The context is you're inside a room and want to throw a pen outside the room through an open window. Now, the pen is outside. Do the sentences below have the same meaning?
I've mostly heard Number 1 but if it's "out the window" then the original location of the pen is inside the window (the window was melted with the pen when making it) hence you throw it out the window.
You can say out the window. It doesn't mean that the pen was embedded in the glass, that would be ridiculous. It mean "out of the building" Compare
Walk out the door.
In context "through the window" could mean the same as "out the window", but you could use it from out of the building. It might also be used if the window is closed. "Throw the brick through the window."
I'm a little worried that you have heard "throw the pen out the window" more often. What kind of school is that??
This sounded like an extremely easy question at first glance but as I think about it, I can see why this might be confusing. I'm not even certain anymore and English is the only language I can speak.
Here's how I would understand those three sentences out of context:
1. Throw the pen out the window.
Take a pen that is currently inside and throw it through the open window such that it is inside no longer.
2. Throw the pen through the window
Take a pen (that may be inside or outside) and throw it through the closed window, breaking the glass in the process.
NOTE: This understanding is ambiguous in that the original sentence does not make it clear whether the window was open or not. Another way of putting this is that the English word "window" is ambiguous because it refers to both the glass part and the hole itself.
If a larger object like a ball or a brick had been thrown "through" the window, it would definitely imply breaking the window. A pen however, is too small. Thus it is unclear.
3. Throw the pen out of the room through the window.
Take a pen that is currently inside and throw it through the open window such that it is inside the room no longer.
Consider a generic adverbial phrase "out the NOUN".
There are two types of nouns that can replace NOUN.
NOUN can be a location, or
NOUN can be a barrier between locations
When NOUN is a location (1 above), often times and following far more complex rules than I can summarize or even understand, "out of" can be used instead of just "out".
For these reasons, if you wanted to make it clear that window was a location rather than a barrier (meaning that the pen is physically inside the window, you could clarify by stating "throw the pen out of the window."
At risk of not answering the question, it may be easier to use a brick rather than a pen.
Throwing a brick through a window implies broken glass and the brick finishing up in the room. Bricks are thrown into rooms by default.
Throwing a brick through an open window definitively excludes broken glass but the brick may be assumed to finish up in the room again by default.
Throwing a brick out of a window is ambiguous about the glass but definite about the direction of travel. The brick finishes up outside the room.
Throwing the brick out of the room is ambiguous about the route taken by the brick, window or door, but again the brick definitely finishes outside.
