Clustering eye-movement data uncovers students' strategies for coordinating equations and diagrams of vector fields: Strategies for coordinating vector field equations and diagrams: L. Hahn, P. Klein.
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| Title: | Clustering eye-movement data uncovers students' strategies for coordinating equations and diagrams of vector fields: Strategies for coordinating vector field equations and diagrams: L. Hahn, P. Klein. |
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| Authors: | Hahn, Larissa1 (AUTHOR) larissa.hahn@uni-goettingen.de, Klein, Pascal1 (AUTHOR) pascal.klein@uni-goettingen.de |
| Source: | Educational Studies in Mathematics. Mar2025, Vol. 118 Issue 3, p359-385. 27p. |
| Subject Terms: | *Mathematics education, Vector fields, Spatial ability, Eye tracking, Executive orders, Triangulation, Saccadic eye movements, Eye movements |
| Abstract: | In mathematics education, students are repeatedly confronted with the tasks of interpreting and relating different representations. In particular, switching between equations and diagrams plays a major role in learning mathematical procedures and solving mathematical problems. In this article, we investigate a rather unexplored topic with precisely such requirements—that is, vector fields. In our study, we first presented a series of multiple-choice tasks to 147 introductory university students at the beginning of their studies and recorded students' eye movements while they matched vector field diagrams and equations. Thereafter, students had to solve a similar coordination task on paper and justify their reasoning. Two cluster analyses were performed including (i) transition and fixation data on diagrams and options (Model 1), and (ii) additionally the number of horizontal and vertical saccades on the diagram (Model 2). In both models, two clusters emerge—with Model 1 distinguishing behaviors related to representational mapping and Model 2 additionally differentiating students according to representation-specific demands. Model 2 leads to a better distinction between the groups in terms of different performance indicators (test score, response confidence, and spatial ability) which also transfers to another task format. We conclude that vertical and horizontal saccades reflect executive actions of perception when approaching vector field coordination tasks. Thus, we recommend targeted interventions for mathematics lessons; these lessons must focus on a visual handling of the vector field diagram. Further, we infer that students' difficulties can be attributed to covariational reasoning, thereby indicating the need for further investigations. From a methodological perspective, we reflect on the triangulation of eye-tracking and verbal data in (multiple-choice) assessment scenarios. [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: 183641023 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Clustering eye-movement data uncovers students' strategies for coordinating equations and diagrams of vector fields: Strategies for coordinating vector field equations and diagrams: L. Hahn, P. Klein. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hahn%2C+Larissa%22">Hahn, Larissa</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> larissa.hahn@uni-goettingen.de</i><br /><searchLink fieldCode="AR" term="%22Klein%2C+Pascal%22">Klein, Pascal</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> pascal.klein@uni-goettingen.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Educational+Studies+in+Mathematics%22">Educational Studies in Mathematics</searchLink>. Mar2025, Vol. 118 Issue 3, p359-385. 27p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Mathematics+education%22">Mathematics education</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+fields%22">Vector fields</searchLink><br /><searchLink fieldCode="DE" term="%22Spatial+ability%22">Spatial ability</searchLink><br /><searchLink fieldCode="DE" term="%22Eye+tracking%22">Eye tracking</searchLink><br /><searchLink fieldCode="DE" term="%22Executive+orders%22">Executive orders</searchLink><br /><searchLink fieldCode="DE" term="%22Triangulation%22">Triangulation</searchLink><br /><searchLink fieldCode="DE" term="%22Saccadic+eye+movements%22">Saccadic eye movements</searchLink><br /><searchLink fieldCode="DE" term="%22Eye+movements%22">Eye movements</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In mathematics education, students are repeatedly confronted with the tasks of interpreting and relating different representations. In particular, switching between equations and diagrams plays a major role in learning mathematical procedures and solving mathematical problems. In this article, we investigate a rather unexplored topic with precisely such requirements—that is, vector fields. In our study, we first presented a series of multiple-choice tasks to 147 introductory university students at the beginning of their studies and recorded students' eye movements while they matched vector field diagrams and equations. Thereafter, students had to solve a similar coordination task on paper and justify their reasoning. Two cluster analyses were performed including (i) transition and fixation data on diagrams and options (Model 1), and (ii) additionally the number of horizontal and vertical saccades on the diagram (Model 2). In both models, two clusters emerge—with Model 1 distinguishing behaviors related to representational mapping and Model 2 additionally differentiating students according to representation-specific demands. Model 2 leads to a better distinction between the groups in terms of different performance indicators (test score, response confidence, and spatial ability) which also transfers to another task format. We conclude that vertical and horizontal saccades reflect executive actions of perception when approaching vector field coordination tasks. Thus, we recommend targeted interventions for mathematics lessons; these lessons must focus on a visual handling of the vector field diagram. Further, we infer that students' difficulties can be attributed to covariational reasoning, thereby indicating the need for further investigations. From a methodological perspective, we reflect on the triangulation of eye-tracking and verbal data in (multiple-choice) assessment scenarios. [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/s10649-023-10243-y Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 27 StartPage: 359 Subjects: – SubjectFull: Mathematics education Type: general – SubjectFull: Vector fields Type: general – SubjectFull: Spatial ability Type: general – SubjectFull: Eye tracking Type: general – SubjectFull: Executive orders Type: general – SubjectFull: Triangulation Type: general – SubjectFull: Saccadic eye movements Type: general – SubjectFull: Eye movements Type: general Titles: – TitleFull: Clustering eye-movement data uncovers students' strategies for coordinating equations and diagrams of vector fields: Strategies for coordinating vector field equations and diagrams: L. Hahn, P. Klein. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hahn, Larissa – PersonEntity: Name: NameFull: Klein, Pascal IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00131954 Numbering: – Type: volume Value: 118 – Type: issue Value: 3 Titles: – TitleFull: Educational Studies in Mathematics Type: main |
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