In terms of things you can offer, if university policy allows it, you could also have a later alternative date for the final for any students who want it. This has a possible side-benefit of making effective proctoring more possible since you would be online proctoring fewer students at a time.

Patricia's suggestion is great. Calculus word problems are taken from a pretty weird subset of life experience (lighthouses, boats, swimming, farming) that can almost certainly be improved and made more inclusive, but I would really worry that most white faculty trying to rewrite those to be inclusive would end up veering into offensive stereotypes. Asking for suggestions deftly avoids that pitfall, while also getting students to engage with the material. I'd recommend giving extra credit for suggestions, otherwise it looks like you're asking students to do your work for you for free.

" I won't be able to assign a grade to these students" This might be a lie.

@AnonymousPhysicist, In this case, it is probably true that without a final exam, the grades can be very difficult to assign due to the compressed schedule --- the final exam may be the only exam.

@AnonymousPhysicist OP says that cancelling the exam is not "realistic" this semester. This example suggests one reason why it might not be possible to cancel the exam, OP can substitute whatever reason actually applies in the situation.

Of course you can assign grades. Just give all the minority students an A+, and see how many of them complain that they weren't "entitled" to it! As for the exam, try asking questions that only involve math - but I suppose the problem would be that then every student would fail.

@NoahSnyder Could you please give an example of a more inclusive question in Calculus?

@NoahSnyder I don't think it ever occurred to me before, but after reading your comment I realize that I always thought math word problems were designed not to be relatable to most people's life experiences.

@DmitrySavostyanov As Noah has written, this is difficult for cisgender white males to come up with without reaching into stereotypes (OPs colleague should talk to students). What can be done, is getting exclusive life experiences out of the questions: replace skiing questions with questions about a weird animal with a skiing-like behaviour, replace boating questions with physics of a swimming animal; that way you can at least avoid physics question to drive a wedge between the experiences of those privileged to go boating and swimming and those who don't. Nobody included, nobody excluded.

@gerrit the point of using a sport such as skiing for problems involving object sliding down a slope is that pretty much everyone (depending on geography) knows what skiing is. It helps set the problem for everyone, whereas explaining the mechanics of a fictitious animal with skiing-like behaviours would confuse more students than it would help. I don't think setting the problem as a "skiing problem" gives skiers an advantage in solving it properly.

@DmitrySavostyanov: Here's a very nice blog post including a few specific suggestions. That post is less focused on racial inclusion, but I think the concrete examples are still helpful as a starting point.

@AlexandreAubrey Maybe you're right. I don't know if using examples from skiing or boating actually contributes to some students feeling excluded, I just imagine that it could be the case. If it's presented as James Bond ski jumping it probably wouldn't. As I wrote elsewhere, OPs colleague should talk to the students.

Re: Noah's link, item #6: readers should be aware that Dweck's "growth mindset" theory failed replication attempts in large studies in the last few years.

@DanielR.Collins: Point taken, though I was suggesting it primarily for item #1 which included concrete related rates problems.

The skiing one isn't too bad, but there certainly are some math problems that are inadvertently harder for some students because of the non-math context of the problem. Poker hands and tennis scores come to mind.

Might be fine for an intro course but how are you suppose to relate abstract algebra or infinite dimensional analysis to ANYONES experience

@Alexandre Aubrey: Pretty much everyone knows what skiing is? IDK about that, since I have known people who think skiing involves being towed around behind a power boat :-( And even among those of us who ski on snow, there are those who think it involves getting to the top of a mountain on a lift and sliding down, and people like me who go on their own muscle power.

Since the instructor knows that (some, particular) minorities have in the past performed worse in their exam, it may be good to try and break this down e.g. to "pure math questions" (differentiate the following functions) vs. word problems that have the potential to relate to life experience. Better matching to actual life experience will after all not help with the pure math questions.