Transforming equations into equivalent equations—an empirical study of the equation transformation capability as a multidimensional construct.
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| Title: | Transforming equations into equivalent equations—an empirical study of the equation transformation capability as a multidimensional construct. |
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| Authors: | Noster, Norbert1 (AUTHOR) norbert.noster@uni-wuerzburg.de, Siller, Hans-Stefan1 (AUTHOR) hans-stefan.siller@uni-wuerzburg.de |
| Source: | Educational Studies in Mathematics. Oct2025, Vol. 120 Issue 2, p249-267. 19p. |
| Subject Terms: | *Mathematical ability, *Secondary education, *Statistical correlation, *Academic achievement, Confirmatory factor analysis, Mathematical transformations, Latent variables, Empirical research |
| Geographic Terms: | Germany |
| Abstract: | This study focuses on equivalent transformations of equations in the context of secondary school education. Solving (determining the solution set of an equation), normalizing (transforming an equation to reach a certain form), and reorganizing equations (isolating variables in formulae) are discussed as different possible applications of these transformations. An equation transformation capability is defined, incorporating these activities, and is empirically studied. A confirmatory factor analysis is performed to investigate the capability as a construct concerning each application (not) representing a single latent variable. Furthermore, success rates for individual applications are analyzed. Additionally, statistical implicative analysis is performed to study possible implicative relations between the different applications. The analyses are based on a test that 271 secondary school students took at the end of the 9th and 10th grades in Germany. Results suggest a three-dimensional model, with each of the mentioned applications representing individual latent variables. Regarding the reorganization of equations, it does not seem to matter whether the equation is embedded in a context or not. This application also appears to be the most challenging one, whereas the other two do not differ regarding the solution rate. The implicative analysis suggests that learners who are able to reorganize equations are more likely to solve or normalize equations compared to the reverse implications. [ABSTRACT FROM AUTHOR] |
| Copyright of Educational Studies in Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Education Research Complete |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 188451644 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Transforming equations into equivalent equations—an empirical study of the equation transformation capability as a multidimensional construct. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Noster%2C+Norbert%22">Noster, Norbert</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> norbert.noster@uni-wuerzburg.de</i><br /><searchLink fieldCode="AR" term="%22Siller%2C+Hans-Stefan%22">Siller, Hans-Stefan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> hans-stefan.siller@uni-wuerzburg.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Educational+Studies+in+Mathematics%22">Educational Studies in Mathematics</searchLink>. Oct2025, Vol. 120 Issue 2, p249-267. 19p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Mathematical+ability%22">Mathematical ability</searchLink><br />*<searchLink fieldCode="DE" term="%22Secondary+education%22">Secondary education</searchLink><br />*<searchLink fieldCode="DE" term="%22Statistical+correlation%22">Statistical correlation</searchLink><br />*<searchLink fieldCode="DE" term="%22Academic+achievement%22">Academic achievement</searchLink><br /><searchLink fieldCode="DE" term="%22Confirmatory+factor+analysis%22">Confirmatory factor analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+transformations%22">Mathematical transformations</searchLink><br /><searchLink fieldCode="DE" term="%22Latent+variables%22">Latent variables</searchLink><br /><searchLink fieldCode="DE" term="%22Empirical+research%22">Empirical research</searchLink> – Name: SubjectGeographic Label: Geographic Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Germany%22">Germany</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This study focuses on equivalent transformations of equations in the context of secondary school education. Solving (determining the solution set of an equation), normalizing (transforming an equation to reach a certain form), and reorganizing equations (isolating variables in formulae) are discussed as different possible applications of these transformations. An equation transformation capability is defined, incorporating these activities, and is empirically studied. A confirmatory factor analysis is performed to investigate the capability as a construct concerning each application (not) representing a single latent variable. Furthermore, success rates for individual applications are analyzed. Additionally, statistical implicative analysis is performed to study possible implicative relations between the different applications. The analyses are based on a test that 271 secondary school students took at the end of the 9th and 10th grades in Germany. Results suggest a three-dimensional model, with each of the mentioned applications representing individual latent variables. Regarding the reorganization of equations, it does not seem to matter whether the equation is embedded in a context or not. This application also appears to be the most challenging one, whereas the other two do not differ regarding the solution rate. The implicative analysis suggests that learners who are able to reorganize equations are more likely to solve or normalize equations compared to the reverse implications. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Educational Studies in Mathematics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=ehh&AN=188451644 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10649-025-10419-8 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 19 StartPage: 249 Subjects: – SubjectFull: Mathematical ability Type: general – SubjectFull: Secondary education Type: general – SubjectFull: Statistical correlation Type: general – SubjectFull: Academic achievement Type: general – SubjectFull: Confirmatory factor analysis Type: general – SubjectFull: Mathematical transformations Type: general – SubjectFull: Latent variables Type: general – SubjectFull: Empirical research Type: general – SubjectFull: Germany Type: general Titles: – TitleFull: Transforming equations into equivalent equations—an empirical study of the equation transformation capability as a multidimensional construct. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Noster, Norbert – PersonEntity: Name: NameFull: Siller, Hans-Stefan IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: Oct2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00131954 Numbering: – Type: volume Value: 120 – Type: issue Value: 2 Titles: – TitleFull: Educational Studies in Mathematics Type: main |
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