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Research Spending & Results

Award Detail

Doing Business As Name:Oklahoma State University
  • John Paul Cook
  • (405) 744-9995
Award Date:06/10/2021
Estimated Total Award Amount: $ 500,000
Funds Obligated to Date: $ 500,000
  • FY 2021=$500,000
Start Date:09/01/2021
End Date:08/31/2024
Transaction Type:Grant
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.076
Primary Program Source:040106 NSF Education & Human Resource
Award Title or Description:Undergraduate Students' Reasoning about Equivalence in Multiple Mathematical Domains: Exploration and Theory-Building
Federal Award ID Number:2055590
DUNS ID:049987720
Parent DUNS ID:049987720
Program:ECR-EHR Core Research
Program Officer:
  • Michael Ferrara
  • (703) 292-2635

Awardee Location

Awardee Cong. District:03

Primary Place of Performance

Organization Name:Oklahoma State University
Street:401 Mathematical Sciences
Cong. District:03

Abstract at Time of Award

Equivalence, the idea that two objects can be considered “the same” in some way, is one of the most important concepts in mathematics. Learners from elementary through graduate school encounter equivalence in many ways across many mathematical topics. Unfortunately, students can have difficulties in understanding ideas of equivalence in more advanced mathematics courses. One possible challenge is that equivalence is often treated as a new concept each time it is introduced within or across courses. In addition, students’ ways of thinking about this fundamental idea are not yet well understood. To begin to fill this knowledge gap, this project aims to develop a theory about how students reason with equivalence across two mathematical disciplines: combinatorics and abstract algebra. To gather data on which to base the theory, the project will examine the current body of literature on equivalence, analyze textbooks, and conduct interviews with mathematicians and students. The theory that emerges from this research will help researchers and educators better understand different ways to reason about equivalence across mathematical domains. This work also may have long-term benefits: such a theory could inform the design of curricular materials to help students at all levels see instances of equivalence in a more consistent, linked fashion. Equivalence is one of the most fundamental, far-reaching concepts in all of mathematics and an essential component of the K-16 mathematics curriculum. Its importance is particularly evident at the postsecondary level, where equivalence manifests and plays a key role in virtually every domain from calculus to abstract algebra. Despite its prevalence and importance, undergraduate students can be challenged to understand instances of equivalence, especially if similar concepts are introduced in a disconnected way. Moreover, characterizations of equivalence in research are often implicit or domain-specific, speaking to the need for cognitive models that might prove useful within and across mathematical disciplines. This project will work toward a crosscutting theory of equivalence that could be applied in multiple contexts. Focusing on the domains of combinatorics and abstract algebra, the project’s primary research questions are: (1) What is entailed in undergraduate students’ ways of thinking about equivalence within the domains of abstract algebra and combinatorics? (2) What is entailed in undergraduate students’ ways of thinking about equivalence across these domains? To answer these questions, the project will leverage existing literature, textbook analysis, and interviews with mathematicians to develop an initial theory and then rigorously refine that theory via sequences of exploratory and targeted task-based clinical interviews with students, focusing on abstract algebra in Year 1, combinatorics in Year 2, and both domains in Year 3. This project is funded by the EHR Core Research (ECR) program, which supports work that advances fundamental research on STEM learning and learning environments, broadening participation in STEM, and STEM workforce development. 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.

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