well. She confidently explained to the observer that the first step to do is finding the discount. Then, subtracting the discount from the initial price.

From interview, it was clearly seen that Athia understood the discount concept quite well. She claimed that because of discount the bike price will be reduced from the initial price.

Findings

Jika harga sebuah sepeda Rp 600.000,- dan kamumendapatkan diskon 15% maka berapa uang yangharus kamu bayar jika ingin membelinya?

3

Therefore, to know the amount of money to paid if you want to buy a

bike with initial price 600.000 and 15 % discount, strategy used by

Athia was looking for discount by multiplying 15/100 with 600.000 to

obtain 90.000. But in this part Athia made a mistake in notating such

number, since she wrote 900000.

After obtaining discount, Athia found that the final price of bike is

510,000, which is obtained by subtracting the discount (90,000) from

the initial price of bicycle (600,000).