Teaching Math is Sometimes Like Using an Etch-a-Sketch

A recent chat with my sister-in-law (who I am extremely proud of) brought up the topic of Common Core Math Standards. Words and ideas were bandied about, like "high level of support for teachers" and "deciphering the students' depth of understanding" and "instructional strategies". One item suddenly caught my attention: CGI. Now, my sister-in-law is a Presidential Award Winner for California and so when she talks, I listen.
 
I did a little research about Cognitive Guided Instruction and a light bulb went off inside my head. In a nutshell, (hopefully I have the crux of it fairly accurate) CGI is understanding the preformed ideas that children come to mathematics with, along with identifying the developmental stages children go through as they learn concepts and to use this knowledge as a framework, or foundation, to teach on.
 
I love to create analogies, so here goes..... Remember using an Etch-a-Sketch when you were younger? You had an idea of a picture you wanted to create but you had to get used to the knobs and which way you needed to turn them to get the line going in the direction you wanted. Many times, you intended the line to go one way, but it went the opposite direction. It was impossible to back up or erase the mistake. Uggggghhhhh!!!! After a whole lot of work, you get something that slightly resembles what you want, but it is kind of crude. The fleeting thought crosses your mind that maybe the Etch-a-Sketch is not the right medium for what you had in mind.
 
Teaching math using the principles of CGI feels the same way. You know what the end result should look like. You are teaching and turning knobs like crazy, trying to interpret student thinking and depth of understanding. In the end, it never quite resembles what you were hoping for in the beginning. Childrens' developmental stages will limit you just as much as trying to use an Etch-a-Sketch to draw a masterpiece.
 
Then again, I have seen some pretty amazing art come from an Etch-a-Sketch!