The first connections were to elements of their own stories, and were interesting. Then one of the students brought up a connection with how Robinson describes us as being educated out of creativity. Her sister is interested in being a soloist, and it took ears of retraining or untraining to get her out of what she had been taught to do as a choral member. I'd never heard of that before, but it connected exactly to the point I wanted to make.

They have been educated - and successfully so, as college calc students - in school mathematics, which has almost nothing to do with mathematics as practiced by mathematicians. (Which really needs a descriptor. Real mathematics isn't going to interest anyone. Creative mathematics? Cool vs. school or cruel mathematics?) Instead of being able to repeat what someone shows you, it should be about solving problems that you don't know how to solve. In which situations mathematicians excel, because they are entirely willing to be wrong, and even glad to be wrong if they learn from it. They're willing to, as my friend Dave says (quoting his favorite Australian, Brian Cambourne) to "Give it a go!"

As long ago as 1982, my calc instructor, John Hocking, worked mightily to convince us to have no fear. To be wrong 100 times if it teaches you something. That math was exploratory, and creative. He shared his topological research with us... which was amazing and fun. He's the reason I added the math major in the first place. Often he put it as "blank pages are just waiting to be filled."

Now can I help my calc students to do the same?

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