For GDP purposes, do economists classify education spending as consumption, investment, or gov't spending?

I don’t think you can make that kind of generalization, lumping public and private education together. I’ve only taken AP Macroeconomics so I’m certainly no expert, but I would think that publicly funded education would fall under government spending; spending for private education, on the other hand, would be considered investment and consumption, depending on the type of spending, since a private school is a business. Even then, though, that’s a large generalization, the types of spending would have to be further broken down.

The Congressional Budget Office has higher education under “Other” on this, tab 3–2.

Actual Education expenditures involve capital projects like new schools, renovations, equipment, and it involves salaries for everyone from researchers to janitors and clerks in the facilities.

Ok, how about the money that college students spend on tuition? Is that counted as consumption?

For one thing that’s a completely different budget, the student’s.
Depending on how you approach college, it’s either training (a long-term investment) or entertainment (recreation expense).

@submariner Payment from the students has nothing to do with “education spending” which implies spending from the government, unless you are factoring in federal student grants, loans, etc., which is a whole other monster. In short, yes, it would most likely fall under consumption, because the student is paying for a service (education).