A common thread to my recent practices as a writer, researcher, and yogi, is around the theme of finding my purpose, passions, and igniting activity the is true to my way or ~dharma~.
By opening my mind and my sensibilities to learning from every experience, I’ve re-learned that having my own ideas, finding clarity in those ideas, and sharing them with others is something to celebrate.
I’m learning to let go of feelings and experiences of shutting in and shutting down. This frees up space for pursuing new connections that build toward my own ideas.
The practice of deep breathing and offering through the physical aspects or asanas of yoga are transformative. These physical offerings afford deep insight into the cognitive and spiritual facets of our beings. You just need to be open to listening. Trust in your self. Believe in yourself.
The world is your playground. Don’t be stymied by others putting you down. Accept those experiences for what they are – experiences. Those experiences and associated feelings do not define who you are as a person. There is always a silver lining, a learning opportunity. To grow, to change, to be a better person.
Living with the acceptance of change is a powerful mantra.
It’s quite liberating to acknowledge an openness to new ideas and opportunities. Now having space for those ideas, I also need time to support and nourish those ideas into fruition. My ideas lately are centered around representational fluency in problem solving with technology. Time to turn that progress in press to published ideas…
A characterization of a students’ sophistication in representational fluency tells an important story regarding their ability to solve problems using multiple representations, and their ability to create, interpret and connect these representations in communicating their strategies. The processes of creating, interpreting, and connecting representations are universal across the activity of doing mathematics (and are not specific to algebra, for example). This leads to many questions…
How do students use multiple representations in solving problems? My hypothesis is that a student who has a higher level of representational fluency is able to demonstrate a great deal of persistence and perseverance in their problem solving. They are able to take a problem situation and view it from multiple perspectives, creating and interpreting multiple representations in order to come to some success in solving the problem. An untested hypothesis is that a student who has a higher level of representational fluency in solving problems with technology has a richer conception of the mathematical idea being represented.
There is much theory around the notion that multiple representations help support students’ meaning making in mathematics, but less support for the notion that students actually understand what the representations mean with respect to the mathematical idea or concept being represented.
Do students see these representations as signifiers for a sign? How can instruction be designed to foster and cultivate representationally fluent students whilst at the same time supporting rich conceptions of mathematical ideas in technology-rich settings?