Functionary: Learning to Communicate Mathematically in Online Environments
I took a collection of recommendations from researchers in the fields of online education and mathematics education and asked our friends at Desmos to tie them all together in a digital middle-school math lesson. These recommendations had never been synthesized before. We piloted and iterated that lesson for a year. I then tested that Desmos lesson against a typical online math lesson (lecture-based instruction followed by recall exercises) in a pretest-posttest design. Both conditions learned. The Desmos lesson learned more. (Read the technical abstract.)
True story: I wrote it with you, the reader of math blogs, in mind.
That is to say, it’s awfully tempting in grad school to lard up your writing with jargon as some kind of shield against criticism. (If your critics can’t understand your writing, they probably can’t criticize it and if you’re lucky they’ll think that’s their fault.) Instead I tried to write as conversationally as possible with as much precision and clarity as I could manage. This didn’t always work. Occasionally, my advisers would chide me for being “too chatty.” That was helpful. Then I stocked my committee with four of my favorite writers from Stanford’s Graduate School of Education and let the chips fall.
Everything from my methods section and beyond gets fairly technical, but if you’re looking for a review of online education and the language of mathematics, I think the early chapters offer a readable summary of important research.