CTK Insights

Probably every math teacher has the experience of facing such questions; most likely the students who asked them were not looking for the answers as arguments to study mathematics, but rather in support of their conviction that the effort is not necessary. Most of the answers teachers give perfectly serve this purpose.

I wrote about that quandary on two occasions:

Motivation, where does it come from? and
What Is Your Answer to That Question?

Very recently the questions have been discussed in the August 2011 issue of Mathematics Teacher. Author Samuel Otten offers a short catalogue of common answers and describes the effect that the answers commonly have on students. Here's a short write-up.

Citing a Real-World Situation

"You would use area functions like this if you were carpeting your floors. The ability to solve systems of equations is important when you're comparing different phone plans."

Whatever real-world utility of mathematics is mentioned, most students may usually argue that for their future the cited examples won't be relevant. Further, in most cases it could be argued that those real world problem could always be solved without a recourse to mathematics.

Citing a Profession

"You can't become a nurse without a solid foundation in algebra. Engineers use this stuff all the time."

There are too many professions to convincingly satisfy every student. Moreover, most of the professions require at best the most rudimentary mathematics.

Citing the Mathematics That Underlies Useful Technology

"Matrix algebra is a basis for Internet search engines. That cell phone you're using wouldn't exist without mathematics."

This goes counter the students' daily experience. Everyone uses Internet and a cell phone without so much as giving a thought to matrices or other aspects of mathematics.

Citing a Future Mathematics Class

"You’ll need this stuff from algebra when you get to advanced algebra. This is one of the pieces that’s building up to calculus."

Students who question the utility of the present math class are unlikely to be convinced by the utility of a future class.

Citing a Future Event in the Current Class

"You’ll use these trig functions in the next chapter. This material will be on the upcoming exam."

The argument may cause students to make a short term effort, but actually avoids answering their deeper concerns.

Other responses

... students could be asked whether they challenge other classes in a similar way.

This approach carries little conviction, for everyone has his or her personal inclinations. Not every one who plays basketball plays soccer and vice versa.

A frequent answer induced by the common way of thinking is that mathematics helps develop logical thinking that could be applied in many real life situations. However, this thinking is faulty on to counts. First, it assumes at best - contrary to the recurring experience - that the whole of the student body may succeed in mathematics, which is simply not universally true. Secondly, that thinking does not consider the possibility that the same logical thinking skills could be acquired by means other than through the study of mathematics. But there are of course many ways to achieve that goal.

Samuel Otten rightfully observes that the best situation is where

the students are happily engaged in learning mathematics and unlikely to challenge its purpose (e.g., students are finding intrinsic value in mathematical discovery and sense making)

This is the situation every teacher could dream of, but it needs to be admitted that the study of mathematics may have its ups and downs; there could not be guarantee that on occasion students may be inclined to inquire into the utility of what they are required to do. This may happen even with the best teachers.

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In my view the article eschews a possibility that answering students' quandary may be less important than having a real justification for the requirement to study mathematics by all and sundry. When questions are asked, the answers must be given. The problem is to give an answer that would be convincing to the teacher even more than to the students. This is practically impossible in view of the simple fact that - importance of mathematics notwithstanding - it is used very rarely by most of the population, if at all.

When discussed, those questions and answers are most often considered in the context of a classroom, as a two-way conversation, a conversation between students and a teacher. But there is a third component that has bearings on the whole situation: the system. It's the system that prevents some of students - those who can - to enjoy mathematics, while forcing many others - those who can't - to suffer the burden.

Perhaps, changing the system that requires every student to take more or less the same classes, with a relatively high minimum scope, would be a better response to the perpetual students and teachers plight - why to study mathematics. Perhaps, as a society, we need to admit that some students may benefit more focusing on other subjects, that putting so much emphasis on mathematics and its importance we do disservice both to students and to the subject - beautiful and important as it is.

References

1. Samuel Otten, Cornered by the Real World: A Defense of Mathematics, Mathematics Teacher, August 2011, Volume 105, Issue 1, 20-25

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