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TERTIARY STUDENTS’ UNDERSTANDING OF SECOND ORDER RELATIONSHIPS IN FUNCTION NOTATION

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TERTIARY STUDENTS’ UNDERSTANDING OF SECOND ORDER RELATIONSHIPS IN FUNCTION NOTATION

Author: Carmel Coady & John Pegg

Publication Year: 1994

Abstract

The function concept permeates many aspects of the mathematics curriculum at both the secondary and tertiQlY levels. Students' use and conceptualization of the function concept have been the subject of a number of research studies (see for example, Arnold (1992), Barnes (1988)). These studies have found that the overwhelming view students hold of this concept is that a function is a rule of correspondence, or more precisely, an algebraic formula, into which values are substituted. However, this rather narrow interpretation begins to breakdov.m H!hen questions that require the use of more advanced reasoning skills are encountered. The competent use offimctionnotation, given this stance, relies heavily on students' understanding of the symbolism involved. Thus the notion of a variable and how different variables relate are critical factors in students' ability to use the junction concept purely within an algebraic context. The purpose of this study was to explore this feature by examining tertialY students' responses to a series of questions, in which relationships between variables were set within the framework offimctionnotatiol1. To assess such responses, the SOLO Taxonomy was used. The study has highlighted the difficulties students experience with second order relationships in non-routine function questions and the value of the SOLO Taxonomy in interpreting students' responses.

Type: Research Paper

Carmel Coady & John Pegg
TERTIARY STUDENTS’ UNDERSTANDING OF SECOND ORDER RELATIONSHIPS IN FUNCTION NOTATION

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