Educational Studies in Mathematics

, Volume 51, Issue 1–2, pp 71–94 | Cite as

Sensitivity and Challenge in University Mathematics Tutorial Teaching

  • Barbara Jaworski


Data from observations of first year university mathematics tutorials were analyzed to elicit characteristics of teaching using a tool, the teaching triad, developed in earlier research. Analysis explored elements of `sensitivity to students' and `mathematical challenge' in the observed teaching. Initial analyses suggested teaching to consist mainly of tutor exposition and closed questions embodying little challenge for the student. More finely grained analyses provided insights into pedagogic processes relating teaching actions, processes and strategies and their learning outcomes, and providing alternative perspectives on sensitivity and challenge. The research, distinctively, shows approaches to analyzing teaching that start to address tutor-student interactions related to cognitive construction of mathematics (here abstract algebra) by undergraduates within the social dimensions of the tutorial setting.


Mathematics Teacher Mathematical Thinking Educational Study Concept Image Abstract Algebra 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bauersfeld, H.: 1988, ‘Interaction, construction and knowledge: Alternative perspectives for mathematics education,’ in Grouws, D.A. and Cooney, T.J. (eds.), Perspectives on Research on Effective Mathematics Teaching, National Council of Teachers of Mathematics, Reston, Va.Google Scholar
  2. Burn, R.P.: 1998, Participating in the Learning of Group Theory, Primus, Volume VIII number 4.Google Scholar
  3. Dubinsky, E., Dautermann, J., Leron, U. and Zazkis, R.: 1994, ‘On learning fundamental concepts of group theory,’ Educational Studies in Mathematics 27, 267–305.CrossRefGoogle Scholar
  4. Dubinsky, E.: 2000, Towards a Theory of Learning Advanced Mathematical Concepts, Paper presented at ICME9, the 9th International Congress on Mathematical Education, Tokyo.Google Scholar
  5. Even, R. and Tirosh, D.: 1995, ‘Subject-matter knowledge and knowledge about students as sources of teacher presentations of the subject matter,’ Educational Studies in Mathematics 29(1), 1–20.CrossRefGoogle Scholar
  6. Even, R. and Tirosh, D.: 2002, ‘Teacher knowledge and understanding of students’ mathematical learning,’ in English, L. (ed.), Handbook of International Research in Mathematics Education, Laurence Erlbaum, Mahwah, NJ, pp. 219–240.Google Scholar
  7. Glasersfeld, E. von: 1987, ‘Learning as a constructive activity,’ in Janvier, C. (ed.), Problems of Representation in the Teaching and Learning of Mathematics, Erlbaum, Hillslade, NJ.Google Scholar
  8. Jaworski, B.: 1994, Investigating Mathematics Teaching: A Constructivist Enquiry, Falmer, London.Google Scholar
  9. Jaworski, B.: 2001, ‘University mathematics teaching: Where is the challenge?,’ in Van den Heuvel-Panhuizen, (ed.), Proceedings of the 25th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3 pp. 193–200.Google Scholar
  10. Jaworski, B., Nardi, N. and Hegedus, S.: 1999, Characterizing Mathematics Teaching - A Collaboration between Educators and Mathematicians: A Methodological Perspective, Paper presented at the British Educational Research Association Conference, Brighton, September.Google Scholar
  11. Kieran, C., Forman, E. and Sfard, A.: 2001, ‘Bridging the individual and the social: Discursive approaches to research in mathematics education. A PME special issue,’ Educational Studies in Mathematics 46.Google Scholar
  12. Ledermann, W.: 1961, Introduction to the Theory of Finite Groups, Oliver and Boyd, London.Google Scholar
