"Cogito ergo sum." These famous words from the philosopher René Descartes summarize his view, or maybe his thought experiment, on how we know. For Descartes, knowledge is knowledge if it originates in the thinker. Any knowledge that originates outside of the thinker must be doubted, questioned, examined, and reasoned by the thinker so as to make it knowledge that could have originated within the thinker. Until the knowledge originates in the thinker, it cannot be considered actual knowledge.
There are three kinds of people in this word, it has been said. Those that think math is a waste of time beyond learning to count, add, subtract, multiply, and divide and thus is primarily useful for consumerism. Those that think that math is amazing because it is extremely useful for the construction of bridges, building, airplanes, cars, and more. These are the engineers. And, finally, those that think math is beautiful for its own sake. Each group is smaller than the previous.
A person's approach to teaching math will differ based on which group he is in.
At the 2015 CiRCE Conference, A Contemplation of Harmony, Andrew Kern and I led a breakout session called "Transcending Method: The Art of Classical Teaching". What did we mean?
Over the last few years, I've read several books that seem to be beckoning me to home. Almost any of Wendell Berry's books, especially the one I've read most recently, Jayber Crow, will stir your thoughts to home and community. In June, I attended the CiRCE Summer Institute's inaugural retreat, where we read and discussed Homer's The Odyssey.
I teach a group of homeschooled 12th graders. This is my second year teaching them, having followed them from 11th to 12th grade. I introduced them to The Lost Tools of Writing Level 1 at the beginning of the 11th grade and we’ve continued the lessons into this second year.