An Investigation of Primary School Teachers’ Experiences in Teaching Division
Year 2026,
Volume: 11 Issue: 1, 119 - 141, 15.03.2026
Özlem Doğan Temur
,
Hülya Coşkun
,
Abdullah Yavuz Yeşil
Abstract
Primary school mathematics education places significant emphasis on the teaching of arithmetic operations. Among these, the instruction of division has a structure that requires careful and sensitive handling by classroom teachers. The aim of this study is to examine classroom teachers’ experiences regarding the teaching of division. The research was designed using a qualitative approach and employed a phenomenological research method. The study group consisted of 20 experienced classroom teachers working in the provinces of Afyonkarahisar and Kütahya. Criterion sampling and convenience sampling methods were used. Data were collected through a semi-structured interview form consisting of six questions developed by the researchers. Thematic analysis was employed in the data analysis process. The findings indicate that only a limited number of teachers used problem statements and real-life connections in the teaching of division. Although teachers considered the use of models necessary for teaching division, they experienced difficulties in establishing meaningful instructional connections through these models. Furthermore, analysis of teachers’ instructional processes and problem constructions related to remainders revealed a predominantly one-dimensional and non-relational structure.
Ethical Statement
CONFLICT OF INTEREST STATEMENT
The authors declare that there is no conflict of interest in this study.
RESEARCH AND PUBLICATION ETHICS STATEMENT
The authors declare that research and publication ethics are followed in this study.
The necessary permission to conduct the study was obtained from Social and Human Sciences Research and Publication Ethics Committee of Kütahya Dumlupınar University (April 28, 2025-2025/04)
AUTHOR LIABILITY STATEMENT
The authors declare that they have done every step of this work themselves.
GENERATIVE AI USE DECLARATION
The authors declare that GenAI tools were not used in this study.
References
-
Aronson, J. (1995). A pragmatic view of thematic analysis: Thematic analysis of qualitative data. The Qualitative Report, 2(1), 1–3. https://doi.org/10.46743/2160-3715/1995.2069
-
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://journals.sagepub.com/doi/abs/10.1177/0022487108324554
-
Berliner, D. C. 2004. Describing the Behavior and Documenting the Accomplishments of Expert Teachers. Bulletin of Science, Technology and Society 24 (3): 200–212. https://doi.org/10.1177/0270467604265535.
-
Bloomberg, L. D., & Volpe, M. (2008). Completing your qualitative dissertation: A roadmap from beginning to end. Sage. https://doi.org/10.4135/9781452226613
-
Boyatzis, R. E. (1998). Transforming qualitative information: Thematic analysis and code development. Sage Publications.
-
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa
-
Braun, V., & Clarke, V. (2019). Reflecting on thematic analysis as a set of phases or steps. Qualitative Research in Psychology, 16(2), 115–123. https://doi.org/10.1080/2159676X.2019.1628806
-
Christensen, L. B., Johnson, R. B., & Turner, L. A. (2015). Araştırma yöntemleri: Desen ve analiz, (Çev. A. Alpay), Anı Yayıncılık.
-
Cohen, L., Manion, L., & Morrison, K. (2002). Research methods in education. Routledge.
-
Creswell, J. W. & Plano Clark, V. L. (2011). Designing and conducting mixed method research. Sage. https://doi.org/10.4135/9781483398341
-
Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for research in mathematics education, 16(1), 3-17. https://doi.org/10.5951/jresematheduc.16.1.0003
-
Fox, S. & Surtees, L. (2010). Mathematics across the curriculum. Continuum International Pub. Group.
-
Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F., & Yoon, K. S. (2001). What makes professional development effective? Results from a national sample of teachers. American educational research journal, 38(4), 915-945. https://doi.org/10.3102/00028312038004915
-
Hammersley, M. (2013). What is qualitative research? What is? Research methods. Continuum/Bloomsbury.
-
Haylock, D. (2006). Mathematics explained for primary teachers. SAGE Publications.
