Advertisement

Interactions Between Teacher, Student, Software and Mathematics: Getting a Purchase on Learning with Technology

  • John Mason
  • John Mason
Chapter
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 2)

Abstract

In this chapter three examples of teacher-guided use of ICT stimuli for learning mathematics (screencast, animation and applet) are critically examined using a range of distinctions derived from a complex framework. Six modes of interaction between teacher, student and mathematics are used to distinguish different affordances and constraints; five different structured forms of attention are used to refine the grain size of analysis; four aspects of activity are used to highlight the importance of balance between resources and motivation; and the triadic structure of the human psyche (cognition, affect and enaction, or intellect, emotion and behaviour) is used to shed light on how affordances may or may not be manifested, and on how constraints may or may not be effective, depending on the attunements of teachers and students. The conclusion is that what matters is the way of working within an established milieu. The same stimulus can be used in multiple modes according to the teacher’s awareness and aims, the classroom ethos and according to the students’ commitment to learning/thinking. The analytic frameworks used can provide teachers with structured ways of informing their choices of pedagogic strategies.

Keywords

Interaction Teacher-guided Ways of working e-screensScreencast Animation Activity 

References

  1. Ainley, J., & Pratt, D. (2002). Purpose and utility in pedagogic task design. In A. Cockburn & E. Nardi (Eds.), Proceedings of the 26th annual conference of the international group for the psychology of mathematics education Vol. 2 (pp. 17–24). Norwich: PME.Google Scholar
  2. Ascari, M. (2011). Networking different theoretical lenses to analyze students’ reasoning and teacher’s actions in the mathematics classroom. Unpublished Ph.D. Thesis, Universita’ Degli Studi Di Torino.Google Scholar
  3. Atkinson, R., Derry, S., Renkl, A., & Wortham, D. (2000). Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70(2), 181–214.CrossRefGoogle Scholar
  4. Baird, J., & Northfield, F. (1992). Learning from the peel experience. Melbourne: Monash University.Google Scholar
  5. Bennett, J. (1966). The dramatic universe (Vol. 4). London: Routledge.Google Scholar
  6. Bennett, J. (1993). Elementary systematics: A tool for understanding wholes. Santa Fe: Bennett Books.Google Scholar
  7. Brousseau, G. (1997). Theory of Didactical Situations in Mathematics: didactiques des mathématiques (1970–1990). (trans: Balacheff N., Cooper M., Sutherland R., Warfield V.). Dordrecht: Kluwer.Google Scholar
  8. Brown, S., Collins, A., & Duguid, P. (1989). Situated cognition and the culture of learning. Educational Researcher, 18(1), 32–41.CrossRefGoogle Scholar
  9. Bruner, J. (1966). Towards a theory of instruction. Cambridge: Harvard University Press.Google Scholar
  10. Bruner, J. (1990). Acts of meaning. Cambridge: Harvard University Press.Google Scholar
  11. Claxton, G. (1984). Live and learn: An introduction to the psychology of growth and change in everyday life. London: Harper and Row.Google Scholar
  12. Davis, B. (1996). Teaching mathematics: Towards a sound alternative. New York: Ablex.Google Scholar
  13. Davis, B., & Simmt, E. (2006). Mathematics-for-teaching: An ongoing investigation of the mathematics that teachers (need) to know. Educational Studies in Mathematics, 61(3), 293–319.CrossRefGoogle Scholar
  14. Dawes, L., Mercer, N., & Wegerif, R. (2004). Thinking together: A programme of activities for developing speaking, listening and thinking skills (2nd ed.). Birmingham: Imaginative Minds Ltd.Google Scholar
  15. Festinger, L. (1957). A theory of cognitive dissonance. Stanford: Stanford University Press.Google Scholar
  16. Gardiner, A. (1992). Recurring themes in school mathematics: Part 1 direct and inverse operations. Mathematics in School, 21(5), 5–7.Google Scholar
  17. Gardiner, A. (1993a). Recurring themes in school mathematics: Part 2 reasons and reasoning. Mathematics in School, 23(1), 20–21.Google Scholar
