Applying covariational reasoning while modeling dynamic events: A framework and a study

Marilyn Carlson, Sally Jacobs, Edward Coe, Sean Larsen, Eric Hsu

Research output: Contribution to journalArticle

144 Citations (Scopus)

Abstract

The article develops the notion of covariational reasoning and proposes a framework for describing the mental actions involved in applying covariational reasoning when interpreting and representing dynamic function events. It also reports on an investigation of high-performing 2nd-semester calculus students' ability to reason about covarying quantities in dynamic situations. The study revealed that these students were able to construct images of a function's dependent variable changing in tandem with the imagined change of the independent variable, and in some situations, were able to construct images of rate of change for contiguous intervals of a function's domain. However, students appeared to have difficulty forming images of continuously changing rate and could not accurately represent or interpret inflection points or increasing and decreasing rate for dynamic function situations. These findings suggest that curriculum and instruction should place increased emphasis on moving students from a coordinated image of two variables changing in tandem to a coordinated image of the instantaneous rate of change with continuous changes in the independent variable for dynamic function situations.

Original languageEnglish (US)
Pages (from-to)352-378
Number of pages27
JournalJournal for Research in Mathematics Education
Volume33
Issue number5
StatePublished - Nov 2002

Fingerprint

Dynamic Modeling
Reasoning
event
Instantaneous rate of change
student
Point of inflection
Rate of change
semester
Calculus
Framework
instruction
curriculum
Interval
Dependent
ability

Keywords

  • Applications
  • Calculus
  • Cognitive development
  • College mathematics
  • Functions
  • Mathematical modeling
  • Reasoning

ASJC Scopus subject areas

  • Education

Cite this

Applying covariational reasoning while modeling dynamic events : A framework and a study. / Carlson, Marilyn; Jacobs, Sally; Coe, Edward; Larsen, Sean; Hsu, Eric.

In: Journal for Research in Mathematics Education, Vol. 33, No. 5, 11.2002, p. 352-378.

Research output: Contribution to journalArticle

Carlson, Marilyn ; Jacobs, Sally ; Coe, Edward ; Larsen, Sean ; Hsu, Eric. / Applying covariational reasoning while modeling dynamic events : A framework and a study. In: Journal for Research in Mathematics Education. 2002 ; Vol. 33, No. 5. pp. 352-378.
@article{34adeb2347fd487fb4636929a908702d,
title = "Applying covariational reasoning while modeling dynamic events: A framework and a study",
abstract = "The article develops the notion of covariational reasoning and proposes a framework for describing the mental actions involved in applying covariational reasoning when interpreting and representing dynamic function events. It also reports on an investigation of high-performing 2nd-semester calculus students' ability to reason about covarying quantities in dynamic situations. The study revealed that these students were able to construct images of a function's dependent variable changing in tandem with the imagined change of the independent variable, and in some situations, were able to construct images of rate of change for contiguous intervals of a function's domain. However, students appeared to have difficulty forming images of continuously changing rate and could not accurately represent or interpret inflection points or increasing and decreasing rate for dynamic function situations. These findings suggest that curriculum and instruction should place increased emphasis on moving students from a coordinated image of two variables changing in tandem to a coordinated image of the instantaneous rate of change with continuous changes in the independent variable for dynamic function situations.",
keywords = "Applications, Calculus, Cognitive development, College mathematics, Functions, Mathematical modeling, Reasoning",
author = "Marilyn Carlson and Sally Jacobs and Edward Coe and Sean Larsen and Eric Hsu",
year = "2002",
month = "11",
language = "English (US)",
volume = "33",
pages = "352--378",
journal = "Journal for Research in Mathematics Education",
issn = "0021-8251",
publisher = "National Council of Teachers of Mathematics",
number = "5",

}

TY - JOUR

T1 - Applying covariational reasoning while modeling dynamic events

T2 - A framework and a study

AU - Carlson, Marilyn

AU - Jacobs, Sally

AU - Coe, Edward

AU - Larsen, Sean

AU - Hsu, Eric

PY - 2002/11

Y1 - 2002/11

N2 - The article develops the notion of covariational reasoning and proposes a framework for describing the mental actions involved in applying covariational reasoning when interpreting and representing dynamic function events. It also reports on an investigation of high-performing 2nd-semester calculus students' ability to reason about covarying quantities in dynamic situations. The study revealed that these students were able to construct images of a function's dependent variable changing in tandem with the imagined change of the independent variable, and in some situations, were able to construct images of rate of change for contiguous intervals of a function's domain. However, students appeared to have difficulty forming images of continuously changing rate and could not accurately represent or interpret inflection points or increasing and decreasing rate for dynamic function situations. These findings suggest that curriculum and instruction should place increased emphasis on moving students from a coordinated image of two variables changing in tandem to a coordinated image of the instantaneous rate of change with continuous changes in the independent variable for dynamic function situations.

AB - The article develops the notion of covariational reasoning and proposes a framework for describing the mental actions involved in applying covariational reasoning when interpreting and representing dynamic function events. It also reports on an investigation of high-performing 2nd-semester calculus students' ability to reason about covarying quantities in dynamic situations. The study revealed that these students were able to construct images of a function's dependent variable changing in tandem with the imagined change of the independent variable, and in some situations, were able to construct images of rate of change for contiguous intervals of a function's domain. However, students appeared to have difficulty forming images of continuously changing rate and could not accurately represent or interpret inflection points or increasing and decreasing rate for dynamic function situations. These findings suggest that curriculum and instruction should place increased emphasis on moving students from a coordinated image of two variables changing in tandem to a coordinated image of the instantaneous rate of change with continuous changes in the independent variable for dynamic function situations.

KW - Applications

KW - Calculus

KW - Cognitive development

KW - College mathematics

KW - Functions

KW - Mathematical modeling

KW - Reasoning

UR - http://www.scopus.com/inward/record.url?scp=0036860479&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036860479&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036860479

VL - 33

SP - 352

EP - 378

JO - Journal for Research in Mathematics Education

JF - Journal for Research in Mathematics Education

SN - 0021-8251

IS - 5

ER -