This is from the 2011 Common Core of data, showing all personnel in each state who work in public primary and secondary education. Click here to see the data table and read all the footnotes, especially if you want to argue.
There are many things that can explain this data: States that have mostly urban areas (like California and New York) are likely to have bigger schools and classrooms, and thus fewer teachers per student. Different states with similar populations may have more district administrators if they manage schools locally, or fewer if they do it in bigger geographies (by county, for instance.)
I added a couple data pieces to the table: First, the 2010 census data of the population under 18, which is not a perfect proxy for public school enrollment, but it's probably close enough. I used Data Ferret to extract the data, and used those figures to compute the ratios (students per teacher, for instance.) Again, a state with a younger population (more in elementary schools) might have fewer students per teacher than one with an older population (more in secondary schools).
Second, I downloaded 2012 election results, to see if data might sort out by Republican and Democrat states. I'm pleased to say they generally don't, as I suspect that might avoid more colorful "discussion" on the topic. The colors are applied to all but the top tab; Republicans in red and Democrats in blue.
There are four views, with the tabs across the top. If you want to sort any of this data by any column, just hover over the x-axis labels at the bottom and click on the little bars icon to the right of the text.