Dear Barbara, it is not a quantitative method, but I like very much the series of books collected by Pitici (you know: 2010, 2011, 2012…) pertaining a collection of the best papers On mathematics - by many of the most distinguished mathematicians. It is a most valuable tool for the issues raised by your question.

Thank you, Carlos. I was able to identify the series, and I can scan the collection for information about mathematical dialogue. Do you know of any particular article that might review peer dialogue in mathematics?

Here are two:

Kiuhara, S. A. & Witzel, B. S. (2014. Focus on Inclusive Education: Math Literacy Strategies for Students with Learning Difficulties. Childhood Education, 90 (3), p234-238

Knudsen, J., Lara-Meloy, T., Stallworth Stevens, H, & Wise Rutstein, D. (2014). Advice for Mathematical Argumentation. Mathematics in the Middle School, 19(8), p494-500.

Thank you, Susan. The title of the second one sounds particularly promising, and I like that both are from this year. I'll look for them now.

Here you have a few more:

Daniel, M. F. (2013). Engaging in critical dialogue about mathematics. Analytic Teaching and Philosophical Praxis, 34(1).

http://journal.viterbo.edu/index.php/atpp/article/view/926

Shahrill, M., & Clarke, D. J. (2014). Brunei teachers’ perspectives on questioning: Investigating the opportunities to “Talk” in mathematics lessons. International Education Studies, 7(7), 

http://www.ccsenet.org/journal/index.php/ies/article/view/35568

Langer-Osuna, J. M., & Avalos, M. A. (2015). “I’m trying to figure this out. Why don’t you come up here?”: heterogeneous talk and dialogic space in a mathematics discussion. ZDM, 1-10.

Díez-Palomar, J., & Olivé, J. C. (2015). Using dialogic talk to teach mathematics: the case of interactive groups. ZDM, 1-14.

THIS ONE IS LESS ESPECIFIC:

Moorehead, T., & Grillo, K. (2013). Celebrating the Reality of Inclusive STEM Education Co-Teaching in Science and Mathematics. TEACHING Exceptional Children, 45(4), 50-57.

http://tcx.sagepub.com/content/45/4/50.extract

Best regards,

María