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It seems to me that we all might benefit from an answer to this question, since math departments must defend their performance within their institutions.

I imagine there will be standard answers like:

  • Cultivate a culture of diversity, where everyone can be a "math person", and growth mindset is emphasized. "Launch" instead of "weed".
  • Have applied and pure offerings, as well as a robust math education presence in the department.
  • Do outreach and actively recruit (what are the most effective ways to do this?)
  • Help students find internships, jobs and careers
  • Have a super passionate, engaged faculty who share the excitement for mathematics all the time!!

Any other concrete articles or suggestions would be very helpful.

I know there are articles about doing this in the literature (maa publications, etc). My reason for posting this is that I think math professors may have personal "best of" lists of these that they could share.

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    $\begingroup$ You are a very experienced MESE member from whom I've benefited, so I hesitate to try to edit ... but this question is VERY broad. I'm not even sure what "more robust" should mean here - probably all of "stable/increasing number of students", "healthy outcomes for graduates", "valued in concrete ways by campus constituents", and so forth. Obviously it's a very important question, but I don't know if it fits the Q&A format so well, since there are long documents prepared by organizations like the MAA trying to answer it. But I could be off base with that - it just seems really hard to answer. $\endgroup$ – kcrisman Oct 18 at 22:19
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    $\begingroup$ No worries kcrisman. I wrote the post in a bit of a hurry, and don't think I'm too experienced to be told to edit! Thanks! $\endgroup$ – Jon Bannon Oct 18 at 22:28
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    $\begingroup$ Now I know what you're asking! Rock on. $\endgroup$ – kcrisman Oct 19 at 0:19
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    $\begingroup$ (Also, congrats on the promotion.) $\endgroup$ – kcrisman Oct 19 at 0:21
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    $\begingroup$ @user1527: My first question would be why do you want to attract more majors? --- To decrease the possibilities of things like reduction of math faculty, reduction of departmental money and support staff and such, elimination of the major or consolidation of the math department with another department, etc. Also, to decrease the amount of departmental effort needed to defend existing levels of the previous things should they be viewed as potentially being on the chopping block at some future time. $\endgroup$ – Dave L Renfro Oct 21 at 5:51
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This might go over differently at a liberal arts school, but we've had some success inviting students to an optional, uncredited program where they work in groups on fun problems from various topics in math (ideally associated with upper level courses, so we can say, "and if you liked this, you should take..."), supervised by two older undergrads. (There are similar programs at a number of other schools - we got ours from Columbia, and one of our grad students went to Northwestern and started it there. The name that gets used is usually "Emerging Scholars Program".)

The premise is that some of the big factors that keep students away from math are:

  1. Not knowing what a major is actually like, and thinking it will all be more calculus and algebra,
  2. Not knowing other people in the major (this may be a bigger issue in a larger school),
  3. Seeing a lot of posturing and competitive, macho culture from the students who excelled in math in high school.

We've found that the number of students who later enroll in the major from the program is pretty high, though we haven't done anything rigorous enough to determine how many would have enrolled without it.

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For both options below, first and foremost the Math Department should be institutionally

  • Friendly

In my book this means letting students try to do what they want. Err on the side of bending policy to help students with unusual paths. Don't make students retake things they've already taken if at all possible. But, do give warnings if your institution has above average content in the course in question, this sort of advice requires some individualized care and attention to detail. On a personal note, this is one of the things which pushed me away from engineering and towards math and physics as an undergraduate. Both the math and physics departments had faculty who cared to advise me personally and I never felt appreciated or challenged in a positive fashion.

A possible high road to growing the major: (here I echo the excellent suggestions of the OP)

  • Share scholarship in general education courses. Don't succumb to teaching the course from the book. Instead, spend a summer to read old books, brush up on the history and write your own notes with which to teach the course. Also, write your own homework which is shockingly dissimilar from the math your general audience has seen throughout previous course work. Prove things like it matters. If you do this right you can attract elite students from majors outside math who thirst for analysis which is not surface level. Once upon a time, I taught such a course and it helped me earn us a new math major who went on to do significant work in graduate school and beyond.
  • Generally, try to make the major as serious as possible. Build two or three semester sequences which dive deeper into core subjects. The goal here is not to weed out students, the goal is to teach students a broad and reasonably mature picture of math which sets them up for success in their future endeavors.

Downside, you will scare some students in the above approach. Certainly the weaker students need individualized reassurance in the midst of the above style. But, if you have a relatively small class size with a few good students then it can work. Also, if you have no students who endorse the program of excellence then it creates an unfortunate dynamic where excellence on the part of faculty is perceived as unreasonable behavior by the students. When the philosophy of the faculty and students are unaligned there is real danger for damaged morale for all parties. Upside, the new students you add the major will be sincere in their focus on math since sincere mathematics is what drew them in to begin.

