Preservice education of math teachers using paradoxes

This is a report on a naturalistic study of the role mathematical paradoxes can play in the preservice education of high school mathematics teachers. The study examined the potential of paradoxes as a vehicle for: (a) sharpening student-teachers' mathematical concepts; (b) raising their pedagogical awareness of the constructive role of fallacious reasoning in the development of mathematical knowledge. Course material development and data collection procedures are described. Results obtained in parts of the study through written responses and class-videotapes are analyzed and discussed. The findings indicate that the model of dealing with paradoxes as applied in this study has relevance to such aspects of mathematics education as cognitive conflicts, motivation, misconceptions and constructive learning.

[1]  Edward E. Smith,et al.  The Teaching of Thinking , 1985 .

[2]  I. Sigel.  On becoming a thinker: A psychoeducational model , 1979 .

[3]  I. Kleiner.  Thinking the Unthinkable : The Story of Complex Numbers (with a Moral) , 1988 .

[4]  Jean Piaget.  Piaget’s Theory , 1976 .

[5]  Nitsa Movshovitz-Hadar,et al.  AN EMPIRICAL CLASSIFICATION MODEL FOR ERRORS IN HIGH SCHOOL MATHEMATICS , 1987 .

[6]  Conflict, learning, and Piaget: Comments on Zimmerman and Blom's “Toward an empirical test of the role of cognitive conflict in learning” , 1983 .

[7]  Raymond M. Smullyan,et al.  What is the name of this book , 1978 .

[8]  C. Bereiter.  Toward a Solution of the Learning Paradox , 1985 .

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

[10]  P. Woods.  Sociology, ethnography and teacher practice , 1985 .

[11]  Robert J. Marzano,et al.  Dimensions of Thinking: A Framework for Curriculum and Instruction , 1988 .

[12]  Bryan H. Bunch.  Mathematical Fallacies and Paradoxes , 1982 .

[13]  J. Piaget,et al.  The Development of Thought: Equilibration of Cognitive Structures , 1977 .

[14]  J. Flavell.  Speculations about the nature and development of metacognition , 1987 .

[15]  Martin Gardner,et al.  Wheels, life, and other mathematical amusements , 1983 .

[16]  R. Skemp.  Relational Understanding and Instrumental Understanding. , 2006 .

[17]  Martin Gardner,et al.  Aha! Gotcha: Paradoxes to Puzzle and Delight , 1982 .

[18]  Barry J. Zimmerman,et al.  Toward an empirical test of the role of cognitive conflict in learning , 1983 .