Eurasia Journal of Mathematics, Science and Technology Education

• Asvat, Z. J. (2024). Pedagogical content knowledge development within pre-service mathematics teacher education: A bibliometric analysis. Journal of Educational Studies, 23(4), 182-213. https://doi.org/10.59915/jes.2024.23.4.8
• 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://doi.org/10.1177/0022487108324554
• Behr, M. J., Khoury, H. A., Harel, G., Post, T., & Lesh, R. (1997). Conceptual units analysis of preservice elementary school teachers’ strategies on a rational-number-as-operator task. Journal for Research in Mathematics Education, 28(1), 48-69. https://doi.org/10.2307/749663
• Blömeke, S., & Delaney, S. (2012). Assessment of teacher knowledge across countries: A review of the state of research. ZDM Mathematics Education, 44, 223-247. https://doi.org/10.1007/s11858-012-0429-7
• Buforn, Á., Llinares, S., & Fernández, C. (2018). Características del conocimiento de los estudiantes para maestro españoles en relación con la fracción, razón y proporción [Characteristics of Spanish preservice teachers’ knowledge of fraction, ratio, and proportion]. Revista Mexicana de Investigación Educativa, 23(76), 229-251.
• Butto, C. (2013). El aprendizaje de fracciones de educación primaria: una propuesta de enseñanza en dos ambientes [Learning fractions in primary education: A two-environment teaching proposal]. Horizontales Pedagógicos, 15(1), 33-45.
• Candray, J. C. (2021). Concepciones docentes acerca de los errores que cometen los estudiantes al resolver operaciones básicas con fracciones [Teachers’ conceptions about students’ errors when solving basic fraction operations]. Revista Paradigma, 62(1), 130-155. https://doi.org/10.37618/PARADIGMA.1011-2251.2021.p130-155.id998
• Chick, H. (2012). God-like educators in a fallen world [Conference paper]. University of Tasmania. https://hdl.handle.net/102.100.100/525599
• Contreras, M. (2013). Problemas multiplicativos relacionados con la división de fracciones: Un estudio sobre su enseñanza y aprendizaje [Multiplicative problems related to fraction division: A study of teaching and learning] [PhD thesis, University of Valencia].
• Copur-Gencturk, Y. (2015). The effects of changes in mathematical knowledge on teaching: A longitudinal study of teachers’ knowledge and instruction. Journal for Research in Mathematics Education, 46(3), 280-330. https://doi.org/10.5951/jresematheduc.46.3.0280
• Copur-Gencturk, Y., & Li, J. (2023). Teaching matters: A longitudinal study of mathematics teachers’ knowledge growth. Teaching and Teacher Education, 121, Article 103949. https://doi.org/10.1016/j.tate.2022.103949
• Depaepe, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Kelchtermans, G., Verschaffel, L., & Van Dooren, W. (2015). Teachers’ content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary school teachers. Teaching and Teacher Education, 47, 82-92. https://doi.org/10.1016/j.tate.2014.12.009
• Dragnić-Cindrić, D., & Anderson, J. L. (2025). Developing pre-service teachers’ pedagogical content knowledge: Lessons from a science methods class. Education Sciences, 15(7), Article 860. https://doi.org/10.3390/educsci15070860
• Ekiz-Kiran, B., Boz, Y., & Oztay, E. S. (2021). Development of pre-service teachers’ pedagogical content knowledge through a PCK-based school experience course. Chemistry Education Research and Practice, 22(2), 415-430. https://doi.org/10.1039/D0RP00225A
• Eraut, M. (1994). Developing professional knowledge and competence. Falmer Press. https://doi.org/10.4324/9780203486016
• Fernández, D. E., & Roa, D. N. (2022). Propuesta didáctica lúdica para la resolución de problemas con números racionales para el mejoramiento del desempeño académico estudiantil [A playful didactic proposal for solving rational-number problems to improve students’ academic performance] [PhD thesis, Corporación Universidad de la Costa].
• Fukaya, T., Nakamura, D., Kitayama, Y., & Nakagoshi, T. (2024). A systematic review and meta-analysis of intervention studies on mathematics and science pedagogical content knowledge. Frontiers in Education, 9. https://doi.org/10.3389/feduc.2024.1435758
• Gess-Newsome, J. (2015). A model of teacher professional knowledge and skill including PCK: Results of the thinking from the PCK summit. In A. Berry, P. Friedrichsen, & J. Loughran (Eds.), Re-examining pedagogical content knowledge in science education (pp. 28-42). Routledge.
• Herreros-Torres, D., Sanz, M. T., & Gómez-Ferragud, C. B. (2025). CoRe as a tool to evaluate the pedagogical knowledge of future teachers about the fraction as an operator. Frontiers in Educaciton, 10, Article 1274102. https://doi.org/10.3389/feduc.2025.1274102
• Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406. https://doi.org/10.3102/00028312042002371
• 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
• Hsieh, F. J., Law, C. K., Shy, H. Y., Wang, T. Y., Hsieh, C. J., & Tang, S. J. (2011). Mathematics teacher education quality in TEDS-M: Globalizing the views of future teachers and teacher educators. Journal of Teacher Education, 62(2), 172-187. https://doi.org/10.1177/0022487110390819
• Hsieh, H.-F., & Shannon, S. E. (2005). Three approaches to qualitative content analysis. Qualitative Health Research, 15(9), 1277-1288. https://doi.org/10.1177/1049732305276687
