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The Role of Multiplicative Objects in Students' Reasoning with Formulas

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Title: The Role of Multiplicative Objects in Students' Reasoning with Formulas
Language: English
Authors: Irma E. Stevens
Source: Journal for Research in Mathematics Education. 2026 57(1):30-52.
Availability: National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail: publicationsdept@nctm.org; Web site: https://pubs.nctm.org/
Peer Reviewed: Y
Page Count: 23
Publication Date: 2026
Sponsoring Agency: National Science Foundation (NSF), Division of Research on Learning in Formal and Informal Settings (DRL)
Contract Number: 1350342
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Secondary Education
Descriptors: Mathematical Formulas, Logical Thinking, Preservice Teachers, Secondary School Teachers, Mathematics Teachers, Mental Computation, Geometric Concepts
DOI: 10.5951/jresematheduc-2023-0092
ISSN: 0021-8251
1945-2306
Abstract: Researchers have identified both the affordances of engaging students in symbolization activities and the difficulties students have in constructing meaningful representations of contexts through algebraic expressions and formulas. This article includes clinical interviews and teaching experiments with preservice secondary mathematics teachers focused on engaging them with dynamic geometric contexts to understand their representational activity with formulas. I introduce the notion of a multiplicative object in the context of formulas and express its importance in the construction of productive meanings for constructing formulas via covariational reasoning. Specifically, I provide a framework for the different types of multiplicative objects for formulas and connect students' constructions of a multiplicative object with their covariational reasoning within and across different geometric contexts.
Abstractor: As Provided
Entry Date: 2026
Accession Number: EJ1494711
Database: ERIC
FullText Text:
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  Data: Researchers have identified both the affordances of engaging students in symbolization activities and the difficulties students have in constructing meaningful representations of contexts through algebraic expressions and formulas. This article includes clinical interviews and teaching experiments with preservice secondary mathematics teachers focused on engaging them with dynamic geometric contexts to understand their representational activity with formulas. I introduce the notion of a multiplicative object in the context of formulas and express its importance in the construction of productive meanings for constructing formulas via covariational reasoning. Specifically, I provide a framework for the different types of multiplicative objects for formulas and connect students' constructions of a multiplicative object with their covariational reasoning within and across different geometric contexts.
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      – SubjectFull: Mathematical Formulas
        Type: general
      – SubjectFull: Logical Thinking
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      – SubjectFull: Preservice Teachers
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      – SubjectFull: Geometric Concepts
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