Skip to main content

Theory and Practice in Mathematics Teaching Development: Critical Inquiry as a Mode of Learning in Teaching

Journal of Mathematics Teacher Education volume 9, pages 187–211 (2006)Cite this article

Abstract

In this paper I address the challenge of developing theory in relation to the practices of mathematics teaching and its development. I do this by exploring a notion of ‘teaching as learning in practice’ through overt use of ‘inquiry’ in mathematics learning, mathematics teaching and the development of practices of teaching in communities involving teachers and educators. The roles and goals of mathematics teachers and educators in such communities are both distinct and deeply intertwined. I see an aim of inquiry in teaching to be the ‘critical alignment’ (Wenger, 1998) of teaching within the communities in which teaching takes place. Inquiry ‘as a tool’ and inquiry ‘as a way of being’ are important concepts in reflexive developmental processes in which inquiry practice leads to better understandings and development of theory.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

References

  • InstitutionalAuthorNameAssociation of Teachers of Mathematics (1987) Teacher is/as researcher ATM Derby

    Google Scholar 

  • C. S. Banwell K. D. Saunders D. S. Tahta (1972) Starting points Oxford University Press Oxford

    Google Scholar 

  • M. Bassey (1995) Creating education through research British Educational Research Association Edinburgh

    Google Scholar 

  • M. G. Bartolini-Bussi (1994) Theoretical and empirical approaches to classroom interaction R. Biehler R. W. Scholtz R. Strässer B. Winkelmann (Eds) The didactics of mathematics as a scientific discipline Kluwer Dordrecht 121–132

    Google Scholar 

  • H. Bauersfeld (1995) The structuring of the structures: development and function of mathematizing as a social practice L. P. Steffe J. Gale (Eds) Constructivism in education Lawrence Erlbaum Associates Hillslade, NJ

    Google Scholar 

  • H. Bauersfeld (1988) Interaction, construction, and knowledge: Alternative perspectives for mathematics education D. A. Grouws T. J. Cooney (Eds) Perspectives on research on effective mathematics teaching National Council of Teachers of Mathematics Reston, VA

    Google Scholar 

  • M. S. Britt K. C. Irwin J. Ellis G. Ritchie (1993) Teachers raising achievement in mathematics: Final report to the Ministry of Education Centre for Mathematics Education, Auckland College of Education Auckland, NZ

    Google Scholar 

  • L. Brown A. Coles (2000) Complex decision making in the classroom: The teacher as intuitive practitioner T. Atkinson G. Claxton (Eds) The intuitive practitioner Open University Press Buckingham 165–181

    Google Scholar 

  • S. Brown R. Carter J. Richards (1999) Dilemmas of constructivist mathematics teaching: Instances from classroom practice B. Jaworski T. Wood S. Dawson (Eds) Mathematics teacher education: Critical international perspectives Falmer Press London

    Google Scholar 

  • T. Carpenter E. Fennema P. Peterson D. Carey (1988) ArticleTitleTeachers’ pedagogical content knowledge of students’ problem-solving in elementary arithmetic Journal for Research in Mathematics Education 19 385–401 Occurrence Handle10.2307/749173

    Article  Google Scholar 

  • Cestari, M. L., Daland, E., Eriksen, S., & Jaworski, B. (2005, Feb.) Working in a developmental research paradigm: The role of didactician/researcher working with teachers to promote inquiry practices in developing mathematics learning and teaching. Paper presented at CERME4 Working Group 11, European Society for Research in Mathematics Education, Sant Feliu, Spain.

  • S. Chaiklin (1993) Understanding the social scientific practice of understanding practice S. Chaiklin J. Lave (Eds) Understanding practice: Perspectives on activity and context Cambridge University Press Cambridge

    Google Scholar 

  • Clare, J. (2004) Ministers and unruly pupils ‘causing collapse of schools’. The Daily Telegraph, Thursday, May 27th, 2004.