• Ismail, S. A. S., Maat, S. M., & Khalid, F. (2024). 35 years of fraction learning: Integrating systematic review and bibliometric analysis on a global scale. Eurasia Journal of Mathematics, Science and Technology Education, 20(12), Article em2543. https://doi.org/10.29333/ejmste/15657
• Izsák, A. (2008). Mathematical knowledge for teaching fraction multiplication. Cognition and Instruction, 26(1), 95-143. https://doi.org/10.1080/07370000701798529
• Jamovi Project. (2022). jamovi (version 2.3.16). Jamovi. https://www.jamovi.org
• Kelcey, B., Hill, H. C., & Chin, M. J. (2019). Teacher mathematical knowledge, instructional quality, and student outcomes: A multilevel quantile mediation analysis. School Effectiveness and School Improvement, 30(4), 398-431. https://doi.org/10.1080/09243453.2019.1570944
• Kieren, T. E. (1980). Five faces of mathematical knowledge building. Department of Secondary Education, University of Alberta.
• Kieren, T. E. (2020). Rational and fractional numbers as mathematical and personal knowledge: Implications for curriculum and instruction. In T. E. Kieren (Ed.), Analysis of arithmetic for mathematics teaching (pp. 323-371). Routledge. https://doi.org/10.4324/9781315044606
• Kieren, T. E., & Nelson, D. (1978). The operator construct of rational numbers in childhood and adolescence: An exploratory study. Alberta Journal of Educational Research, 24(1), 22-30.
• Kind, V. (2009). Pedagogical content knowledge in science education: Potential and perspectives for progress. Studies in Science Education, 45(2), 169-204. https://doi.org/10.1080/03057260903142285
• Kleickmann, T., Richter, D., Kunter, M., Elsner, J., Besser, M., Krauss, S., & Baumert, J. (2013). Teachers’ content knowledge and pedagogical content knowledge: The role of structural differences in teacher education. Journal of Teacher Education, 64(1), 90-106. https://doi.org/10.1177/0022487112460398
• Kunter, M., Baumert, J., Blum, W., Klusmann, U., Krauss, S., & Neubrand, M. (2013). The effect of content knowledge and pedagogical content knowledge on instructional quality and student achievement. In M. Kunter, J. Baumert, W. Blum, U. Klusmann, S. Krauss, & M. Neubrand (Eds.), Cognitive activation in the mathematics classroom and professional competence of teachers. Mathematics teacher education, vol 8 (pp. 175-205). Springer. https://doi.org/10.1007/978-1-4614-5149-5_9
• Landis, J. R., & Koch, G. G. (1977). The measurement of observer agreement for categorical data. Biometrics, 33(1), 159-174. https://doi.org/10.2307/2529310
• Li, Y., & Kulm, G. (2008). Knowledge and confidence of preservice mathematics teachers: the case of fraction division. ZDM Mathematics Education, 40, 833-843. https://doi.org/10.1007/s11858-008-0148-2
• Llinares, S., Fernández, C., Ivars, P., González-Forte, J. M., & Zorrilla, C. (2025). Features of pre-service primary school teachers’ curricular noticing: The fraction concept. ZDM Mathematics Education. https://doi.org/10.1007/s11858-025-01726-8
• Lo, JJ., & Luo, F. (2012). Prospective elementary teachers’ knowledge of fraction division. Journal of Mathematics Teacher Education, 15, 481-500. https://doi.org/10.1007/s10857-012-9221-4
• López-Martín, M. D. M., Aguayo-Arriagada, C. G., & García López, M. D. M. (2022). Preservice elementary teachers’ mathematical knowledge on fractions as operator in word problems. Mathematics, 10(3), Article 423. https://doi.org/10.3390/math10030423
• Loughran, J. J., Berry, A. K., & Mulhall, P. (2012). Understanding and developing science teachers’ pedagogical content knowledge. Sense Publishers. https://doi.org/10.1007/978-94-6091-821-6
• Loughran, J., Mulhall, P., & Berry, A. (2004). In search of pedagogical content knowledge in science: Developing ways of articulating and documenting professional practice. Journal of Research in Science Teaching, 41(4), 370-391. https://doi.org/10.1002/tea.20007
• Maryono, A., Sutawidjaja, A., Subanji, & Irawati, S. (2017). Implementation of pedagogical content knowledge (PCK) of mathematics teachers in teaching practice: A case study. International Education Studies, 10(3), 11-25. https://doi.org/10.5539/ies.v10n3p11
• Mientus, L., Hume, A., Wulff, P., Meiners, A., & Borowski, A. (2022). Modelling STEM teachers’ pedagogical content knowledge in the framework of the refined consensus model: A systematic literature review. Education Sciences, 12(6), Article 385. https://doi.org/10.3390/educsci12060385
• Murniasih, T. R., Sa’dijah, C., & Muksar, M. (2020). Fraction sense: An analysis of preservice mathematics teachers’ cognitive obstacles. CEPS Journal, 10(2), 27-47. https://doi.org/10.26529/cepsj.742
• Olanoff, D., Lo, J. J., & Tobias, J. (2014). Mathematical content knowledge for teaching elementary mathematics: A focus on fractions. The Mathematics Enthusiast, 11(2), 267-310. https://doi.org/10.54870/1551-3440.1304
• Parra-Sandoval, H., Hernández, A. G. P., & Prieto, G. (2023). Interacciones promovidas por formadores de profesores a partir de un planteamiento erróneo acerca del tema de las fracciones [Interactions promoted by teacher educators based on an erroneous statement about fractions]. Acta Scientiae, 25(3), 154-179. https://doi.org/10.17648/acta.scientiae.7642
• Pramudiani, P., & Dolk, M. (2025). Engaging primary school students in developing fraction sense through Animaker in a realistic context. Mathematics Education Journal, 19(2), 323-342. https://doi.org/10.22342/mej.v19i2.pp323-342
