A new framework for designing qualitative studies is described to optimize the emergence, representation and presentation of insights. The framework, called Reflection Methodology, is presented as a "Conversational Paradigm" that includes four components--interviewer (researcher as participant); child, task situation, and observing technology (including a second researcher as external observer)--in three phases--reflection/performance, judgmental reflection question, and reflection simulation. The involvement of the researcher team embodies the "complementarity" of the wholistic perspective with the separation perspective. The core subsystem within the paradigm is the child as an autonomous living system interacting with a task. The task, traditionally seen as input from the environment, is in contrast a perturbation and also a perturbation within the interviewer system. Accordingly, the conversational system evolves around the common perturbation--the task. It is through the joint participation of the child-task system and the interviewer-task system in the larger conversational system that the task gains any living meaning as an aspect of a larger social system. Descriptions of the task are representations of order which emerges from Reflection Methodology as a conversational system to provide a framework for clinical studies that are becoming central in mathematics education. Methods of a 1985 study in partitioning by children using Reflection Methodology are described to exemplify the Conversational Paradigm. (PN)