The issue addressed in this chapter is age-old: How can learners be stimulated to move from assenting (passively and silently accepting what they are told, doing what they are shown how to do) to asserting (actively taking initiative, by making, testing and modifying conjectures, and by taking responsibility for making subject pertinent choices). How can learners be provoked into actively working on and making sense of the ideas and techniques that they encounter, and how can this cultural ethos be fostered and sustained?
I use the term asserting because of the assonance with assenting, but also because it signals that the learner is taking initiative and making significant choices. It is not intended to indicate that learners become either arrogant or garrulous. Much of the most desirable assertive behaviour is internal, and need not have visibly overt external behaviour. It involves taking initiative, taking control, making choices, and becoming independent.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
- Information Communication Technology
- Sense Impression
- Dynamic Geometry Software
- Natural Power
- Didactic Contract
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Boaler, J. (1997). Experiencing School Mathematics: Teaching Styles, Sex and Setting. Buckingham: Open University Press
Brousseau, G. (1984). The Crucial Role of the Didactical Contract in the Analysis and Construction of Situations in Teaching and Learning Mathematics. In H. Steiner (Ed.), Theory of Mathematics Education, Paper 54 (pp. 110–119). Institut fur Didaktik der Mathematik der Universitat Bielefeld.Boaler
Brousseau, G. (1997). Theory of Didactical Situations in Mathematics: Didactiques des mathéma-tiques, 1970–1990, N. Balacheff, M. Cooper, R. Sutherland & V. Warfield (Trans. & Eds.). Dordrecht: Kluwer
Brown, S., Collins, A. & Duguid, P. (1989). Situated Cognition and the Culture of Learning. Educational Researcher, 18(1), 32–41
Bruner, J. (1996). The Culture of Education. Cambridge: Harvard University Press
Bruner, J., Goodnow, J. & Austin, A. (1956). A Study of Thinking. New York: Wiley
Davis, B. (1996). Teaching Mathematics: Toward a Sound Alternative. London: Garland
diSessa, A. (1987). Phenomenology and the Evolution of Intuition. In C. Janvier (Ed.), Problems of Representation in the Teaching and Learning of Mathematics (pp. 83–96). Mahwah: Erlbaum
Festinger, L. (1957). A Theory of Cognitive Dissonance. Stanford: Stanford University Press
Fischbein, E. (1987). Intuition in Science and Mathematics: An Educational Approach. Dordecht: Reidel
Fischbein, E. (1993). The Theory of Figural Concepts. Educational Studies in Mathematics, 24(2), 139–162
Floyd, A., Burton, L., James, N. & Mason, J. (1981). EM235: Developing Mathematical Thinking. Milton Keynes: Open University
Gattegno, C. (1970). What We Owe Children: The Subordination of Teaching to Learning. London: Routledge & Kegan Paul
Gattegno, C. (1987). The Science of Education Part I: Theoretical Considerations. New York: Educational Solutions
Gattegno, C. (1988). The Mind Teaches the Brain. New York: Educational Solutions
Halmos, P. (1994). What is Teaching? American Mathematical Monthly, 101(9), 848–854
Hamilton, E. & Cairns, H. (Eds.) (1961). Plato: The Collected Dialogues Including the Letters. Bollingen Series LXXI. Princeton: Princeton University Press
Harré, R. & van Langenhove, L. (1999). Introducing Positioning Theory. In R. Harré & L. van Langenhove (Eds.), Positioning Theory (pp. 14–31). Oxford: Blackwell
Johansson, B., Marton, F. & Svensson, L. (1985). An Approach to Describing Learning as Change Between Qualitatively Different Conceptions. In L. West & A. Pines (Eds.), Cognitive Structure and Conceptual Change (pp. 233–257). New York: Academic
King, A. (1993). From Sage on the Stage to Guide on the Side. College Teaching, 41(1), 30–35
Krutetskii, V.A. (1976). J. Teller, Trans.) In Kilpatrick, J. & Wirszup, I. (Eds.), The Psychology of Mathematical Abilities in School Children. Chicago: University of Chicago Press
Laborde, C. (1995). Designing Tasks for Learning Geometry in a Computer Environment. In L. Burton & B. Jaworski (Eds.), Technology in Mathematics Teaching: A Bridge Between Teaching and Learning(pp. 35–67). London: Chartwell-Bratt
Lakatos, I. (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge: Cambridge University Press
Lave, J. & Wenger, E. (1991). Situated Learning: Legitimate Peripheral Participation. Cambridge: Cambridge University Press
Legrand, M. (1990). Débat scientifique en cours de mathématiques. Repères-IREM, 10, 123–158
Legrand, M. (1998/2000). Scientific Debate in Mathematics Course. La Lettre de la Preuve Novembre/Décembre 2000 on-line text. Retrieved May 2008 Http://europa.eu.int/comm/ research/conferences/2004/univ/pdf/univ_sciencediss_mathematics_290704_en.pdf
Lin, J. (2004). A Chinese Cultural Model of Learning. In F. Lianghuo, N.-Y. Wong, J. Cai & S. Li. (Eds.), How Chinese Learn Mathematics: Perspectives from Insiders (pp. 124–156). Singapore: World Scientific
