Professional Developments
The first three weeks that I was back at work, I had to deliver five days of professional development! Three of those days I was presenting on making connections with representations. The Virginia Department of Education made this easy because they have the PowerPoints and the facilitator's guides for each grade band: K-2, 3-5, 6-8, Algebra, and Geometry!http://www.doe.virginia.gov/instruction/mathematics/professional_development/index.shtml
I was presenting the K-2 band, but the people running the first sets of workshops failed to put that into the program, which meant that high school teachers came into my workshop.
During one session, two high school and one middle school teachers attended. As we went through the activities I could see that the two gentlemen were increasingly put off with having to go through the activities. I even overheard one of them say, "They don't need all of this stuff! They just need to learn the algorithms!"
I assured him that if he went onto the VDOE website, he could see that ALL students needed to work through the five representations, whether they were in elementary school or high school (or college for that matter!) I know what the high school scores are like in our district, and I wanted to ask him how his scores were and that perhaps he needed to learn new strategies and representations to increase those scores!
Albert Einstein said the definition of insanity is doing something over and over again and expecting the same result.
The other high school teacher, I am pleased to say, came to me and said that she could see how these representations could help her students increase their understanding. We were able to talk for a few minutes and I suggested she look into Dan Meyer's 3 Act Problems http://blog.mrmeyer.com/2011/the-three-acts-of-a-mathematical-story/