I feel very fortunate to be able to easily recall my favorite math teachers and struggle to bring to mind a least favourite. In reflecting on all of my experiences, though, I can certainly identify some qualities and methods that I appreciated seeing and some that I disliked.
In my favourite math classes, each class was a journey of discovery. This sounds overwhelmingly cliché, but it's true. Part of the reason that I love math is that a math problem has always felt like a puzzle to me. I never had much patience as a student for repetitive practice and much preferred complex problems that forced me to develop new ideas or ways of using a technique. I'm also a big fan of vertical classrooms, working in visibly random groups to solve problems so that I can get insight into how other people approach the problem as well as cement my own understanding by explaining to the rest of the group how I approached the task.
Many of the negative experiences I had as a learner of math came from a year in which I studied independently through modules (without a teacher, just someone supervising progress). I still have the modules from all those years ago and was idly looking through them the other day, in fact. My biggest frustration was when the module would insist that I approach a problem in a set way (i.e. solve geometrically). It felt as though the module didn't understand the way that my brain was working and, since it wasn't a person, I couldn't explain anything to it. It's very important to me as a teacher and a learner that everyone's ideas are heard and valued, even if they go against a conventional strategy or might not be the most efficient solution.
Great!
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