Dynamics of Symmetry Group Theorizing (Non-Kairos references)
[Parts: First | All] [Links: To-K | From-K | From-Kx ]
Alexander, Christopher. The Nature of Order: an essay on the art of building and the nature of the universe. Center for Environmental Structure, 2003-2004. [
summary]
Atkin, Ronald H. Multidimensional Man: Can man live in three dimensional space? London, Penguin, 1981. [
review]
Atkin, Ronald H. Combinatorial Connectivities in Social Systems; an application of simplicial complex structures to the study of large organizations. Basel, Birkhauser, 1977.
Bagni, Giorgio T. /
Furinghetti, Fulvia /
Spagnolo, Filippo. History and epistemology in mathematics education. In: Cannizzato, L., Pesci A., Robutti, O. (Eds.),
Italian research in Mathematics Education, 2000-2003. [
text]
Bateson, Gregory. Mind and Nature: a necessary unity, 1979.
Branford, Benchara. A Study of Mathematical Education. Oxford, Clarendon Press, 1908/1921. [
review]
Bringuier, Jean Claude. Conversations with Jean Piaget. University of Chicago Press, 1980.
Conway, John Horton /
Curtis, R. T. /
Norton, Simon P. /
Parker, R. A. /
Wilson, R. A. Atlas of Finite Groups: maximal subgroups and ordinary characters for simple groups. Oxford University Press, 1985.. [
summary]
Davis, Philip J. /
Hersh, Reuben. The Mathematical Experience. Houghton Mifflin, 1981.
Davydov, V. V. Types of Generalization in Instruction: logical and psychological problems in the structuring of school curricula. Soviet Studies in Mathematics Education, 1990, Volume 2.. [
abstract]
de Bono, Edward. I Am Right, You Are Wrong: New Renaissance: From Rock Logic to Water Logic. Penguin, 1990.
de Nicolas, Antonio T. Habits of Mind: an introduction to the philosophy of education. iUniverse, 2000. [
text]
Detienne, F. Assessing the Cognitive Consequences of the Object-oriented Approach: a survey of empirical research on object-oriented design by individuals and teams.
Interacting with Computers, 9, 1997, pp. 47-72.
Dorier, J. L. Meta Level in the Teaching of Generalizing Concepts in Mathematics.
Educational Studies in Mathematics, 29, 1995, pp. 175-197.
du Sautoy, Marcus. Finding Moonshine: a mathematician's journey through symmetry. Fourth Estate, 2008.
Dubinksy, Ed. Reflective Abstraction in Advanced Mathematical Thinking. In: D. Tall (Ed.). Advanced Mathematical Thinking. Kluwer, 1991, pp. 95-123.
Dubinksy, Ed. Mathematical Literacy and Abstraction in the 21st Century.
School Science and Mathematics, 100, 2000. [
abstract]
Duval, Raymond. A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics.
Educational Studies in Mathematics, Volume 61, Numbers 1-2, February 2006, pp. 103-131(29). [
abstract]
Edling, Agnes. Abstraction and Authority in Textbooks: the textual paths towards specialized language. Uppsala, Acta Universitatis Uppsaliensis, 2006. [
text]
Eppstein, David. The Geometry Junkyard: Symmetry and Group Theory. [
text]
Eppstein, David. The Geometry Junkyard: Polyhedra and Polytopes. [
text]
Fambrough, Mary J. The Changing Epistemological Assumptions of Group Theory.
The Journal of Applied Behavioral Science, 42, 2006, 3, pp. 330-349. [
text]
Fauvel, John /
Maanen, Jan A. (Eds.). History in Mathematics Education: the ICMI Study. Springer, 2000). [
text]
Feldman, Jacob. Perceptual Grouping into Visual "objects": a detailed chronology.
Journal of Vision, 2, 2003, 7. [
abstract]
Frorer, P. /
Hazzan, Orrit. and M. Manes. Revealing the Faces of Abstraction.
International Journal of Computers for Mathematical Learning, 2, 1997, pp. 217-228.
