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I've fortunately gotten a placement to do supervised mathematical research over the summer. The field is probability/statistics. My research topic has already been given to me. I'm planning on asking this in my next meeting, but I'd like to gather some thoughts ahead of time on what success means in such a project.

In general, what does success look like in an undergraduate research project? The timespan is relatively short (6-8 weeks), and I'll have to learn and apply my knowledge quickly. So what does success mean? How can I ensure that measurable achievements come out of such a project? What kinds of measurable achievements are there to aim for?

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    One of two things will happen. You'll either pick an easy project and finish it, or pick a difficult project and not finish it. It's not always possible to know what will be easy and what will be difficult, unless you do something somebody else has done already. Even if you don't finish the project though, you won't generally fail if you write up what you did manage to do well enough. This is an undergraduate project, not a PhD!
    – Crazymoomin
    Mar 24, 2022 at 6:15

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Consider both internal and external success.

At this level and for such a short duration, external success might be quite modest and defined by your supervisor. It is probably too short to result in a publication, but anything is possible. If it is graded, that will also measure success. Even if the results aren't publishable, a written (and maybe oral) report at the end is good experience. If the supervisor is happy with the work, then you have an item for your CV when it comes time to apply to graduate school or some kinds of industry work.

In between, developing a good relationship with the supervisor is a kind of success that might help you along a bit later.

Internal success, however, can be quite broad and deep. If it introduces you to research process and if it helps you decide whether you want more of it then it is a plus. But diving quickly into a research topic and immersing yourself in it can have a profound effect on your mind. That is harder to measure objectively, but you will know it if it happens.

Getting some collaboration skills is also a good thing if it is part of the project. Teamwork is valued in lots of later career positions.

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    +1 for the internal success. I think there are very few people even much later in their career who do not occasionally write a paper where the prime motivation is not to get an interesting result, but simply to use it as an excuse to learn a new topic.
    – mlk
    Mar 23, 2022 at 16:36
  • Nice answer Buffy. I like your mention of soft skills: Getting some collaboration skills is also a good thing if it is part of the project. Teamwork is valued in lots of later career positions.
    – Richard Erickson
    Mar 23, 2022 at 19:14
  • One particular form of relevant external success is that a project supervisor or similar is very well placed to write recommendation letters for both jobs and future academic applications. There may even be openings for further study within the same lab - taking on a promising undergrad for a placement can be a good way to recruit if there are postgrad positions coming up
    – Chris H
    Mar 24, 2022 at 12:56
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I have mentored NSF funded REU students through a math bio program. My collaborators described our experience in a paper, Using a Summer REU to Help Develop the Next Generation of Mathematical Ecologists. Here's my answers to questions given my experiences mentoring over 3 summers over the past 7 years:

In general, what does success look like in an undergraduate research project?

For the students, learning about research through doing research. I have had students discover they want to go to grad school. I have also had students learn they do not want to go to grad school. Both outcomes are successes because they positively shaped the students' lives.

An added bonus is that I have had 2 student first-authored papers from their projects. However, the mentorship was my greatest personal success.

The timespan is relatively short (6-8 weeks), and I'll have to learn and apply my knowledge quickly. So what does success mean?

Be organized. Plan out a schedule before you start. We treated our REU like a mini-biology master's program for 10 weeks.

  • We spend about 2 weeks in a coding and math/stats/biology boot camp. This ensures all students have the skills they need.
  • We then gave the students a focused project, usually in groups of 2-3. For some students, the project would take all summer. But, they would have something to present at future meetings. These projects could be simple questions we had about data or existing models. Or, they might be recreating an existing paper. We selected projects given our (the mentors' interests) that also naturally lent themselves to bigger questions. For stronger students, these projects would springboard into bigger questions they would discover on their own.
  • We would spend the last 2 weeks winding down. The students would create a poster of their work. This gives them something to share at their home university. We also would send students to a national meeting to present after the REU. Also, we would do a de-brief with the student.

Throughout the REU, we would have guest speakers talk about the softer sides of science and research. For example, we have regular speakers on careers in science and also people talking about how they got their jobs.

We also ensured our REU students' research was impactful and novel because we applied the models to new systems used by managers. For example, we would have the students work on problems US Fish and Wildlife Service biologists could use the results from for their management. Thus, even if the math and statistics were not new, the biological application were novel and impactful because agency biologists could use the results for decision making.

How can I ensure that measurable achievements come out of such a project? What kinds of measurable achievements are there to aim for?

Look at the paper I shared. My collaborators did formal pre- and post-REU assessments. These allowed them to describe how they changed students likelihood for going to grad school and learned about science.

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