Expanding a concept-specific measure of mathematical knowledge for teaching: Validation of the fractions instrument

Maryam Zolfaghari; Christine Kathryn Austin; Karl Wesley Kosko; Hanan Alyami

doi:10.29333/iejme/18096

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Maryam Zolfaghari ¹ ^* , Christine Kathryn Austin ² , Karl Wesley Kosko ¹ , Hanan Alyami ³

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¹ Kent State University, USA² The University of Akron, USA³ Purdue University in Fort Wayn, USA^* Corresponding Author

Abstract

This study extends prior efforts to assess mathematical knowledge for teaching (MKT) by advancing the MKT-Fractions instrument, focusing specifically on teachers’ knowledge for teaching fractions. Building an earlier measure centered on Knowledge of Content and Students (KCS), this phase integrates items targeting Specialized Content Knowledge (SCK) and Knowledge of Content and Teaching (KCT). Drawing on responses from 103 preservice teachers across two teacher preparation programs, we employed Rasch modeling to examine evidence for internal structure and item functioning. Results indicated strong item reliability, unidimensionality, and a coherent item hierarchy aligned with a construct map that represents the developmental trajectory of knowledge needed to teach fractions. The instrument effectively differentiated item difficulty across domains without significant variation in performance across programs. These findings support the use of the MKT-Fractions instrument as a tool for assessing preservice teachers’ readiness and for informing teacher education practices focused on fraction instruction.

Keywords

mathematical knowledge for teaching
fraction
preservise teachers
Rasch modeling

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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 2, May 2026, Article No: em0871

https://doi.org/10.29333/iejme/18096

Publication date: 01 Apr 2026

Online publication date: 13 Mar 2026

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Article Downloads: 7

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How to cite this article

APA

Zolfaghari, M., Austin, C. K., Kosko, K. W., & Alyami, H. (2026). Expanding a concept-specific measure of mathematical knowledge for teaching: Validation of the fractions instrument. International Electronic Journal of Mathematics Education, 21(2), em0871. https://doi.org/10.29333/iejme/18096

Vancouver

Zolfaghari M, Austin CK, Kosko KW, Alyami H. Expanding a concept-specific measure of mathematical knowledge for teaching: Validation of the fractions instrument. INT ELECT J MATH ED. 2026;21(2):em0871. https://doi.org/10.29333/iejme/18096

AMA

Zolfaghari M, Austin CK, Kosko KW, Alyami H. Expanding a concept-specific measure of mathematical knowledge for teaching: Validation of the fractions instrument. INT ELECT J MATH ED. 2026;21(2), em0871. https://doi.org/10.29333/iejme/18096

Chicago

Zolfaghari, Maryam, Christine Kathryn Austin, Karl Wesley Kosko, and Hanan Alyami. "Expanding a concept-specific measure of mathematical knowledge for teaching: Validation of the fractions instrument". International Electronic Journal of Mathematics Education 2026 21 no. 2 (2026): em0871. https://doi.org/10.29333/iejme/18096

Harvard

Zolfaghari, M., Austin, C. K., Kosko, K. W., and Alyami, H. (2026). Expanding a concept-specific measure of mathematical knowledge for teaching: Validation of the fractions instrument. International Electronic Journal of Mathematics Education, 21(2), em0871. https://doi.org/10.29333/iejme/18096

MLA

Zolfaghari, Maryam et al. "Expanding a concept-specific measure of mathematical knowledge for teaching: Validation of the fractions instrument". International Electronic Journal of Mathematics Education, vol. 21, no. 2, 2026, em0871. https://doi.org/10.29333/iejme/18096