# Sensitivity and Challenge in University Mathematics Tutorial Teaching

- 290 Downloads
- 16 Citations

## Abstract

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.

## Keywords

Mathematics Teacher Mathematical Thinking Educational Study Concept Image Abstract Algebra## Preview

Unable to display preview. Download preview PDF.

## REFERENCES

- 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 - Burn, R.P.: 1998,
*Participating in the Learning of Group Theory*,*Primus*, Volume VIII number 4.Google Scholar - 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 - 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 - 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 - 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 - 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 - Jaworski, B.: 1994,
*Investigating Mathematics Teaching: A Constructivist Enquiry*, Falmer, London.Google Scholar - 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 - 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 - 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 - Ledermann, W.: 1961,
*Introduction to the Theory of Finite Groups*, Oliver and Boyd, London.Google Scholar - 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 - Moore, W.G.: 1968,
*The Tutorial System and its Future*, Pergamon Press, Oxford.Google Scholar - 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 - 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 - 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 - Pearson, T.A.: 1989,
*The Teacher: Theory and Practice in Teacher Education*, Routledge, London.Google Scholar - Pimm, D.: 1987,
*Speaking Mathematically*, Routledge, London.Google Scholar - 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 - Sfard, A.: 1994, ‘Reification as the birth of metaphor,’
*For the Learning of Mathematics*14(1), 44–55.Google Scholar - Shulman, L.S.: 1987, ‘Knowledge and teaching: Foundations of the new reform,’
*Harvard Educational Review*57(1), 1–22.Google Scholar - Sierpinska, A.: 1994,
*Understanding in Mathematics*, Falmer Press, London.Google Scholar - Simon, M.: 1995, ‘Reconstructing mathematics pedagogy from a constructivist perspective,’
*Journal for Research in Mathematics Education*26(2), 114–145.CrossRefGoogle Scholar - 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 - 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 - 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 - Steinbring, H.: 1998, ‘Elements of epistemological knowledge for mathematics teachers,’
*Journal of Mathematics Teacher Education*1(2), 157–189.CrossRefGoogle Scholar - Tall, D.: 1991,
*Advanced Mathematical Thinking*, Kluwer Academic Publishers, Dordrecht / Boston / London, England.Google Scholar - 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 - Wenger, E.: 1998,
*Communities of Practice: Learning, Meaning and Identity*, Cambridge University Press, Cambridge.Google Scholar - 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 - 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