### Abstract

In this study, we investigate students’ ways of understanding graphing tasks involving quantitative relationships in which time functions as an implicit variable. Through task-based interviews of students ages 14–16 in a summer mathematics program, we observe a variety of ways of understanding, including thematic or visual association, pointwise thinking, and reasoning parametrically about changes in the two variables to be graphed. We argue that, rather than comprising a hierarchy, these ways of understanding complement one another in helping students discover an invariant relationship between two dynamically varying quantities, and develop a graph of the relationship that captures this invariance. From these ways of understanding, we conjecture several mathematical meanings for graphing that may account for students’ behavior when graphing quantitative relationships.

Original language | English (US) |
---|---|

Pages (from-to) | 295-323 |

Number of pages | 29 |

Journal | Mathematical Thinking and Learning |

Volume | 20 |

Issue number | 4 |

DOIs | |

State | Published - Oct 2 2018 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Education
- Developmental and Educational Psychology

### Cite this

**When time is an implicit variable : An investigation of students’ ways of understanding graphing tasks.** / Patterson, Cody L.; Mcgraw, Rebecca H.

Research output: Contribution to journal › Article

*Mathematical Thinking and Learning*, vol. 20, no. 4, pp. 295-323. https://doi.org/10.1080/10986065.2018.1509421

}

TY - JOUR

T1 - When time is an implicit variable

T2 - An investigation of students’ ways of understanding graphing tasks

AU - Patterson, Cody L.

AU - Mcgraw, Rebecca H

PY - 2018/10/2

Y1 - 2018/10/2

N2 - In this study, we investigate students’ ways of understanding graphing tasks involving quantitative relationships in which time functions as an implicit variable. Through task-based interviews of students ages 14–16 in a summer mathematics program, we observe a variety of ways of understanding, including thematic or visual association, pointwise thinking, and reasoning parametrically about changes in the two variables to be graphed. We argue that, rather than comprising a hierarchy, these ways of understanding complement one another in helping students discover an invariant relationship between two dynamically varying quantities, and develop a graph of the relationship that captures this invariance. From these ways of understanding, we conjecture several mathematical meanings for graphing that may account for students’ behavior when graphing quantitative relationships.

AB - In this study, we investigate students’ ways of understanding graphing tasks involving quantitative relationships in which time functions as an implicit variable. Through task-based interviews of students ages 14–16 in a summer mathematics program, we observe a variety of ways of understanding, including thematic or visual association, pointwise thinking, and reasoning parametrically about changes in the two variables to be graphed. We argue that, rather than comprising a hierarchy, these ways of understanding complement one another in helping students discover an invariant relationship between two dynamically varying quantities, and develop a graph of the relationship that captures this invariance. From these ways of understanding, we conjecture several mathematical meanings for graphing that may account for students’ behavior when graphing quantitative relationships.

UR - http://www.scopus.com/inward/record.url?scp=85053625593&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053625593&partnerID=8YFLogxK

U2 - 10.1080/10986065.2018.1509421

DO - 10.1080/10986065.2018.1509421

M3 - Article

AN - SCOPUS:85053625593

VL - 20

SP - 295

EP - 323

JO - Mathematical Thinking and Learning

JF - Mathematical Thinking and Learning

SN - 1098-6065

IS - 4

ER -