# >> How to Modify a Math Problem

By: Al Jupri

Question: How the hell do I modify the math problem?

The word “modification” in the English Dictionary means “alteration” or “change”. Usually if we modify “something”, then this action can be interpreted as an activity of converting that “something” into “something else”. ‘”Something else” made changes could be better than the original or could have been worse than the beginning. What is often done is to change the original shape to a better thing. Goal? Certainly to increase the value of the use of something that we change to achieve our goals. For example, a vegetable man modified his motorcycle, which was originally two-wheeled, into a tricycle. The modification is a motorcycle in the form of a rickshaw, so it can be used to carry a lot of merchandise.

Well, can the modification activity also be done in mathematics? I suspect, as long as the mathematics is seen as the fruit of human thought, the answer to that question is “yes”. If the answer to this question is “yes”, and by referring to the question at the beginning of this article, then how do I modify the math question? As an illustration, here I give you one example. In this way, hopefully the way I will present it is easier to understand.

Supposing in certain math textbooks we find examples of the following questions:

If $x + y = 2$ and $x^2 + y^2 = 5$, then specify the value of $x^3 + y^3.$

Furthermore in the discussion of the example the question is known that the $x^3 + y^3 = 11.$

If we as teachers want to make a test question, whether for a daily replay or a general replay based on the example of the question, then what modification process can we do to the question?

Based on experience and observation, there are at least two basic ways that can be done. The first way, which is common, is to change the “numbers” in the known part of the question without changing the shape and editorial of the question. So the result is a question that almost makes no difference when compared to the original question. If this is done, then the question for example will be changed to the following question:

If $x + y = 8$ and $x^2 + y^2 = 50$, then specify the value of $x^3 + y^3.$

To be able to answer this question, students only need to remember and understand the procedure for resolving the example of the question. According to the theory of educational psychology, the process of learning that is merely remembering is a low-level thought process. I suspect that this first modification is what the problem makers often do. In fact, whether it’s a daily replay, a public replay, or a national exam, most questions have the same type of questions as the questions that have been discussed in the textbooks. As a result of this action, we should not be surprised if the results of international studies, such as PISA or TIMSS, put our students in a very low position, well below the international average.

The second way that can be done is to change the question section asked. For example, the known part remains the same, but what is asked for example is the value of $x^5 + y^5.$ In addition, it can also change the known section and the questioned section simultaneously by utilizing the results of the discussion in the original question example above. If this is done, then the question for example is changed to the following:

If $x + y = 2$ and $x^3 + y^3 = 11$, then specify the value of $x^4 + y^4.$

It appears that the question of modification of this second way is better than the modification of the first way. In to be able to answer the question of the results of this second way, the necessary skills are not only memorized procedures, but also necessary for further understanding and mathematical skills. I think the question of modifying this second way can encourage students to think to a higher level.

Well, it’s easy not to modify that math problem? If so, please practice! Hopefully the example outlined is only useful for us as math teachers. Amin.

If you have any other way of modifying the problem, please pour it in the comments field. Thank.