Table Of ContentIt’s Just Math: Research on Students’ Understanding
of Chemistry and Mathematics
1316
ACS SYMPOSIUM SERIES
It’s Just Math: Research on Students’ Understanding of
Chemistry and Mathematics
Marcy H. Towns,Editor
Purdue University
West Lafayette, Indiana
Kinsey Bain,Editor
Michigan State University
East Lansing, Michigan
Jon-Marc G. Rodriguez,Editor
Purdue University
West Lafayette, Indiana
Sponsored by the
ACS Division of Chemical Education
American Chemical Society, Washington, DC
Library of Congress Cataloging-in-Publication Data
Names: Towns, Marcy H., editor. | Bain, Kinsey, editor. | Rodriguez, Jon-Marc
G., editor. | American Chemical Society. Division of Chemical Education.
Title: It's just math : research on students' understanding of chemistry and
mathematics / Marcy H. Towns, editor (Purdue University, West Lafayette,
Indiana), Kinsey Bain, editor (Michigan State University, East Lansing,
Michigan), Jon-Marc G. Rodriguez, editor (Purdue University, West
Lafayette, Indiana) ; sponsored by the ACS Division of Chemical Education.
Other titles: It is just math
Description: Washington, DC : American Chemical Society, [2019] | Series: ACS
symposium series ; 1316 | Includes bibliographical references and index.
Identifiers: LCCN 2019004262 (print) | LCCN 2019011824 (ebook) | ISBN
9780841234345 (ebook) | ISBN 9780841234352 (alk. paper)
Subjects: LCSH: Chemistry--Mathematics. | Chemistry--Study and teaching. |
Mathematics--Study and teaching.
Classification: LCC QD39.3.M3 (ebook) | LCC QD39.3.M3 I87 2019 (print) | DDC
540.1/51--dc23
LC record available at https://lccn.loc.gov/2019004262
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Foreword
Thepurposeoftheseriesistopublishtimely,comprehensivebooksdevelopedfromtheACS
sponsoredsymposiabasedoncurrentscientificresearch.Occasionally,booksaredevelopedfrom
symposia sponsored by other organizations when the topic is of keen interest to the chemistry
audience.
Beforeabookproposalisaccepted,theproposedtableofcontentsisreviewedforappropriate
andcomprehensivecoverageandforinteresttotheaudience.Somepapersmaybeexcludedtobetter
focusthebook;othersmaybeaddedtoprovidecomprehensiveness.Whenappropriate,overview
orintroductorychaptersareadded.Draftsofchaptersarepeer-reviewedpriortofinalacceptanceor
rejection.
Asarule,onlyoriginalresearchpapersandoriginalreviewpapersareincludedinthevolumes.
Verbatim reproductions of previous published papers are not accepted.
ACS Books Department
Contents
1. How Did We Get Here? Using and Applying Mathematics in Chemistry. . . . . . . . . . . . . . . . . . . . . 1
Marcy H. Towns, Kinsey Bain, and Jon-Marc G. Rodriguez
2. A Modeling Perspective on Supporting Students’ Reasoning with Mathematics in
Chemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Katherine Lazenby and Nicole M. Becker
3. Mathematics in Chemical Kinetics: Which Is the Cart and Which Is the Horse?. . . . . . . . . 25
Kinsey Bain, Jon-Marc G. Rodriguez, Alena Moon, and Marcy H. Towns
4. Graphs: Working with Models at the Crossroad between Chemistry and
Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Felix M. Ho, Maja Elmgren, Jon-Marc G. Rodriguez, Kinsey R. Bain, and Marcy H. Towns
5. Graphs as Objects: Mathematical Resources Used by Undergraduate Biochemistry
Students To Reason about Enzyme Kinetics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Jon-Marc G. Rodriguez, Kinsey Bain, and Marcy H. Towns
6. Math Self-Beliefs Relate to Achievement in Introductory Chemistry Courses. . . . . . . . . . . . . 81
Michael R. Mack, Cynthia A. Stanich, and Lawrence M. Goldman
7. “But You Didn’t Give Me the Formula!” and Other Math Challenges in the Context
of a Chemistry Course. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Amy J. Phelps
8. Transition of Mathematics Skills into Introductory Chemistry Problem Solving. . . . . . . . 119
Benjamin P. Cooke and Dorian A. Canelas
9. Mathematical Knowledge for Teaching in Chemistry: Identifying Opportunities To
Advance Instruction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
LynmarieA.Posey,KristenN.Bieda,PamelaL.Mosley,CharlesJ.Fessler,andValentinA.B.
Kuechle
10. The Logic of Proportional Reasoning and Its Transfer into Chemistry. . . . . . . . . . . . . . . . . . . . . . . . 157
Donald J. Wink and Stephanie A. C. Ryan
11. Making Sense of Mathematical Relationships in Physical Chemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . 173
Renée Cole and Tricia Shepherd
12. What Education Research Related to Calculus Derivatives and Integrals Implies for
Chemistry Instruction and Learning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
Steven R. Jones
vii
13. Developing an Active Approach to Chemistry-Based Group Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . 213
Anna Marie Bergman and Timothy A. French
14. Systems Thinking as a Vehicle To Introduce Additional Computational Thinking
Skills in General Chemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
Thomas Holme
15. Video-Based Kinetic Analysis of Period Variations and Oscillation Patterns in the
Ce/Fe-Catalyzed Four-Color Belousov–Zhabotinsky Oscillating Reaction. . . . . . . . . . . . . . . . 251
Rainer Glaser, Marco Downing, Ethan Zars, Joseph Schell, and Carmen Chicone
Editors’ Biographies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
Indexes
Author Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
Subject Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
viii
Chapter1
How Did We Get Here? Using and Applying Mathematics in
Chemistry
Marcy H.Towns,1,*KinseyBain,2andJon-Marc G.Rodriguez1
1Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States
2Department of Chemistry, Michigan State University, East Lansing, Michigan 48824,
United States
*E-mail:[email protected]
Concernsabouttheabilityofstudentstoapplymathematicsinchemistrycourses
havebeenpartofthechemistrylandscapeintheUnitedStatessinceatleastthe
1920s. Improving the mathematical preparation of undergraduate and graduate
studentshasbeenasorepointthathasledtoresearchdocumentingdeficiencies.
This book may help researchers and chemists understand current research on
mathematical reasoning including covatiational reasoning, graphical reasoning,
andmathematicalmodelinginthecontextofchemistry.Buttoaccomplishthat
loftygoal,we’dliketotakereadersbackintimetotheturnofthe20thcenturyto
brieflyexaminethelandscapeasitpertainedtomathematicsinchemistry.Taking
a historical perspective may help researchers understand where we are now in
the 21st century, and it may drive forward the type of novel and innovative
consideration of frameworks and literature that can guide important research
questions that span both chemistry and mathematics.
Introduction
“Inadequateexperienceinmathematicsisthegreatestsinglehandicapintheprogressofchemistry
in America”(1).
The ability of students to transfer and meaningfully apply their mathematical knowledge in
chemistry has been a concern in undergraduate chemistry for decades, as Dr. Farrington Daniels
pointedoutin1929(1).Onemightask,howdidwegethereandwhydidDanielsframethelack
ofexperienceandknowledgeofmathematicsinthisway?Tobeginthissymposiumseriesbook,we
shall look back over the educational landscape in the United States and in Europe to gain a bit of
perspectiveaboutthefieldofmathematicsandundergraduateandgraduateprogramsinchemistry,
then launch forward toward the present day.
© 2019 American Chemical Society
