It may be true that very few middle school student can grasp the meaning of lines and points in Euclidean geometry prior to a direct instruction. For example, it's possible that such a conversation occur in a classroom:
T: How many line pass through two points?
S: It depends on size of the points!
How should the teacher explain the nature of points and lines to overcome such misconceptions? Any book, article or online source would be appreciated too!
Thanks.
Well, the answer is quite easy to understand. A point only remains a point when the size is infinitely small (the first diagram) and if the size increases (as shown in the second diagram) it becomes a collection of many points.
A point is basically like a pixel on a screen, for better understanding you could make use of this example. So, when 2 pixels on screen are considered, the computer can't draw more than one line passing through them.
Moreover, even the thinkness of line is the same as the point, so, no matter how large the point is, if you consider Euclidean geometry, only one line can pass through two points.