Skip to main content
Log in

Mathematics Teachers Acting as Informal Assessors: Practices, Problems and Recommendations

  • Published:
Educational Studies in Mathematics Aims and scope Submit manuscript

Abstract

The purpose of this paper is initially to present findings which identify components of the practices of teachers acting as assessors of students' mathematics in the normal course of classroom work. At an informal level such practice is found to be complex and intimately related to every aspect of teaching and learning. It is found that even teachers who have undergone some assessment training may underestimate the role of interpretation of evidence, and questions about equity in the uses of teachers' judgements are raised in relation to awareness and practice. It is suggested that more care needs to be taken over the formation and use of ‘professional judgements’ within systems of assessment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  • Askew, M., Brown, M., Johnson, D., Millett, A., Prestage, S. and Walsh, A.: 1993, Evaluation of the Implementation of National Curriculum Mathematics at Key Stages 1, 2 and 3, School Curriculum and Assessment Authority, London.

    Google Scholar 

  • Atkinson, P.: 1985, Language, Structure and Reproduction, Methuen, London.

    Google Scholar 

  • Bauersfeld, H.: 1988, 'Interaction, Construction and Knowledge: alternative perspectives for mathematics education', in D.A. Grouws and T.J. Cooney (eds.), Perspectives on Research on Effective Mathematics Teaching vol 1. Erlbaum, New Jersey.

    Google Scholar 

  • Bernstein, B.: 1971, Class, Codes and Control, vol 1 RKP, London.

    Google Scholar 

  • Blease, D.: 1983, 'Teacher Expectations and the Self-fulfilling Prophecy', Educational Studies 9, 123.

    Google Scholar 

  • Blumer, H.: 1969, Symbolic Interactionism: perspective and method, Prentice-Hall, Englewood Cliffs.

    Google Scholar 

  • Boaler, J.: 1997, Experiencing School Mathematics: teaching styles, sex and setting, Open University Press, Buckingham, UK.

    Google Scholar 

  • Brown, M.L.: 1993, 'Assessment Philosophy and Practice in the UK', in M. Niss (ed.), Cases of Assessment in Mathematics Education, Kluwer, Dordrecht.

    Google Scholar 

  • Brown, T.: 1996, 'The Phenomenology of the Mathematics Classroom', Educational Studies in Mathematics 31, 115-150.

    Article  Google Scholar 

  • Clarke, D.: 1996, 'Assessment' in A. Bishop (ed.), International Handbook of Mathematics Education, Kluwer, Dordrecht.

    Google Scholar 

  • Conner, C.: 1991, Assessment and Testing in Primary School, Falmer, London.

    Google Scholar 

  • Dearing, Sir R.: 1994, The National Curriculum and its Assessment, School Curriculum and Assessment Authority, London.

    Google Scholar 

  • Delamont, S.: 1976, Interaction in the Classroom, Methuen, London.

    Google Scholar 

  • Dwyer, C.A.: 1990, 'Trends in the Assessment of Teaching and Learning', in P. Broadfoot (ed.), Changing Educational Assessment, RKP, London.

    Google Scholar 

  • Ernest, P.: 1998, Social Constructivism as a Philosophy of Mathematics SUNY, New York.

    Google Scholar 

  • Galbraith, P. (1993): 'Paradigms, Problems and Assessment: some ideological implications', in M. Niss (ed.), Investigations into Assessment in Mathematics Education, Kluwer, Dordrecht.

    Google Scholar 

  • Gipps, C. and Murphy, P.: 1994, A Fair Test, Open University Press, Buckingham.

    Google Scholar 

  • Glaser, B.G. and Strauss, A.L.: 1967, The Discovery of Grounded Theory: strategies for qualitative research, Aldine, Chicago.

    Google Scholar 

  • Hargreaves, D.: 1972, Interpersonal Relations in Education, RKP, London.

    Google Scholar 

  • Harre, R. and Gillett, G.: 1994, The Discursive Mind, Sage, London.

    Google Scholar 

  • HMSO, Her Majesty's Stationery Office: 1988, The Education Reform Act, HMSO, London.

    Google Scholar 

  • Koehler, M. and Grouws, D.A.: 1992, 'Mathematics Teaching Practices and Their Effects', in D.A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, MacMillan, New York.

    Google Scholar 

  • Lerman, S.: 1989, 'Investigations: where to now?' in P. Ernest (ed.), Mathematics Teaching: the State of the Art, Falmer, London.

    Google Scholar 

  • Lorenz, J.H.: 1982, 'On Some Psychological Aspects of Mathematics Achievement Assessment and Classroom Interaction', Educational Studies in Mathematics 13, 1-19.

    Article  Google Scholar 

  • Love, E.: 1994, 'Mathematics Teachers' Accounts Seen as Narratives' in L. Bazzini (ed.), Proceedings of Fifth International Conference on Systematic Cooperation Between Theory and Practice in Mathematics Education, Grado, Italy, pp. 43-155.