Love, E. & Mason, J. (1992). Teaching Mathematics: Action and Awareness. Milton Keynes: Open University
MacHale, D. (1980). The Predictability of Counterexamples. American Mathematical Monthly, 87, 752
Marton, F. & Booth, S. (1997). Learning and Awareness. Hillsdale, USA: Lawrence Erlbaum
Marton, F. & Trigwell, K. (2000). ‘Variatio est Mater Studiorum’.Higher Education Research and Development, 19(3), 381–395
Mason, J. (2002a). Mathematics Teaching Practice: A Guide for University and College Lecturers. Chichester: Horwood Publishing
Mason, J. (2002b). Researching Your Own Practice: The Discipline of Noticing. London: RoutledgeFalmer
Mason, J. (2003). On the Structure of Attention in the Learning of Mathematics. AAMT, 59(4), 17–25
Mason, J. (2004). Doing ≠Construing and Doing + Discussing ≠ Learning: The importance of the structure of attention. Regular Lecture at the 10th International Congress on Mathematics Education. Copenhagen, July 2004
Mason, J. (2007). Making Use of Children's Powers to Produce Algebraic Thinking. In D. Carraher, J. Kaput & M. Blanton (Eds.), Algebra in the early grades. Hillsdale: Erlbaum
Mason, J., Burton, L. & Stacey, K. (1982). Thinking Mathematically. London: Addison Wesley
Mason, J. & Johnston-Wilder, S. (2004). Fundamental Constructs in Mathematics education. London: RoutledgeFalmer
Mason, J. & Johnston-Wilder, S. (2004/2006). Designing and Using Mathematical tasks. Milton Keynes: Open University, republished (2006). St. Albans: Tarquin
Mason, J. & Watson, A. (2001). Stimulating Students to Construct Boundary Examples, Quaestiones Mathematicae, 24 (Suppl 1), 123–132
Montessori, M. (1912 reprinted 1964). (George, A. Trans.) The Montessori Method. New York: Schocken Books
Norretranders, T. (1998). (J. Sydenham, Trans.). The User Illusion: Cutting Consciousness Down to Size. London: Allen Lane
Noss, R. & Hoyles, C. (1996). Windows on Mathematical Meanings: Learning Cultures and Computers. Dordrecht: Kluwer
Piaget, J. (1971). Biology and Knowledge. Chicago: University of Chicago Press
Pólya, G. (1962). Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving. New York: Wiley
Popper, K. (1972). Objective Knowledge: An Evolutionary Approach. Oxford: Oxford University Press
Renkl, A., Stark, R., Gruber, H. & Mandl, H. (1998). Learning from Worked-out Examples: The Effects of Example Variability and Elicited Self-explanations. Contemporary Educational Psychology, 23, 90–108
Rissland, E.L. (1991). Example-based Reasoning. In J.F. Voss, D.N. Parkins & J.W. Segal (Eds.), Informal Reasoning in Education (pp. 187–208). Hillsdale, NJ: Lawrence Erlbaum
Rowland, T. (2001). Generic Proofs in Number Theory. In S. Campbell & R. Zazkis (Eds.), Learning and Teaching Number Theory: Research in Cognition and Instruction (pp. 157–184). Westport, CT: Ablex
Salomon, G. (1979). Interaction of Media, Cognition and Learning. London: Jossey-Bass
Spencer, H. (1878). Education: Intellectual, Moral, and Physical. London: Williams and Norgate
Sweller, J. & Cooper, G.A. (1985). The Use of Worked Examples as a Substitute for Problem Solving in Learning Algebra. Cognition and Instruction, 2, 59–85
Thompson, P. (2002). Didactic Objects and Didactic Models in Radical Constructivism. In K. Gravemeijer, R. Lehrer, B. van Oers & L. Verschaffel (Eds.), Symbolizing, Modeling and Tool Use in Mathematics Education (pp. 191–212). Dordrecht: Kluwer
van Hiele, P. (1986). Structure and Insight: A Theory of Mathematics Education. London: Academic Press
Walker, J. (1975). The Flying Circus of Physics with Answers. New York: Wiley
Warfield, V. (2005). (accessed June 05). Calculus by Scientific Debate as an Application of didac-tique. On line document. Retrieved May 2008. Http://www.math.washington.edu/warfield/ articles/Calc&Didactique.html
Watson, A. & Mason, J. (2005). Mathematics as a Constructive Activity: The Role of Learner-Generated Examples. Mahwah: Erlbaum
Wertheimer, M. (1945). Productive Thinking. New York: Harper
Whitehead, A. (1932). The Aims of Education and Other Essays. London: Williams and Norgate
Winston, P. (1975). Learning Structural Descriptions from Examples. In P. Winston (Ed.), The Psychology of Computer Vision (pp. 157–210). New York: McGraw-Hill
Wood, D., Bruner, J. & Ross, G. (1976). The Role of Tutoring in Problem Solving. Journal of Child Psychology, 17, 89–100
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Mason, J. (2009). From Assenting to Asserting. In: Skovsmose, O., Valero, P., Christensen, O.R. (eds) University Science and Mathematics Education in Transition. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09829-6_2
Download citation
DOI: https://doi.org/10.1007/978-0-387-09829-6_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-09828-9
Online ISBN: 978-0-387-09829-6
eBook Packages: Humanities, Social Sciences and LawEducation (R0)