1) The document analyzes students' thinking when solving percentage problems. It observes two students, Athia and Kartika, solving three percentage word problems. 2) For the first problem, Athia was able to convert a fraction to a percentage by multiplying the numerator and denominator by 10. For the second problem, Athia struggled at first but then used a visual representation strategy to solve it. 3) For the third problem, Athia confidently explained how to find the discount percentage and subtract it from the original price to determine the amount to pay. She understood the discount concept well although made a notation mistake.

1. Analysis of Student’ Way of Thinking
in Solving Percentage Problems
in grade VA MIN 2 Model Palembang
A.Harpeni D.

2. 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 Ratih
Ayu Apsari interviewed Kartika.


3. There are three questions given to students in this
activity, those are:
1
3/10 dari sepeda yang diperiksa ternyata rusak.
Berapa persen kah sepeda yang rusak tersebut?
Berapa persentase dari siswa kelas 5 yang merupakan anggota
ekskul sepak bola?
Hasil dari pendaftaran ekskul kelas 5
2
Apakah kamu anggota ekskul sepak bola?
YA
:
TIDAK :
3
Jika harga sebuah sepeda Rp 600.000,- dan kamu
mendapatkan diskon 15% maka berapa uang yang harus
kamu bayar jika ingin membelinya?

4. 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.

5. Result of interviews and analysis of
student’s answer.

6. 1
3/10 dari sepeda yang diperiksa ternyata rusak.
Berapa persen kah sepeda yang rusak tersebut?
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.

7. Strategy she used was by multiplying 3/10 to 10/10. In other
words, Athia multiplied each numerator and denominator by 10
to 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.

9. Berapa persentase dari siswa kelas 5 yang merupakan anggota
ekskul sepak bola?
Hasil dari pendaftaran ekskul kelas 5
2
Apakah kamu anggota ekskul sepak bola?
YA
:
TIDAK :
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

10. Steps;
Finding the number of students who enrolled and didn’t enrolled the soccer extracurricular.
Notating the fraction representing the number of students who enrolled
(15/20) and didn’t enrolled (5/20) the soccer extracurricular.
Converting both 15/20 and 5/20 to percent
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%.
Concluding that students who attended soccer extracurricular is as much as 75%,

12. 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.

14. 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%.

15. Jika harga sebuah sepeda Rp 600.000,- dan kamu
mendapatkan diskon 15% maka berapa uang yang
harus kamu bayar jika ingin membelinya?
3
Findings


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.

16. 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).