Distance university students' processing of mathematics exercises
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This study reports the development and use of a taxonomy for describing the way distance students plant their work and use course materials to complete mathematics exercises. A taxonomy of 12 component procedures of cognitive operations was developed from a set of propositions about problem-solving. Two undergraduate students of mathematics and one graduate thought aloud as they completed an exercise using standard course materials under distance study conditions. The verbal protocols of the students' problem-solving processes and use of course materials were described and compared using the taxonomy.
The two undergraduates centred on single aspects of the problem. They used examples rather than conceptual information presented in the written materials. The graduate made greater use of theories and definitions, but like the undergraduates, neglected the expository material. No student planned the work.
The data are discussed in terms of the usefulness of a taxonomic description of thinking-aloud data for course designers and mathematics teachers.
KeywordsCognitive Operation Undergraduate Student Study Condition Mathematics Teacher Verbal Protocol
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- Bates, T.: 1976, ‘Survey of student use of broadcasting’,Teaching at a Distance 5, 45–52.Google Scholar
- Benjafield, J.: 1969, ‘Evidence that “thinking aloud” constitutes an externalization of inner speech’,Psychonomic Science 14, 83–84.Google Scholar
- Burt, G.: 1976, ‘Detailed evaluation: A framework for understanding...a rich treasury of experience’,Teaching at a Distance 7, 42–48.Google Scholar
- Casey, D. P.: 1978, ‘Failing students: A strategy of error analysis’, in P.Costello (ed.):Aspects of Motivation, Melbourne, Mathematical Association of Victoria, pp. 295–306.Google Scholar
- Chase, W. G., and Simon, H. A.: 1973, ‘Perception in chess’,Cognitive Psychology 4, 55–81.Google Scholar
- Clements, M. A.: 1980, ‘Analysing children's erros in written mathematical tasks’,Educational Studies in Mathematics 11, 1–21.Google Scholar
- Dodds, A. E., Lawrence, J. A., and Guiton, P. de C.: 1981, ‘Distance university students' perceptions of the influence of their study’, paper presented at the Forum of the Australian and South Pacific External Studies Association, Fiji, ERIC Ref. No. ED 210000.Google Scholar
- Dodds, A. E. and Lawrence, J. A.: 1979, ‘Towards the development of a heuristic for describing studying processes of adult distance students’, paper presented at the Forum of the Australian and South Pacific External Studies Association, Perth, ERIC Ref. No. ED209992.Google Scholar
- Ericsson, K. A.: 1975, ‘Instructions to verbalize as a means to study problem-solving processes with the 8-puzzle: Preliminary study’, reports from the Department of Psychology, University of Stockholm, No. 458.Google Scholar
- Ericsson, K. A. and Simon, H. A.: 1980, ‘Verbal reports as data’,Psychological Review 87, 215–251.Google Scholar
- Gagné, R. H. and Smith, E. C.: 1962, ‘A study of the effects of verbalization on problemsolving’,Journal of Experimental Psychology 63, 12–18.Google Scholar
- Hollander, S. K.: 1978, ‘A literature review: Thought processes employed in the solution of verbal mathematical problems’,School Science and Mathematics 78, 327–335.Google Scholar
- Lawrence, J. A.: 1979, ‘Components of moral judgement-making responses’, paper presented at the Annual Meeting of the Australian Psychological Society, Hobart, Tasmania.Google Scholar
- Lawrence, J. A.: 1981, ‘A case for the usefulness and plausibility of Thinking Aloud verbal data’, in M. J. Lawson and R. Linke (eds.).Inquiry and Action in Education: Papers presented at the 1981 AARE Conference, Adelaide, Australian Association for Research in Education, Vol. 1, 95–103.Google Scholar
- Newell, A. and Simon, H. A.: 1972,Human Problem-solving, Prentice-Hall, Englewood Cliffs.Google Scholar
- Newman, M. A.: 1977, ‘An analysis of 6th grade pupils' errors on written mathematical tasks’, in M. A. Clements and J. Foyster (eds.):Research in Mathematical Education in Australia, 1977, Melbourne, Vol. 1, 239–258.Google Scholar
- Nisbett, R. E. and Wilson, T. D.: 1977, ‘Telling more than we can know: Verbal reports on mental processes’,Psychological Review 84, 231–259.Google Scholar
- Pitt, R. B.: 1976, Toward a comprehensive model of problem solving: Application to solutions of chemistry problems by high school and college students, Doctoral dissertation, University of California,Dissertation Abstracts International 37, 4730B, University Microfilms No. 77-4218, 145.Google Scholar
- Polya, G.: 1954,Induction and Analogy in Mathematics, Princeton, Princeton University Press.Google Scholar
- Polya, G.: 1957,How to Solve It: A New Aspect of Mathematical Method, Princeton, Princeton University Press, 2nd edn.Google Scholar
- Purcell, E. J.: 1976,Calculus with Analytical Geometry, Prentice Hall, Englewood Cliffs, 2nd edn.Google Scholar
- Radatz, H.: 1979, ‘Error analysis in mathematics education’,Journal of Research in Mathematics Education 10, 163–172.Google Scholar
- Svenson, I. F.: 1982, A process analysis of distance mathematics students' solution of set exercises. Unpublished master's dissertation, Murdoch University.Google Scholar
- Svenson, I. F. and Lawrence, J. A.: 1980, ‘Distance students' use of tutor feedback in a university introductory mathematics course’, unpublished manuscript, Murdoch University.Google Scholar
- Swokowski, E. W.: 1975,Calculus with Analytic Geometry, Prindle, Weber and Schmidt, Boston.Google Scholar