  18. Gardiner, A. (1993b). Recurring themes in school mathematics: Part 3 generalised arithmetic. Mathematics in School, 22(2), 20–21.Google Scholar
  19. Gardiner, A. (1993c). Recurring themes in school mathematics, part 4 infinity. Mathematics in School, 22(4), 19–21.Google Scholar
  20. Gattegno, C. (1970). What we owe children: The subordination of teaching to learning. London: Routledge & Kegan Paul.Google Scholar
  21. Gattegno, C. (1987). The science of education part I: Theoretical considerations. New York: Educational Solutions.Google Scholar
  22. Gibson, J. (1979). The ecological approach to visual perception. London: Houghton Mifflin.Google Scholar
  23. Habermas, J. (1998). In M. Cooke (Ed.), On the pragmatics of communication (pp. 307–342). Cambridge: The MIT Press.Google Scholar
  24. Handa, Y. (2011). What does understanding mathematics mean for teachers? Relationship as a metaphor for knowing (Studies in curriculum theory series). London: Routledge.Google Scholar
  25. Heidegger, M. (1962). Being and time. New York: Harper & Row.Google Scholar
  26. Hein, P. (1966). T.T.T. in Grooks. Copenhagen: Borgen.Google Scholar
  27. Hewitt, D. (1994). The principle of economy in the learning and teaching of mathematics, unpublished Ph.D. dissertation, Open University, Milton Keynes.Google Scholar
  28. Hewitt, D. (1996). Mathematical fluency: The nature of practice and the role of subordination. For the Learning of Mathematics, 16(2), 28–35.Google Scholar
  29. James, W. (1890 reprinted 1950). Principles of psychology (Vol. 1). New York: Dover.Google Scholar
  30. Jaworski, B. (1994). Investigating mathematics teaching: A constructivist enquiry. London: Falmer Press.Google Scholar
  31. Jordan, C., Loch, B., Lowe, T., Mestel, B., & Wilkins, C. (2011). Do short screencasts improve student learning of mathematics? MSOR Connections, 12(1), 11–14.CrossRefGoogle Scholar
  32. Kang, W., & Kilpatrick, J. (1992). Didactic transposition in mathematics textbooks. For the Learning of Mathematics., 12(1), 2–7.Google Scholar
  33. Leapfrogs. (1982). Geometric images. Derby: Association of Teachers of Mathematics.Google Scholar
  34. Marton, F., & Booth, S. (1997). Learning and awareness. Hillsdale: Lawrence Erlbaum.Google Scholar
  35. Marton, F., & Säljö, R. (1976). On qualitative differences in learning—1: Outcome and process. British Journal of Educational Psychology, 46, 4–11.CrossRefGoogle Scholar
  36. Marton, F., & Tsui, A. (Eds.). (2004). Classroom discourse and the space for learning. Marwah: Erlbaum.Google Scholar
  37. Mason, J. (1979). Which medium, Which message, Visual Education, February, 29–33.Google Scholar
  38. Mason, J. (1985). What do you do when you turn off the machine? Preparatory paper for ICMI conference: The influence of computers and informatics on mathematics and its teaching (pp. 251–256). Strasburg: Inst. de Recherche Sur L’Enseignement des Mathematiques.Google Scholar
  39. Mason, J. (1994a). Learning from experience. In D. Boud & J. Walker (Eds.), Using experience for learning. Buckingham: Open University Press.Google Scholar
  40. Mason, J. (1994b). Professional development and practitioner research. Chreods, 7, 3–12.Google Scholar
  41. Mason, J. (1998). Enabling teachers to be real teachers: Necessary levels of awareness and structure of attention. Journal of Mathematics Teacher Education, 1(3), 243–267.CrossRefGoogle Scholar
  42. Mason, J. (2003). Structure of attention in the learning of mathematics. In J. Novotná (Ed.), Proceedings, international symposium on elementary mathematics teaching (pp. 9–16). Prague: Charles University.Google Scholar
  43. Mason, J. (2004). A phenomenal approach to mathematics. Paper presented at Working Group 16, ICME, Copenhagen.Google Scholar
  44. Mason, J. (2007). Hyper-learning from hyper-teaching: What might the future hold for learning mathematics from & with electronic screens? Interactive Educational Multimedia 14, 19–39. (refereed e-journal) 14 (April). Accessed May 2007.Google Scholar
  45. Mason, J. (2008). Phenomenal mathematics. Plenary presentation. Proceedings of the 11th RUME Conference. San Diego.Google Scholar
