To determine what was taught requires investigating what was learned.
"What radical constructivism may suggest to educators is this: the art of teaching has little to do with the traffic of knowledge, its fundamental purpose must be to foster the art of learning."
- Ernst von Glasersfeld
Picture a traditional textbook, drawn up by a mathematician in her or his office as a way to sort out and present her or his understandings to another. Such a textbook can provide beautiful expositions of mathematical ideas, but it is typically absent of something critical: an image of the learner. Teaching and curricula often emphasize an adult's mathematics, a mathematics as already learned.
Drawing from the radical constructivist movement in mathematics education, I take a scientific-inquiry approach to developing models of students' mathematical learning. My specific interest is understanding how students' quantitative and covariational reasoning is a generative foundation for their learning precalculus and calculus concepts. Through better understanding students' mathematical learning, I work to construct epistemic learners and ultimately design instructional experiences that foreground their mathematical experiences.
To understand something requires an attempt to change it.
A great project inspires those involved to learn more.
The quality of our work is defined by what students learn.