-
Hill, H., & Ball, D. L. (2009). The curious—and crucial—case of mathematical knowledge for teaching. Phi Delta Kappan, 91(2), 68-71. https://doi.org/10.1177/003172170909100215
-
Husserl, E. (2012). Ideas: General introduction to pure phenomenology. Routledge. https://doi.org/10.4324/9780203120330
-
Joutsenlahti, J., & Kulju, P. (2017). Multimodal languaging as a pedagogical model—A case study of the concept of division in school mathematics. Education Sciences, 7(1), 9. https://doi.org/10.3390/educsci7010009
-
Kinach, B. M. (2002). A cognitive strategy for developing prospective teachers‟ pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education, 18(1), 51-71. https://doi.org/10.1016/S0742-051X(01)00050-6
-
Korkmaz, E. (2021). Instructional explanations of class teachers and primary school mathematics teachers about division. International Journal of Progressive Education, 17(2), 29-54. https://doi.org/10.29329/ijpe.2020.332.3
-
Lamberg, T., & Wiest, L. R. (2012). Conceptualizing division with remainders. Teaching Children Mathematics, 18(7), 426-433. https://doi.org/10.5951/TEACCHILMATH.18.7.0426
-
Morgan, C. (2001). The place of pupil writing in learning, teaching and assessing mathematics. In P. Gates (Ed.), Issues in mathematics teaching (pp. 232–244). Routledge
-
Moustakas, C. (1994). Phenomenological research methods. Sage. https://doi.org/10.4135/9781412995658
-
Patton, M. Q. (2015). Qualitative research & evaluation methods: Integrating theory and practice (4th ed.). Sage Publications.
-
Patton, M. Q. (2018). Nitel araştırma ve değerlendirme yöntemleri. (2. baskı). (M. Bütün & S. B. Demir, Çev. Ed.), Pegem.
-
Ping, O. W. & Hua, A. K. (2015). Effectiveness of Division Wheel in Basic Mathematics Operation Case Study: Primary School Perspective. IOSR Journal of Research & Method in Education, 5 (3), 52-56. https://doi.org/10.9790/7388-05345256
-
Polat, A. (2022). Nitel araştırmalarda yarı-yapılandırılmış görüşme soruları: Soru form ve türleri, nitelikler ve sıralama. Anadolu Üniversitesi Sosyal Bilimler Dergisi, 22(Özel Sayı 2), 161-182. https://doi.org/10.18037/ausbd.1227335
-
Pope, S. (2012). The problem with division. Mathematics Teaching, 23, 42-45.
-
Richardson, K., Pratt, S., & Kurtts, S. (2010). Imagery and utilization of an area model as a way of teaching long division: Meeting diverse student needs. Oklahoma Journal of School Mathematics, 2(1), 14-24.
-
Rizvi, N. F., & Lawson, M. J. (2007). Prospective teachers' knowledge: Concept of division. International Education Journal, 8(2), 377-392.
-
Roche, A., & Clarke, D. M. (2013). Primary teachers’ representations of division: Assessing mathematical knowledge that has pedagogical potential. Mathematics Education Research Journal, 25(2), 257-278. https://doi.org/10.1007/s13394-012-0060-5
-
Rowland, T. (2008). The purpose, design and use of examples in the teaching of elementary mathematics. Educational studies in mathematics, 69(2), 149-163. DOİ 10.1007/s10649-008-9148-y
-
Ryan, J., & Williams, J. (2007). Children's mathematics 4-15: learning from errors and misconceptions: Learning from errors and misconceptions. McGraw-Hill Education.
-
Samuel, K. (2010). A quasi-experimental case study involving teaching division to low attaining grade 5 learners using variation theory. [Doctoral dissertation], University of the Witwatersrand). http://hdl.handle.net/10539/9805
-
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14. http://dx.doi.org/10.3102/0013189X015002004
-
Sitrava, R. T., Özel, Z., & Işık, A. (2020). Sınıf Öğretmeni adaylarının bölme işleminin anlamına dair alan bilgilerinin incelenmesi. Kastamonu Education Journal, 28(2), 931-946. https://doi.org/10.24106/kefdergi.697844
-
Thompson, P. W., Carlson, M. P., & Silverman, J. (2007). The design of tasks in support of teachers’ development of coherent mathematical meanings. Journal of Mathematics Teacher Education, 10(4), 415-432.
-
Troutman, A. P., & Lichtenberg, B. K. (2003). Mathematics: A new Beginning. Thomson Wadsworth.