Furinghetti, Fulvia /
Radford, Luis. Hisotrical Conceptual Developments and the Teaching of Mathematics: from phylogenesis and ontogenesis theory to classroom practice. In: John Fauvel and Jan A. Maanen (Eds.). History in Mathematics Education: the ICMI Study. Springer, 2000). [
text]
Fysik, KTH. A timeline of symmetry in physics, chemistry and mathematics. [
text]
Fysik, KTH. Web links to resources on Symmetry, Group Theory, and related subjects in Mathematics and Physics. [
text]
Goonatilake, Susantha. Toward a Global Science: mining civilizational knowledge. Indiana University Press, 1999.
Hazzan, Orrit. Reducing Abstraction Level when Learning Abstract Algebra Concepts.
Educational Studies in Mathematics, 40, 1999, pp. 71-90.
Hazzan, Orrit. Reflections on Teaching Abstraction and other Soft Ideas.
ACM SIGCSE Bulletin, 40, 2008, 2, pp. 40-43. [
abstract]
Hughes, Martin. Children and Number: difficulties in learning mathematics. Blackwell Publishing, 1986.
Inchbald, Guy. Polytopes, duality and precursors. 2005. [
text]
Katz, Victor /
Dorier, Jean-Luc /
Bekken, Otto /
Sierpinska, Anna. The Role of Historical Analysis in Predicting and Interpreting Students' Difficulties in Mathematics. In: John Fauvel and Jan A. Maanen (Eds.). History in Mathematics Education: the ICMI Study. Springer, 2000. [
text]
Knapp, Anthony W. Group Representations and Harmonic Analysis from Euler to Langlands.
Notices of the AMS, 3, 1996, 4. [
text]
Kramer, Jeff. Abstraction - the key to Computing?.. [
text]
Kvasz, Ladislav. The History of Algebra and the Development of the Form of its Language.
Philosophia Mathematica 2006 14(3):287-317. [
abstract]
Lévy-Leblond, J. M. The pedagogical role and epistemological significance of group theory in quantum mechanics.
La Rivista del Nuovo Cimento, 4, 1, January, 1974 pp. 99-143. [
abstract]
Lakoff, George /
Johnson, Mark. Metaphors We Live By. University of Chicago Press, 2003.
Lakoff, George /
Núñez, Rafael E. Where Mathematics Comes From: how the embodied mind brings mathematics into being. Basic Books, 2000. [
summary]
Lam, T. Y. Representations of Finite Groups: A Hundred Years, Part I.
Notices of the AMS, 45, 1998, 3. [
text]
Lam, T. Y. Representations of Finite Groups: A Hundred Years, Part II.
Notices of the AMS, 45, 1998, 4. [
text]
Leyton, Michael. Symmetry, Causality, Mind. MIT Press, 1992.
Leyton, Michael. Shape as Memory: a geometric theory of architecture. Birkhäuser, 2006.
Leyton, Michael. A Generative Theory of Shape. Springer, 2001. [
text]
Limón, Margarita /
Mason, Lucia. Reconsidering Conceptual Change: issues in theory and practice. Springer, 2002. [
text]
Martin, J. R. Technicality and Abstraction: language for the creation of specialized texts, In: M.A.K. Halliday and J.R. Martin.
Writing Science: Literacy and Discursive Power, London, Falmer Press, 1993.
Martin, J. R. Life as a Noun: arresting the universe in science and humanities. In: M.A.K. Halliday and J.R. Martin, 1993.
Maryniarczyk, Andrzej. Abstraction.
Powszechna Encyklopedia Filozofii. [
text]
Mason, J. Mathematical Abstraction as a Result of a Delicate Shift of Attention.
For the Learning of Mathematics, 9, 1989, pp. 2-8.
Masters, Alexander. The Genius in My Basement: the biography of a happy man. Fourth Estate, 2011.
Mazzola, Guerino. Mathematical Music Theory: Status Quo 2000. 2001. [
text]
McGee, Vann. How We Learn Mathematical Language.
Philosophical Review, 106, 1997, pp. 35- 68.
Mengal, P. (Ed.). Histoire du concept de récapitulation. Paris, Masson, 1993.
Miller, George A. The Magical Number Seven, Plus or Minus Two: some limits on our capacity for processing information.
Psychological Review, 63, 1956, pp. 81-97. [
summary]
Nicolescu, Basarab. Levels of Reality and the Sacred, 2002. [
text]
Nicolescu, Basarab. Transdisciplinarity and Complexity: levels of reality as source of indeterminacy.