  • P. Cobb (1996) Where is the mind? A coordination of sociocultural and cognitive constructivist perspectives C. Twomey Fosnot (Eds) Constructivism: Theory, perspectives, and practice Teachers College Press NY

    Google Scholar 

  • P. Cobb J. Bowers (1999) ArticleTitleCognitive and situated learning perspectives in theory and practice Educational Researcher 28 IssueID2 4–15 Occurrence Handle10.2307/1177185

    Article  Google Scholar 

  • P. Cobb J. Confrey A. diSessa R. Lehrer L. Schauble (2003) ArticleTitleDesign experiments in educational research Educational Researcher 32 IssueID1 9–13

    Google Scholar 

  • Cobb, P., Wood, T., & Yackel, E. (1990). ‘Classrooms as learning environments for teachers and researchers.’ In R. Davis, C. Maher & N. Noddings (Eds.), Constructivist views on the teaching and learning of mathematics: Journal for Research in Mathematics Education, Monograph No. 4 (pp. 125–146). Reston, VA: National Council of Teachers of Mathematics.

  • M. Cochran Smith S. L. Lytle (1999) Relationships of knowledge and practice: Teacher learning in communities A. Iran-Nejad P. D. Pearson (Eds) Review of research in education American Educational Research Association Washington 249–305

    Google Scholar 

  • A. Collins (1988) ArticleTitleDifferent goals of inquiry teaching Questioning Exchange 2 IssueID1 39–45

    Google Scholar 

  • J. Confrey (1995) How compatible are radical constructivism, sociocultural approaches, and social constructivism? L. P. Steffe J. Gale (Eds) Constructivism in education Lawrence Erlbaum Associates Hillslade, NJ

    Google Scholar 

  • T. Cooney (1994) Teacher education as an exercise in adaptation D. B. Aichele A. F. Coxford (Eds) Professional development for teachers of mathematics: 1994 Yearbook National Council of Teacher of Mathematics Reston, VA

    Google Scholar 

  • Davis, R. B., Maher, C. A., & Noddings, N. (Eds.), (1990). Constructivist Views on the Learning and Teaching of Mathematics. Journal for Research in Mathematics Education, Monograph Number 4. Reston, Virginia: National Council of Teachers of Mathematics.

  • InstitutionalAuthorNameDES (Department of Education and Science) (1982) Mathematics Counts: Report of the committee of inquiry into the teaching of mathematics in schools under the chairmanship of W. H. Cockcroft HMSO London

    Google Scholar 

  • C. Desforges A. Cockburn (1987) Understanding the mathematics teacher Falmer Press Lewes

    Google Scholar 

  • J. Dewey (1902/1956/1990) The school and society and the child and the curriculum The University of Chicago Press London

    Google Scholar 

  • J. Dewey (1938) Education and experience Collier Macmillan New York

    Google Scholar 

  • J. Elliott (1991) Action research for educational change Open University Press Milton Keynes

    Google Scholar 

  • J. Elliott C. Adelman (1975) The language and logic of informal teaching. The Ford Teaching Project, Unit 1, Patterns of Teaching University of East Anglia Norwich

    Google Scholar 

  • P. Ernest (1991) The philosophy of mathematics education Falmer Press London

    Google Scholar 

  • J. D. Farmer H. Gerretson M. Lassak (2003) ArticleTitleWhat teachers take from professional development: Cases and implications Journal of Mathematics Teacher Education 6 IssueID4 331–360 Occurrence Handle10.1023/A:1026318709074

    Article  Google Scholar 

  • H. Freudental (1978) Weeding and sowing D. Reidel Dordrecht

    Google Scholar 

  • E. Glasersfeld Particlevon (1984) An introduction to radical constructivism P. Watzlavik (Eds) The invented reality W. W. Naughton & Co London

    Google Scholar 

  • E. Glasersfeld von (1987) Learning as a constructive activity C. Janvier (Eds) Problems of representation in the teaching and learning of mathematics Erlbaum Hillslade, NJ

    Google Scholar 

  • R. M. Heaton W. T. Mickelson (2002) ArticleTitleThe learning and teaching of statistical investigation in teaching and teacher education Journal of Mathematics Teacher Education 5 IssueID1 35–59 Occurrence Handle10.1023/A:1013886730487

    Article  Google Scholar 

  • B. Jaworski (1994) Investigating mathematics teaching: A constructivist enquiry Falmer Press London

    Google Scholar 

  • Jaworski, B. (1995). The critical nature of teaching decisions. Mathematics Teaching, 150.

