Main Article Content
Abstract
The ability to measure quantities is a fundamental component of primary mathematics education due to its relevance in both real-world applications and mathematical horizontality. However, the concept of time measurement remains one of the most challenging topics for students to grasp due to its abstract nature. Despite the recognized difficulties, there is a lack of effective instructional strategies that integrate constructivist approaches to enhance students' conceptual understanding of time. Addressing this gap, this study presents the design and implementation of a constructivist didactic sequence based on active learning within an Inquiry-Based Learning (IBL) framework. The study involved 31 pre-service teachers in their final year of training, aiming to enhance their pedagogical competence in teaching time measurement through the use of sundials. The research explores how these future educators conceptualize time and how they interpret sundials as a means to represent its passage. To evaluate their assimilation and comprehension of the topic, a phenomenographic analysis was conducted, comparing their depth of knowledge before and after the intervention. The findings indicate a significant improvement in both conceptual understanding and didactic application. The results underscore the effectiveness of sundials as instructional tools, not only for illustrating the passage of time and calendar cycles but also for highlighting the social and historical contexts associated with timekeeping. This study contributes to the field of mathematics education by providing empirical evidence supporting the integration of inquiry-based, constructivist methods in the teaching of time measurement, ultimately enhancing pre-service teachers’ instructional competencies and students’ conceptual grasp of temporal concepts.
Keywords
Article Details

This work is licensed under a Creative Commons Attribution 4.0 International License.
References
- Akerlind, G. L. (2005). Learning about phenomenography: Interviewing, data analysis and the qualitative research paradigm. In Doing developmental phenomenography. RMIT Publishing.
- 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
- Bell, P. (2004). On the theoretical breadth of design-based research in education. Educational Psychologist, 39(4), 243-253. https://doi.org/10.1207/s15326985ep3904_6
- Bonotto, C. (2001). How to connect school mathematics with students' out-of-school knowledge. ZDM, 33(3), 75-84. https://doi.org/10.1007/bf02655698
- Bowden, J. A. (2000). The nature of phenomenographic research. Phenomenography, 154(1), 1-18.
- Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13. https://doi.org/10.3102/0013189x032001009
- Da Ponte, J. P., & Chapman, O. (2006). Mathematics teachers’ knowledge and practices. In Handbook of Research on the Psychology of Mathematics Education (pp. 461-494). Brill. https://doi.org/10.1163/9789087901127_017
- Duschl, R., Maeng, S., & Sezen, A. (2011). Learning progressions and teaching sequences: A review and analysis. Studies in Science Education, 47(2), 123-182. https://doi.org/10.1080/03057267.2011.604476
- Dýrfjörð, K., Hreinsdóttir, A. M., Visnjic-Jevtic, A., & Clark, A. (2023). Young children's perspectives of time: New directions for co-constructing understandings of quality in ECEC. British Educational Research Journal, 2023, 1-18. https://doi.org/10.1002/berj.3935
- Edelson, D. C., Gordin, D. N., & Pea, R. D. (1999). Addressing the challenges of inquiry-based learning through technology and curriculum design. Journal of the Learning Sciences, 8(3-4), 391-450. https://doi.org/10.1207/s15327809jls0803&4_3
- Ernst, D. C., Hodge, A., & Yoshinobu, S. (2017). What is inquiry-based learning. Notices of the AMS, 64(6), 570-574. https://doi.org/10.1090/noti1536
- Euler, M. (2004). The role of experiments in the teaching and learning of physics. In Research on Physics Education (pp. 175-221). Ios Press. https://doi.org/10.1007/978-3-319-96184-2_1
- Fulmer, G. W. (2013). Constraints on conceptual change: How elementary teachers’ attitudes and understanding of conceptual change relate to changes in students’ conceptions. Journal of Science Teacher Education, 24(7), 1219-1236. https://doi.org/10.1007/s10972-013-9334-3
- García, M., Sánchez, V., & Escudero, I. (2007). Learning through reflection in mathematics teacher education. Educational Studies in Mathematics, 64, 1-17. https://doi.org/10.1007/s10649-006-9021-9
