Award Abstract # 1611946
Collaborative Research: Raising Physics to the Surface

NSF Org: DUE
Division Of Undergraduate Education
Recipient: WINONA STATE UNIVERSITY
Initial Amendment Date: September 20, 2016
Latest Amendment Date: December 7, 2021
Award Number: 1611946
Award Instrument: Standard Grant
Program Manager: R. Corby Hovis
chovis@nsf.gov
 (703)292-4625
DUE
 Division Of Undergraduate Education
EDU
 Directorate for STEM Education
Start Date: March 1, 2017
End Date: September 30, 2022 (Estimated)
Total Intended Award Amount: $87,580.00
Total Awarded Amount to Date: $87,580.00
Funds Obligated to Date: FY 2016 = $87,580.00
History of Investigator:
  • Aaron Wangberg (Principal Investigator)
    awangberg@winona.edu
Recipient Sponsored Research Office: Winona State University
175 W MARK ST
WINONA
MN  US  55987-3384
(507)457-5519
Sponsor Congressional District: 01
Primary Place of Performance: Winona State University
175 W. Mark St.
Winona
MN  US  55987-5838
Primary Place of Performance
Congressional District:
01
Unique Entity Identifier (UEI): MQBGMELWH9M3
Parent UEI:
NSF Program(s): ECR-EDU Core Research
Primary Program Source: 04001617DB NSF Education & Human Resource
Program Reference Code(s): 8209, 9178
Program Element Code(s): 798000
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.076

ABSTRACT

The significance of the Raising Physics to the Surface project is that it will yield a set of hands-on, discovery-style, discussion-based classroom activities where students develop meaningful understandings of physical systems that depend on multiple variables. Most physical systems depend on more than one variable. However, when solving problems about these systems, many students merely apply pointless algebraic manipulations to memorized formulas. Students gain meaningful understandings by thinking conceptually and geometrically about the relationships between variables. During the Raising Physics activities, students will develop these understandings by working with custom, dry-erasable, 3D surfaces, corresponding contour and gradient maps, and computer-based models. The activities will span physics topics in classical mechanics, electricity and magnetism, and thermal physics. Instructors from various colleges and universities will learn how to use the Raising Physics materials effectively during a summer workshop then deploy the materials in their physics courses.

The goals of the Raising Physics project are to (a) produce and disseminate curricular materials, (b) identify the best practices for using these materials in various classroom settings, and (c) study the impact of these materials on student learning and on instructors' attitudes, beliefs, and teaching practices. The curricular materials will be informed by results from research in physics and math education that demonstrate the importance of (1) using tangible models, maps and tools to explore geometric relationships, (2) representing physical quantities in multiple ways, and (3) discussing ideas in small groups for meaningful and flexible learning. The research components of this project will investigate the effectiveness of the activities and will advance understanding of how students reason about multivariable functions in physics using multiple representations.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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Aaron Wangberg and Elizabeth Gire "Raising Calculus to the Surface: Extending derivatives and concepts with multiple representations" Calculus in upper secondary and beginning university mathematics , 2019 , p.171
Aaron Wangberg and Elizabeth Gire and Tevian Dray "Measuring the derivative using Surfaces" Teaching Mathematics and its Applications: An International Journal of the IMA , 2021 10.1093/teamat/hrab030
Aaron Wangberg, Elizabeth Gire, Tevian Dray "Measuring the derivative using surfaces" Teaching Mathematics and its Applications: An International Journal of the IMA , v.41 , 2022 , p.110 https://doi.org/10.1093/teamat/hrab030
Abigail Kimbrough and Kelby T. Hahn and Paul J. Emigh and Elizabeth Gire "Teaching gravitational potential energy: Student Interactions with Surface Manipulatives" 2019 Physics Education Research Conference , 2019 10.1119/perc.2019.pr.Kimbrough
Alfson, Jonathan W., Paul J. Emigh, Aaron Wangberg, Robyn Wangberg, and Elizabeth Gire "Surface Models and Multiple External Representations in Paradigms" American Association of Physics Teachers Annual Winter Meeting , 2021
Emigh, P., Alfson, J., and Gire, E. "Student Sensemaking about Equipotential Graphs." Proceedings of the 2018 Physics Education Research Conference, Washington, D.C. , 2018
Gire, E., Wangberg, A., & Wangberg, R. "Multiple tools for visualizing equipotential surfaces: Optimizing for instructional goals" In (Eds.) L. Ding, A. Traxler, and Y. Cao, Proceedings of the 2017 Physics Education Research Conference, Cincinnati , 2017
Paul J. Emigh and Reese R. Siegel and Jonathan W. Alfson and Elizabeth Gire "Student reasoning about multivariable covariation in thermodynamics" 2019 Physics Education Research Conference , 2019 10.1119/perc.2019.pr.Emigh
Wangberg, A. "Fostering Student Discovery and Conjecture in Multivariable Calculus" Journal of Humanistic Mathematics , 2020
Wangberg, A. "Student Reasoning with Graphs, Contour Maps, and Rate of Change for Multivariable Functions" Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education. , 2020

PROJECT OUTCOMES REPORT

Disclaimer

This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.

In the Raising Physics to the Surface project, we designed 7 3D plastic graphs for college-level physics instruction. We created and tested 15 classroom activities for topics in classical mechanics, electricity and magnetism, and thermal physics. In these activities, students work in groups with the plastic graphs and contour maps to explore quantitative relationships for context-rich physical systems, using the physical materials to coordinate geometric, algebraic, and conceptual ways of reasoning. The activities feature physical systems that are algebraically involved (e.,g. the internal energy of water vapor or the electric potential of a quadrupole) or commonly studied (e.g., gravitational potential for a spherical planet, electric potential due to a parallel plate capacitor). The 3D plastic graphs are large, dry-erasable, transparent, and each are engineered with specific, pedagogically useful features. 


Beyond instructors at the host institutions, six beta testing faculty attended a professional development workshop to learn how to use these student-centered pedagogies with the 3D graphs. The beta testing faculty received classroom sets of the 3D graphs and contour maps, used the activities in their own classes, and then provided feedback that was used to refine and revise the activities and instructor guides. A total of 511 plastic graphs were manufactured for this project and were distributed to 9 institutions.


The activities provided a context for research about how students’ reason with multiple representations in these physics contexts. We found that the 3D plastic graphs have important structural features that make them particularly powerful pedagogical tools and support students in engaging in scientific practices: the ease with which students can discern relative values of the function (ease of use), the spatial separation between the value of the function and the domain (individuation), the dry-erasable nature promoting brainstorming and serving as a place to store ideas (configurability), and the large size of the graph allow multiple students to annotate and promoting collaboration (accessibility). However, although the 3D plastic graphs can be annotated with a dry-erase marker, they have limited configurability in that they cannot be reformed to represent a different system. This has implications for the cost of obtaining and storing the graphs, particularly for large classes, and designing activities in which student groups work with different physical systems and share knowledge across groups by comparing and contrasting features of their system.


 


Last Modified: 12/28/2022
Modified by: Aaron Wangberg

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