Covariational reasoning and invariance among coordinate systems

Kevin C. Moore, Teo Paoletti, Stacy Musgrave

Research output: Contribution to journalArticleResearchpeer-review

17 Citations (Scopus)

Abstract

Researchers continue to emphasize the importance of covariational reasoning in the context of students' function concept, particularly when graphing in the Cartesian coordinate system (CCS). In this article, we extend the body of literature on function by characterizing two pre-service teachers' thinking during a teaching experiment focused on graphing in the polar coordinate system (PCS). We illustrate how the participants engaged in covariational reasoning to make sense of graphing in the PCS and make connections with graphing in the CCS. By foregrounding covariational relationships, the students came to understand graphs in different coordinate systems as representative of the same relationship despite differences in the perceptual shapes of these graphs. In synthesizing the students' activity, we provide remarks on instructional approaches to graphing and how the PCS forms a potential context for promoting covariational reasoning.

Original languageEnglish
Pages (from-to)461-473
Number of pages13
JournalJournal of Mathematical Behavior
Volume32
Issue number3
DOIs
StatePublished - 1 Sep 2013

Fingerprint

Invariance
Polar coordinates
Reasoning
Students
Cartesian coordinate system
Pre-service Teachers
Teaching
Graph in graph theory
Research Personnel
Continue
student
Experiments
Experiment
experiment
teacher
Relationships
Context

Keywords

  • Covariational reasoning
  • Function
  • Graphing
  • Multiple representations
  • Polar coordinates

Cite this

Moore, Kevin C. ; Paoletti, Teo ; Musgrave, Stacy. / Covariational reasoning and invariance among coordinate systems. In: Journal of Mathematical Behavior. 2013 ; Vol. 32, No. 3. pp. 461-473.
@article{dcc3b1db5c5a4cef82ebf2eab5bfb5dd,
title = "Covariational reasoning and invariance among coordinate systems",
abstract = "Researchers continue to emphasize the importance of covariational reasoning in the context of students' function concept, particularly when graphing in the Cartesian coordinate system (CCS). In this article, we extend the body of literature on function by characterizing two pre-service teachers' thinking during a teaching experiment focused on graphing in the polar coordinate system (PCS). We illustrate how the participants engaged in covariational reasoning to make sense of graphing in the PCS and make connections with graphing in the CCS. By foregrounding covariational relationships, the students came to understand graphs in different coordinate systems as representative of the same relationship despite differences in the perceptual shapes of these graphs. In synthesizing the students' activity, we provide remarks on instructional approaches to graphing and how the PCS forms a potential context for promoting covariational reasoning.",
keywords = "Covariational reasoning, Function, Graphing, Multiple representations, Polar coordinates",
author = "Moore, {Kevin C.} and Teo Paoletti and Stacy Musgrave",
year = "2013",
month = "9",
day = "1",
doi = "10.1016/j.jmathb.2013.05.002",
language = "English",
volume = "32",
pages = "461--473",
journal = "Journal of Mathematical Behavior",
issn = "0732-3123",
publisher = "Elsevier Inc.",
number = "3",

}

Covariational reasoning and invariance among coordinate systems. / Moore, Kevin C.; Paoletti, Teo; Musgrave, Stacy.

In: Journal of Mathematical Behavior, Vol. 32, No. 3, 01.09.2013, p. 461-473.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Covariational reasoning and invariance among coordinate systems

AU - Moore, Kevin C.

AU - Paoletti, Teo

AU - Musgrave, Stacy

PY - 2013/9/1

Y1 - 2013/9/1

N2 - Researchers continue to emphasize the importance of covariational reasoning in the context of students' function concept, particularly when graphing in the Cartesian coordinate system (CCS). In this article, we extend the body of literature on function by characterizing two pre-service teachers' thinking during a teaching experiment focused on graphing in the polar coordinate system (PCS). We illustrate how the participants engaged in covariational reasoning to make sense of graphing in the PCS and make connections with graphing in the CCS. By foregrounding covariational relationships, the students came to understand graphs in different coordinate systems as representative of the same relationship despite differences in the perceptual shapes of these graphs. In synthesizing the students' activity, we provide remarks on instructional approaches to graphing and how the PCS forms a potential context for promoting covariational reasoning.

AB - Researchers continue to emphasize the importance of covariational reasoning in the context of students' function concept, particularly when graphing in the Cartesian coordinate system (CCS). In this article, we extend the body of literature on function by characterizing two pre-service teachers' thinking during a teaching experiment focused on graphing in the polar coordinate system (PCS). We illustrate how the participants engaged in covariational reasoning to make sense of graphing in the PCS and make connections with graphing in the CCS. By foregrounding covariational relationships, the students came to understand graphs in different coordinate systems as representative of the same relationship despite differences in the perceptual shapes of these graphs. In synthesizing the students' activity, we provide remarks on instructional approaches to graphing and how the PCS forms a potential context for promoting covariational reasoning.

KW - Covariational reasoning

KW - Function

KW - Graphing

KW - Multiple representations

KW - Polar coordinates

UR - http://www.scopus.com/inward/record.url?scp=84880308612&partnerID=8YFLogxK

U2 - 10.1016/j.jmathb.2013.05.002

DO - 10.1016/j.jmathb.2013.05.002

M3 - Article

VL - 32

SP - 461

EP - 473

JO - Journal of Mathematical Behavior

JF - Journal of Mathematical Behavior

SN - 0732-3123

IS - 3

ER -