- González-Ugalde, C. (2014). Investigación fenomenográfica. Magis, Revista Internacional de Investigación en Educación, 7(14), 141-158. https://doi.org/10.11144/javeriana.m7-14.infe
- Guisasola, J., Zuza, K., Ametller, J., & Gutierrez-Berraondo, J. (2017). Evaluating and redesigning teaching learning sequences at the introductory physics level. Physical Review Physics Education Research, 13(2), 020139. https://doi.org/10.1103/physrevphyseducres.13.020139
- Guisasola, J., Ametller, J., & Zuza, K. (2021). Investigación basada en el diseño de Secuencias de Enseñanza-Aprendizaje: Una línea de investigación emergente en Enseñanza de las Ciencias. Revista Eureka sobre Enseñanza y Divulgación de las Ciencias, 18(1), 180101-180117. https://doi.org/10.25267/rev_eureka_ensen_divulg_cienc.2021.v18.i1.1801
- Han, F., & Ellis, R. A. (2019). Using phenomenography to tackle key challenges in science education. Frontiers in Psychology, 10, 1414. https://doi.org/10.3389/fpsyg.2019.01414
- Kavelashvili, N. (2019). Conserving the past for today: Politics of Georgian government towards cultural heritage protection in the context of political uncertainty. Athenaeum. Polskie Studia Politologiczne, 63, 199-219. https://doi.org/10.15804/athena.2019.63.13
- Laursen, S., Hassi, M. L., Kogan, M., Hunter, A. B., & Weston, T. (2011). Evaluation of the IBL mathematics project: Student and instructor outcomes of inquiry-based learning in college mathematics. Colorado University.
- Llinares, S. (2014). Experimentos de enseñanza e investigación. Una dualidad en la práctica del formador de profesores de matemáticas. Educación Matemática, 25, 31-51. https://www.redalyc.org/pdf/405/40540854003.pdf
- Meaney, T. (2011). Only two more sleeps until the school holidays: One child's home experiences of measurement. For the Learning of Mathematics, 31(1), 31-36. https://flm-journal.org/Articles/40F05816C462CF38FE0A7864677344.pdf
- Méheut, M., & Psillos, D. (2004). Teaching–learning sequences: Aims and tools for science education research. International Journal of Science Education, 26(5), 515-535. https://doi.org/10.1080/09500690310001614762
- Michelini, M., & Stefanel, A. (2011). Prospective primary teachers and physics Pedagogical Content Knowledge’s. C. Constantinou & N. Papadouris, Physics curriculum design, development and validation.
- Minasian‐Batmanian, L. C., Lingard, J., & Prosser, M. (2006). Variation in student reflections on their conceptions of and approaches to learning biochemistry in a first‐year health sciences’ service subject. International Journal of Science Education, 28(15), 1887-1904. https://doi.org/10.1080/09500690600621274
- Murillo, J. C., Michelini, M., & Perea, C. (2021). Fundamental Physics and Physics Education Research. Springer. https://doi.org/10.1007/978-3-030-52923-9
- National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA.
- Nuangchalerm, P. (2010). Engaging students to perceive nature of science through socioscientific issues-based instruction. European Journal of Social Sciences, 13(1), 34-37. https://files.eric.ed.gov/fulltext/ED508531.pdf
- Palau, M. (1977). Rellotges de sol: història i l'art de construir-los: primer tractat de gnomònica en català, amb un apèndix de solucions analítiques. Editorial Millà.
- Paola, F. D. (2019). Geometry/time measurement/sundials graphical resolution via algorithmic and parametric processes. In International Conference on Geometry and Graphics (pp. 1945-1957). Springer. https://doi.org/10.1007/978-3-319-95588-9_173
- Panasan, M., & Nuangchalerm, P. (2010). Learning outcomes of project-based and inquiry-based learning activities. Journal of Social Sciences, 6(2), 252-255. https://doi.org/10.3844/jssp.2010.252.255
- Piaget, J., Grize, J. B., Henry, K., Balcks, M. M., Orsine, F., & Van den Bogaert Rombouts, N. (1971). La epistemología del tiempo. El Ateneo.
- Plomp, T. (2013) Educational design research: An introduction. In T. Plomp and N. Nieveen (Eds.), Educational design research. Part A: An introduction (pp. 10-51). SLO. https://www.fi.uu.nl/publicaties/literatuur/educational-design-research-part-a.pdf#page=12
- Prosser, M. (2000). Using phenomenographic research methodology in the context of research in teaching and learning. In Bowden, J. A., & Green, P. (eds.). Doing Developmental Phenomenography (pp. 34-46). RMIT University Press.
