I'm at work, so just a few seconds to chime in: Educational spending is primarily sourced from the states. If you were to sum state spending on education, you would come up with another eye-watering pile of money. It's just that this money is usually sourced from property taxes and sales taxes and so doesn't show up on a "Here's how your income taxes were spent" analysis.

In fact, a lot of educational spending is local. I think something like 65% (maybe more) of my town's property taxes go to K-12 education with a decent chunk of the rest going to emergency services. There are various grants at the state and federal levels but it's mostly local.