A possible low road to growing the major:

  • maximize the number of electives in the Degree Completion Plan (DCP)
  • minimize the difficulty in required courses in the DCP
  • maximize the choices of math electives so students can avoid subdisciplines they don't care for. For example, provide a path around too much probabilty or statistics. Or, provide a path around applied math for pure folks. Or provide a path around pure math for applied folks etc... general idea: don't make people do things they don't want to do.
  • don't require physics or computer science, allow many courses to fill these slots in the DCP.

In summary, make the major as easy as possible. Upside to this approach: you will get more students. Also, with so much flexibility in scheduling, there is a good chance the students taking a given course actually want to be there. Downside, these new "math" majors may not really want to take all your math classes. Also, you will need to warn students that your "major" doesn't really prepare them for graduate math. Also, the lack of computer science and general lack of well-rounding in physics, chemistry etc. may give some employers pause on the applied side.

Probably the low road better describes the position we are pushed towards when there is fear of downsizing and such. The high road is not easily maintained.

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  • $\begingroup$ Other structural answers: If you're real goal is to get more students in classes there are a couple of options: On the high road, build out courses for a meaningful dual or combined major (geometry/diffeq for physics, prob and stat for compsci/ML, etc). On the low road end make and advertise a minor that just involves tacking one or two classes onto a physics, engineering or comp-sci degree. $\endgroup$ – Nate Bade Oct 24 at 12:41
  • $\begingroup$ @NateBade yes the minor can be useful. For best effect, it must be structured so at least two classes in the minor are not automatically inside the targeted major. However, there are sometimes unintended consequences. At my old school, I had students take theoretical linear algebra rather than a more computational one just to kill off the major requirement and satisfy the minor. Poor choice for some since they were not big on proofs. Ideally, the minor should route students to courses they benefit from in their major. Maybe math modeling, numerical methods, a second DEs course etc. $\endgroup$ – James S. Cook Oct 25 at 23:27
  • $\begingroup$ @JamesSCook That's a very real concern. I think it can also cause the problem that it doesn't really help higher level courses get run, just mid-level courses. $\endgroup$ – Nate Bade Oct 26 at 21:34
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I wrote to a professor of mathematics at a liberal arts college that has, in recent years, found great success in attracting more math majors. Here are lightly edited excerpts from the two emails I received in response:

Initial email:

Excellent teaching, welcoming classrooms, caring attitudes, support in and out of the classroom, etc. Don't make it a tough-guy "who is awesome enough to make it through the crucible of the math major" thing. Make it tough, but provide students with the support they need to succeed --- even, and especially, the at-promise students. [Have math professors of different backgrounds - race, gender, etc - teaching students.]

Unprompted follow-up:

Accurate placement of students at the lower level is important, too. Too many well-prepared students try to weasel their way into lower-level courses (to get an easy A), while too many underprepared students try to shoot for the stars by trying to push upwards into higher-level starting courses (putting them at great risk of crashing and burning). So gentle but firm placement is key, BUT THEN, you ALSO need the instructors of the courses to teach at the appropriate level for the course. If a Calc 2 instructor gets excited that there are students in the class who are really getting the material so well, and starts talking about everything at a higher level to continue to inspire those students (who are actually the lazy weasels who should have been taking multivariable calc instead of a class they already got an A+ in in high school), then the students who actually belong in the class get lost and think, "I guess I'm just no good at math".

So it needs to be a team effort.

Oh, I thought of another thing: personal notes on exams when you hand them back, to invite struggling students to office hours, to congratulate students doing well, and to suggest to students doing well that they should take the next math class, or maybe even consider a math major.

Basically, all the time, actively make math and math classes a welcoming place where students feel supported. Challenged, but supported.

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Here is one very easy thing that has gotten good results at the University of Michigan: Every term , a few weeks before the end of the term, our director of undergraduate studies sends an e-mail to the math faculty saying roughly "if you are teaching a class with a lot of undergraduate non-math majors, please choose 1-3 students in it who you think would do well as math majors, and tell them so." Students who receive this feedback very often become math majors and, while correlation is not causation, we do a survey of our senior majors when they graduate which includes the question "why did you choose to be a math major", and they often mention this interaction.