An Investigation of Primary School Teachers’ Experiences in Teaching Division
Year 2026,
Volume: 11 Issue: 1, 119 - 141, 15.03.2026
Özlem Doğan Temur
,
Hülya Coşkun
,
Abdullah Yavuz Yeşil
Abstract
Primary school mathematics education places significant emphasis on the teaching of arithmetic operations. Among these, the instruction of division has a structure that requires careful and sensitive handling by classroom teachers. The aim of this study is to examine classroom teachers’ experiences regarding the teaching of division. The research was designed using a qualitative approach and employed a phenomenological research method. The study group consisted of 20 experienced classroom teachers working in the provinces of Afyonkarahisar and Kütahya. Criterion sampling and convenience sampling methods were used. Data were collected through a semi-structured interview form consisting of six questions developed by the researchers. Thematic analysis was employed in the data analysis process. The findings indicate that only a limited number of teachers used problem statements and real-life connections in the teaching of division. Although teachers considered the use of models necessary for teaching division, they experienced difficulties in establishing meaningful instructional connections through these models. Furthermore, analysis of teachers’ instructional processes and problem constructions related to remainders revealed a predominantly one-dimensional and non-relational structure.
Ethical Statement
CONFLICT OF INTEREST STATEMENT
The authors declare that there is no conflict of interest in this study.
RESEARCH AND PUBLICATION ETHICS STATEMENT
The authors declare that research and publication ethics are followed in this study.
The necessary permission to conduct the study was obtained from Social and Human Sciences Research and Publication Ethics Committee of Kütahya Dumlupınar University (April 28, 2025-2025/04)
AUTHOR LIABILITY STATEMENT
The authors declare that they have done every step of this work themselves.
GENERATIVE AI USE DECLARATION
The authors declare that GenAI tools were not used in this study.
References
-
Aronson, J. (1995). A pragmatic view of thematic analysis: Thematic analysis of qualitative data. The Qualitative Report, 2(1), 1–3. https://doi.org/10.46743/2160-3715/1995.2069
-
Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. https://journals.sagepub.com/doi/abs/10.1177/0022487108324554
-
Berliner, D. C. 2004. Describing the Behavior and Documenting the Accomplishments of Expert Teachers. Bulletin of Science, Technology and Society 24 (3): 200–212. https://doi.org/10.1177/0270467604265535.
-
Bloomberg, L. D., & Volpe, M. (2008). Completing your qualitative dissertation: A roadmap from beginning to end. Sage. https://doi.org/10.4135/9781452226613
-
Boyatzis, R. E. (1998). Transforming qualitative information: Thematic analysis and code development. Sage Publications.
-
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa
-
Braun, V., & Clarke, V. (2019). Reflecting on thematic analysis as a set of phases or steps. Qualitative Research in Psychology, 16(2), 115–123. https://doi.org/10.1080/2159676X.2019.1628806
-
Christensen, L. B., Johnson, R. B., & Turner, L. A. (2015). Araştırma yöntemleri: Desen ve analiz, (Çev. A. Alpay), Anı Yayıncılık.
-
Cohen, L., Manion, L., & Morrison, K. (2002). Research methods in education. Routledge.
-
Creswell, J. W. & Plano Clark, V. L. (2011). Designing and conducting mixed method research. Sage. https://doi.org/10.4135/9781483398341
-
Fischbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for research in mathematics education, 16(1), 3-17. https://doi.org/10.5951/jresematheduc.16.1.0003
-
Fox, S. & Surtees, L. (2010). Mathematics across the curriculum. Continuum International Pub. Group.
-
Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F., & Yoon, K. S. (2001). What makes professional development effective? Results from a national sample of teachers. American educational research journal, 38(4), 915-945. https://doi.org/10.3102/00028312038004915
-
Hammersley, M. (2013). What is qualitative research? What is? Research methods. Continuum/Bloomsbury.
-
Haylock, D. (2006). Mathematics explained for primary teachers. SAGE Publications.