Bulletin Interactif du Centre International de Recherches et Études transdisciplinaires, 15, Mai 2000. [
text]
Nicolis, John S. /
Tsuda, Ichiro. Chaotic Dynamics of Information Processing: the 'magic number seven plus-minus two' revisited.
Bulletin of Mathematical Biology, 47, 1985, 3, pp. 343-365. [
abstract]
O'Connor, J. J. /
Robertson, E. F. The Development of Group Theory. 1996. [
text]
Ohlsson, S. /
Lehtinen, E. Abstraction and the Acquisition of Complex Ideas.
International Journal of Educational Research, 27, 1997, pp. 37-48.
Ozmantar, Mehmet Fatih. An investigation of the formation of mathematical abstractions through scaffolding. Unpublished Ph.D. thesis, University of Leeds, 2005.
Ozmantar, Mehmet Fatih /
Monaghan, John. A Dialectical Approach to the Formation of Mathematical Abstractions.
Mathematics Education Research Journal, 2007, 19, No. 2, pp. 89-112. [
text]
Pennington, N. /
Lee, A. Y. /
Rehder, B. Cognitive Activities and Levels of Abstraction in Procedural and Object-oriented Design.
Human-Computer Interaction, 10, 1995, pp. 171-226.
Piaget, Jean /
Garcia, Rolando. Psychogenesis and the History of Science. Columbia University Press, 1989.
Piaget, Jean /
Garcia, Rolando /
Davidson, Philip M. /
Easley, Jack. Toward a Logic of Meanings. Hillsdale NJ, Lawrence Erlbaum Associates, 1991. [
contents]
Plaisted, David A. Abstraction using Generalization Functions.
8th International Conference on Automated Deduction, Volume 230/1986, pp. 365- 376. [
abstract]
Posey, Darrell A. (Ed.). Cultural and Spiritual Values of Biodiversity: a complementary contribution to Global Biodiversity Assessment, Intermediate Technology, 1999 (for the United Nations Environment Programme).
Radford, Luis /
Boero, Paolo /
Vasco, Carlos. Epistemological Assumptions Framing Interpretations of Students Understanding of Mathematics. In: John Fauvel and Jan A. Maanen (Eds.). History in Mathematics Education: the ICMI Study. Springer, 2000, pp. 162-167. [
text]
Radford, Luis. On psychology, historical epistemology and the teaching of mathematics: towards a socio-cultural history of mathematics.
For the Learning of Mathematics, 17, 1997, 1, pp. 26-33.
Ronan, Mark. Symmetry and the Monster: one of the greatest quests of mathematics. Oxford University Press, 2006. [
review]
Sfard, Anna. On the Dual Nature of Mathematical Conceptions: reflections on processes and objects as different sides of the same coin.
Educational Studies in Mathematics, 22, 1991, pp. 1-36..
Sfard, Anna. The Development of Algebra: confronting historical and psychological perspectives.
Journal of Mathematical Behavior, 14, 1995, pp. 15-39.
Sierpinska, Anna. Understanding in Mathematics. Falmer Press, 1994.
Stehliková, N. Emergence of Mathematical Knowledge Structures: introspection. In: N. A. Pateman, B. J. Dougherty and J. T. Zilliox (Eds.), Proceedings of the 27th International Conference for the Psychology of Mathematics Education, 4, 2003, pp. 251-258.
Stolze, Radegundis. Levels of Abstraction in Specialist Concepts as a Translation Problem. In: C. Zelinsky-Wibbelt (Ed.)
Text, Context, Concepts, Berlin, Mouton de Gruyter, 2003.
Vasco, C. E. History of Mathematics as a Tool for Teaching Mathematics for Understanding. In: D. N. Perkins., Software Goes to School: teaching for understanding with new technologies. Oxford University Press, 1995, pp 56-69.
Vygotsky, Lev S. The History of the Development of Higher Mental Functions. Plenum Press, 1997.
Wigner, Eugene P. Symmetries and Reflections: Scientific Essays. MIT Press, 1970.
Wolpert, David H. The Mathematics of Generalization. Addison Wesley Longman, 1995.