From Searle’s Chinese room to the mathematics classroom: technical and cognitive mathematics
 Dimitris Gavalas
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Employing Searle’s views, I begin by arguing that students of Mathematics behave similarly to machines that manage symbols using a set of rules. I then consider two types of Mathematics, which I call Cognitive Mathematics and Technical Mathematics respectively. The former type relates to concepts and meanings, logic and sense, whilst the latter relates to algorithms, heuristics, rules and application of various techniques. I claim that an upgrade in the school teaching of Cognitive Mathematics is necessary. The aim is to change the current mentality of the stakeholders so as to compensate for the undue value presently attached to Technical Mathematics, due to advances in technology and its applications, and thus render the two sides of Mathematics equal. Furthermore, I suggest a reorganization/systematization of School Mathematics into a cognitive network to facilitate students’ understanding of the subject. The final goal is the transition from mechanical execution of rules to better understanding and indepth knowledge of Mathematics.
 Anderson, J. R. (1993). Rules of the mind. Hillsdale, N.J.: Lawrence Erlbaum Associates, Publishers.
 Bloom, B. S. (1956). Taxonomy of educational objectives, handbook I: The cognitive domain. N.Y.: David McKay Co, Inc.
 Bradshaw, J. L. & Nettleton, N. C. (1981). The nature of hemispheric specialization in man. The Behavioural and Brain Sciences, 7, 51–91.
 Byers, V. & Herscovics, N. (1978). Understanding school mathematics. Mathematics Teaching 81.
 Carlson, M. P. & Bloom, I. (2005). The cyclic nature of problem solving: An emergent multidimensional problemsolving framework. Educational Studies in Mathematics, 58, 45–75. CrossRef
 Carpenter, T. P., Fennema, E. & Romberg, T. A. (Eds.) (1992). Rational numbers: An integration of research. Hillsdale, N.J.: Lawrence Erlbaum Associates, Publishers.
 Charles, D. (2001). Wittgenstein’s builders and Aristotle’s craftsmen. In Charles, D. & Child, W. (Eds.), Wittgensteinian themes. (pp. 49–79). Oxford: Clarendon Press.
 Churchland, P. & Churchland, P. S. (1990). Could a machine think? Scientific American, 262, 32–39.
 Dave, R. H. (1975). Developing and writing behavioural objectives. N.Y.: Educational Innovators Press.
 Davis, P. J. & Hersh, R. (1984). The mathematical experience. N.Y.: Penguin Books.
 Dehaene, S. (1997). The number sense: How the mind creates mathematics. N. Y.: Penguin Books.
 Drossos, C. (1987). Cognition, mathematics and synthetic reasoning. General Seminar of Mathematics 13, 107–151. Edited by Department of Mathematics, University of Patras, Greece. (2nd revised edition 2006).
 Entrekin, V. S. (1992). Mathematical mind mapping. The Mathematics Teacher, 85(6), 444–445.
 Eysenck, M. W. & Keane, M. T. (2000). Cognitive psychology. Philadelphia, PA: Psychology Press/Tailor & Francis.
 Fennema, E. & Romberg, T. A. (Eds.) (1999). Mathematics classrooms that promote understanding. Mahwah, NJ: Lawrence Erlbaum Associates.
 Gavalas, D. (1999). A foursided view of ‘function’. For the Learning of Mathematics, 19(2), 38–41
 Gavalas, D. (2000). Study of the ‘Teaching System’ according to systems theory. International Journal of Mathematical Education in Science and Technology, 31(2), 261–268. CrossRef
 Gentner, D. & Markman, A. (1997). Structure mapping in analogy and similarity. American sychologist, 52(1), 45–56. CrossRef
 Grenander, U. (1997). Geometries of knowledge. Proceedings of the National Academy of Sciences of the United States America, 94, 783–789. CrossRef
 Grouws, D. A. (Ed.) (1997). Handbook on research on mathematics teaching and learning. N.Y.: Simon and Schuster Macmillan.
 Harrison, D. (1999). The Searle workout: Connectionism hits the Chinese gym. http://gort.ucsd.edu/newjour/c/msg02500.html.
 Hasemann, K. & Mansfield, H. (1995). Concept mapping in research on mathematical knowledge development: Background, methods, findings and conclusions. ESM, 29, 45–72.
 Hauser, L. (1996). The Chinese room argument. The Internet Encyclopaedia of Philosophy. www.utm.edu/research/iep.
 Hegel, G. W. F. (1969). Science of logic. Trans. A. V. Miller. London: Allen & Unwin; repr. Atlantic Highlands, N.J.: Humanities Press, 1993. (Translation of Hegel (1812–1816)).
 Heylighen, F. & Joslyn, C. (1992). What is systems theory? Edited by Cambridge Dictionary of Philosophy, Cambridge University Press.
