Currently, the badge progress for the Curious, Inquisitive and Socratic badges looks like this:
When I don't have a positive question record, it only says "need a positive question record", without saying anything about how close I am to having a positive question record. So I therefore have no idea about how close I am to earning this badge, and I can't check either because of this issue.
I would therefore suggest changing the design so that instead of just saying "need a positive question record", it actually says how close I am to having a positive question record, using the
(total questions - negative questions - closed - deleted)/total questions formula. Doing so would also solve this feature request which is asking for there to be a way to see the question record (note that this is not a duplicate since that question is asking that there should be a way to see the question record and I'm asking that the badge progress should be displayed differently).
I also think that the badge progress without clicking on the button should show the question record instead of the days asked when the user has asked a well-received question on more days than the badge requires (otherwise still show the days asked, for example if a user has asked a well-received question on four separate days the Curious badge progress should continue showing 4/5). This is because I think that it looks weird seeing a 12/5 progress (and I'm not the only one), and it would make more sense seeing for example 0.4/0.5. Note that a similar feature is already implemented for the Elecorate badge (see screenshots of my badge progress and Jon Skeet's badge progress).
It would also be useful to add a link explaining what a positive question record is in case a user doesn't know what it means (which is fairly common, I myself misunderstood completely what it meant when I was a new user). I therefore think that the words "positive question record" should be turned into a link to a Meta post explaining what a positive question record is, for example this answer.
In case the above wasn't really clear, I've made a picture in Paint illustrating my feature request:
Note that the picture is just supposed to illustrate the main ideas, so it's totally OK to me if the moderators decide to design it a little bit differently.