• Rafiepour, A., Kazemi, F., & Fadaee, M. (2019). Investigate content knowledge and pedagogy content knowledge of the primary school teachers and its relation with the students’ problem-solving ability at mathematical fractions. Research in Curriculum Planning, 16(60), 104-120.
• Ríos-Cuesta, W. (2021). Aplicación de las representaciones gráficas y la visualización a la resolución de problemas con fracciones: una transición hacia el algoritmo [Applying graphic representations and visualization to fraction-problem solving: A transition to the algorithm]. Revista Virtual Universidad Católica del Norte, 63, 196-222. https://doi.org/10.35575/rvucn.n63a8
• Rodríguez Rojas, P. D. L. C., & Navarrete Rojas, C. A. (2020). Influencia del conocimiento profundo del profesor sobre fracciones en el aprendizaje de alumnos de 4º grado [Influence of teachers’ deep knowledge of fractions on 4th-grade students’ learning]. Revista Electrónica de Investigación Educativa, 22, Article e10. https://doi.org/10.24320/redie.2020.22.e10.2285
• Royal Decree 126/2014 of February 28. (2014). Establece el currículo básico de la educación primaria [Establishes the basic curriculum of primary education]. Official State Gazette Agency. https://www.boe.es/eli/es/rd/2014/02/28/126
• Şahin, Ö., Gökkurt, B., & Soylu, Y. (2016). Examining prospective mathematics teachers’ pedagogical content knowledge on fractions in terms of students’ mistakes. International Journal of Mathematical Education in Science and Technology, 47(4), 531-551. https://doi.org/10.1080/0020739X.2015.1092178
• Sakaria, D. A., Maat, S. M. B., & Matore, M. E. E. (2023). Factors influencing mathematics teachers’ pedagogical content knowledge (PCK): A systematic review. Pegem Journal of Education and Instruction, 13(2), 1-14. https://doi.org/10.47750/pegegog.13.02.01
• Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
• Sin, S. (2021). Examining Cambodian pre-service primary school teachers’ mathematical knowledge for teaching (MKT) on fractions. Cambodian Journal of Educational Development, 1, 86-107.
• Star, J. R. (2023). Revisiting the origin of, and reflections on the future of, pedagogical content knowledge. Asian Journal for Mathematics Education, 2(2), 147-160. https://doi.org/10.1177/27527263231175885
• Stelzer, F., Andrés, M. L., Canet-Juric, L., Introzzi, I., & Urquijo, S. (2016). Relaciones entre el conocimiento conceptual y el procedimental en el aprendizaje de las fracciones [Relations between conceptual and procedural knowledge in fraction learning]. Cuadernos de Investigación Educativa, 7(1), 13-27. https://doi.org/10.18861/cied.2016.7.1.2573
• Suripah, S., Suyata, S., & Retnawati, H. (2021). Pedagogical content knowledge (PCK) mathematics pre-service teachers in developing content representations (CoRes). International Journal On Emerging Mathematics Education, 5(1), 41-50. https://doi.org/10.12928/ijeme.v5i1.19954
• Tirosh, D. (2000). Enhancing prospective teachers’ knowledge of children’s conceptions: The case of division of fractions. Journal for Research in Mathematics Education, 31(1), 5-25. https://doi.org/10.2307/749817
• Tsai, T. L., & Li, H. C. (2016). Towards a framework for developing students’ fraction proficiency. International. International Journal of Mathematical Education in Science and Technology, 48(2), 244-255. https://doi.org/10.1080/0020739X.2016.1238520
• Vallespín, I. (2024, diciembre 15). El problema de los malos resultados de los alumnos catalanes: “Hay maestros que han huido de las matemáticas y acaban enseñándolas” [The problem of poor results among Catalan students: “Some teachers have fled from mathematics and end up teaching it”]. El País. https://elpais.com/espana/catalunya/2024-12-15/el-problema-de-los-malos-resultados-de-los-alumnos-catalanes-hay-maestros-que-han-huido-de-las-matematicas-y-acaban-ensenandolas.html
• Verdugo-Perona, J. J., Solaz-Portolés, J. J., & Sanjosé López, V. (2018). Assessment of pre-service primary teachers’ pedagogical knowledge in elementary science: Effects from science education training. Periódico Tchê Química, 15(29), 171-183. https://doi.org/10.52571/PTQ.v15.n29.2018.171_Periodico29_pgs_171_183.pdf
• Vergara, C., & Cofré S, H. (2014). Conocimiento Pedagógico del Contenido: ¿El paradigma perdido en la formación inicial y continua de profesores en Chile [Pedagogical content knowledge: The lost paradigm in preservice and in-service teacher education in Chile]? Estudio Pedagógico, 40(2), 323-Article 338. https://doi.org/10.4067/S0718-07052014000200019
• Zakaryan, D., Estrella, S., Espinoza-Vásquez, G., Morales, S., Olfos, R., Flores-Medrano, E., & Carrillo, J. (2018). Relaciones entre el conocimiento de la enseñanza y el conocimiento de las características del aprendizaje de las matemáticas: Caso de una profesora de secundaria [Relations between teaching knowledge and knowledge of students’ learning characteristics in mathematics: A secondary-teacher case]. Enseñanza de las Ciencias, 36(2), 105-123. https://doi.org/10.5565/rev/ensciencias.2260
• Zolfaghari, M., Austin, C. K., & Kosko, K. W. (2021). Exploring teachers’ pedagogical content knowledge of teaching fractions. Investigations in Mathematics Learning, 13(3), 230-248. https://doi.org/10.1080/19477503.2021.1963145

