Many of my most successful classroom STEM experiences are ones where I give my students challenges and problems that I did not really know how to solve myself, or at least admitted that I may not know the best solution or only solution to. Joining my students in research, tinkering, trial and error, and eventually success gave them the OK to struggle and work through failures in part because they saw me doing the same thing.
Please realize that this goes for all parts of STEM, including math! There are many times that I came ready with the "right" answer only to work with a group of students (and I mean 5th graders, not just older students) and have them figure out something better or even show me that I was incorrect. Tinkering with Math is just as important and powerful as tinkering with physical things.