- Psillos, D., & Kariotoglou, P. (2016) Iterative Design of Teaching-Learning Sequences. Springer. https://doi.org/10.1007/978-94-007-7808-5
- Ravanis, K., & Kaliampos, G. (2018). Mental representations of 14-15 years old students about the light propagation time. Jurnal Pendidikan Progresif, 8(2), 44-52.
- Sharma, M. D., Stewart, C., & Prosser, M. (2004). On the use of phenomenography in the analysis of qualitative data. AIP Conference Proceedings, 720(1), 41-44. https://doi.org/10.1063/1.1807249
- Schwarz, C. (2009). Developing preservice elementary teachers' knowledge and practices through modeling‐centered scientific inquiry. Science Education, 93(4), 720-744. https://doi.org/10.1002/sce.20324
- Tesar, M., Farquhar, S., Gibbons, A., Myers, C. Y., & Bloch, M. N. (2016). Childhoods and time: Rethinking notions of temporality in early childhood education. Contemporary Issues in Early Childhood, 17(4), 359-366. https://doi.org/10.1177/1463949116677931
- Tight, M. (2016). Phenomenography: The development and application of an innovative research design in higher education research. International Journal of Social Research Methodology, 19(3), 319-338. https://doi.org/10.1080/13645579.2015.1010284
- Tirosh, D., & Wood, T. (2008). The International Handbook of Mathematics Teacher Education, Volume 2: Tools and Processes in Mathematics Teacher Education. Sense Publishers. https://doi.org/10.1163/9789087905460_002
- Thomas, M., Clarke, D. M., McDonough, A., & Clarkson, P. C. (2023). Assessing students’ understanding of time concepts in Years 3 and 4: Insights from the development and use of a one-to-one task-based interview. Mathematics Education Research Journal, 35(Suppl 1), 1-22. https://doi.org/10.1007/s13394-023-00451-3
- van Manen, M. (1990). Researching lived experience: Human science for an action sensitive pedagogy. The Althouse Press. https://doi.org/10.29173/pandp15124
- Vos, P. (2018). ‘How real people really need mathematics in the real world’—Authenticity in mathematics education. Education Sciences, 8(4), 195. https://doi.org/10.3390/educsci8040195
- Xirouchaki, E., & Boilevin, J. M. (2019). The notion of time from a didactics' point of view. Conceptions of 5 to 7-years-old students about time perception. Journal of Interdisciplinary Methodologies and Issues in Sciences, 7, 1-10. http://dx.doi.org/10.18713/JIMIS-160419-7-10
- Zuazagoitia, D., Aragón, L., González, A. R., & Gozalbo, M. E. (2021). ¿Podemos cultivar este suelo? Una secuencia didáctica para futuros maestros contextualizada en el huerto. Investigación en la Escuela, (103), 32-47. https://doi.org/10.12795/ie.2021.i103.03
References
Akerlind, G. L. (2005). Learning about phenomenography: Interviewing, data analysis and the qualitative research paradigm. In Doing developmental phenomenography. RMIT Publishing.
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
Bell, P. (2004). On the theoretical breadth of design-based research in education. Educational Psychologist, 39(4), 243-253. https://doi.org/10.1207/s15326985ep3904_6
Bonotto, C. (2001). How to connect school mathematics with students' out-of-school knowledge. ZDM, 33(3), 75-84. https://doi.org/10.1007/bf02655698
Bowden, J. A. (2000). The nature of phenomenographic research. Phenomenography, 154(1), 1-18.
Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design experiments in educational research. Educational Researcher, 32(1), 9-13. https://doi.org/10.3102/0013189x032001009
Da Ponte, J. P., & Chapman, O. (2006). Mathematics teachers’ knowledge and practices. In Handbook of Research on the Psychology of Mathematics Education (pp. 461-494). Brill. https://doi.org/10.1163/9789087901127_017
Duschl, R., Maeng, S., & Sezen, A. (2011). Learning progressions and teaching sequences: A review and analysis. Studies in Science Education, 47(2), 123-182. https://doi.org/10.1080/03057267.2011.604476
Dýrfjörð, K., Hreinsdóttir, A. M., Visnjic-Jevtic, A., & Clark, A. (2023). Young children's perspectives of time: New directions for co-constructing understandings of quality in ECEC. British Educational Research Journal, 2023, 1-18. https://doi.org/10.1002/berj.3935
Edelson, D. C., Gordin, D. N., & Pea, R. D. (1999). Addressing the challenges of inquiry-based learning through technology and curriculum design. Journal of the Learning Sciences, 8(3-4), 391-450. https://doi.org/10.1207/s15327809jls0803&4_3
Ernst, D. C., Hodge, A., & Yoshinobu, S. (2017). What is inquiry-based learning. Notices of the AMS, 64(6), 570-574. https://doi.org/10.1090/noti1536
Euler, M. (2004). The role of experiments in the teaching and learning of physics. In Research on Physics Education (pp. 175-221). Ios Press. https://doi.org/10.1007/978-3-319-96184-2_1
Fulmer, G. W. (2013). Constraints on conceptual change: How elementary teachers’ attitudes and understanding of conceptual change relate to changes in students’ conceptions. Journal of Science Teacher Education, 24(7), 1219-1236. https://doi.org/10.1007/s10972-013-9334-3
García, M., Sánchez, V., & Escudero, I. (2007). Learning through reflection in mathematics teacher education. Educational Studies in Mathematics, 64, 1-17. https://doi.org/10.1007/s10649-006-9021-9
González-Ugalde, C. (2014). Investigación fenomenográfica. Magis, Revista Internacional de Investigación en Educación, 7(14), 141-158. https://doi.org/10.11144/javeriana.m7-14.infe
Guisasola, J., Zuza, K., Ametller, J., & Gutierrez-Berraondo, J. (2017). Evaluating and redesigning teaching learning sequences at the introductory physics level. Physical Review Physics Education Research, 13(2), 020139. https://doi.org/10.1103/physrevphyseducres.13.020139
Guisasola, J., Ametller, J., & Zuza, K. (2021). Investigación basada en el diseño de Secuencias de Enseñanza-Aprendizaje: Una línea de investigación emergente en Enseñanza de las Ciencias. Revista Eureka sobre Enseñanza y Divulgación de las Ciencias, 18(1), 180101-180117. https://doi.org/10.25267/rev_eureka_ensen_divulg_cienc.2021.v18.i1.1801
Han, F., & Ellis, R. A. (2019). Using phenomenography to tackle key challenges in science education. Frontiers in Psychology, 10, 1414. https://doi.org/10.3389/fpsyg.2019.01414
Kavelashvili, N. (2019). Conserving the past for today: Politics of Georgian government towards cultural heritage protection in the context of political uncertainty. Athenaeum. Polskie Studia Politologiczne, 63, 199-219. https://doi.org/10.15804/athena.2019.63.13
Laursen, S., Hassi, M. L., Kogan, M., Hunter, A. B., & Weston, T. (2011). Evaluation of the IBL mathematics project: Student and instructor outcomes of inquiry-based learning in college mathematics. Colorado University.
Llinares, S. (2014). Experimentos de enseñanza e investigación. Una dualidad en la práctica del formador de profesores de matemáticas. Educación Matemática, 25, 31-51. https://www.redalyc.org/pdf/405/40540854003.pdf
Meaney, T. (2011). Only two more sleeps until the school holidays: One child's home experiences of measurement. For the Learning of Mathematics, 31(1), 31-36. https://flm-journal.org/Articles/40F05816C462CF38FE0A7864677344.pdf
Méheut, M., & Psillos, D. (2004). Teaching–learning sequences: Aims and tools for science education research. International Journal of Science Education, 26(5), 515-535. https://doi.org/10.1080/09500690310001614762
Michelini, M., & Stefanel, A. (2011). Prospective primary teachers and physics Pedagogical Content Knowledge’s. C. Constantinou & N. Papadouris, Physics curriculum design, development and validation.
Minasian‐Batmanian, L. C., Lingard, J., & Prosser, M. (2006). Variation in student reflections on their conceptions of and approaches to learning biochemistry in a first‐year health sciences’ service subject. International Journal of Science Education, 28(15), 1887-1904. https://doi.org/10.1080/09500690600621274
Murillo, J. C., Michelini, M., & Perea, C. (2021). Fundamental Physics and Physics Education Research. Springer. https://doi.org/10.1007/978-3-030-52923-9
National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA.
