Main Article Content
Abstract
The integration of computational thinking into mathematics learning is increasingly important in preparing students for problem-solving in the digital era, and visual programming tools such as Flowgorithm offer potential pedagogical support. This study analyzes the effect of Flowgorithm-assisted instruction on students’ computational thinking skills and mathematical problem-solving abilities. A quasi-experimental pretest–posttest control group design was employed and implemented in two phases: a programming phase and a mathematics learning phase. The population consisted of all eighth-grade students at Madrasah Tsanawiyah in Bali Province, Indonesia, from which 34 students were selected using cluster random sampling (20 in the experimental group and 14 in the control group). Data on computational thinking and mathematical problem-solving abilities were collected using achievement tests and analyzed using MANCOVA, followed by post hoc tests, with effect sizes reported using partial eta squared. The findings reveal significant differences between the experimental and control groups, with post hoc analysis indicating that Flowgorithm-assisted mathematics learning significantly improved students’ computational thinking skills, while no significant difference was found in mathematical problem-solving abilities. Despite a non-significant effect on problem-solving, the integration of Flowgorithm showed no negative impact, suggesting that Flowgorithm-assisted instruction can be a viable approach for embedding computational thinking concepts into mathematics curricula and instructional practices.
Keywords
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References
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- Carboni, A., Koleszar, V., Tejera, G., Viera, M., & Wagner, J. (2018). MateFun: Functional Programming and Math with Adolescents. Proceedings - 2018 44th Latin American Computing Conference, CLEI 2018, 849–858. https://doi.org/10.1109/CLEI.2018.00106
- Chan, S. W., Looi, C.-K., Ho, W. K., & Kim, M. S. (2022). Tools and Approaches for Integrating Computational Thinking and Mathematics: A Scoping Review of Current Empirical Studies. Journal of Educational Computing Research. https://doi.org/10.1177/07356331221098793
- Chiang, F. K., Zhang, Y., Zhu, D., Shang, X., & Jiang, Z. (2022). The influence of online STEM education camps on students’ self-efficacy, computational thinking, and task value. Journal of science education and technology, 31(4), 461-472. https://doi.org/10.1007/s10956-022-09967-y
- Costa, E. J. F., Campos, L. M. R. S., & Guerrero, D. D. S. (2017). Computational thinking in mathematics education: A joint approach to encourage problem-solving ability. Proceedings - Frontiers in Education Conference, FIE, 2017-Octob, 1–8. https://doi.org/10.1109/FIE.2017.8190655
- Gajewski, R. R., and Smyrnova-Trybulska, E. (2018). Algorithms, programming, flowcharts and flowgorithm. E-Learning and Smart Learning Environment for the Preparation of New Generation Specialists, 393–408. Retrieved from http://www.studio-noa.pl/ig/pub/us/E-l-10/10-393.pdf
- Gignac, G. E., & Szodorai, E. T. (2016). Effect size guidelines for individual differences researchers. Personality and Individual Differences, 102, 74–78. https://doi.org/https://doi.org/10.1016/j.paid.2016.06.069
- Goldenberg, E. P., & Carter, C. J. (2021). Programming as a language for young children to express and explore mathematics in school. British Journal of Educational Technology, 52(3), 969-985. https://doi.org/10.1111/bjet.13080
- Grover, S., Pea, R., & Cooper, S. (2015). Designing for deeper learning in a blended computer science course for middle school students. Computer Science Education, 25(2), 199–237. https://doi.org/10.1080/08993408.2015.1033142
- Haseski, H. İ., Ilic, U., & Tugtekin, U. (2018). Defining a New 21st Century Skill-Computational Thinking: Concepts and Trends. International Education Studies. https://doi.org/10.5539/ies.v11n4p29
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- Hoyles, C., & Noss, R. (2015). A Computational Lens on Design Research. ZDM, 47, 1039–1045. https://doi.org/10.1007/s11858-015-0731-2
