The omnipresence of the Letter-as-Object misconception: a multilevel Latent Transition Analysis on understanding variables.
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| Title: | The omnipresence of the Letter-as-Object misconception: a multilevel Latent Transition Analysis on understanding variables. |
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| Authors: | Klingbeil, Katrin1 (AUTHOR) katrin.klingbeil@uni-due.de, Moons, Filip2 (AUTHOR) f.moons@uu.nl |
| Source: | Educational Studies in Mathematics. Nov2025, Vol. 120 Issue 3, p455-476. 22p. |
| Subject Terms: | *Algebra education |
| Abstract: | When students first encounter variables in algebra, they often develop the Letter-as-Object misconception, interpreting letters as labels for objects rather than references to numerical values. This study analysed the response patterns of 2220 German Year 7 and 8 students (aged 12–14) using the SMART test 'Meaning of Letters', designed to assess various subtypes of this misconception. Employing multilevel Latent Transition Analysis, we identified five latent classes and tracked shifts in students' classifications over 4 weeks of algebra instruction. These classes revealed persistent patterns in how the Letter-as-Object misconception and its subtypes manifest. While the majority of students exhibited this misconception, their responses varied depending on the equation type in the test items. Encouragingly, the class of students with mostly correct responses tripled in size after instruction, though it remained small, with a majority of students staying in their original classes. This study highlights the potential of multilevel Latent Transition Analysis to track misconceptions and conceptual changes over time and is among the first to account for the multilevel data structure of students nested within teachers in a Latent Transition Analysis. [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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 188798270 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: The omnipresence of the Letter-as-Object misconception: a multilevel Latent Transition Analysis on understanding variables. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Klingbeil%2C+Katrin%22">Klingbeil, Katrin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> katrin.klingbeil@uni-due.de</i><br /><searchLink fieldCode="AR" term="%22Moons%2C+Filip%22">Moons, Filip</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> f.moons@uu.nl</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Educational+Studies+in+Mathematics%22">Educational Studies in Mathematics</searchLink>. Nov2025, Vol. 120 Issue 3, p455-476. 22p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Algebra+education%22">Algebra education</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: When students first encounter variables in algebra, they often develop the Letter-as-Object misconception, interpreting letters as labels for objects rather than references to numerical values. This study analysed the response patterns of 2220 German Year 7 and 8 students (aged 12–14) using the SMART test 'Meaning of Letters', designed to assess various subtypes of this misconception. Employing multilevel Latent Transition Analysis, we identified five latent classes and tracked shifts in students' classifications over 4 weeks of algebra instruction. These classes revealed persistent patterns in how the Letter-as-Object misconception and its subtypes manifest. While the majority of students exhibited this misconception, their responses varied depending on the equation type in the test items. Encouragingly, the class of students with mostly correct responses tripled in size after instruction, though it remained small, with a majority of students staying in their original classes. This study highlights the potential of multilevel Latent Transition Analysis to track misconceptions and conceptual changes over time and is among the first to account for the multilevel data structure of students nested within teachers in a Latent Transition Analysis. [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.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10649-025-10428-7 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 22 StartPage: 455 Subjects: – SubjectFull: Algebra education Type: general Titles: – TitleFull: The omnipresence of the Letter-as-Object misconception: a multilevel Latent Transition Analysis on understanding variables. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Klingbeil, Katrin – PersonEntity: Name: NameFull: Moons, Filip IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 11 Text: Nov2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00131954 Numbering: – Type: volume Value: 120 – Type: issue Value: 3 Titles: – TitleFull: Educational Studies in Mathematics Type: main |
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