Started reading this blog: Doing Mathematics by Bryan Meyer. The post there has an interesting link to his research and book. You can buy the book or read it online. He also has a link to pdf of a 1994 paper "Mathematics Teaching: Moving From Telling to Listening" by Brent A. Davis.

!! His Book

As teachers, we should be instilling in our students powers of inquiry, confidence, and creativity in problem solving, and a love of learning. ... I want my students to know that we are all mathematical. I want them to recognize their own mathematical thinking and habits. I want them to view themselves as mathematicians, people who view the world with a mathematical lens and make sense of problems in the best way they can. I want them to have confidence in their ownt hinking.

I think his point is that we are all able to think mathematically from a very young age, but through the course of education we learn that we are not or shouldn;t be and depend on other authorities to tell us how to solve a math problem; that the correct way is a learned way from an authority, and not the way we could naturally percieve it. So students lose interest in math and their confidence becuase they think they need to know what the authpority would do, rather than what they would do.

This certainly applies to all subjects as well. Ask me about a piece of art or poem, and I think my opinion may not be useful, since I am not an expert. How opposite it really should be.

Telling to Listening

Certainly not a new idea, but really helps formalate how to use the listening and prodding approach in mathematical education. Certainly would apply to many fields of education.

Presenting math concepts as if they were a pre-existing pre-defined concepts that exist independant of human experience is a common method of teaching math concepts. It is actually the opposite. Math concepts are notions invented by humans to help make human experience more meaningful.

And in the footnotes on the last page

...a greater awareness of the ungroundedness of mathematical kowledge and a newly legitimated interest in attending to "learners" as they construct their own sense of mathematical concepts.

People really can have their own foundation for mathematical experience, and a teacher can be critical in engageing a conversation and listening methods to help them realize that ability.