Things they don't teach in schools:
Understanding how the sun and moon function has been a fascination for me, I don't understand how it all works, but what I do (think I) understand makes a lot of sense to me. Maybe I can explain it in a way that makes sense to other people as well. Or maybe not.
The "dark side" or "shaded side" of the moon is not a shadow of the earth, but the result of lighting from a singular light source, namely the sun. The "phases" of the moon are dependent on the location of the sun and moon on any given day of the month. If you've ever drawn a sketch of a bunch of apples in a bowl, with a lamp on one side, the opposite side will have shading. Put that bowl of fruit in a pitch-black room and turn on the lamp on one side and you'll see a "crescent" of the apple as you move the light source around. It's not a perfect analogy, since when we see the moon shade during the day, we see the blue background of the sky that also appears over the shaded portion of the moon, giving the appearance that that the moon itself is changing shape. It's a strange phenomenon that can't be replicated on earth, but is visible in the sky many times. People have claimed to have witnessed stars viewable through the shaded part of the moon, but I've never seen actual evidence of this, nor witnessed this myself. The moon is solid as best as I can tell.
The other odd phenomenon, is that we all have our own personal "visual sphere": because our eyes are spheres which can only see accurately a certain distance (though we can see farther), the world appears to us as existing as a giant sphere with us in the center... or with the earth cutting off half, more like a half-sphere or "dome". That means that everything viewed beyond our ability to see will appear to be "painted" onto this dome. This is why we see the sun "rise" and "set" even while the sun travels parallel with the earth, just like we see planes "rise" and "set" while they fly parallel with the earth. This is how one person can watch the sun "set" while another person can watch the sun "rise" at the exact same time. This is also how people in the south can see the stars rotating counter-clockwise, while in the north, people observe stars rotating clock-wise. Stars appear to go down under the earth, and appear to come back up from under the earth, when in reality, stars are going out (setting) and coming back (rising) into our personal visual range as in reality they rotate above us, parallel with the earth.
This "dome" causes light to appear to bend, even though it doesn't actually bend: if you draw a straight imaginary line from the sun to the moon during the daytime, the light side and shaded sides of the moon do not appear correctly in perspective to the sun's light source, but if you draw an imaginary curved line following the curved "dome" it works perfectly. Limitations of our own eyes prevent us from accurately perceiving the world as it actually is. Yes, there is curvature, it's in our own eye-balls! Once the mind perceives the "personal visual sphere", we can better understand what we see in relation to how things actually are. The sphere is real, it's in our vision, but it's not in our geography.