- Hooshyar, D., Ahmad, R. B., Yousefi, M., Yusop, F. D., & Horng, S. J. (2015). A flowchart‐based intelligent tutoring system for improving problem‐solving skills of novice programmers. Journal of computer assisted learning, 31(4), 345-361. https://doi.org/10.1111/jcal.12099
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- Iwamoto, T., & Matsumoto, S. (2019). Development of Web-Based Programming Learning Support System with Graph Drawing of Mathematics as a Learning Task. Proceedings - 2019 8th International Congress on Advanced Applied Informatics, IIAI-AAI 2019, 302–305. https://doi.org/10.1109/IIAI-AAI.2019.00067
- Karaliopoulou, M., Apostolakis, I., & Kanidis, E. (2018). Perceptions of Informatics Teachers Regarding the Use of Block and Text Programming Environments. European Journal of Engineering and Technology Research. https://doi.org/10.24018/ejers.2018.0.cie.638
- Maraza-Quispe, B., Sotelo-Jump, A. M., Alejandro-Oviedo, O. M., Quispe-Flores, L. M., Cari-Mogrovejo, L. H., Fernandez-Gambarini, W. C., & Cuadros-Paz, L. E. (2021). Towards the Development of Computational Thinking and Mathematical Logic through Scratch. International Journal Of Advanced Computer Science And Applications, 12(2), 332–338. https://dx.doi.org/10.14569/IJACSA.2021.0120242
- Maryati, S., Lestarika, L., Idi, A., & Tri Samiha, Y. (2023). Madrasah as an Institution of Islamic Education and Social Change. Jurnal Konseling Pendidikan Islam, 4(2), 317–326. https://doi.org/10.32806/jkpi.v4i2.11
- Miller, J. (2019). STEM education in the primary years to support mathematical thinking: using coding to identify mathematical structures and patterns. ZDM-MATHEMATICS EDUCATION, 51(6), 915–927. https://doi.org/10.1007/s11858-019-01096-y
- Miterianifa, M., Ashadi, A., Saputro, S., & Suciati, S. (2021). Higher Order Thinking Skills in the 21st Century: Critical Thinking. https://doi.org/10.4108/eai.30-11-2020.2303766
- Oluk, A., and Çakır, R. (2021). The Effect of Code. Org Activities on Computational Thinking and Algorithm Development Skills. Journal of Teacher Education and Lifelong Learning, 3(2), 32–40. https://doi.org/10.51535/tell.960476
- Park, Y., & Shin, Y. (2022). Text Processing Education Using a Block-Based Programming Language. Ieee Access. https://doi.org/10.1109/access.2022.3227765
- Papadakis, S., & Kalogiannakis, M. (2019). Evaluating a course for teaching advanced programming concepts with Scratch to preservice kindergarten teachers: A case study in Greece. In D. Farland-Smith (Ed.), Early childhood education. IntechOpen. https://doi.org/10.5772/intechopen.81714
- Robins, A., Rountree, J., & Rountree, N. (2003). Learning and Teaching Programming: A Review and Discussion. Computer Science Education. https://doi.org/10.1076/csed.13.2.137.14200
- Rodríguez-Martínez, J. A., González-Calero, J. A., and Sáez-López, J. M. (2020). Computational thinking and mathematics using Scratch: an experiment with sixth-grade students. Interactive Learning Environments, 28(3), 316–327. https://doi.org/10.1080/10494820.2019.1612448
- Román-González, M., Pérez-González, J. C., & Jiménez-Fernández, C. (2017). Which cognitive abilities underlie computational thinking? Criterion validity of the Computational Thinking Test. Computers in human behavior, 72, 678-691. https://doi.org/10.1016/j.chb.2016.08.047
- Selby, C., & Woollard, J. (2014). Refining an understanding of computational thinking. eprints.soton.ac.uk. https://eprints.soton.ac.uk/372410
- Sentance, S, & Csizmadia, A. (2017). Computing in the curriculum: Challenges and strategies from a teacher’s perspective. In Education and Information Technologies. Springer. https://doi.org/10.1007/s10639-016-9482-0
- Sentance, S, & Csizmadia, A. (2016). Computing in the Curriculum: Challenges and Strategies From a Teacher’s Perspective. Education and Information Technologies, 22(2), 469–495. https://doi.org/10.1007/s10639-016-9482-0
- Seehorn, D., Carey, S., Fuschetto, B., Lee, I., Moix, D., O'Grady-Cunniff, D., & Verno, A. (2011). CSTA K--12 Computer Science Standards: Revised 2011. ACM.
