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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.
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References
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- 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. Educ. Psychol, 39, 243. 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. (2000). ‘The nature of phenomenographic research,’ in Phenomenography, eds J. A. Bowden and E. Walsh (Melbourne: RMIT University), 1–18.
- Cobb, P., J. Confrey, A. diSessa, R. Lehrer y L. Schauble (2003), ‘Design experiments in educational research’, Educational Researcher, vol. 32, núm. 1, pp. 9-13. https://doi.org/10.3102/0013189x032001009
- 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. https://doi.org/10.1002/berj.3935
- 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
- 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., V. Sánchez e I. Escudero (2006), ‘Learning through reflection in mathematics teacher education’, Educational Studies in Mathematics, vol. 64, pp. 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). 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
- Knaus, M. (2009). Recognising a Child's Perspective of Time in Daily Practice. New Zealand Research in Early Childhood Education, 12, 23-32.
- 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, 31-51.
- 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.
- 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., Lingard, J., and Prosser, M. (2006). Variation in student reflections on their conceptions of and approaches to learning biochemistry in a first-year health sciences’ service subject. Int. J. Sci. Educ. 28, 1887–1904. https://doi.org/10.1080/09500690600621274
- Murillo, J. C., Michelini, M., & Perea, C. (2021). Fundamental Physics and Physics Education Research. B. G. Sidharth (Ed.). 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. Eur. J. Soc. Sci. 13: 34-37. https://files.eric.ed.gov/fulltext/ED508531.pdf
- 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, Cham. 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. Online Submission, 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. En T. Plomp y N. Nieveen (Eds.), Educational design research. Part A: an introduction (pp. 10-51). Enschede, Netherlands: SLO.
- Ponte, J. P. y O. Chapman (2006), ‘Mathematics teachers’ knowledge and practice’, en A. Gutiérrez y P. Boero (eds.), Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future, Rotterdam/Taipei, Sense Publishers, pp. 461-494. https://doi.org/10.1163/9789087901127_017
- Prosser, M. (2000). Using Phenomenographic Research Methodology in the Context of Research in Teaching and Learning. En Bowden, J. A., & Green, P. (eds.). Doing Developmental Phenomenography. Melbourne: RMIT University Press.
- Psillos D. y Kariotoglou P. (2016) Iterative desing 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. In AIP Conference Proceedings (Vol. 720, No. 1, pp. 41-44). American Institute of Physics. 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.
- Tight, M. (2016). Phenomenography: the development and application of an innovative research design in higher education research. Int. J. Soc. Res. Methodol. 19, 319–338. https://doi.org/10.1080/13645579.2015.1010284
- Tirosh, D. y T. Wood (eds.) (2008), The International Handbook of Mathematics Teacher Education, Volume 2: Tools and Processes in Mathematics Teacher Education, Taiwan/Rotterdam, 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. Math Ed Res J 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. Ontario: 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
- 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. Educ. Psychol, 39, 243. 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. (2000). ‘The nature of phenomenographic research,’ in Phenomenography, eds J. A. Bowden and E. Walsh (Melbourne: RMIT University), 1–18.
Cobb, P., J. Confrey, A. diSessa, R. Lehrer y L. Schauble (2003), ‘Design experiments in educational research’, Educational Researcher, vol. 32, núm. 1, pp. 9-13. https://doi.org/10.3102/0013189x032001009
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. https://doi.org/10.1002/berj.3935
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
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., V. Sánchez e I. Escudero (2006), ‘Learning through reflection in mathematics teacher education’, Educational Studies in Mathematics, vol. 64, pp. 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). 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
Knaus, M. (2009). Recognising a Child's Perspective of Time in Daily Practice. New Zealand Research in Early Childhood Education, 12, 23-32.
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, 31-51.
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.
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., Lingard, J., and Prosser, M. (2006). Variation in student reflections on their conceptions of and approaches to learning biochemistry in a first-year health sciences’ service subject. Int. J. Sci. Educ. 28, 1887–1904. https://doi.org/10.1080/09500690600621274
Murillo, J. C., Michelini, M., & Perea, C. (2021). Fundamental Physics and Physics Education Research. B. G. Sidharth (Ed.). 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. Eur. J. Soc. Sci. 13: 34-37. https://files.eric.ed.gov/fulltext/ED508531.pdf
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, Cham. 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. Online Submission, 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. En T. Plomp y N. Nieveen (Eds.), Educational design research. Part A: an introduction (pp. 10-51). Enschede, Netherlands: SLO.
Ponte, J. P. y O. Chapman (2006), ‘Mathematics teachers’ knowledge and practice’, en A. Gutiérrez y P. Boero (eds.), Handbook of Research on the Psychology of Mathematics Education: Past, Present and Future, Rotterdam/Taipei, Sense Publishers, pp. 461-494. https://doi.org/10.1163/9789087901127_017
Prosser, M. (2000). Using Phenomenographic Research Methodology in the Context of Research in Teaching and Learning. En Bowden, J. A., & Green, P. (eds.). Doing Developmental Phenomenography. Melbourne: RMIT University Press.
Psillos D. y Kariotoglou P. (2016) Iterative desing 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. In AIP Conference Proceedings (Vol. 720, No. 1, pp. 41-44). American Institute of Physics. 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.
Tight, M. (2016). Phenomenography: the development and application of an innovative research design in higher education research. Int. J. Soc. Res. Methodol. 19, 319–338. https://doi.org/10.1080/13645579.2015.1010284
Tirosh, D. y T. Wood (eds.) (2008), The International Handbook of Mathematics Teacher Education, Volume 2: Tools and Processes in Mathematics Teacher Education, Taiwan/Rotterdam, 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. Math Ed Res J 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. Ontario: 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
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