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15 September 2013


by: Ratih Ayu Apsari
Student of International Master Program on Mathematics Education (IMPoME)

Many educators usually use a formal approach to teach about linear equation system. We might invoke the real life experience problem, but we will tell their pupils to do standard strategies to solve it. For example, let considering a beautiful “T-Shirt and Soda” problem given by Romberg and de Lange (1998) on Zulkardi (2002).


Figure 1: T-Shirt and Soda Problem

In what way you will solve that problem?
It might be true that most mathematics teachers will directly use one of three most common use strategies to solve linear equation system, such as by sketch a graph, elimination, or substitution. They will represent the T-Shirt and Soda as the mathematical symbol, let say x and y and start their formal method.
However, why we are not trying to see the problem in different point of view? Assume that we are the grade 8 students who have no experience whit this kind of problem. What will we do?
It is something amazing that our students may solve this problem without knowing anything about x, y and any standard method. Consider this possible strategy.


Figure 2: Example of Non-formal Strategy

This is my strategy:
Because I omit several item, the remainder is one T-Shirt on the first expenditure and one Soda on the second expenditure. From that situation, I can infer that the price for T-Shirt is $14 higher than Soda.
After knowing that fact, I can find the price of each. For instance, I would like to find the price for Soda using the second expenditure. Since I know the price for Soda is $14 cheaper than T-Shirt, I can say that I spent $16 for 4 Soda. Therefore, the price for one Soda is $4. Since the T-Shirt is $14 more than Soda, then the price of T-Shirt should be $18.
What do you feel when your students can answer the question through a creative way like what I have done? It is actually applied the concept of substitution and elimination, but not in a formal scheme.
Feel curious for other creative strategy that might be emerge in your class try to give the similar problem to your students!
Here you can improve the problem into something that experimentally real to the Balinese students. How if you use the context of Sukawati Market? You can change the T-Shirt as the Sukawati Pants with flower pattern and the Soda with the Sukawati Necklace. Change the price from US Dollar ($) to Rupiah (Rp).


Figure 3: Modifying T-Shirt and Soda Problem into Sukawati Market Problem


Enjoy your class!

Note for the readers who doesn’t familiar with the name of Sukawati:
Sukawati is a famous handicraft market located in Gianyar, Bali. It is well-known place to buy a traditional clothes, accessories, statue, painting, and other local industries.

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