Solution proposals of preservice mathematics teachers regarding the cases of 3⁻²·5³ = 15⁻⁶ and 12⁸: 6² = 2⁴

Sümeyye Çakir; Esra Altıntaş

doi:10.5281/zenodo.20648909

Solution proposals of preservice mathematics teachers regarding the cases of 3⁻²·5³ = 15⁻⁶ and 12⁸: 6² = 2⁴

Abstract

This study aims to examine the solution proposals of preservice mathematics teachers regarding students’ incorrect solutions to the expressions 3-2.53= 15-6 and 128:62= 24. The purpose of the study is to identify how teacher candidates approach these error situations, to reveal possible misconceptions related to multiplication and division of exponential expressions, and to explore instructional strategies proposed to correct such errors. In this context, the study seeks to contribute to preventing similar misconceptions from recurring and to guiding teachers who encounter these types of errors in classroom settings. The study was conducted using a qualitative case study design. The study group consisted of thirty-five fourth-year preservice mathematics teachers enrolled at a public university during the fall semester of the 2024–2025 academic year. Data were collected through a written opinion form consisting of two open-ended questions related to errors in multiplication and division of exponential expressions. The collected data were analyzed using content analysis. The findings revealed that preservice teachers most frequently proposed strategies such as explaining exponential expressions through repeated multiplication, using simple examples, and applying factorization. However, it was also observed that some preservice teachers had difficulty in developing effective solution proposals for the given error situations. These findings indicate the importance of strengthening preservice mathematics teachers’ pedagogical content knowledge related to exponential expressions and student misconceptions.

Keywords

Ethical Statement

This study was conducted with the approval of the Educational Research Ethics Committee of Aydın Adnan Menderes University, dated 04/11/2024 and numbered XVI. The purpose of the study was explained to the preservice teachers, and they were informed that participation was voluntary and that they could withdraw from the study at any time. Participants’ identities were kept confidential, and the collected data were used solely for scientific purposes.

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Details

Primary Language

English

Subjects

Mathematics Education

Journal Section

Research Article

Authors

Sümeyye Çakir ^*
Türkiye

Esra Altıntaş
0000-0003-3311-7179
Türkiye

Early Pub Date

June 11, 2026

Publication Date

June 30, 2026

Submission Date

June 26, 2025

Acceptance Date

December 19, 2025

Published in Issue

Year 2026 Volume: 7 Number: 1

DOI

https://doi.org/10.5281/zenodo.20648909

IZ

https://izlik.org/JA65EP92DN

Cite

RIS / Bibtex

APA

Çakir, S., & Altıntaş, E. (2026). Solution proposals of preservice mathematics teachers regarding the cases of 3⁻²·5³ = 15⁻⁶ and 12⁸: 6² = 2⁴. Journal for the Mathematics Education and Teaching Practices, 7(1), 13-29. https://doi.org/10.5281/zenodo.20648909

AMA

1.Çakir S, Altıntaş E. Solution proposals of preservice mathematics teachers regarding the cases of 3⁻²·5³ = 15⁻⁶ and 12⁸: 6² = 2⁴. JMETP. 2026;7(1):13-29. doi:10.5281/zenodo.20648909

Chicago

Çakir, Sümeyye, and Esra Altıntaş. 2026. “Solution Proposals of Preservice Mathematics Teachers Regarding the Cases of 3⁻²·5³ = 15⁻⁶ and 12⁸: 6² = 2⁴”. Journal for the Mathematics Education and Teaching Practices 7 (1): 13-29. https://doi.org/10.5281/zenodo.20648909.

EndNote

Çakir S, Altıntaş E (June 1, 2026) Solution proposals of preservice mathematics teachers regarding the cases of 3⁻²·5³ = 15⁻⁶ and 12⁸: 6² = 2⁴. Journal for the Mathematics Education and Teaching Practices 7 1 13–29.

IEEE

[1]S. Çakir and E. Altıntaş, “Solution proposals of preservice mathematics teachers regarding the cases of 3⁻²·5³ = 15⁻⁶ and 12⁸: 6² = 2⁴”, JMETP, vol. 7, no. 1, pp. 13–29, June 2026, doi: 10.5281/zenodo.20648909.

ISNAD

Çakir, Sümeyye - Altıntaş, Esra. “Solution Proposals of Preservice Mathematics Teachers Regarding the Cases of 3⁻²·5³ = 15⁻⁶ and 12⁸: 6² = 2⁴”. Journal for the Mathematics Education and Teaching Practices 7/1 (June 1, 2026): 13-29. https://doi.org/10.5281/zenodo.20648909.

JAMA

1.Çakir S, Altıntaş E. Solution proposals of preservice mathematics teachers regarding the cases of 3⁻²·5³ = 15⁻⁶ and 12⁸: 6² = 2⁴. JMETP. 2026;7:13–29.

MLA

Çakir, Sümeyye, and Esra Altıntaş. “Solution Proposals of Preservice Mathematics Teachers Regarding the Cases of 3⁻²·5³ = 15⁻⁶ and 12⁸: 6² = 2⁴”. Journal for the Mathematics Education and Teaching Practices, vol. 7, no. 1, June 2026, pp. 13-29, doi:10.5281/zenodo.20648909.

Vancouver

1.Sümeyye Çakir, Esra Altıntaş. Solution proposals of preservice mathematics teachers regarding the cases of 3⁻²·5³ = 15⁻⁶ and 12⁸: 6² = 2⁴. JMETP. 2026 Jun. 1;7(1):13-29. doi:10.5281/zenodo.20648909