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Proficiency in the Explanation of Procedures: A Test of the Intuitive Understanding of Teachers of Undergraduate Mathematics
Ist Teil von
Higher education, 1993-12, Vol.26 (4), p.355-386
Ort / Verlag
Kluwer Academic Publishers
Erscheinungsjahr
1993
Link zum Volltext
Quelle
ERIC
Beschreibungen/Notizen
A discussion of production system approaches to the representation of learned procedures, and of stage models of the acquisition of procedures, yielded four general principles applicable to the construction of effective explanations. The intuitive appreciation of these principles by tertiary teachers was tested in two studies. In the first, separate versions of an explanation of a standard undergraduate mathematics problem solution procedure were prepared, these versions differing in the extent to which they exemplified the derived principles. Subjects ranked the explanations in terms of their perceived effectiveness. In the second study, subjects of varying experience at teaching tertiary level mathematics were video recorded while they individually explained three standard undergraduate problems. Their explanations were scored for the extent to which some awareness of the general principles was evidenced. In general terms the findings from these two studies suggested that mathematics teachers might be well able to discriminate between explanations which differ in their compliance with the derived general principles, but that they were not well skilled at employing these principles in explanations which they generated themselves.