We designed our first lesson to talk about the difference between an inch and a cm, and then were going to have them measure various items in both to make sure they did know the difference.  As the lesson began, each teacher watched his or her designated child diligently.  Then, all of a sudden, as many children came to the document camera to show how they measured an item, a light bulb came on for us educators.  See we thought the reason the students were missing the test items had to do with them just reading the last number on the ruler.  In Kansas students have to read a broken ruler.  So if they show a pencil starting at the 4

" line and ending at the 10" line, then students have to state it is 6".  We all thoughts many students would say the pencil is 10".  Boy were we surprised when they stated "seven inches".  Seven inches, really, show us how.  One by one students would come to the document camera and measure each object. This is when we had the ahha!  Students did not understand the concept of an inch.  They were counting the lines on the ruler, not the space in between the lines.  All the teachers in the room, including myself, couldn't wait to get out of the room.  Now we know how to fix this misconception.

Our second lesson, after being revised, made us realize we need to clarify students' concept of an inch.  I believe this is what happens when we move to a procedure or skill before a concept is deepened and understood completely.  This time we started with the one-inch square tiles.  Making sure students understood, by measuring with their ruler that yes it is an inch.  Measuring objects with the square tiles, then laying a broken ruler on the object, made students question their own understanding. 

True learning took place that day, not just with students but with also many great educators.