Abstract
This article links two areas of contemporary interest in mathematics education. These are respectively; mathematical characteristics of prospective teachers, and the notion of levels of understanding.
The study reported here considered questions relating to the mathematical appreciation of successful students at both senior secondary (university entrance) and tertiary level. The tertiary students were graduates embarking upon a post-graduate course of teacher-training.
It was found that response patterns were stable across a variety of institutions, geographical regions (Australian States), and education systems. Mathematical malfunctions present among secondary graduates were found to exist in substantially the same proportions among the graduate teacher trainees. It was found that the type of understanding sought in this study was not enhanced merely by taking more mathematics courses. The problem of recycling of attitudes and mathematical misconceptions within the secondary teaching structure is addressed, and the question of the approach to the study of mathematics at both secondary and tertiary level is raised as a matter of continuing concern.
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References
Begle, E. G.: 1972, ‘Teacher knowledge and student achievement in algebra’, SMSG Reports, No. 9, Stanford, School Mathematics Study Group, 1972.
Buckland, P. R.: 1969, ‘The mathematical background of teachers in training’, The Mathematical Gazette 386, 357–362.
Clement, J., Lochead, J. and Soloway, E.: 1980, ‘Positive effects of computer programming on the student's understanding of variables and equations’, Cognitive Development Project, Dept. of Physics and Astronomy, University of Massachusetts.
Eisenberg, T. A.: 1977, ‘Begle revisited: teacher knowledge and student achievement in algebra’, Journal for Research in Mathematics Education 8, 216–222.
Galbraith, P. L.: 1981, ‘Aspects of proving: a clinical investigation of process’, Educational Studies in Mathematics 12, 1–28.
Gray, J. D.: 1975, ‘Criticism in the mathematics class’, Educational Studies in Mathematics 6, 77–86.
Howson, A. G.: 1975, ‘University courses for future teachers’, Educational Studies in Mathematics 6, 273–292.
Lakatos, I.: 1976, Proofs and Refutations, Cambridge University Press, Cambridge.
McGarvey, C.: 1981, ‘Mathematics and miseducation: toward the next school curricula’, The Mathematics Teacher 74, 90–95.
Neumann, Hanna: 1973, ‘Teaching first year undergraduates: fads and fancies’, The Australian Mathematics Teacher 29, 23–28.
Skemp, R. R.: 1976, ‘Relational understanding and instrumental understanding’, Mathematics Teaching 77, 20–26.
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Galbraith, P.L. The mathematical vitality of secondary mathematics graduates and prospective teachers: A comparative study. Educ Stud Math 13, 89–112 (1982). https://doi.org/10.1007/BF00305499
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DOI: https://doi.org/10.1007/BF00305499