I hate to tell you that all of your elementary school teachers lied to you, but chances are they probably did. Not because they were trying to harm your education, but so you could better understand the topic they were trying to teach. It surely made their life a lot easier to leave out some important details. I have a very high opinion of all teachers and there dedication to the education of youth, but some of the information I am about to share, I doubt many of your elementary teachers knew/know it. This strategy often used by early grade school teachers, frusturated one of my teachers, who had the duty of breaking down all of these false ideas, which the children accepted as fact. So the question I am asking myself is, "Does this strategy harm the child's mathematical education in the future?"

I bet your elemenatry school teachers always told you that you can never subtract by a larger number. (5-8) This is false of course, you can get a negative number. (5-8=-3) This information is fact, and fairly simple, but which teacher wants to explain negative numbers to a first or second grader. Your teacher might have also told you that you cannot divide by a larger number. This too is false, since it is possible to get a decimal or fraction.

Another misconception is that parallel lines are the only lines which do not intersect. This idea is more complex, which is why I understand why you wouldn't want to explain this to a fifth grader. In order to prove that this idea is wrong, you must think of a 3-D figure. It is difficult to explain this simply, but it is possible to take two lines from the figure and draw them out forever, and they will never intersect, yet they are not parallel. These lines are named skew lines. This can be a complicated idea, though. I didn't learn about skew lines until my high school geometry class.

These misconceptions pushed by your early teachers, might now seem so bad, and most of the time I would agree with that. Though these ideas are normally easily remedied, they can cause some major headaches for you later teachers. When you have a young impressionable child and you tell them in a matter-of-fact manner that you cannot subtract by a larger number, then you graduate them to the next grade and the teacher starts talking about negative numbers, which can get pretty complicated, it messes with them. In mathematics there are certain basic rules which are never or very rarely broken. Now, when you take a false idea and include it with those basic rules it can ham the later education of the child. Now, I don't think it is that serious, but I wouldn't mind if the teachers could explain it a different way. They should make it clear that you can subtract by a larger number, or whatever they are teaching you, is just for some cases and that, chances are, will be furthur complicated later. Math can be very confusing and when you complicate something beyond where it needs to be it can get even worse. I think the teachers need to work out a new system where the students are more encouraged to think freely. Though it helps the younger teachers it can hurt you and your later teachers in mathematics.