Greenhaus Education and Other "Effects"

I can't believe how long it's been since I posted!  Lord - obviously my life is a lot busier than I thought, and I thought it was pretty busy. Alright, let's get to it. Last year I did an entire series on hybrid professional development centered around teaching mathematics with technology and the Common Core, with specific use of Sketchpad as the technology tool (series listed at the bottom of this post).  It was a really exciting experience for me, and one that I have to say has sort of become my mantra - long term, supportive PD that provides time, practice, support, and collaboration using both a face-to-face and online component. Time is a key factor here - long-term, slow integration of technology into instructional practice where the focus is on how knowledge of the technology, the content being taught, and teaching strategies work together to provide learning experiences that help students.  For those of you in the know, this is TPACK - Technological, Pedagog...

I have been writing a piece about dynamic geometry® software, and have had a really difficult time conveying the power of dynamic mathematics environments in the static environment of the written word. Let me clarify what I mean by dynamic geometry software - I do NOT mean software that is just for geometry.  Dynamic geometry means the ability to take all sorts of mathematics visualizations (shapes, graphs, plots, functions) and drag and manipulate them to create infinite examples. These dynamic movements follow mathematical behaviors and allows for exploration, discovery of relationships and properties and allow students to interact directly with the mathematics because the mathematics is visual and tangible. Dynamic geometry software is specifically mentioned in the Common Core Standards of Mathematical Practice because of it's ability to be a tool that promotes reasoning, questioning, making conjectures, persevering, modeling, and communicating. Naturally, I have a strong bia...