 is a much better approximation of what a mathematician actually does. I think unfortunately the way math is generally taught, people see math as just a sequence of procedures or rules that have to be followed and they don't really see the creativity that goes into it. I mean really mathematics is sort of a process of discovery. You're kind of figuring out what's going on, how things are connected, what the patterns are, and you're recognizing these things and then trying to make general statements that represent what's happening. And then once you understand why it's happening, the proof is just sort of the finishing touch where you write a logical argument that explains why something is true. And so I think when they're working on the worksheets and they're able to sort of figure things out for themselves they get much better kind of concrete understanding of why things are the way they are. In terms of getting them prepared, a lot of onus is on them to really keep a record of their work because I don't collect a lot of this stuff. The investigations they make on the worksheet, I don't collect any of that, that's for them to understand and discover for themselves. And then even with the theorems they get graded on their proof presentations but they don't do that many of those in a quarter. So they really are responsible for keeping a good record of their work, keeping a sort of a polished version of each theorem even if they're the ones that they don't present, they really should be keeping their written proofs for all of the theorems. Another thing that I do to help them have sort of kind of a class set of finished proofs is we use our learning management system for the course and so each person that presents a proof is responsible for after they've had the feedback from the class writing their final version as a page on the learning management system so that everybody can go and view that and actually they can even edit on there and give responses on there if they want. But that way we have sort of one version of kind of a polished proof for each of the theorems that everybody can access and so they can use that to study from as well. The vibe can it's it's really dependent on the group of students I mean I've had I've had quarters where unfortunately whatever the whatever the chemistry of the class of the group of students is it just somehow they don't gel and it's kind of harder and they're more quiet and more reticent and those are tough quarters. This quarter is actually great from the get-go they were just ready to go and really excited about it. When it's going well you know I pass on a worksheet and they just dive right in and they're excited and they're talking about it right away and they're trying things out and then they're kind of checking in with each other to see you know if they're in agreement on certain questions and then sometimes someone will go up to one of the boards because they're trying to work something out. So yeah it is messy and it's kind of it's not really loud because they're sort of working in groups but it's you know people are sort of all over the place and sometimes working on the board and sometimes doing what they're doing. That's on the worksheet days the presentation days look a bit more normal because we're all at least sitting facing the front and someone's at the board.