  • B. Jaworski (1998) ArticleTitleMathematics teacher research: Process practice and the development of teaching Journal of Mathematics Teacher Education 1 IssueID1 3–31 Occurrence Handle10.1023/A:1009903013682

    Article  Google Scholar 

  • B. Jaworski (2001) Developing mathematics teaching: Teachers, teacher-educators, and researchers as co-learners F.-L. Lin T. J. Cooney (Eds) Making sense of mathematics teacher education Kluwer Dordrecht, The Netherlands 295–320

    Google Scholar 

  • Jaworski, B. (2004). Grappling with complexity: Co-learning in inquiry communities in mathematics teaching development. Proceedings of the 28th PME Conference. Bergen, Norway: Bergen University College

  • B. Jaworski T. Wood S. Dawson (1999) Mathematics teacher education: Critical international perspectives Falmer Press London

    Google Scholar 

  • C. Kieran E. Forman A. Sfard (2001) ArticleTitleBridging the individual and the social: Discursive approaches to research in mathematics education. A PME Special Issue Educational Studies in Mathematics 46 1–3 Occurrence Handle10.1023/A:1014276102421

    Article  Google Scholar 

  • Krainer, K. (1993). Understanding students’ understanding: On the importance of co-operation between teachers and researchers. In P. Boero (Ed.), Proceedings of the 3rd Bratislava International Symposium on Mathematical Teacher Education. Bratislava: Comenius University

  • Krainer, K., Goffree, F., & Berger, P. (Eds.) (1999). European research in mathematics education, I.III: On research in mathematics teacher education. Proceedings of the first conference of the european society in mathematics education, vol III. Osnabrück

  • M. Lampert (1998) ArticleTitleWhat can research on teacher education tell us about improving quality in mathematics education? Teaching and Teacher Education 4 IssueID2 157–170 Occurrence Handle10.1016/0742-051X(88)90015-7

    Article  Google Scholar 

  • J. Lave (1996) ArticleTitleTeaching as learning, in practice Mind Culture and Activity 3 IssueID3 149–164 Occurrence Handle10.1207/s15327884mca0303_2

    Article  Google Scholar 

  • J. Lave E. Wenger (1991) Situated learning: Legitimate peripheral participation Cambridge University Press Cambridge, MA

    Google Scholar 

  • S. Lerman (1996) ArticleTitleIntersubjectivity in mathematics learning: A challenge to the radical constructivist paradigm? Journal for Research in Mathematics Education 27 IssueID2 133–150 Occurrence Handle10.2307/749597

    Article  Google Scholar 

  • S. Lerman (2000) ArticleTitleSome problems of socio-cultural research in mathematics teaching and learning Nordisk Matematic Didaktic (NOMAD) 8 IssueID3 55–72

    Google Scholar 

  • S. Lerman (2001) ArticleTitleCultural and discursive psychology: A sociocultural approach to studying the teaching and learning of mathematics Educational Studies in Mathematics 46 87–113 Occurrence Handle10.1023/A:1014031004832

    Article  Google Scholar 

  • F.-L. Lin T. Cooney (2001) Making sense of mathematics teacher education Kluwer The Netherlands

    Google Scholar 

  • J. Mason L. Burton K. Stacey (1982) Thinking mathematically Addison-Wesley London

    Google Scholar 

  • InstitutionalAuthorNameMathematical Association (1991) Develop your teaching Stanley Thornes Cheltenham, UK

    Google Scholar 

  • A. R. McDuffie (2004) ArticleTitleMathematics teaching as a deliberate practice: An investigation of elementary pre-service teachers’ reflective thinking during student teaching Journal of Mathematics Teacher Education 7 IssueID1 33–61 Occurrence Handle10.1023/B:JMTE.0000009970.12529.f4

