What is rate? Does context or representation matter?

Herbert, Sandra and Pierce, Robyn 2011, What is rate? Does context or representation matter?, Mathematics education research journal, vol. 23, no. 4, pp. 455-477.

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Title What is rate? Does context or representation matter?
Author(s) Herbert, Sandra
Pierce, Robyn
Journal name Mathematics education research journal
Volume number 23
Issue number 4
Start page 455
End page 477
Publisher Springer
Place of publication Dordrecht, Netherlands
Publication date 2011
ISSN 1033-2170
2211-050X
Keyword(s) secondary school mathematics
rate
speed
representation
pre-calculus
educationally critical aspects
Summary Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students’ conceptions of rate, focussing on the influence of representation and context on their expression of their understanding of rate. This analysis shows that different representations of functions provide varying levels of rate-related information for individual students. Understandings of rate in one representation or context are not necessarily transferred to another representation or context. Rate is an important, but commonly misunderstood, mathematical concept with many everyday applications (Swedosh, Dowsey, Caruso, Flynn, & Tynan, 2007). It is a complicated concept comprising many interwoven ideas such as the ratio of two numeric, measurable quantities but in a context where both quantities are changing. In mathematics classes, this is commonly expressed as change in the dependent variable resulting from a unit change in the independent variable, and variously described as constant or variable rate; average or instantaneous rate. In addition, rate may be seen as a purely abstract mathematical notion or embedded in the understanding of real-world applications. This paper explores the research question: Are students’ expressions of their conceptions of rate affected by either context or mathematical representation? This question was part of a larger study (Herbert, 2010) conducted with Grade 10 students from the Australian state of Victoria.
Language eng
Field of Research 130208 Mathematics and Numeracy Curriculum and Pedagogy
Socio Economic Objective 930302 Syllabus and Curriculum Development
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
HERDC collection year 2011
Copyright notice ©2011, Springer
Persistent URL http://hdl.handle.net/10536/DRO/DU:30041038

Document type: Journal Article
Collection: School of Education
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