finding out what you already know

I came across a quote one day, from Richard Bach, of "Jonathan Livingston Seagull" fame: "Learning is finding out what you already know. Doing is demonstrating that you know it. Teaching is reminding others that they know just as well as you. You are all learners, doers, teachers." It reminded me of a question that was posed to the students in an education class by one of my favorite professors in graduate school. She asked whether teachers always had to know about something they were teaching, or if they could guide students into going ahead into places where the teacher might be unfamiliar. Herein lies the whole crux, I think, of teaching as guiding, of life-long learning, and of the delicate interplay between teaching and learning. Is it possible to teach without learning? Is it possible to learn without teaching? Great questions to ponder. Here's an example: once a third grade student and I learned together about bases other than ten, using Cuisinaire Rods to build models. Until then, I had never understood the concept of bases other than ten. Had I been the kind of teacher who needed to know something before I introduced it to a student, that student would never have had the opportunity for that individual mathematical exploration -- nor would I have learned how other bases worked! Sometimes as teachers and leaders we can easily slip into the idea that we are in charge, that we know the answers, that our answers are the only answers, and that only we know which direction to head.