    Article  Google Scholar 

  • J. McNiff (1988) Action research: Principles and practice Macmillan London

    Google Scholar 

  • Nardi, E. (1996). The Novice mathematician’s encounter with mathematical abstraction: Tensions in concept-image construction and formulisation. Unpublished D. Phil. Thesis. Oxford: University of Oxford

  • G. Polya (1945) How to solve it Princeton University Press New Jersey

    Google Scholar 

  • J. P. Ponte da (2001) Investigating mathematics and learning to teach mathematics F.-L. Lin T. J. Cooney (Eds) Making sense of mathematics teacher education Kluwer Academic Publishers The Netherlands

    Google Scholar 

  • D. Potari B. Jaworski (2002) ArticleTitleTackling complexity in mathematics teaaching development: Using the teaching triad as a tool for reflection and analysis Journal of Mathematics Teacher Education 5 IssueID4 351–380 Occurrence Handle10.1023/A:1021214604230

    Article  Google Scholar 

  • B. Rogoff (1994) ArticleTitleDeveloping understanding of the idea of communities of learners Mind, Culture and Activity 1 IssueID4 209–229

    Google Scholar 

  • K. Ruthven (2001) Mathematics teacher education and educational research: Developing “practical theorising” in initial teacher education F. L. Lin T. Cooney (Eds) Making sense of mathematics teacher education Kluwer The Netherlands 165–183

    Google Scholar 

  • A. H. Schoenfeld (1985) Mathematical problem solving Academic Press New York

    Google Scholar 

  • R. Skemp (1976) ArticleTitleRelational understanding and instrumental understanding Mathematics Teaching 77 20–26

    Google Scholar 

  • L. P. Steffe P. W. Thompson (2000) ArticleTitleInteraction or intersubjectivity? A reply to Lerman Journal for Research in Mathematics Education 31 IssueID2 191–209 Occurrence Handle10.2307/749751

    Article  Google Scholar 

  • L. Stenhouse (1984) Evaluating curriculum evaluation C. Adelman (Eds) The politics and ethics of evaluation Croom Helm London

    Google Scholar 

  • L. S. Vygotsky (1978) Mind in Society. The development of the higher psychological processes Harvard University Press London

    Google Scholar 

  • J. Wagner (1997) ArticleTitleThe unavoidable intervention of educational research: A framework for reconsidering research-practitioner cooperation Educational Researcher 26 IssueID7 13–22 Occurrence Handle10.2307/1177125

    Article  Google Scholar 

  • G. Wells (1999) Dialogic inquiry: Towards a sociocultural practice and theory of education Cambridge University Press Cambridge

    Google Scholar 

  • E. Wenger (1998) Communities of practice: Learning, meaning and identity Cambridge University Press Cambridge

    Google Scholar 

  • T. Wood (1999) Approaching teacher development: Practice into theory B. Jaworski T. Wood S. Dawson (Eds) Mathematics teacher education: Critical international perspectives Falmer Press London 163–179

    Google Scholar 

  • T. Wood B. Scott Nelson J. Warfield (2001) Beyond classical pedagogy: Teaching elementary school mathematics Lawrence Erlbaum Mahwah, NJ

    Google Scholar 

  • Zack, V., Mousley, J., & Breen, C. (Eds.), (1997). Developing practice: Teachers’ inquiry and educational change in classrooms. Geelong, Australia: Centre for Studies in Mathematics, Science and Environmental Education, Deakin University.

Download references

Author information

Authors and Affiliations

  1. Agder University College, Serviceboks 422, 4604, Kristiansand, Norway

    Barbara Jaworski

Authors
  1. Barbara Jaworski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Barbara Jaworski.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Jaworski, B. Theory and Practice in Mathematics Teaching Development: Critical Inquiry as a Mode of Learning in Teaching. J Math Teacher Educ 9, 187–211 (2006). https://doi.org/10.1007/s10857-005-1223-z

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10857-005-1223-z

Keywords

  • Teacher Education
  • Mathematics Teacher
  • Mathematics Learning
  • Teaching Development
  • Critical Awareness