The Impact of Inquiry-Oriented, Differential-Equations Instruction on Students' Performance and Beliefs about Mathematics

Julia Spencer; Megan Ryals; Gianluca Guadagni

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Conference: 2024 ASEE Annual Conference & Exposition
Location: Portland, Oregon
Publication Date: June 23, 2024
Start Date: June 23, 2024
End Date: July 12, 2024
Conference Session: Mathematics Division (MATH) Technical Session 3
Tagged Division: Mathematics Division (MATH)
Tagged Topic: Diversity
Permanent URL: https://peer.asee.org/48110

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Paper Authors

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Julia Spencer University of Virginia

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Julie Spencer finished her Ph.D. in math from the University of Virginia in August of 2014. During graduate school, she developed a deep excitement about teaching math, and was able to spend the last year of her dissertation teaching at Mary Baldwin College (now Mary Baldwin University), a small women's liberal arts school. In Fall of 2015, she started teaching applied math with the School of Engineering and Applied Sciences at the University of Virginia. During her time at the University of Virginia, she has taught ordinary or partial differential equations almost every semester. She has been putting work into refining these classes so that they involve more active learning and critical thinking for students. In 2020-2021, she redesigned ordinary differential equations with two other professors to make it an inquiry-oriented class.

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Megan Ryals University of Virginia

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Gianluca Guadagni University of Virginia orcid.org/0000-0003-4568-0487

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PhD in Mathematics

Associate Professor, School of Data Science, University of Virginia.

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Abstract

Differential equations instruction for engineering students in the United States often follows a traditional lecture format and topics are often presented abstractly with applications subsequently tacked on. Additionally, the past focus has been primarily on symbolic manipulation and memorization and application of specific procedures. This study examines the impact of one department’s implementation of Inquiry Oriented Differential Equations (IODE). Beginning with materials provided by the NSF TIMES project (Teaching Inquiry-Oriented Mathematics) DUE#1431641, instructors developed classroom materials, homework assignments, and assessments aimed at engaging students in mathematical discovery, introducing new mathematics concepts through problems, and integrating symbolic, graphical, and numerical representations of the solutions of differential equations. This study will address the following research questions: 1) How do traditional and inquiry oriented differential equations courses impact students’ views about mathematics and how do these results differ across different student demographics? 2) How does student performance on conceptual and procedural assessment items differ in traditional and IODE classrooms? To address question 1, we administered the View About Mathematics Survey (VAMS) to students at the beginning and end of the semester in two fall semesters, before and after the implementation of the new curriculum. To address question 2, we administered multiple assessment items on the final exam both semesters and compared the scored results. Based on scored final exam questions, initial results suggest that students who took the IODE class demonstrated deeper conceptual understanding than those who took the traditional course without losing procedural fluency. When comparing the scores on the VAMS from the beginning and end of each semester, we saw that there was only a slight difference in the change between the Fall 2019 semester and the Fall 2021 semester. We plan to compare VAMS results from Fall 2023 to Fall 2019 and Fall 2021. We will also collect data on final exam scores from Fall of 2023 for the same questions we asked in Fall of 2019 and 2021. We also plan to do a statistical analysis of the exam scores as well as the VAMS results. Furthermore, we plan to look at changes in individual VAMS questions, as well as looking at VAMS and final exam results across demographic groups.

Citation
Format

Spencer, J., & Ryals, M., & Guadagni, G. (2024, June), The Impact of Inquiry-Oriented, Differential-Equations Instruction on Students' Performance and Beliefs about Mathematics Paper presented at 2024 ASEE Annual Conference & Exposition, Portland, Oregon. https://peer.asee.org/48110

TY  - CPAPER
AB  - Differential equations instruction for engineering students in the United States often follows a traditional lecture format and topics are often presented abstractly with applications subsequently tacked on. Additionally, the past focus has been primarily on symbolic manipulation and memorization and application of specific procedures. This study examines the impact of one department’s implementation of Inquiry Oriented Differential Equations (IODE). Beginning with materials provided by the NSF TIMES project (Teaching Inquiry-Oriented Mathematics) DUE#1431641, instructors developed classroom materials, homework assignments, and assessments aimed at engaging students in mathematical discovery, introducing new mathematics concepts through problems, and integrating symbolic, graphical, and numerical representations of the solutions of differential equations.
 
This study will address the following research questions: 1) How do traditional and inquiry oriented differential equations courses impact students’ views about mathematics and how do these results differ across different student demographics? 2) How does student performance on conceptual and procedural assessment items differ in traditional and IODE classrooms? To address question 1, we administered the View About Mathematics Survey (VAMS) to students at the beginning and end of the semester in two fall semesters, before and after the implementation of the new curriculum. To address question 2, we administered multiple assessment items on the final exam both semesters and compared the scored results.
 
Based on scored final exam questions, initial results suggest that students who took the IODE class  demonstrated deeper conceptual understanding than those who took the traditional course without losing procedural fluency. When comparing the scores on the VAMS from the beginning and end of each semester, we saw that there was only a slight difference in the change between the Fall 2019 semester and the Fall 2021 semester.
 
We plan to compare VAMS results from Fall 2023 to Fall 2019 and Fall 2021. We will also collect data on final exam scores from Fall of 2023 for the same questions we asked in Fall of 2019 and 2021. We also plan to do a statistical analysis of the exam scores as well as the VAMS results. Furthermore, we plan to look at changes in individual VAMS questions, as well as looking at VAMS and final exam results across demographic groups.
AU  - Julia Spencer
AU  - Megan Ryals
AU  - Gianluca Guadagni
CY  - Portland, Oregon
DA  - 2024/06/23
PB  - ASEE Conferences
TI  - The Impact of Inquiry-Oriented, Differential-Equations Instruction on Students' Performance and Beliefs about Mathematics
UR  - https://peer.asee.org/48110
ER  -