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The tutors need training. Any volunteer job has job requirements, and one of the requirements of this job [for it to be done well] is being able to tutor anything that comes along. The training can mainly involve intriguing problems that will help the tutors enjoy math themselves. Then, if they get stuck on a student's problem, they can seek help in a ...

Why does it matter what the research shows? At best, a study might have found that students who were blindly fed recipes did better in the short term on examinations for calculus. But then, what is the ultimate goal of education? For students to pass tests? I really hope not. The goal of any teacher, especially a teacher in mathematics, should first and ...

For math pedagogy, I recommend exploring some of the blogs out there, in particular Dan Meyer's blog. He also has a great TEDx talk. The whole online community of math educators, sometimes called the mathtwitterblogosphere, is worth exploring. What's out there ranges from virtual filing cabinets of creative lessons, to folks venting about common frustrations,...

In my particular case, I was lucky to have some very inspiring teachers, and to be teaching assistant in large, well-organized courses. Yes, other teachers were awful, but I learned how to teach from the ones I admire (and I hope I'm doing them justice in my work). I learned a lot from colleagues, even (or perhaps particularly) from ones in other fields. ...

While my answer is not a book, author, idea, or article, it is a source of ideas: conferences of people who are interested in such things are very good for inspiring you to learn. The American Mathematical Association of Two-Year Colleges (AMATYC) has affiliates in each region and many of them host annual conferences. My first experience at the Illinois ...

The best way is to surround yourself with people who are creative, smart, and actively thinking about and using effective pedagogy in the classroom. Twitter can be great for this. I'm fortunate to be in a department full of such people, such as David Coffey, John Golden, and others. I can just walk down the hall and embroil myself in a fascinating ...

A perhaps unusual recommendation: Lakoff and Núñez's book Where Mathematics Comes From, despite suffering from being mildly repetitive, has made me think very differently about mathematics education, as long as this is defined as the activity of instilling mathematical understanding in students (versus "mere" mathematical knowledge). Lakoff and Núñez, more ...

Most of my job tutoring high school math is giving my students confidence -- it's rare that a student of mine will actually have trouble with math. Switch at least part of your focus to building your students' confidence: "hey, that wasn't so hard, was it?," "See, you can do this!" If you can't show their students how to do something, then you should not ...

To the question about whether or not there is existant literature around some of these ideas, I believe there is a great deal. It seems you are getting at conversations around proof and how this plays out in teachers beliefs about mathematics. Several researchers have engaged in such pursuits. Immediately two things come to mind. The ICMI study on proof ...

I don't see that there is anything you can do other than teach the non-math volunteers math. Your normal "Joe" isn't going to be able to do pre-cal homework. The only real thing I would push is tell them to find someone who can help, but never, ever, under any circumstances say things like "Everyone has trouble with math, hey" or anything else that pushes ...