The Way of Student’s Thinking about Percentage Problems

By: Sari Saraswati

International Master Program on Mathematics Education (IMPoME) 2013

Sriwijaya University

Email: Sarisaraswati7@gmail.com

Introduction

The interview was conducted to know the students’ thinking related with percentage. The interview conducted in SD IBA Palembang. The subject of this observation is M. Dzar Alghifari who is one of students grade 5 SD IBA Palembang. The problems consist of three levels which are easy, intermediate, hard.

Problem 1

Student’s Answer

Jadi, persen sepeda yang rusak adalah

30%

Analyze Problem 1 Based on the student’s answer, it have been gotten

that bikes turned out represented by the fraction which is .

The student know that percentage is hundredth. Therefore, it is , so that the student only changed the fraction become percentage such that have been gotten .

From the concept that had been gotten by the student, so that the student presented that equal to 30%.

So, the perncentage is 30%.

Problem 2

Student’s Answer

From the student’s answer, known that the student sum all of students in class such that had been gotten 20 child in class.

The student used the rectangle to represent the fraction of the number in class.

Satu persegi panjang yang diarsir sebanding dengan 20 anak

¾ bagian persegi panjang yang diarsir sebanding dengan 15 anak

½ bagian persegi panjang yang diarsir sebanding dengan 10 anak

¼ bagian persegi panjang yang diarsir sebanding dengan 5 anak

1/20 bagian persegi panjang yang diarsir sebanding dengan 1 anak

Analyze Problem 2

The student explained that 20 child represent 100%.

because a half of 20 is 10, so that the percentage is 50% which is a half of 100%.

Then, a half of 10 is 5, so that a half of 50% is 25%.

Then, 5 child divide by 5 is 1, so a child represent 5%.

So, percentage of the children in class 5 a member of a sports club is 75%.

Dialog the observer and student Observer : Dua puluh itu apanya?

Alghi : Dua puluh jumlah semua siswa.

Observer : He’em..terus?

Alghi : Kalau semuanya dua puluh anak ikut, ada seratus persen. Tapi Kalau hanya lima belas yang ikut.. tujuh puluh lima persen.

Observer : He’em

Alghi : Karena dua puluh sama dengan....(siswa menulis)

Obserever : He’em

Alghi : lima belas...tiga per empatnya.

Observer : Iya..terus?

Alghi : Kalau sepuluh anak setengahnya. Kalau lima anak se per empatnya. Kalau satu anak....sama dengan lima persennya.

Observer : iya..berarti kesimpulannya.. berapa persen yang termasuk dalam kelompok yang suka sepak bola?

Alghi : Ada tujuh puluh lima persen.

Problem 3

Student’s Answer

The student explained that Rp. 600.000 represent 100%Then, he found a half of 100% is 50% so that a half of

Rp.600.000 is Rp. 300.000 which have to be paid.Then, a half of 50% is 25% such that a half of Rp.300.000

is Rp. 150.000, so the number of money which have to be paid is Rp.450.000 (Rp.300.000 + Rp.150.000)

Then, a half of 25% is 12.5 % such that a half of Rp.150.000 is Rp75.000 so that the number of money which have to be paid is Rp.525.000 (Rp.450.000 + Rp.75.000)

But, to find 15% of Rp.600.000, the student was difficult.

Analyze Problem 3

The student used the rectangle to find 15% of Rp.600.000.

The dialogue between observer and student Alghi : Kalau seratus persen, berarti enam ratus ribu, jadi satu full.

Setengahnya tiga ratus ribu...seperempatnya...seratus li...

Observer : Tiga piluh ribu daa..dari?...tiga ratus ribu darimana?

Alghi : Dibagi setengah..

Observer : Dibagi..dibagi?

Alghi : Dibagi dua.

Observer : Iya...terus kalau yang ini?

Alghi : Dibagi empat..

Observer : Dari? siapa yang dibagi empat? Berapa yang dibagi empat?

Alghi : Satu dibagi empat. Enam ratus ribu dibagi empat.

Observer : He’em..

Alghi : Jadi seratus lima puluh ribu.

Observer : He’em..

Alghi : Sedangkan lima persen ini sama dengan satu per dua puluh.

Observer : he’em..

Alghi : Satu per dua puluh.

Using the particular of rectangle, the student found that 5% of Rp.600.000 is Rp.30.000.

Then, he multiplied 5% by 3 such that had been gotten Rp.90.000.

Therefore, the price of bike is Rp.600.000, while the discount is Rp.90.000, so the total money that have been paid is (Rp. 600.000 – Rp. 90.000 equal to Rp. 510.000,-.

Thank You