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I have always been wondering why some mathematics professors choose to publish problems in journals such as Crux Mathematicorum, Mathematical Reflections etc, which only focus on elementary mathematics.
I don't think that these journals are highly regarded by the academic community and I don't see how publishing problems here helps them in their career(of course, they may only be doing it as a hobby, but it seems highly unlikely for those who publish lots of such problems). Such journals seem more suited for high school teachers, even though I don't see how they may benefit from publishing there either.

  • @SolarMike I've thought about this, but I don't think it is likely. This is why I posted here, to see other opinions. – Math Guy Jul 24 at 12:12
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    Hmmm, do you think that everything possible or valuable has already been said/written about elementary math? – Buffy Jul 24 at 12:22
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    I'm not in math so I can't tell if the American Journal of Physics, from the American Association of Physics Teachers, is vaguely similar. Different audience than Physical Review, but useful to that other audience. – Jon Custer Jul 24 at 12:31
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    @JonCuster very highly regarded journal as a matter of fact. Anyways: Martin Gardner (en.m.wikipedia.org/wiki/Martin_Gardner) would disagree with the Op. – ZeroTheHero Jul 24 at 21:53
  • @ZeroTheHero - I would agree fully. It isn't Phys. Rev. Letters, and is not supposed to be, but has some really neat stuff in it. – Jon Custer Jul 25 at 13:40
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There appears to be a mismatch between your view of "Math" and what math means to a broader community. Sure, there are those doing leading edge research, publishing bold new results, and so forth. But, there are also those who have a calling to do things like teach mathematics, including dedicated high school teachers. Why should there not be a journal for them to read? And if there is such a journal, somebody has to write for it, and those people are normally professionals closely engaged with teaching (remember that many professors, including in math, are at teaching-focused institutions).

In a non-math context, I would point to the American Association of Physics Teachers (aapt.org), associated with the American Physical Society. Their mission statement reads (AAPT Mission):

Mission:

AAPT's mission is to enhance the understanding and appreciation of physics through teaching.

When the organization was established in 1930, our goal was clear: "ensuring the dissemination of the knowledge of physics, particularly by way of teaching." Decades later, we remain committed to that core value, but with a new emphasis and meaning provided by our current mission statement.

Our vision is to be the leader in physics education. We are committed to providing the most current resources and up-to-date research needed to enhance a physics educator's professional development. The results are not only a deeper appreciation of the teaching profession, but most importantly, more enthusiastic involvement from their students.

The Association has identified four critical issues that will guide our future activities:

Increase AAPT's outreach to and impact on physics teachers

Increase the diversity and numbers of physics teachers and students

Improve the pedagogical skills and physics knowledge of teachers at all levels

Increase our understanding of physics learning and of ways to improve teaching effectiveness

The twenty-first century will provide the greatest opportunities and challenges for us as we take an active role in shaping the future. Our success will depend on the commitment, dedication, and continued input of our members and the physics education community. Join us in this journey to enhance the quality and effectiveness of physics education at all levels.

They publish several journals, the American Journal of Physics and The Physics Teacher, focused on slightly different audiences within their society. Frankly, some of their stuff is pretty interesting (in the spring there was a nice paper on the production of polonium in the Manhattan Project, physics included).

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I hope it isn't a radical position to say that math can be "interesting" and "enlightening" at any level. If it weren't then no one would ever study it long enough to reach the edge that the OP seems to prefer. It would just be too boring and uninteresting to pursue.

Unfortunately too many young students find it boring, I suppose, which makes the importance of such endeavors into elementary math more important, and actually gives them added interest.

How can we bring math insight to youngsters who are only studying arithmetic? Algebra?

Math insight is hard gained. But to truly be a mathematician requires it. That insight isn't in the individual statements (theorems, if you like) of math, but in the spaces between the more easily stated things. What is algebra? Really, what is it? How do its parts fit together into a whole?

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I have always been wondering why some mathematics professors choose to publish problems in journals such as Crux Mathematicorum, Mathematical Reflections etc, which only focus on elementary mathematics.

I think that in this case the obvious answer is the correct one: some mathematics professors choose to publish problems in the journals you list because they enjoy working on and constructing interesting problems that are difficult yet have elementary solutions.