- Spencer, D., Mark, J., Reed, K., Goldenberg, P., Coleman, K., Chiappinelli, K., and Kolar, Z. (2023). Using Programming to Express Mathematical Ideas. Mathematics Teacher: Learning and Teaching PK-12, 116(5), 322–329. https://doi.org/https://doi.org/10.5951/MTLT.2022.0354
- Stephen, J. S., & Rockinson-Szapkiw, A. J. (2021). A high-impact practice for online students: the use of a first-semester seminar course to promote self-regulation, self-direction, online learning self-efficacy. Smart Learning Environments, 8(1), 6. https://doi.org/https://doi.org/10.1186/s40561-021-00151-0
- Tsarava, K., Moeller, K., Román-González, M., Golle, J., Leifheit, L., Butz, M. V., & Ninaus, M. (2022). A cognitive definition of computational thinking in primary education. Computers & Education, 179, 104425. https://doi.org/10.1016/j.compedu.2021.104425
- Varela, C., Rebollar, C., Garcia, O., Bravo, E., & Bilbao, J. (2019). Skills in computational thinking of engineering students of the first school year. HELIYON, 5(11). https://doi.org/10.1016/j.heliyon.2019.e02820
- Veerasamy, A. K., D’Souza, D., Lindén, R., & Laakso, M. (2018). Relationship Between Perceived Problem‐solving Skills and Academic Performance of Novice Learners in Introductory Programming Courses. Journal of Computer Assisted Learning, 35(2), 246–255. https://doi.org/10.1111/jcal.12326
- Weintrop, D. (2015). Comparing Text-Based, Blocks-Based, and Hybrid Blocks/Text Programming Tools. https://doi.org/10.1145/2787622.2787752
- Weintrop, D., & Wilensky, U. (2017). Comparing block-based and text-based programming in high school computer science classrooms. ACM Transactions on Computing Education (TOCE), 18(1), 1–25. https://doi.org/https://doi.org/10.1145/3089799
- Witherspoon, E. B., Higashi, R. M., Schunn, C. D., Baehr, E. C., & Shoop, R. (2017). Developing Computational Thinking through a Virtual Robotics Programming Curriculum. ACM Transactions on Computing Education, 18(1). https://doi.org/10.1145/3104982
- Xu, Z., Ritzhaupt, A. D., Tian, F., & Umapathy, K. (2019). Block-based versus text-based programming environments on novice student learning outcomes: a meta-analysis study. Computer Science Education, 29(2–3), 177–204. https://doi.org/10.1080/08993408.2019.1565233
- Yadav, A., Gretter, S., Hambrusch, S., & Sands, P. (2016). Expanding computer science education in schools: understanding teacher experiences and challenges. Computer Science Education, 26(4), 235–254. https://doi.org/10.1080/08993408.2016.1257418
- Ye, H., Liang, B., Ng, O. L., & Chai, C. S. (2023). Integration of computational thinking in K-12 mathematics education: A systematic review on CT-based mathematics instruction and student learning. International Journal of STEM Education, 10(1), 3. https://doi.org/10.1186/s40594-023-00396-w
- Ye, H., Ng, O.-L., & Cui, Z. (2023). Conceptualizing Flexibility in Programming-Based Mathematical Problem-Solving. Journal of Educational Computing Research. https://doi.org/10.1177/07356331231209773
- Yi, S., & Lee, Y.-J. (2018). An Educational System Design to Support Learning Transfer From Block-Based Programming Language to Text-Based Programming Language. International Journal on Advanced Science Engineering and Information Technology. https://doi.org/10.18517/ijaseit.8.4-2.5735
- Yuana, R. A., Faisal, M., Pangestu, D., & Putri, Y. R. L. (2015). Math thematic learning through the introduction of basic science-based programming games virtual robot for high school students. Advanced Science Letters, 21(7), 2235–2238. https://doi.org/10.1166/asl.2015.6318
- Zeng, Y., Yang, W., and Bautista, A. (2023). Teaching programming and computational thinking in early childhood education: a case study of content knowledge and pedagogical knowledge. Frontiers in Psychology, 14, 1252718. https://doi.org/10.3389/fpsyg.2023.1252718