  46. Mason, J. (2009). From assenting to asserting. In O. Skvovemose, P. Valero, & O. Christensen (Eds.), University science and mathematics education in transition (pp. 17–40). Berlin: Springer.CrossRefGoogle Scholar
  47. Mason, J., & Klymchuk, S. (2009). Counter examples in calculus. London: Imperial College Press.CrossRefGoogle Scholar
  48. Mason, J., & Watson, A. (2005). Mathematical Exercises: What is exercised, what is attended to, and how does the structure of the exercises influence these? Invited Presentation to SIG on Variation and Attention. Nicosia: EARLI.Google Scholar
  49. Mason, J., Burton, L., & Stacey, K. (1982/2010). Thinking mathematically (Second Extended Edition). Harlow: Prentice Hall (Pearson).Google Scholar
  50. Mason, J., Drury, H., & Bills, E. (2007). Explorations in the zone of proximal awareness. In J. Watson & K. Beswick (Eds.), Mathematics: Essential research, essential practice: Proceedings of the 30th annual conference of the Mathematics Education Research Group of Australasia Vol. 1 (pp. 42–58). Adelaide: MERGA.Google Scholar
  51. Norretranders, T. (1998). The user illusion: Cutting consciousness down to size (trans: Sydenham, J.). London: Allen Lane.Google Scholar
  52. O’Brien, T. (2006). What is fifth grade? Phi Beta Kappan, January, 373–376.Google Scholar
  53. Piaget, J. (1970). Genetic epistemology. New York: Norton.Google Scholar
  54. Piaget, J. (1971). Biology and knowledge. Chicago: University of Chicago Press.Google Scholar
  55. Poincaré, H. (1956 reprinted 1960). Mathematical creation: Lecture to the psychology society of Paris. In J. Newman (Ed.), The world of mathematics (pp. 2041–2050). London: George Allen & Unwin.Google Scholar
  56. Pólya, G. (1962) Mathematical discovery: On understanding, learning, and teaching problem solving (combined edition). New York: Wiley.Google Scholar
  57. Ravindra, R. (2009). The wisdom of Patañjali’s Yoga sutras. Sandpoint: Morning Light Press.Google Scholar
  58. Redmond, K. (2012). Professors without borders. Prospect, July, 42–46.Google Scholar
  59. Renkl, A. (1997). Learning from worked-out examples: A study on individual differences. Cognitive Science, 21, 1–29.CrossRefGoogle Scholar
  60. Renkl, A. (2002). Worked-out examples: Instructional explanations support learning by self-explanations. Learning and Instruction, 12, 529–556.CrossRefGoogle Scholar
  61. Rhadakrishnan, S. (1953). The principal Upanishads. London: George Allen & Unwin.Google Scholar
  62. Salomon, G. (1979). Interaction of media, cognition and learning. London: Jossey-Bass.Google Scholar
  63. Sangwin, C. (2005). On Building Polynomials. The Mathematical Gazette, November, 441–450. See http://web.mat.bham.ac.uk/C.J.Sangwin/Publications/BuildPoly.pdf
  64. Shah, I. (1978). Learning how to learn. London: Octagon.Google Scholar
  65. Shulman, L. (1986). Those who understand: Knowledge and growth in teaching. Educational Researcher, 15(2), 4–14.CrossRefGoogle Scholar
  66. Skinner, B. F. (1954). The science of learning and the art of teaching. Harvard Educational Review, 24(2), 86–97.Google Scholar
  67. Swift, J. (1726). In H. Davis (Ed.), Gulliver’s travels Vol. XI (p. 267). Oxford: Blackwell.Google Scholar
  68. Tahta, D. (1981). Some thoughts arising from the new Nicolet films. Mathematics Teaching, 94, 25–29.Google Scholar
  69. van der Veer, R., & Valsiner, J. (1991). Understanding Vygotsky. London: Blackwell.Google Scholar
  70. van Hiele, P. (1986). Structure and insight: A theory of mathematics education (Developmental psychology series). London: Academic Press.Google Scholar
  71. Varela, F., Thompson, E., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge: MIT Press.Google Scholar
  72. Watson, A., & Mason, J. (2005). Mathematics as a constructive activity: Learners generating examples. Mahwah: Erlbaum.Google Scholar
  73. Watson, A., & Mason, J. (2006). Seeing an exercise as a single mathematical object: Using variation to structure sense-making. Mathematical Thinking and Learning, 8(2), 91–111.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Open UniversityMilton KeynesUK
  2. 2.University of OxfordOxfordUK

Personalised recommendations