Sandlin tells us that knowledge is not understanding, and I completely agree. As I was working on my undergraduate degree , I discovered that I knew a lot about how to solve mathematical problems, but that didn't mean I have a deep understanding of the concepts. And for me it's the same way with technology. I feel that I "pick it up" more slowly than other people do. Perhaps, as Sandlin puts it, my "thinking is in a rut." I have learned a lot about using technology in education, but I honestly don't think I have as deep an understanding as my fellow teacher candidates. It makes me wonder, "How can I use technology to enhance my ability to teach and lead in a global society?" My instructor asks me this very question. The answer is a lot simpler than it seems--start by learning new tools. That will help you to acquire knowledge. But you have to connect to others who use those tools and learn what they do in order to develop a deeper understanding of how to use them and how to devise new ways for using them. For me, finding new tools wasn't so difficult. I made my first PowerPoint presentation just one year ago. Today, I'm on the Twitter (yes, I said "the" Twitter), I've had my students using Desmos to graph, I've shared a little bit on Google+, and I've been bookmarking websites with Diigo. I've certainly gained knowledge about these tools, but I still need to develop a deeper understanding of how to really use them.
As for thinking in a rut, I was surprised a few weeks ago when my cooperating teacher decided that our students would use electronic graphing utilities to graph polynomial functions and find rational roots for those functions. I hadn't thought of allowing our students to do this. I just assumed that our students would do it the way I did--by hand, I paper and pencil. But when we taught this lesson, it was amazing. Our students were talking with each other about math, engaging in discourse about how to write the polynomial in factored form and how the roots they see in Desmos relate to the factors they pull off the original polynomial. They did this rather than get all caught up and flustered in the Rational Root Theorem and a myriad of synthetic divisions. I have been thinking in a rut.
Sandlin, D. (2015, April 24). The Backwards Brain Bicycle - Smarter Every Day 133. [Video File]. Retrieved from https://www.youtube.com/watch?v=MFzDaBzBlL0&list=PLbRLdW37G3oMquOaC-HeUIt6CWk-FzaGp&index=2.