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The Physics Teacher
written by Edward F. Redish
When students are learning to use math in physics, one of the most important ideas they need to learn is that equations are not just calculational tools; they represent relationships between physical variables that change together (co-vary). How much a change in one variable or parameter is associated with a change in another depends on how they appear in the equation--their functional dependence. Understanding this sort of relationship is rarely emphasized in introductory mathematics classes, and students who have not yet learned to blend conceptual ideas with mathematical symbols may not see the relevance and power of this idea. We need to explicitly teach functional dependence as part of our effort to help students learn to use math productively in science.

This paper is the fifth in a series of five articles on how to help students develop the scientific reasoning skills required to effectively use mathematics in science.

See Related Materials for links to the additional articles that comprise this series: Collection Overview, plus articles addressing dimensional analysis, estimation, anchor equations, and toy models.
The Physics Teacher: Volume 60, Issue 1, Pages 18-21
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© 2022 American Association of Physics Teachers (AAPT)
DOI:
10.1119/5.0040055
Keywords:
covariation, math symbology, mathematics reasoning, physics reasoning
Record Creator:
Metadata instance created May 18, 2023 by Sam McKagan
Record Updated:
October 20, 2023 by Sam McKagan
Last Update
when Cataloged:
January 1, 2022
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AIP Format
E. Redish, , Phys. Teach. 60 (1), 18 (2022), WWW Document, (https://doi.org/10.1119/5.0040055).
AJP/PRST-PER
E. Redish, Using Math in Physics: 5. Functional dependence, Phys. Teach. 60 (1), 18 (2022), <https://doi.org/10.1119/5.0040055>.
APA Format
Redish, E. (2022, January 1). Using Math in Physics: 5. Functional dependence. Phys. Teach., 60(1), 18-21. Retrieved May 27, 2024, from https://doi.org/10.1119/5.0040055
Chicago Format
Redish, Edward F.. "Using Math in Physics: 5. Functional dependence." Phys. Teach. 60, no. 1, (January 1, 2022): 18-21, https://doi.org/10.1119/5.0040055 (accessed 27 May 2024).
MLA Format
Redish, Edward F.. "Using Math in Physics: 5. Functional dependence." Phys. Teach. 60.1 (2022): 18-21. 27 May 2024 <https://doi.org/10.1119/5.0040055>.
BibTeX Export Format
@article{ Author = "Edward F. Redish", Title = {Using Math in Physics: 5. Functional dependence}, Journal = {Phys. Teach.}, Volume = {60}, Number = {1}, Pages = {18-21}, Month = {January}, Year = {2022} }
Refer Export Format

%A Edward F. Redish %T Using Math in Physics: 5. Functional dependence %J Phys. Teach. %V 60 %N 1 %D January 1, 2022 %P 18-21 %U https://doi.org/10.1119/5.0040055 %O application/pdf

EndNote Export Format

%0 Journal Article %A Redish, Edward F. %D January 1, 2022 %T Using Math in Physics: 5. Functional dependence %J Phys. Teach. %V 60 %N 1 %P 18-21 %8 January 1, 2022 %U https://doi.org/10.1119/5.0040055


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Using Math in Physics: 5. Functional dependence:

Accompanies Using Math in Physics: Overview

A link to the overview article by E.F. Redish that explains how all six items in this collection are related to the topic, "Using Math in Physics".

relation by Caroline Hall
Accompanies Using Math in Physics: 1. Dimensional Analysis

A link to the first in this series of five articles: "Using Math in Physics 1: Dimensional Analysis".

relation by Caroline Hall
Accompanies Using Math in Physics: 2. Estimation

A link to the second in this series of five articles: "Using Math in Physics 2: Estimation".

relation by Caroline Hall
Accompanies Using Math in Physics: 3. Anchor equations

A link to the third in this series of five articles, "Using Math in Physics 3: Anchor Equations".

relation by Caroline Hall
Accompanies Using Math in Physics: 4. Toy models

A link to the fourth in this series of five articles, "Using Math in Physics 4: Toy Models".

relation by Caroline Hall

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