'Magical' Moments in Mathematics: Insights into the Process of Coming To Know.

That sudden flash of understanding which Naidra described as magical is often referred to in the literature as the 'Aha!' or 'Eureka! ' experience. It has frequently been described by mathematicians writing about the creative process. Gauss spoke of "a sudden flash of lightning" (cited in Hadamard, 1945, p. 15). Hadamard, drawing on the ideas of Poincare, described stages in the creative process as preparation (a period of intensive conscious work on a problem), incubation (a period of rest or relaxation away from the problem) and illumination (when a solution suddenly becomes clear). Poincare also linked mathematical insight to an appreciation of the aesthetics of mathematics. Polya (1965/1981) spoke of:

[1]  Leone Burton,et al.  Why Is Intuition So Important to Mathematicians but Missing from Mathematics Education , 1999 .

[2]  George Polya,et al.  Mathematical discovery : on understanding, learning, and teaching problem solving , 1962 .

[3]  J. Meece,et al.  Sex Differences in Math Achievement: Toward a Model of Academic Choice. , 1982 .

[4]  C. Thompson,et al.  Memory for personal events occurring in different modalities , 1984 .

[5]  Seymour Papert,et al.  Mindstorms: Children, Computers, and Powerful Ideas , 1981 .

[6]  C. Hirsch.  Curriculum and Evaluation Standards for School Mathematics , 1988 .

[7]  Philip J. Davis,et al.  The Mathematical Experience , 1982 .

[8]  Douglas B. McLeod,et al.  Research on affect in mathematics education: A reconceptualization. , 1992 .

[9]  R. White.  Achievements and Directions in Research on Intellectual Skills , 1981 .

[10]  Leone Burton,et al.  Mathematical Thinking: The Struggle for Meaning. , 1984 .

[11]  Paul Cobb,et al.  Young Children’s Emotional Acts While Engaged in Mathematical Problem Solving , 1989 .

[12]  Mark A. Runco,et al.  Creativity and Affect , 1994 .

[13]  Leone Burton,et al.  The Practices of Mathematicians: What do They Tell us About Coming to Know Mathematics? , 1998 .

[14]  Richard T. White,et al.  Recall of autobiographical events , 1989 .

[15]  Vadim Andreevich Krutet︠s︡kiĭ.  The Psychology of Mathematical Abilities in Schoolchildren , 1976 .

[16]  P. Cobb,et al.  Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. , 1996 .

[17]  T. Dreyfus,et al.  On the Aesthetics of Mathematical Thought. , 1986 .

[18]  Douglas B. McLeod,et al.  The Role of Affect in Mathematical Problem Solving , 1989 .

[19]  Jo Boaler,et al.  Experiencing School Mathematics: Teaching Styles, Sex, and Setting , 1997 .