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    $\begingroup$ Given that at colleges like the OP is describing, faculty are even more likely to have good pre-existing relationships with students, this is a no-brainer, glad you mentioned it. $\endgroup$ – kcrisman Oct 23 at 17:52
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My advice is to emphasize the "get a job" aspect. The university is filled with the dreamy beauty of knowledge stuff. (And that's fine. But you need to distinguish yourself and provide additional info that kids might not have.) Do you even know what percent of graduating kids go into what fields? How easy/hard it is to get jobs (like some sort of semiquantitative analysis)? Is there a lot of "option value" to the degree? Is it relatively recession proof. Etc.

Donno the exact story, but if you've done a little bit of work to figure this out and then tout it on the department website at least it would show you care. If story is mixed feel free to play up the positive aspects...everyone is rushing the froshes after all. I just wouldn't be too overtly comparitive. But find some subtle way to show that your kids won't end up as English major baristas. And saying you care, doesn't show you care. Showing work (analysis) you did...shows you care. ;-) Heck...you might even learn something interesting. I mean even though you're a God-like professor, sir. ;-)

I do also think it is important to have an applied track or two. And show clearly (with a matrix) what the difference is. I.e. get out of real analysis but have to take DOE...or whatever.

I also quite like the idea of an applied track that can be portrayed as business friendly. All these little kids want to be consultants. They shouldn't. But the world is sort of heading that way. It doesn't need to be as hard core as a finance/econ/business degree. But something where they can take a few classes with business application (OR, options pricing, etc.) would be helpful. Think about how to position this.

Caveat: Just ideas. I'm not a teacher.

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This is a fairly minor issue, but probably worth a mention.

At a technical university there was (and probably still is) a question about how to attract more female students. One aspect was the diversity in promotional material. The outcome was that

  • male students reacted equally well to diverse promotional material than to material with mostly white male students

  • female students greatly preferred more diverse promotional material.

Hence, to the extent that the university has a "modern" website with lots of pictures of smiling people or people in "classroom" situations and in front of blackboards etc., it is a good idea to have diverse people as students and teachers, and to have groups of mixed students.

Of course, the results might not generalize to USA culture, so one should be a little bit careful here.

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  • $\begingroup$ I work in a technical engineering school in Spain. It offers a degree in mechanical engineering and one in industrial design and product development. Two thirds of the classes are the same. The students in mechanical engineering are 1/4-1/5 female, while about half of the students of the design degree (which has stronger entrance requirements) are female. The difference appears to be in some social aspect of how these degree programs are perceived (they are "sold" in the same way). The technical content is not that different. A mere name seems to matter a lot. $\endgroup$ – Dan Fox Oct 21 at 8:32
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There is quite a bit of literature under the banner "humanizing mathematics" (or cognate phrases). I am just beginning to read this literature, so I can do no more than point to a few references. This seems a slightly different emphasis than your first bullet on "a culture of diversity."

Luis A. Leyva. "Toward humanizing undergraduate mathematics education: A re-imagining through historical perspectives in mathematics." AMS blog. May 2018. AMS link.

Hottinger, Sara N. Inventing the mathematician: Gender, race, and our cultural understanding of mathematics. SUNY Press, 2016. SUNY Press link.

Bonner, Emily P., and Thomasenia L. Adams. "Culturally responsive teaching in the context of mathematics: A grounded theory case study." Journal of Mathematics Teacher Education 15, no. 1 (2012): 25-38. Springer link.

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One very brief answer is to have multiple entry points to the major, or even just to taking more courses. That is to say, at many colleges the typical Calc I-II-III entry sequence may not be attended by a very large number of students who would love to take more math. So have clear options for them.


To elaborate into something not so brief, consider a university where perhaps there will be a biocalculus option, a business calculus, a finite math, or even a "no math required" option in many areas that might still entice people to math. Having very clear pathways of "what your next math course is if you liked this one" helps a lot with allowing people to at least become a math minor, or even just a "math tag-along" person. That may mean having a couple different linear algebra courses, or a "calc II for people without calc I".

Similarly, having options for people who might not even get a minor, which fulfill additional core/distribution requirements, or having a couple different non-calculus options for people to start taking even if they didn't have a particularly strong high school experience can be useful. Not everyone will be ready for these courses, but often students who did not have calculus in high school come out of the woodwork when they take some initial math course and experience success.

Naturally, the smaller your college (or at least your department), the harder it will be to do this; we are quite small so it's been difficult to develop such courses. Even so, we probably get half or more of our majors as people who add math or switch to it starting sophomore year by realizing they missed math. I admit that many of those are people who started in related science fields, but definitely not all - and we have a number who start in math then drop it for something else ("easier"? not always) so it is good that we have them come in! If most of your load is consumed with having multiple sections of the required service courses and then upper-level major courses, this is a tough row to hoe. But a sympathetic dean might make it possible to try it out if you can point out the benefits of having a stronger program to them.

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