Nuangchalerm, P. (2010). Engaging students to perceive nature of science through socioscientific issues-based instruction. European Journal of Social Sciences, 13(1), 34-37. https://files.eric.ed.gov/fulltext/ED508531.pdf
Palau, M. (1977). Rellotges de sol: història i l'art de construir-los: primer tractat de gnomònica en català, amb un apèndix de solucions analítiques. Editorial Millà.
Paola, F. D. (2019). Geometry/time measurement/sundials graphical resolution via algorithmic and parametric processes. In International Conference on Geometry and Graphics (pp. 1945-1957). Springer. https://doi.org/10.1007/978-3-319-95588-9_173
Panasan, M., & Nuangchalerm, P. (2010). Learning outcomes of project-based and inquiry-based learning activities. Journal of Social Sciences, 6(2), 252-255. https://doi.org/10.3844/jssp.2010.252.255
Piaget, J., Grize, J. B., Henry, K., Balcks, M. M., Orsine, F., & Van den Bogaert Rombouts, N. (1971). La epistemología del tiempo. El Ateneo.
Plomp, T. (2013) Educational design research: An introduction. In T. Plomp and N. Nieveen (Eds.), Educational design research. Part A: An introduction (pp. 10-51). SLO. https://www.fi.uu.nl/publicaties/literatuur/educational-design-research-part-a.pdf#page=12
Prosser, M. (2000). Using phenomenographic research methodology in the context of research in teaching and learning. In Bowden, J. A., & Green, P. (eds.). Doing Developmental Phenomenography (pp. 34-46). RMIT University Press.
Psillos, D., & Kariotoglou, P. (2016) Iterative Design of Teaching-Learning Sequences. Springer. https://doi.org/10.1007/978-94-007-7808-5
Ravanis, K., & Kaliampos, G. (2018). Mental representations of 14-15 years old students about the light propagation time. Jurnal Pendidikan Progresif, 8(2), 44-52.
Sharma, M. D., Stewart, C., & Prosser, M. (2004). On the use of phenomenography in the analysis of qualitative data. AIP Conference Proceedings, 720(1), 41-44. https://doi.org/10.1063/1.1807249
Schwarz, C. (2009). Developing preservice elementary teachers' knowledge and practices through modeling‐centered scientific inquiry. Science Education, 93(4), 720-744. https://doi.org/10.1002/sce.20324
Tesar, M., Farquhar, S., Gibbons, A., Myers, C. Y., & Bloch, M. N. (2016). Childhoods and time: Rethinking notions of temporality in early childhood education. Contemporary Issues in Early Childhood, 17(4), 359-366. https://doi.org/10.1177/1463949116677931
Tight, M. (2016). Phenomenography: The development and application of an innovative research design in higher education research. International Journal of Social Research Methodology, 19(3), 319-338. https://doi.org/10.1080/13645579.2015.1010284
Tirosh, D., & Wood, T. (2008). The International Handbook of Mathematics Teacher Education, Volume 2: Tools and Processes in Mathematics Teacher Education. Sense Publishers. https://doi.org/10.1163/9789087905460_002
Thomas, M., Clarke, D. M., McDonough, A., & Clarkson, P. C. (2023). Assessing students’ understanding of time concepts in Years 3 and 4: Insights from the development and use of a one-to-one task-based interview. Mathematics Education Research Journal, 35(Suppl 1), 1-22. https://doi.org/10.1007/s13394-023-00451-3
van Manen, M. (1990). Researching lived experience: Human science for an action sensitive pedagogy. The Althouse Press. https://doi.org/10.29173/pandp15124
Vos, P. (2018). ‘How real people really need mathematics in the real world’—Authenticity in mathematics education. Education Sciences, 8(4), 195. https://doi.org/10.3390/educsci8040195
Xirouchaki, E., & Boilevin, J. M. (2019). The notion of time from a didactics' point of view. Conceptions of 5 to 7-years-old students about time perception. Journal of Interdisciplinary Methodologies and Issues in Sciences, 7, 1-10. http://dx.doi.org/10.18713/JIMIS-160419-7-10
Zuazagoitia, D., Aragón, L., González, A. R., & Gozalbo, M. E. (2021). ¿Podemos cultivar este suelo? Una secuencia didáctica para futuros maestros contextualizada en el huerto. Investigación en la Escuela, (103), 32-47. https://doi.org/10.12795/ie.2021.i103.03