Teaching and grieving in a classroom where perfect math meets a broken world

I've known a lot of fourth-graders in my life. The law of the excluded middle is a technique of logical argumentation that most famously rears its head in "proofs by contradiction", wherein you show a statement is true by assuming otherwise and use this contrary assumption as a starting point of an argument that leads to a known mathematical falsehood, like 0=1. When, last week, my students walked into class, still mourning last week's tragedy – since when did teaching require training in grief counseling? It's because I've got to go teach this class, but I'm a lousy compartmentalizer and I'm thinking about tragedy in terms of vectors and I feel like I need to have another moment — that this moment requires its own moment of recognition everywhere, that we should all be aligned in sadness and anger – and at least a moment in our class so that we can air it all out before entering the safe place of Platonic objects. Brouwer's Theorem says that there is no way to comb those glancing locks to get them all aligned while keeping them tangent, that no matter how carefully you nudge them like the balding man carefully arranging his combover, you'll always end up with a cowlick, a place where suddenly the flow goes the other way.