Connecting with people from around the world who have similar interests and understand your passion for education can be inspiring. Although educators get accused of accepting the status quo and not wanting to move forward, Twitter is a place where that accusation is proven wrong.

We live in the 21st century where our students don't just "do" social networking; it is a part of who they are as digital citizens. To us, it's a big deal to get on Facebook or Twitter, and to our students it is something they cannot fathom living without. Understanding their connection with those sites will increase an educator's connection with their students. Being able to talk their language may even provide an opportunity to breakthrough to a hard to reach student.

Critically, pushing around symbols on paper is just a symbolic representation of the real math taking place within one’s head. When one does a calculation, whether it is by hand or by machine, an important feature of whether or not one can be said to be doing the calculation is whether or not one can predict the potential output from the algorithm, or if one understands the process they are using.

We also require, as a system, much more flexibility in the mathematics taught at the K-to-12 level. I’d like to see a system where many different types of mathematics are taught besides just the standard hierarchy leading to calculus.