I am curious as to why, as the moon goes through the different phases, do we see the visible part sometimes be crescent shaped, then as we get to the time that we 'see' only half the moon, it is no longer crescent shaped, but appears to be virtually bisected or straight across. I always thought that the earth was casting a shadow, which created the crescent that we see or said another way, the earth was blocking the light from the sun that was hitting the moon, which caused the crescent shape that we 'see'. If this is true, why is the visible part of the moon, as we approach being able to see half of it, no longer crescent shaped?

The Earth is only casting a shadow on the moon during a lunar eclipse, this only happens when the moon is full.

The phases of the moon are an effect of what portion of the moon facing us is lit by the sun. Take a ball (a globe will work great), turn on 1 light, hold the ball at arms length. Rotate so the ball is "orbiting" around your head and watch the phase change. You might even see an "eclipse" where your head is blocking the light from reaching the ball.