Familiarize yourself with the standards themselves (reading and writing [pdf], mathematics [pdf]). Notice that assessment against the standards is done by overall teacher judgement and not entirely, or even principally, by standardized testing.
If you want to play with the shiny data set, Luis A Apiolaza has done you a favour by putting it into something sensible and R-friendly. I recommend reading all of the case studies on Stuff before diving in. Context matters.
My own prejudices. I am a policy analyst with nil expertise in education. I support publication of national standards data. I am agnostic as to whether national standards should have been introduced in the first place, but furious at those “public servants” who sought to obstruct implementation of a lawful Government policy: no integrity.
I’m mainly interested in what the standards data can and can’t tell us, and how they might be used to improve education outcomes. The lens I’m trying to look through is how would I tackle this if I were at the Ministry of Education?