 Holland J.H. et al (1986). Induction: Processes of inference. Learning and discovery. Cambridge, Mass: MIT Press.
 Jung, C. G.: The collected works. 20 vols. Bollingen Series XX. Translated by R. F. C. Hull, edited by H. Read, M. Fordham, G. Adler, and Wm. McGuire. Princeton N.J.: Princeton University Press (1953–1979).
 Kim, J. (1996). Philosophy of mind. Boulder, Colorado: Westview Press.
 Kofman, F. & Senge, P. (1995). Communities of commitment: The heart of learning organizations. In Chawla & Reneschs (Eds.), Learning organizations: Developing cultures for tomorrow’s workplace (pp. 14–43). Portland, Oregon: Productivity Press.
 Krathwohl, D., Bloom, B., & Masia, B. (1956). Taxonomy of educational objectives, Handbook II: Affective domain. N. Y.: David McKay.
 Krathwohl, D. R., Bloom, B. S., & Bertram, B. M. (1973). Taxonomy of educational objectives, the classification of educational goal. Handbook II: Affective domain. New York: David McKay Co., Inc.
 Lawvere, F. W. (1976). Variable quantities and variable structures in Topoi. In algebra, topology and category theory: A collection of papers in honour of S. Eilenberg (pp. 101–131). N.Y.: Academic press.
 Lawvere, F. W. & Schanuel, S. H. (2001). Conceptual mathematics: A first introduction to categories. Cambridge, UK: Cambridge University Press.
 Lester, F. K. (1994). Musings about mathematical problem solving research: 1970–1994. Journal for Research in Mathematics Education, 25, 660–675. CrossRef
 Mac Lane, S. (1986).Mathematics: Form and function N.Y.: SpringerVerlag.
 Mayer, R. E. (1992).Thinking, problem solving, cognition. N.Y.: Freeman & Co.
 NCTM (2000). Principals and standards for school mathematics. Reston, VA.
 Piaget, J. (1978). Judgment and reasoning in the child. London: Routledge and Kegan Paul.
 Rey, G. (1997). Contemporary philosophy of mind. Cambridge, MA: Blackwell.
 Rosenbloom, P. S. et al. (1993). The soar papers: Research on integrated intelligence. Cambridge, Mass.: MIT Press.
 Rucker, R. (1988). Mind tools: The mathematics of information. N.Y.: Penguin Books.
 Searle, J. (1980). Minds, brains and programs. The Behavioural and Brain Sciences, 3, 417–457.
 Searle, J. (1984). Minds, brains and science. Cambridge, MA: Harvard University Press.
 Searle, J. (1989). Reply to Jacquette. Philosophy and Phenomenological Research, XLIX, 701–708. CrossRef
 Searle, J. (1990). Is the brain’s mind a computer program? Scientific American, 262, 26–31. CrossRef
 Senge, P. et al. (2003). Schools that learn. London: Nicholas Brealey Publishing.
 Shoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition and sensemaking in mathematics. In D. A. Grouws (Ed.), Handbook for research on mathematics teaching and learning. (pp. 334–370). N.Y.: Macmillan Publishing Co.
 Simpson E. J. (1972). The classification of educational objectives in the psychomotor domain. Washington, DC: Gryphon House.
 Skemp, R. R. (1972). The psychology of learning mathematics N.Y.: Penguin Books.
 Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
 Skemp, R. (1987). The psychology of learning mathematics. Hillsdale, N.J.: Lawrence Erlbaum Associates, Publishers.
 Sterenly, K. (1990). The representational theory of mind. Cambridge, MA: Blackwell.
 Tall, D. O. (1978). The dynamics of understanding mathematics. Mathematics Teaching, 81, 50–52.
 Tall, D. & Thomas, M. (Eds.) (2002). Intelligence, learning and understanding in mathematics: a tribute to Richard Skemp. Post Pressed, Teneriffe, Brisbane.
 Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge: Harvard University Press.
 Wilson, P. S. (Ed.) (1993). Research ideas for the classroom: High school mathematics. N.Y.: Macmillan Publishing Company.
 Yalom, I. (2002). Religious and psychotherapy. American Journal of Psychotherapy 3.
 Zeleke, A. & Lee, C. (2002). On students’ conceptual understanding of ‘variation’ in introductory statistics. www.hicstatistics.org/2003StatsProceedings/Akilulu%20Zeleke.pdf.
 Title
 From Searle’s Chinese room to the mathematics classroom: technical and cognitive mathematics
 Journal

Studies in Philosophy and Education
Volume 26, Issue 2 , pp 127146
 Cover Date
 20070301
 DOI
 10.1007/s112170069018y
 Print ISSN
 00393746
 Online ISSN
 1573191X
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Chinese room
 Mathematics classroom
 Education
 Cognitive mathematics
 Technical mathematics
 Authors

 Dimitris Gavalas ^{(1)}
 Author Affiliations

 1. Mathematics, Pedagogical InstituteGreece, Folois 6, Athens, 11256, Greece