This story begins yesterday when 7 year-old AR came to ask a question. The beauty was that I was giving a lesson to 12 year-old JV on the relationship between circles. She came and sat near me. She listened as I spoke with JV about tangental circles (internal and external), exterior and interior placement, secant circles, and even concentric circles and their annulus. She waited staring at the circles as we reviewed the nomenclature. She then interrupted. I didn’t stop her because her question was germain to the topic, “How do you measure a perimeter of a circle?”
We’ve been spending lots of time in geometry. She and BW have covered the nomenclature of lines, closed figures, triangles (including the theorem of the relationship of the length of the arms to hypotenuse), and quadrilaterals. She has the background for polygons; but circles? I was still in my lesson and time was short. I led her to the book case and handed her the Sir Circumference book series. She was hooked. She poured over the books. Then the day was over.
Today, she spent the day reading and working on her own thoughts. She wondered about measuring circles. She tried several ways to measures them by inscribing them in squares (lunch circle was a blur to her as she was very pre-occupied with this problem). She worked out making a square shaped object into multiple shapes from triangles to parallelogram to an approximate circle. She read some more and decided she didn’t get cones as pure geometry, but she liked the circles and the angles and the story.
All this wasn’t part of the plan. Lucky for us, following the plan is not the goal. Learning is the goal. AR is in the pursuit of wonder. Goal met.