    Google Scholar 

  • MacNamara, A. and Roper, T.: 1992, 'Attainment Target 1-is all the evidence there?', Mathematics Teaching 140, 26-27.

    Google Scholar 

  • Mellin-Olsen, S.: 1993, 'Where is the Student as a Subject?', in M. Niss (ed.), Investigations into Assessment in Mathematics Education, Kluwer, Dordrecht.

    Google Scholar 

  • Morgan, C.: 1996, An Analysis of the Discourse of Written Reports of Investigative Work in GCSE Mathematics, Unpublished PhD thesis, University of London, Institute of Education.

  • Morgan, C.: 1998, WritingMathematically: the discourse of investigation, Falmer, London.

    Google Scholar 

  • NCTM, National Council for Teachers of Mathematics: 1989, Curriculum and Evaluation Standards for School Mathematics, NCTM, Reston, VA.

    Google Scholar 

  • Ofsted: 1994, Science and Mathematics in Schools: a review, HMSO, London.

    Google Scholar 

  • Rico, L., Fernandez, F., Gil, F., Castro, E., del Olmo, A., Moreno, F. and Segovia, I.: 1995, 'Teachers' Conceptual Frameworks of Mathematics Assessment', in D. Carraher and L. Meira (eds.), Proceedings of the Proceedings 19th Conference of the International Group for Psychology of Mathematics Education, Recife, Brazil.

    Google Scholar 

  • Ridgway, J. and Schoenfeld, A.: 1994, Balanced Assessment: designing assessment schemes to promote desirable change in mathematics education, EAR1 email conference on Assessment.

  • Romberg, T.A. (ed.): 1995, Reform in School Mathematics and Authentic Assessment, SUNY Press, New York.

    Google Scholar 

  • Ruthven, K.: 1987, 'Ability Stereotyping in Mathematics' Educational Studies in Mathematics 18, 243-253.

    Article  Google Scholar 

  • Ruthven, K.: 1994, 'Better Judgement: rethinking assessment in mathematics education', Educational Studies in Mathematics 27, 433-450.

    Article  Google Scholar 

  • SEAC: 1991, NC Assessment: a moderator's handbook 1991/2, Key Stage 1, HMSO, London.

    Google Scholar 

  • TTA, Teacher Training Agency: 1997, Standards for the Award of Qualified Teacher Status, TTA, London.

    Google Scholar 

  • Thompson, A.: 1992, 'Teachers' Beliefs and Conceptions: a synthesis of research', in D.A. Grouws (ed.), Handbook of Research on Mathematics Teaching and Learning, Macmillan, New York.

    Google Scholar 

  • Van den Heuvel-Panhuizen, M.: 1996, 'How pencil-and-paper assessments can provide footholds for further instruction', paper presented to AERA symposium, New York.

  • Van den Heuvel-Panhuizen, M.: 1996, Assessment and Realistic Mathematics Education, Freudenthal Institute, Utrecht.

    Google Scholar 

  • Vile, A.: 1997, 'What can Semiotics offer Mathematics Education', Proceedings of British Society for Research into Learning Mathematics, Oxford, 93-105.

  • Voigt, J.: 1994, 'Negotiation of Mathematical Meaning and Learning Mathematics' Educational Studies in Mathematics 26, 275-298.

    Article  Google Scholar 

  • Vygotsky, L.S.: 1978, Mind in Society: the development of higher psychological processes, Harvard University Press, Cambridge, Mass.

    Google Scholar 

  • Walkerdine, V.: 1984, 'Developmental Psychology and the Child-centred Pedagogy: the insertion of Piaget into early education', in J. Henriques (ed.), Changing the Subject: Psychology, Social Regulation and Subjectivity, Methuen, London.

    Google Scholar 

  • Walkerdine, V.: 1988, Mastery of Reason, London, Routledge.

    Google Scholar 

  • Watson, A.: 1995, 'Evidence for Pupils' Mathematical Achievements' For the Learning of Mathematics 15, 16-21.

    Google Scholar 

  • Watson, A.: 1997, 'Coming to Know Pupils: a study of informal teacher assessment of mathematics' Proceedings of the 21st Conference of the International Group for Psychology of Mathematics Education, University of Helsinki, Finland.

    Google Scholar 

  • Watson, A.: 1998a, An investigation into how teachers make judgements about what pupils know and can do in mathematics, Unpublished DPhil thesis, University of Oxford, UK.

    Google Scholar 

  • Watson, A.: 1998b, 'Potential Sources of inequity in teachers' informal judgements about pupils' mathematics', in P. Gates (ed.), Proceedings of the First International Mathematics Education and Society Conference, University of Nottingham, UK.

    Google Scholar 

  • Webb, N.L.: 1993, 'Visualising a Theory of Assessment' in M. Niss (ed.), Investigations into Assessment in Mathematics Education, Kluwer, Dordrecht.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Watson, A. Mathematics Teachers Acting as Informal Assessors: Practices, Problems and Recommendations. Educational Studies in Mathematics 41, 69–91 (2000). https://doi.org/10.1023/A:1003933431489

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1003933431489

Navigation