APA

Herreros-Torres, D., Sanz, M. T., & Gómez-Ferragud, C. B. (2026). Exploring preservice teachers’ PCK on fractions: Insights from the fraction-as-operator sub-construct. Eurasia Journal of Mathematics, Science and Technology Education, 22(2), em2779. https://doi.org/10.29333/ejmste/17833

Vancouver

Herreros-Torres D, Sanz MT, Gómez-Ferragud CB. Exploring preservice teachers’ PCK on fractions: Insights from the fraction-as-operator sub-construct. EURASIA J Math Sci Tech Ed. 2026;22(2):em2779. https://doi.org/10.29333/ejmste/17833

AMA

Herreros-Torres D, Sanz MT, Gómez-Ferragud CB. Exploring preservice teachers’ PCK on fractions: Insights from the fraction-as-operator sub-construct. EURASIA J Math Sci Tech Ed. 2026;22(2), em2779. https://doi.org/10.29333/ejmste/17833

Chicago

Herreros-Torres, Diana, Maria T. Sanz, and Carlos B. Gómez-Ferragud. "Exploring preservice teachers’ PCK on fractions: Insights from the fraction-as-operator sub-construct". Eurasia Journal of Mathematics, Science and Technology Education 2026 22 no. 2 (2026): em2779. https://doi.org/10.29333/ejmste/17833

Harvard

Herreros-Torres, D., Sanz, M. T., and Gómez-Ferragud, C. B. (2026). Exploring preservice teachers’ PCK on fractions: Insights from the fraction-as-operator sub-construct. Eurasia Journal of Mathematics, Science and Technology Education, 22(2), em2779. https://doi.org/10.29333/ejmste/17833

MLA

Herreros-Torres, Diana et al. "Exploring preservice teachers’ PCK on fractions: Insights from the fraction-as-operator sub-construct". Eurasia Journal of Mathematics, Science and Technology Education, vol. 22, no. 2, 2026, em2779. https://doi.org/10.29333/ejmste/17833