Award Abstract # 1835946
Tracking the Longitudinal Development of STEM Majors' Autonomy and Agency in Mathematical Proof and Proving

NSF Org: DUE
Division Of Undergraduate Education
Recipient: MICHIGAN STATE UNIVERSITY
Initial Amendment Date: March 11, 2019
Latest Amendment Date: March 11, 2019
Award Number: 1835946
Award Instrument: Standard Grant
Program Manager: Mike Ferrara
mferrara@nsf.gov
 (703)292-2635
DUE
 Division Of Undergraduate Education
EDU
 Directorate for STEM Education
Start Date: March 15, 2019
End Date: February 28, 2023 (Estimated)
Total Intended Award Amount: $299,179.00
Total Awarded Amount to Date: $299,179.00
Funds Obligated to Date: FY 2019 = $299,179.00
History of Investigator:
  • Shiv Karunakaran (Principal Investigator)
    karunak3@msu.edu
  • Mariana Levin (Co-Principal Investigator)
  • John Smith III (Co-Principal Investigator)
Recipient Sponsored Research Office: Michigan State University
426 AUDITORIUM RD RM 2
EAST LANSING
MI  US  48824-2600
(517)355-5040
Sponsor Congressional District: 07
Primary Place of Performance: Michigan State University
East Lansing
MI  US  48824-1000
Primary Place of Performance
Congressional District:
07
Unique Entity Identifier (UEI): R28EKN92ZTZ9
Parent UEI: VJKZC4D1JN36
NSF Program(s): IUSE
Primary Program Source: 04001920DB NSF Education & Human Resource
Program Reference Code(s): 8209, 9178
Program Element Code(s): 1998
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.076

ABSTRACT

Student attrition from STEM majors undermines the nation's ability to develop a STEM workforce that can lead the knowledge-based economy. A poorly studied point of attrition occurs at the transition from lower- to upper-division mathematics courses. This three-year research project intends to examine this transition by tracking the development of college students' mathematical agency and autonomy as they move into upper division math courses that emphasize mathematical proofs and argumentation. For this work, agency refers to the student's capacity to take the initiative for their learning; autonomy refers to the student's ability to take responsibility for their learning. The project team will investigate the agency and autonomy of students who are majoring or minoring in mathematics over time, as the students work through an introduction to proof course and into advanced proof-based courses. The project will contribute new knowledge about students' development as mathematicians over the course of their college education.

Learning the concepts and skills needed for mathematical proofs and proving is a fundamental learning challenge for most college students, as their prior mathematics work has emphasized "exercises" (not problems), procedures modeled by instructors, and mastery via practice. This project aims to understand the dynamics of the change that happens as students move from computation-focused work to proof-focused work. This information could inform improvements in introduction to proofs courses, in instructional practices, and in support structures such as Math Help Centers, so that students are better supported as they make the change. More broadly, this information can deepen understanding of how college students make choices about whether to continue in or leave challenging courses and majors. Consequently, this study holds promise for improving both students' experience in and the overall "flow" through the STEM pipeline. The project will recruit a sample of 20 students and track their experiences in proof-based courses for five semesters. In that period, mathematics minors will take two proof-based courses, and mathematics majors typically will take four or five. Primary data will include interviews with students early and at the end of their mathematics courses (including work on proof tasks), observations of students as they work inside and outside of class, and course materials such as assignments and exams. A qualitative analysis will produce dynamic profiles of the of positive and negative changes in students' agency and autonomy over the five semesters. These results will complement and potentially help to explain student outcomes such as course grades, enrollment in additional math courses, and persistence in the mathematics major or minor.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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Smith III, J. "Dimensions of Variation in group work within the ?same? multi-section undergraduate course" Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education , 2020 https://doi.org/ Citation Details
Küchle, Valentin and Karunakaran, Shiv and Levin, Mariana and Smith III, John and Castle, Sarah and Hwang, Jihye and Lu, Yaomingxin and Elmore, Robert "Collapsing Spaces, Colliding Places: Leveraging Constructs from Humanistic Geography to Explore Mathematics Classes" Journal of Humanistic Mathematics , v.13 , 2023 https://doi.org/10.5642/jhummath.LMPQ5945 Citation Details
Levin, M. "Math and moral reasoning in the age of the internet: Undergraduate students? perspectives on the line between acceptable use of resources and cheating" Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education , 2020 https://doi.org/ Citation Details

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.

Proof and proving presents most college students with fundamental learning challenges, as their prior mathematics work has emphasized "excercises" (not problems), procedures modeled by instructors, and mastery via practice. Most introduction to proofs (ITP) courses violate these assumptions. Prior research shows that students find proof and proving work different and deeply challenging. These courses set the conditions where students' agency and autonomy change, often in dynamic ways. This project aimed to understand the dynamics of this change and development so that ITP courses, instructional practices, and external structures can better support it. As college students make choices about continuing in challenging mathematics courses, we aimed to learn more about students' experiences in and the "flow" out of the STEM pipeline.

In the course of the study, we generated operationalized definitions of mathematical agency and mathematical autonomy. The former is defined as the felt capacity to take action in the face of challenges related to mathematical work. This capacity is jointly shaped by contextual norms and resources in specific courses and students’ narratives about their views of mathematics, their future in it, their learning processes, their selves relative to authorities. The latter is definted as a quality of actions, that reflects the student’s active resistance to endorsing, following, or replicating the reasoning of mathematical authorities (e.g., texts, internet sources, instructors, peers), without engaging in sufficient sense-making to make that reasoning their own. What is unique about these definitions is that they are entirely developed from the empirical data collected, and were developed to be operationalizable and observable. 

The project tracked 2 cohorts of about 15 students each as they proceeded through their proof-based mathematical coursework. This longitunal study allowed for the generation of detailed and rich profiles/narratives of students that highlight how their agency and autonomy develops and evolves within and without their instructional environments. This project was also directly effected by the onset of the COVID-19 pandemic. This life-changing event also offered insight into how these students coped with and managed their mathematics learning, along with the added pressures of the pandemic.

 

grad students 

pandemic impact

definitions of agency and autonomy

longitudinal nature of study 

transition from computation to proof


Last Modified: 06/29/2023
Modified by: Shiv S Karunakaran

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