How to Create a Math Problem

By: Al Jupri, M.Sc.*

“Sir, please teach me how to make a good math problem!”

That’s one question a math teacher once asked me. Yes, one question that is rarely asked, can even be said to be a rare question worth asking. Frequently asked questions usually revolve around how to find a solution to a math problem, especially a math problem that is considered difficult.

What did I answer to the question? Am I able to answer it well? Before answering the question, I thought about what the teacher actually asked.

Did he ask about how to make a question that fits the theory of evaluation in learning? If this is asked, then I will answer that a good question should meet the standards of validity, reliability, difficulty, differentiation, and others. Therefore, make a question that meets those standards! But, I think, that’s not the question!

Did the teacher ask about how to make a question that fits the theory of psychology, especially Bloom’s taxonomy? If this is asked, then I will answer that a good question should be made according to the cognitive stage of the student who will answer the question. In Bloom taxonomy, there are six levels of cognitive domain, namely: knowledge, understanding (simple), application, analysis, synthesis, and evaluation. Again, I think, it doesn’t seem like this is the case.

I think the teacher asked about how to make a math problem reviewed from the side of mathematics itself. To answer this, I don’t think it’s easy–because of course what you want is not just a regular problem that can be easily created by cheating the questions already in the book.

Finally, after thinking, the way I did to answer the question was to create a simple example that could be understood and show how the process of a math problem is made. In this way I hope to be easily emulated, practiced, and creatively developed. In that way, I also learned to make good math problems.

This is the (creative) process I’ve done to create a math problem. In this case, I give an example in the row and series topics.

1, 4, 16, 64, 256, …

This line is a geometric row with the first tribe 1 and a ratio of 4. “Regular” questions, which are often exemplified in books, such as this:

(i) Determine the 6th tribe; 10th tribe; and the nth tribe;

(ii) What ethnicity is 65,536?

(iii) Is 2,091,754 one of the tribes in the line?

Not that the questions that are often exemplified in books are not good. But, the problem is how to make a better and interesting question than the usual problem? Here, it will be exemplified how twisting the ordinary problem that we already understand becomes a better and more interesting question.

Note that the geometry lines can be written as follows:

1, 1.(1 + 3), 4.(1 + 3), 16(1 + 3), 64 (1 + 3), …

If the numbers 1 and 3 we replace in a row with m and n for example, then the row will be as follows:

m, m(m + n), 4(m + n), 16(m + n), 64(m + n), …

Is this last line enough to make a good math problem? Hmm… it seems that the tribes are known to still be exaggerated to be a question. It needs to be simplified to look like the following:

m, m(m+n), 4(m +n), …

Up here, from various possibilities, the questions that can be made can be as follows:

If m > 0, n > 0 and both are integers, and: m, m(m+n), and 4(m + n) are three consecutive syllables of a geometric series, then specify a comparison between m and n!

Well, is this question enough to be a math problem that can be answered? If so, then this is the process of making simple math problems, which I see as better and more interesting than the problems we usually find in textbooks. Otherwise, with my hands open, I await a better example of you.

I hope, with the example I gave recently, the teacher’s question that I wrote at the beginning of this article has been answered. If not, hopefully the example can give a drop of “water” that slightly reduces the thirst of curiosity. Amin.

*PhD student at Utrecht University, The Netherlands.

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