Using learning progression-based interactive dynamic geometry instruction to develop quadrilateral reasoning in preservice teachers

Michael L. Winer; Michael T. Battista; Viktoria Taroudaki

doi:10.29333/iejme/19419

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Michael L. Winer ¹ ^* , Michael T. Battista ² , Viktoria Taroudaki ¹

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¹ Eastern Washington University, UNITED STATES² The Ohio State University, UNITED STATES^* Corresponding Author

Abstract

This study investigated the learning of K–8 preservice teachers (PTs) while enrolled in an in-person class that was integrated with an online, individualized, and interactive Dynamic Geometry curriculum (iDGi), built from empirically derived learning progressions (LP). The research examined PTs’ developing understanding of the prototypical defining properties of quadrilaterals—formal geometric attributes that align with the visually salient features students often use when identifying and reasoning about quadrilateral types and their relationships. It also explored how the curriculum supported PTs’ transition toward more precise and abstract forms of reasoning. The curriculum’s effectiveness was evaluated with 541 PTs across multiple courses, all of whom completed identical online multiple-choice LP-based assessments before and after engaging with iDGi. Findings indicated that iDGi significantly improved PTs’ reasoning about quadrilaterals. Analyses of three whole-class discussions illustrated how related in-class activities complemented and deepened PTs’ conceptual understanding.

Keywords

geometry
learning progressions
elementary preservice teachers
quadrilaterals
dynamic geometry

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

INT ELECT J MATH ED, Volume 21, Issue 4, November 2026, Article No: em0896

https://doi.org/10.29333/iejme/19419

Publication date: 25 Sep 2026

Online publication date: 01 Oct 2026

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How to cite this article

APA

Winer, M. L., Battista, M. T., & Taroudaki, V. (2026). Using learning progression-based interactive dynamic geometry instruction to develop quadrilateral reasoning in preservice teachers. International Electronic Journal of Mathematics Education, 21(4), em0896. https://doi.org/10.29333/iejme/19419

Vancouver

Winer ML, Battista MT, Taroudaki V. Using learning progression-based interactive dynamic geometry instruction to develop quadrilateral reasoning in preservice teachers. INT ELECT J MATH ED. 2026;21(4):em0896. https://doi.org/10.29333/iejme/19419

AMA

Winer ML, Battista MT, Taroudaki V. Using learning progression-based interactive dynamic geometry instruction to develop quadrilateral reasoning in preservice teachers. INT ELECT J MATH ED. 2026;21(4), em0896. https://doi.org/10.29333/iejme/19419

Chicago

Winer, Michael L., Michael T. Battista, and Viktoria Taroudaki. "Using learning progression-based interactive dynamic geometry instruction to develop quadrilateral reasoning in preservice teachers". International Electronic Journal of Mathematics Education 2026 21 no. 4 (2026): em0896. https://doi.org/10.29333/iejme/19419

Harvard

Winer, M. L., Battista, M. T., and Taroudaki, V. (2026). Using learning progression-based interactive dynamic geometry instruction to develop quadrilateral reasoning in preservice teachers. International Electronic Journal of Mathematics Education, 21(4), em0896. https://doi.org/10.29333/iejme/19419

MLA

Winer, Michael L. et al. "Using learning progression-based interactive dynamic geometry instruction to develop quadrilateral reasoning in preservice teachers". International Electronic Journal of Mathematics Education, vol. 21, no. 4, 2026, em0896. https://doi.org/10.29333/iejme/19419