I don't think that these journals are highly regarded by the academic community

There are definitely shady, predatory journals out there (I seem to get unsolicited email from them every day) that are not at all respected by the mathematical community and have a reputation for accepting any paper that is submitted to them, regardless of whether or not the results in the paper are correct.

The journals you listed, on the other hand, do not seem to be traditional math journals that specialize in publishing research articles. Instead the journals are devoted primarily (if not entirely) to publishing various flavors of mathematical problems. This being the case, I wouldn't say that the journals aren't highly regarded by the mainstream mathematical community, per se, just that they're likely off the radar of most practicing mathematicians. I hadn't previously heard of either of the journals, for instance. If I was looking at someone's CV and noticed that they published a problem (or perhaps many problems) in one of these journals it certainly wouldn't make me think less of the person as a mathematician. On the other hand, if I noticed that the majority of someone's publications were in predatory journals of the type I mentioned above, that would definitely be a cause for concern.

and I don't see how publishing problems here helps them in their career...

I agree with you that in most cases publishing problems in these journals (or other similar venues) is unlikely to help someone's career in any significant way. Nor is it likely to hurt someone's career. People publish problems and their solutions because they find it intellectually rewarding.

The most well-known problems section that I can think of is the one that appears in The American Mathematical Monthly. I've never submitted a problem to this journal, but believe it to be very competitive. Still, there probably isn't any number of problems (or solutions) one could publish here that would be viewed (by a hiring committee) as being an adequate substitute for one or more papers published in well respected research journals. But if you think this means that only high school teachers, students and amateur mathematicians submit problems to the Monthly then you'd be wrong. Regular contributors include several very well-known and respected mathematicians: George Andrews, Donald Knuth, Jeffrey Lagarias, and Richard Stanley.

Such journals seem more suited for high school teachers, even though I don't see how they may benefit from publishing there either.

The idea that elementary mathematics is something that is inherently not respected by the mathematical community seems to be implicit in your question. I think that this attitude is incorrect. That a paper concerns an elementary topic doesn't make it trivial or not of interest to the mathematical community. (Nor does the fact that a paper concerns a highly technical topic automatically make the paper "deep" or of broad interest.) As an example, consider the number theory journal INTEGERS. Many of the papers published by INTEGERS concern elementary number theory and closely related fields. Yet the editorial board of INTEGERS is extraordinarily strong and contains many extremely highly respected number theorists. And while I can't say that I've found every article I've read in INTEGERS to have been super interesting, many of the ones I've read there have been.

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    Welcome to this site. +1 for your answer. I like how you cite examples (as well as the content of your answer). – Richard Erickson Jul 25 at 12:44
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Both of these journals target mathematical educators, math outreach people (e.g., K-12, college, Math Olympiad), and people who have a general interest in mathematics.

Look at both journal's homepages, they describe their journal's purposes:

Crux Mathematicorum is an internationally respected source of unique and challenging mathematical problems published by the CMS. Designed primarily for the secondary and undergraduate levels, and also containing some pre-secondary material, it has been referred to as "the best problem solving journal in the world". All the problems and solutions are fully peer-reviewed for clarity, completeness and rigour by academic and professional mathematicians. Crux includes an "Olympiad Corner" which is particularly helpful for students preparing for math competitions

and

Mathematical Reflections intends to fill the editor’s perceived need for a publication aimed primarily at high school students, undergraduates, and everyone interested in mathematics. Through articles and problems, we seek to expose readers to a variety of interesting topics that are fully accessible to the target audience.

Similar journals exist in other fields. For example, biology has Journal of Biological Education and statistics has the Journal of Statistical Education. The American Chemistry Society also has a webpage of resources with several similar journals.

Academics publish in these journals to formally share ideas and methods they have for education and accessible examples. Reasons might include:

  • A genuine interest in advancing the field and sharing what they know.
  • A interest in promoting awareness of their field to recruit more people in it (e.g., teaching people to love math may increase the number of math majors in college).
  • A professor who's research focuses on educational methods at a research university.
  • A professor at a teaching institution who is looking for publications and sees a way to publish their methods.

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