This article is the reflection paper of the article of Frans van Galen and Dolly van Eerde that titles Solving Problems with The Percentage Bar. It was publised in IndoMS JME, Volume 4 Number 1, 1 January 2013, page 1-8. Frans van Galen and Dolly van Eerde are realistic mathematics education experts from Freudenthal Institute, Utrecht University, Nederland.
Percentage is one of the matematics material that is taught from grade 4 until 6 in primary school. We can imagine, how often this material is taught. However, when a group of IMPOME students carried out a study in grade 7 on students’ understanding of percentages, they were surprised because there are only four students from 14 students who they tested were able to give a correct answer on the following problem :
Although the students had a certain area to be a scrap paper, they just used it to wrote calculation. None of them used it to draw model to clarify the relation between the given numbers. It was obvious that most of the students didn’t know a systematics procedure for working with percentages.
A week later, they interviewed the students about the way they solved some of these problems. They find that there are four students’ ways to solve the problem.
- Converting the percentage into a decimal number and multiplied, for example : 0,15 x 600
- Multiply with fractions, for example :
- Trying to make proportions equal, for example :
- Guided by the numbers in the problem, for example : 600 is divided by 15
Eventhought two first solutions are true, but they were not consistent and made calculation error. While, the way solution number 3 made the students were confused.
In a teaching experiment, the students were taught the use of the percentage bar.The researchers has 2 approaches.
- Calculating via 10%. The problem is like that “if the price of the handphone is € 300 and you just pay € 240, how much the percentage of the discount?” The answer of the student is shown below.
First, student calculated 50% and 25% of € 300, but that didn’t lead to a discount of € 60. As a next step, she started with 10% and found € 60 by doubling.
- Calculating via 1%. The problem is about the downloading the computer file. “How many Mb if someone download 11% of 600Mb?” The student answer is shown below.
Student’s strategy is 50% equals 300, 25% equals 150 and 10% equals 60. 11% as 10% + 1%.
Although teaching experiment by percentage bar was carried out just one lesson, the result confirm that the percentage bar is a powerful model that deserves a central place in the teaching of the percentage. It helps the students to make a representation for themselves of the relations between what is given and what is asked, offers scrap paper for the intermediate steps in the calculation process, and offers a natural entry to calculating via 1%.