Frans van Galen, Dolly van Eerde
IndoMS. J.M.E
Vol.4 No.1 January 2013, pp 1-8
Students in the last grade
of primary school must be familiar with ‘percentage’, yet most of them often
struggle with percentage problems. As in the study performed by authors and 10
Indonesian master students in Utrecht that only 4 out of 14 grade 7 students (13
and 14 years old) at an international school were able to answer correctly on
this problem: ‘On a bike that normally costs
600 you get a
discount of 15%. What do you have to pay?’
Data from the written test and interviews reveal that
most of students in this study did not know a systematic procedure for working
with percentages. Only the student with the highest score solved all problems
in the same way: she translated the percentage into a decimal and multiplied. Given the bike problem, for example: 15% of
is
0,15 x 600. Whilst other students solve by multiplying 15/100 x 600.
In addition, several students tried to use another approach
by finding an equal proportion of the given percentage. 15% is known same as
’15 out of 100’ or ‘15/100’ and then they
tried to to find the same proportion in ‘so many 600ths’. Principally, this approach is correct leading
them find 15/100=90/100. Often, however, the unfriendly proportion of ’15 out
of 100’ confused some students. Many students divided 600 by 100. Since they saw
100 cannot be divided by 15 easily, but 600 : 15 is doable.
In a teaching experiment in this study, the students were
then taught the use of percentage bar. Hence, this article discusses how
percentage bar supports students solve the percentage problems and shows a few
examples showing how quick students profited from working with this approach.
Drawing a percentage bar has several advantages (van den
Heuvel, 2003; van Galen et al., 2008; Rianasari et al., 2012). Those are:
1st :
It allows students make a
representation for themselves of the relations between what percentage is given
and what is asked. For some cases, it can be presented as follows;
1. ‘How much is 15% of 600?’
2. ‘€90 of €600, what percentage is that?’
3. ‘€90 is 15% of total price; how much is the total price?’
2nd :
It offers scrap paper for the intermediate steps in
the calculation process. The students can easily decide what to do next after
every step of calculation. For instance, 50% of €600 is €300, 10% is €60, and 5 % is €30. Thus, via 10% and 5%,
student may find that the answer is €60 + €30 = €90, as in the following
figure.
3rd :
It offers a natural entry to calculating via 1%. First, calculate 1% and
from there calculate the percentage that is asked for. This approach is
generally applicable and efficient to do. It helps students to solve the
percentage problem with unfriendly numbers (e.g 26% or 51% of something).
The researcher suggested that a good approach when
students start learning about percentages is calculating via 10%. But, it is
only possible if the number are easy. Later on when working with more
complicated numbers, calculating via 1% systematically seems to be an efficient
and applicable procedure.
One of the problems that was given to the students was a
problem about downloading a computer file:
‘11% of 600 MB has been downloaded already, how many MB is that’
Through percentage bar, student found: 50% = 300, 25% = 150, 10% = 60, and 1% =
6. She, eventually computed 11%=10% + 1% and could easily determine 11% of 600
MB = 66 MB.
Some problems in written test shows how effective the percentage bar in helping
students to solve percentage problems that they probably could not have done
otherwise. The percentage bar offers support, because it helps students to
oversee the relations between the given number. Besides, it should be
prevented, at least, students to decide too quickly solve percentage problems
in their heads.
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