Thank-you to everyone responding, especially those who are helping enormously by giving me real-talk; Here's some more information about my situtation:
The legacy system I referred to has limitations that make it very uncomfortable to contemplate continuing to use it as our sole data source. Some issues: - The database is updated once a day; Any changes you add to it today won't show until tomorrow. - Student absences (important so we can see cutting, lateness, etc) can be recorded once per day; students are either "at school" or not. - There are numerous categories of data that we have that can't be tracked or stored, for expample, whether a student is involved in a sports team. We have a large body of instructional data about how students are doing in class, but we're struggling to bring it together to get a full picture because as far as our main system is concerned, students receive a grade at the end of their course for their transcript, and that's that.
I'm not going to ignore what I'm being told and I think that building a new solution is beyond our capacity; we have to keep our focus on teaching the kids as well as we can. But we have a very young staff and an administration committed to exploring our options. I've already been looking at Tableau and it's so powerful and approachable that we can definitely use it. The difficulty I now face is what tool can we use to complement and expand the system that's causing a lot of grief.
We need to be able to store types of information including absences, student biographical info, grades; we want to be able to store student ID pictures, lesson plans, notes from teachers. Points of contact with parents. What we think we know is that we need a SaaS solution, we have regulatory compliance issues (not to mention ethical requirements) around security and privacy of our data, which many of you noticed.
I'm reading every single comment and will respond by email and here where it makes sense. We know we need help even to understand our problem. YC 2016 would be top of my priorities right now, but there are ethics rules preventing me from being a vendor to any NYC public school while I'm working at one. As much as it makes sense ethically, it really seems like that shouldn't be the department's focus when they have kids who can't read yet and they can't tell you which kids they are.