EDCP 342 Relational Understanding&Instruental Understanding-#1  Entrance Slip

This article opened my mind about mathematical education pedagogy. From my experience as a high school math tutor, I always feel there is something missing upon my students' understanding of math concepts when I try to help them, but I have never had a clear definition of what it was. With the concrete example, the road map Skemp gave, my questions were answered. I totally agree that without relational understanding, learning mathematic won't go far.

I often have students mess up with 3x with x^3, this is an exact example of a lack of relational understanding. They may able to get the right answers when they just learned with instrumental understanding and without really understanding the concept. However, after a period of time, they will forget how to do it and then they will get confused, mess up with other concepts. While I am reading through this article I have to stop a few times to ponder and reflect upon the other examples like the method of teaching fraction multiplication and the circumference of a circle. I realize how severely missing the relational understanding from mathematical teaching.