-
Hill, H., & Ball, D. L. (2009). The curious—and crucial—case of mathematical knowledge for teaching. Phi Delta Kappan, 91(2), 68-71. https://doi.org/10.1177/003172170909100215
-
Husserl, E. (2012). Ideas: General introduction to pure phenomenology. Routledge. https://doi.org/10.4324/9780203120330
-
Joutsenlahti, J., & Kulju, P. (2017). Multimodal languaging as a pedagogical model—A case study of the concept of division in school mathematics. Education Sciences, 7(1), 9. https://doi.org/10.3390/educsci7010009
-
Kinach, B. M. (2002). A cognitive strategy for developing prospective teachers‟ pedagogical content knowledge in the secondary mathematics methods course: Toward a model of effective practice. Teaching and Teacher Education, 18(1), 51-71. https://doi.org/10.1016/S0742-051X(01)00050-6
-
Korkmaz, E. (2021). Instructional explanations of class teachers and primary school mathematics teachers about division. International Journal of Progressive Education, 17(2), 29-54. https://doi.org/10.29329/ijpe.2020.332.3
-
Lamberg, T., & Wiest, L. R. (2012). Conceptualizing division with remainders. Teaching Children Mathematics, 18(7), 426-433. https://doi.org/10.5951/TEACCHILMATH.18.7.0426
-
Morgan, C. (2001). The place of pupil writing in learning, teaching and assessing mathematics. In P. Gates (Ed.), Issues in mathematics teaching (pp. 232–244). Routledge
-
Moustakas, C. (1994). Phenomenological research methods. Sage. https://doi.org/10.4135/9781412995658
-
Patton, M. Q. (2015). Qualitative research & evaluation methods: Integrating theory and practice (4th ed.). Sage Publications.
-
Patton, M. Q. (2018). Nitel araştırma ve değerlendirme yöntemleri. (2. baskı). (M. Bütün & S. B. Demir, Çev. Ed.), Pegem.
-
Ping, O. W. & Hua, A. K. (2015). Effectiveness of Division Wheel in Basic Mathematics Operation Case Study: Primary School Perspective. IOSR Journal of Research & Method in Education, 5 (3), 52-56. https://doi.org/10.9790/7388-05345256
-
Polat, A. (2022). Nitel araştırmalarda yarı-yapılandırılmış görüşme soruları: Soru form ve türleri, nitelikler ve sıralama. Anadolu Üniversitesi Sosyal Bilimler Dergisi, 22(Özel Sayı 2), 161-182. https://doi.org/10.18037/ausbd.1227335
-
Pope, S. (2012). The problem with division. Mathematics Teaching, 23, 42-45.
-
Richardson, K., Pratt, S., & Kurtts, S. (2010). Imagery and utilization of an area model as a way of teaching long division: Meeting diverse student needs. Oklahoma Journal of School Mathematics, 2(1), 14-24.
-
Rizvi, N. F., & Lawson, M. J. (2007). Prospective teachers' knowledge: Concept of division. International Education Journal, 8(2), 377-392.
-
Roche, A., & Clarke, D. M. (2013). Primary teachers’ representations of division: Assessing mathematical knowledge that has pedagogical potential. Mathematics Education Research Journal, 25(2), 257-278. https://doi.org/10.1007/s13394-012-0060-5
-
Rowland, T. (2008). The purpose, design and use of examples in the teaching of elementary mathematics. Educational studies in mathematics, 69(2), 149-163. DOİ 10.1007/s10649-008-9148-y
-
Ryan, J., & Williams, J. (2007). Children's mathematics 4-15: learning from errors and misconceptions: Learning from errors and misconceptions. McGraw-Hill Education.
-
Samuel, K. (2010). A quasi-experimental case study involving teaching division to low attaining grade 5 learners using variation theory. [Doctoral dissertation], University of the Witwatersrand). http://hdl.handle.net/10539/9805
-
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14. http://dx.doi.org/10.3102/0013189X015002004
-
Sitrava, R. T., Özel, Z., & Işık, A. (2020). Sınıf Öğretmeni adaylarının bölme işleminin anlamına dair alan bilgilerinin incelenmesi. Kastamonu Education Journal, 28(2), 931-946. https://doi.org/10.24106/kefdergi.697844
-
Thompson, P. W., Carlson, M. P., & Silverman, J. (2007). The design of tasks in support of teachers’ development of coherent mathematical meanings. Journal of Mathematics Teacher Education, 10(4), 415-432.
-
Troutman, A. P., & Lichtenberg, B. K. (2003). Mathematics: A new Beginning. Thomson Wadsworth.