I am by no means an expert, so the references listed below are likely to be extremely incomplete. Hopefully they can help in hunting down further references. (These are based on a short essay written with Eero Hakavuori.)
Reciprocal teaching/learning/education was introduced in Palincsar's thesis  and in an article of Brown and Palincsar . Their original motivation was helping poor readers to perform better by using reading strategies (I think tactics is more accurate word here) that more skilled readers use.
The method of teaching the tactics: First teacher demonstrates them, and then gradually, step by step, gives more independence to the students.
It seems that the reciprocal teaching process and the tactics taught through it are called reciprocal teaching; at least in the articles I read the concepts were not explicitly separated and named.
There exists a general review of reciprocal teaching .
There is some research on word problems in specific [4,5].
We did not find anything related to understanding or composing proofs, or more general mathematical problem-solving.
 Annemarie Sullivan Palincsar. Improving the reading comprehension of junior high students through the reciprocal teaching of comprehension-monitoring strategies. PhD thesis, University of Illinois, 1982.
 Annemarie Sullivan Palincsar ja Ann L. Brown. Reciprocal teaching of comprehension-fostering and comprehension-monitoring activities. Cognition and instruction, 1(2):117–175, 1984.
 Barak Rosenshine ja Carla Meister. Reciprocal teaching: A review of the research. Review of educational research, 64(4):479–530, 1994.
 Delinda van Garderen. Focus on inclusion: reciprocal teaching as a comprehension strategy for understanding mathematical word problems. Reading & Writing Quarterly: Overcoming learning difficulties, 20(2):225–229, 2004.
 Allan Collins, John Seely Brown ja Susan E. Newman. Cognitive apprenticeship: Teaching the crafts of reading, writing, and mathematics. In a book edited by Lauren B. Resnick: Knowing, learning, and instruction: Essays in honor of Robert Glaser, pages 453–494. Lawrence Erlbaum associates, publishers, Hillsdale, New Jersey, USA, 1989.