**1. Introduction**

This chapter presents a new theory of creativity in mathematics education. The theory has been built from two sources: Prabhu's [1] teaching experiment, which brought about a surprising number of Aha! Moments in students enrolled in her developmental math classes and Arthur Koestler's volume The Act of Creation [2]. The research, or rather the teaching–research pathway that led us to formulating the new theory of creativity in mathematics education, started during the 2010/2011 teaching-experiment conducted by Prabhu and supported by CUNY grant C<sup>3</sup> IRG 7, *Problem Solving in Remedial Mathematics*—*a Jumpstart for the Reform*. The grant was awarded to members of the Teaching-Research (TR) Team of the Bronx anchored in Hostos Community College, New York City. The work on creativity of Aha! Moment took two creative cycles of work each lasting several years, during which we realized we have here a new distinct approach to creativity through Aha! Moment. Since Aha! or epiphanies are common occurrences among the general public in many domains of activity, the presented theory applies equally to the "underserved and underrepresented" as well as to the "talented and gifted".

These separate research ideas coalesce into a whole presented in the work by Czarnocha, Baker, Dias and Prabhu in [3], where the first sketches of the new theory appeared in different chapters. The volume introduced the theory of creativity in its discussion of teaching–research methodology, showing that TR methodology is intrinsically creative. Because teaching and research constitute two matrices of thought, generally and unfortunately not connected with each other, working at the teaching–research interface enables bisociative processes to create/build Aha! bridges between them.

During the second teaching–research creative cycle, we investigated processes of facilitation of an Aha! Moment assessment of the depth of knowledge gained during the insight, and constraints imposed on development of creativity in mathematics classrooms. The full exploration of the phenomenon Aha! Moment took place at the completion of the second creative teaching–research cycle with the volume Creativity of an Aha! Moment and Mathematics Education, Czarnocha [4] which collected our own research as well as that of international experts on Aha! Moments. The Koestler/Prabhu theory of creativity through Aha! Moment was formulated in that volume for the first time. The reflection on this work provided the basis on which to build the Philosophy of Creativity in Mathematics Education [5]. In this chapter, we present the Koestler/Prabhu theory in Section 2 together with some of its application into creativity research. We also provide a method of assessment for the increase of knowledge occasioned by Aha! Moment insight in Section 3. Section 4 presents our investigations into the relationship between the bisociative frame and sociocultural framework. In Section 5, we summarize and connect different threads of the paper.
