What does it mean to be "connected"?
What does it mean to be "connected", as a professional and a learner? I think it is a working definition for many educators, myself included.
Lisa Dabbs from Edutopia attempts to define this concept:
Connected learners develop networks and co-construct knowledge from wherever they live. They collaborate online, use social media to interact with colleagues around the globe, engage in conversations in safe online spaces, and bring what they learn online back to their classrooms, schools, and districts.
That works for me. Just as student learning can become more personalized with technology in the school mix, so to should professional learning. Our level of connectedness is best measured in the depth of our relationships and conversations with others in our social networks.
Volume is great. Having many others who follow you and vice versa on multiple platforms certainly creates a more diverse network of learners at your fingertips. At some point though, we have to develop communities of practice if we expect to engage in deep and meaningful learning experiences.
Harold Jarche, whose blog and professional work were introduced to me by Lyn Hilt, has developed a nice framework for understanding how this progression works (Image source: jarche.com).

Going from right to left, you can see how personal learning networks (PLNs) are only the beginning. My start, like many others, was on Twitter. This channel of knowledge and expertise was essential to helping me become more connected. As a principal, I followed the #cpchat (Connected Principals) hashtag and just started following other administrators. This led to some of them following me back, which led to interactions and sharing of ideas in an open space. Others jumped in when they wanted.
While Twitter was and still is a cornerstone of my professional learning, it is equally important that we develop communities of practice (CoP). Otherwise, our self-directed learning isn't really self-directed at all; it follows the current of the streams of information that Twitter, Facebook, and other social media feeds provide.
CoPs are generally smaller groups in numbers, typically with a more specific focus. My favorite tool right now for developing communities of practice is Google+ Communities. You can create private or public groups, develop as many different pages within the group as you like, and control who has access to the conversations. I currently use these groups to continue the conversation about my book. In my school, we also use Google+ Communities to collaborate as staff teams. I am also facilitating a graduate course/book study for district staff with this tool, in between times where we physically meet.
Voxer is a nice tool for this kind of work as well. While it is a little more challenging to share resources like you can in Google+, the advantage Voxer brings is immediacy in the conversations. It works like a walkie talkie, adding audio, text, and images within a chat room. Voxer also requires some moderation, like Google+ Communities. For instance, conversations can go on and on in Voxer. If you are not able to keep up with what everyone has to share, you can feel left behind in the conversation without any more time to catch up.
And then there is Facebook. Of all the tools listed so far for professional learning, this one confounds me the most. I use it for personal reasons only right now. It just hasn't crept into my personal learning network like it has for other educators. Maybe it is the whole "friending" aspect of it, creating an exclusive mindset for this third space for learning. However, no one can deny the incredible audience that Facebook provides for users.
Tony Sinanis, an elementary principal in New York, shared a novel idea for managing these social media feeds. He uses Instagram as his social media hub for his school. When Tony takes a picture on Instagram, he can then select Facebook and Twitter to also post his image at the same time. This appears to save him a lot of time and reach the widest audience possible.
So going back to my original question: What does it mean to be connected? In my humble opinion, it is what you make of it. Do you want to follow Tony's example, and create an Instagram account for your school and tap into other social media tools that your school families use? Fine. Embed the feed on your school's webpage and post away.
Do you want to take advantage of all the professional learning possibilities available through Twitter, blogs, Google+, and Voxer? Also fine! Check out the flyer I made for the Wisconsin State Reading Association's Digital Learning Lounge for some tips and tricks:

Whatever tool(s) you choose, I suggest keeping your connections manageable, meaningful, and a benefit to both who follow you and who you follow. And have fun!