Intuitions and Schemata in Mathematical Reasoning

The present paper is an attampt to analyze the relationship between intuitions and structural schemata. Intuitions are defined as cognitions which appear subjectively to be self-evident, immediate, certain, global, coercive. Structural schemata are behavioral-mental devices which make possible the assimilation and interpretation of information and the adequate reactions to various stimuli. Structural schemata are characterized by their general relevance for the adaptive behavior. The main thesis of the paper is that intuitions are generally based on structural schemata. The transition from schemata to intuitions is achieved by a particular process of compression described in the paper.

[1]  S. Carey.  Conceptual Change in Childhood , 1985 .

[2]  J. Clement,et al.  Not all preconceptions are misconceptions: finding ‘anchoring conceptions’ for grounding instruction on students’ intuitions , 1989 .

[3]  M. McCloskey,et al.  Intuitive physics: the straight-down belief and its origin. , 1983, Journal of experimental psychology. Learning, memory, and cognition.

[4]  E. Fischbein,et al.  Schemata and Intuitions in Combinatorial Reasoning , 1997 .

[5]  Andrea A. diSessa,et al.  Knowledge in pieces : An evolving framework for understanding knowing and learning , 1988 .

[6]  Dina Tirosh,et al.  Is it possible to measure the intuitive acceptance of a mathematical statement? , 1981 .

[7]  Constance Kamii,et al.  Identification of Multiplicative Thinking in Children in Grades 1-5. , 1996 .

[8]  M. Bunge,et al.  Intuition and Science , 1962 .

[9]  J. Chaplin.  Dictionary of psychology , 1975 .

[10]  J. Bruner.  The Process of Education , 1960 .

[11]  The Role of Intuitive Rules in Science and Mathematics Education , 1996 .

[12]  M. Bunge,et al.  Intuition and Science. , 1963 .

[13]  Friedrich Wilkening,et al.  Information integration by children , 1980 .

[14]  Jean Piaget,et al.  Experiments in Contradiction , 1981 .

[15]  C. Gallistel,et al.  The Child's Understanding of Number , 1979 .

[16]  Jean Piaget,et al.  La géométrie spontanée de l'enfant , 1950 .

[17]  J. Flavell.  The Developmental psychology of Jean Piaget , 1963 .

[18]  E. Fischbein,et al.  Intuition in science and mathematics , 1987 .

[19]  E. Fischbein,et al.  The intuitive sources of probabilistic thinking in children , 1975 .

[20]  D. Hume,et al.  The philosophical works , 1964 .

[21]  T. Bastick,et al.  Intuition--how we think and act , 1982 .

[22]  E. Fischbein,et al.  The Evolution with Age of Probabilistic, Intuitively Based Misconceptions. , 1997 .

[23]  Dina Tirosh,et al.  The intuition of infinity , 1979 .

[24]  David Tall,et al.  Advanced Mathematical Thinking , 1994 .

[25]  M. Kline.  Mathematics: The Loss of Certainty , 1982 .