Several years ago, I was a mathematics teacher in a high school. I was one of those business people who was laid off and found out that the school system was looking for people like me who could learn how to be a teacher. I found out that I was not made to be a classroom teacher but that is a story for another time.
I had an opportunity to attend a meeting with all of the math teachers in the district, from kindergarten through high school. Our task was to map the curriculum for each grade level and determine where we could see gaps. We all took turns writing the curriculum for each grade in a big matrix on the board and then we started to analyze it. I was one of the first to comment and I said that I saw no gaps. Instead I saw duplication or redundancies. Some of the things taught in middle school are also taught in high school. This was not a surprise to me since I was teaching much of the same material in Algebra I as I was in Algebra II.
This evening, I had my first tutoring session with a 7th grader. She was learning how to calculate the surface area and volume of three-dimensional objects. Seems like I just tutored a student on this very same thing two days ago. Except he is in 10th grade.
I wonder how much time we spend teaching kids things they should already know.