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A Framework for Time and Covariational Reasoning

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Title: A Framework for Time and Covariational Reasoning
Language: English
Authors: Kevin C. Moore
Source: The Mathematics Educator. 2025 33(1):61-90.
Availability: Mathematics Education Student Association, University of Georgia. 105 Aderhold Hall, Athens, GA 30602. Tel: 706-542-4194; Fax: 706-542-4551; e-mail: mesaprez@gmail.com; Web site: http://tme.journals.libs.uga.edu/index.php/tme/index
Peer Reviewed: Y
Page Count: 30
Publication Date: 2025
Sponsoring Agency: National Science Foundation (NSF), Division of Research on Learning in Formal and Informal Settings (DRL)
National Science Foundation (NSF), Division of Undergraduate Education (DUE)
Contract Number: 1350342
1419973
Document Type: Journal Articles
Reports - Descriptive
Education Level: Elementary Education
Secondary Education
Higher Education
Postsecondary Education
Descriptors: Mathematics Education, Mathematical Concepts, Mathematical Models, Elementary School Mathematics, Secondary School Mathematics, College Mathematics, Time, Mathematics Skills, Thinking Skills, Mathematical Logic, Task Analysis, Piagetian Theory, Developmental Tasks
ISSN: 1062-9017
Abstract: Covariational reasoning has emerged as a productive construct to characterize students' mathematical development. Researchers have illustrated its importance for major middle, secondary, and undergraduate mathematical concepts, including rate of change, accumulation, and modeling. Within this line of work, several researchers have indicated differences between experiential and conceptual time with respect to the covariational relationships students construct. I draw on this body of literature and return to Piaget's perspective of time to provide a framework for the role of time in students' covariational reasoning. The framework also clarifies the nature of the multiplicative objects underlying students' covariational relationships. To illustrate the framework and capture its emergence from second-order models of students' mathematics, I describe the framework as it relates to students' engagement in a task. [Note: The page range (62-90) shown on the PDF is incorrect. The correct page range is p61-90.]
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1492954
Database: ERIC
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  Data: Mathematics Education Student Association, University of Georgia. 105 Aderhold Hall, Athens, GA 30602. Tel: 706-542-4194; Fax: 706-542-4551; e-mail: mesaprez@gmail.com; Web site: http://tme.journals.libs.uga.edu/index.php/tme/index
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  Data: Covariational reasoning has emerged as a productive construct to characterize students' mathematical development. Researchers have illustrated its importance for major middle, secondary, and undergraduate mathematical concepts, including rate of change, accumulation, and modeling. Within this line of work, several researchers have indicated differences between experiential and conceptual time with respect to the covariational relationships students construct. I draw on this body of literature and return to Piaget's perspective of time to provide a framework for the role of time in students' covariational reasoning. The framework also clarifies the nature of the multiplicative objects underlying students' covariational relationships. To illustrate the framework and capture its emergence from second-order models of students' mathematics, I describe the framework as it relates to students' engagement in a task. [Note: The page range (62-90) shown on the PDF is incorrect. The correct page range is p61-90.]
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      – Text: English
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        StartPage: 61
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      – SubjectFull: Mathematics Education
        Type: general
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      – SubjectFull: Mathematical Models
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      – SubjectFull: Secondary School Mathematics
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      – SubjectFull: College Mathematics
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      – SubjectFull: Time
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