What is rate? Does context or representation matter?

This article explores the research question: Are students' expressions of their conceptions of rate affected by either context or mathematical representation? Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, di...

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Bibliographic Details
Published in:Mathematics education research journal 2011-12, Vol.23 (4), p.455-477
Main Authors: Herbert, Sandra, Pierce, Robyn
Format: Article
Language:English
Subjects:
Australia
Calculus
Concept Formation
Context Effect
Education
Elementary School Students
Foreign Countries
Grade 10
Interviews
Learning Strategies
Mathematical Concepts
Mathematical thinking
Mathematics Education
Mathematics Instruction
Misconceptions
Original Article
Secondary education
Secondary School Mathematics
Secondary school students
Students
Year 10
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Summary:This article explores the research question: Are students' expressions of their conceptions of rate affected by either context or mathematical representation? 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. The article reports the results from analysis of data from 20 Grade 10 students from the Australian state of Victoria. Interviews targeted students' conceptions of rate, focusing on the influence of representation and context on their expression of their understanding of rate. The 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. 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. [Author abstract]
ISSN:1033-2170
2211-050X
DOI:10.1007/s13394-011-0026-z