  13. Lerman, S.: 2001, ‘Cultural and discursive psychology: A sociocultural approach to studying the teaching and learning of mathematics,’ Educational Studies in Mathematics 46, 87–113.CrossRefGoogle Scholar
  14. Moore, W.G.: 1968, The Tutorial System and its Future, Pergamon Press, Oxford.Google Scholar
  15. Nardi, E.: 1996, The Novice Mathematician's Encounter with Mathematical Abstraction: Tensions in Concept-Image Construction and Formalization, University of Oxford: Doctoral thesis.Google Scholar
  16. Nardi, E.: 2001, ‘Mathematics undergraduates’ responses to semantic abbreviations, ‘geometric’ images and multi-level abstractions in group theory,’ Educational Studies in Mathematics 43, 169–189.CrossRefGoogle Scholar
  17. Palfreyman, D.: 2001, ‘The Oxford tutorial: Sacred cow or pedagogical gem?,’ in D. Palfreyman (ed.) The Oxford Tutorial: ‘Thanks, you taught me how to think', Oxford Centre for Higher Education Policy Studies, New College, Oxford.Google Scholar
  18. Pearson, T.A.: 1989, The Teacher: Theory and Practice in Teacher Education, Routledge, London.Google Scholar
  19. Pimm, D.: 1987, Speaking Mathematically, Routledge, London.Google Scholar
  20. Potari, D. and Jaworski, B.: 2002, ‘Tackling the complexity of mathematics teaching: Using the Teaching Triad as a Tool for Reflection and Analysis,’ Journal of Mathematics Teacher Education 5(4), 349–378.CrossRefGoogle Scholar
  21. Sfard, A.: 1994, ‘Reification as the birth of metaphor,’ For the Learning of Mathematics 14(1), 44–55.Google Scholar
  22. Shulman, L.S.: 1987, ‘Knowledge and teaching: Foundations of the new reform,’ Harvard Educational Review 57(1), 1–22.Google Scholar
  23. Sierpinska, A.: 1994, Understanding in Mathematics, Falmer Press, London.Google Scholar
  24. Simon, M.: 1995, ‘Reconstructing mathematics pedagogy from a constructivist perspective,’ Journal for Research in Mathematics Education 26(2), 114–145.CrossRefGoogle Scholar
  25. Sinclair, McH. and Coulthard, R.M.: 1975, Towards an Analysis of Discourse: The English used by Teachers and Pupils, Oxford University Press, London.Google Scholar
  26. Skott, J.: 2001, ‘The emerging practice of a novice teacher: The roles of his school mathematics images, Journal of Mathematics Teacher Education 4(1): 3–28.CrossRefGoogle Scholar
  27. Steffe, L.P. and Thompson, P.W.: 2000, ‘Interaction or intersubjectivity? A reply to Lerman,’ Journal for Research in Mathematics Education 31(2), 191–209.CrossRefGoogle Scholar
  28. Steinbring, H.: 1998, ‘Elements of epistemological knowledge for mathematics teachers,’ Journal of Mathematics Teacher Education 1(2), 157–189.CrossRefGoogle Scholar
  29. Tall, D.: 1991, Advanced Mathematical Thinking, Kluwer Academic Publishers, Dordrecht / Boston / London, England.Google Scholar
  30. Tall, D.O. and Vinner, S.: 1981, ‘Concept images and definition in mathematics with special reference to limits and continuity’, Educational Studies in Mathematics 12, 151–169.CrossRefGoogle Scholar
  31. Wenger, E.: 1998, Communities of Practice: Learning, Meaning and Identity, Cambridge University Press, Cambridge.Google Scholar
  32. Williams, S.R. and Baxter, J.: 1996, ‘Dilemmas of discourse-oriented teaching in one middle school mathematics classroom,’ The Elementary School Journal 97(1), 21–38.CrossRefGoogle Scholar
  33. Zaslavsky, O. and Leikin, R.: 1999, ‘Interweaving the training of mathematics teachereducators and the professional development of mathematics teachers,’ in Zaslavsky, O. (ed.) Proceedings of the 23rd Conference of the International Group for the Psychology of Mathematics Education, Israel Institute of Technology, Haifa, Israel.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Barbara Jaworski
    • 1
  1. 1.Dept. of Educational StudiesUniversity of OxfordOxfordUnited Kingdom

Personalised recommendations