References
Abdullah, A. H., Rahman, S. N. S. A., & Hamzah, M. H. (2017). Metacognitive Skills of Malaysian Students in Non-Routine Mathematical Problem Solving. Bolema Boletim De Educação Matemática, 31(57), 310–322. https://doi.org/10.1590/1980-4415v31n57a15
Brennan, K., & Resnick, M. (2012). New frameworks for studying and assessing the development of computational thinking. In Proceedings of the 2012 annual meeting of the American educational research association, 1, 25. Retrieved from https://scratched.gse.harvard.edu/ct/files/AERA2012.pdf
Cameto, G., Carboni, A., Koleszar, V., Méndez, M., Tejera, G., Viera, M., & Wagner, J. (2019). Using functional programming to promote math learning. Proceedings - 14th Latin American Conference on Learning Technologies, LACLO 2019, 306–313. https://doi.org/10.1109/LACLO49268.2019.00059
Carboni, A., Koleszar, V., Tejera, G., Viera, M., & Wagner, J. (2018). MateFun: Functional Programming and Math with Adolescents. Proceedings - 2018 44th Latin American Computing Conference, CLEI 2018, 849–858. https://doi.org/10.1109/CLEI.2018.00106
Chan, S. W., Looi, C.-K., Ho, W. K., & Kim, M. S. (2022). Tools and Approaches for Integrating Computational Thinking and Mathematics: A Scoping Review of Current Empirical Studies. Journal of Educational Computing Research. https://doi.org/10.1177/07356331221098793
Chiang, F. K., Zhang, Y., Zhu, D., Shang, X., & Jiang, Z. (2022). The influence of online STEM education camps on students’ self-efficacy, computational thinking, and task value. Journal of science education and technology, 31(4), 461-472. https://doi.org/10.1007/s10956-022-09967-y
Costa, E. J. F., Campos, L. M. R. S., & Guerrero, D. D. S. (2017). Computational thinking in mathematics education: A joint approach to encourage problem-solving ability. Proceedings - Frontiers in Education Conference, FIE, 2017-Octob, 1–8. https://doi.org/10.1109/FIE.2017.8190655
Gajewski, R. R., and Smyrnova-Trybulska, E. (2018). Algorithms, programming, flowcharts and flowgorithm. E-Learning and Smart Learning Environment for the Preparation of New Generation Specialists, 393–408. Retrieved from http://www.studio-noa.pl/ig/pub/us/E-l-10/10-393.pdf
Gignac, G. E., & Szodorai, E. T. (2016). Effect size guidelines for individual differences researchers. Personality and Individual Differences, 102, 74–78. https://doi.org/https://doi.org/10.1016/j.paid.2016.06.069
Goldenberg, E. P., & Carter, C. J. (2021). Programming as a language for young children to express and explore mathematics in school. British Journal of Educational Technology, 52(3), 969-985. https://doi.org/10.1111/bjet.13080
Grover, S., Pea, R., & Cooper, S. (2015). Designing for deeper learning in a blended computer science course for middle school students. Computer Science Education, 25(2), 199–237. https://doi.org/10.1080/08993408.2015.1033142
Haseski, H. İ., Ilic, U., & Tugtekin, U. (2018). Defining a New 21st Century Skill-Computational Thinking: Concepts and Trends. International Education Studies. https://doi.org/10.5539/ies.v11n4p29
Ho, W. K., Looi, C. K., Huang, W., Seow, P., & Wu, L. (2021). Computational thinking in mathematics: To be or not to be, that is the question. In T. L. Toh & L. H. Santos (Eds.), In Mathematics—Connection and beyond: Yearbook 2020 association of mathematics educators (pp. 205-234). World Scientific. https://doi.org/10.1142/9789811236983_0011
Hoyles, C., & Noss, R. (2015). A Computational Lens on Design Research. ZDM, 47, 1039–1045. https://doi.org/10.1007/s11858-015-0731-2
Hooshyar, D., Ahmad, R. B., Yousefi, M., Yusop, F. D., & Horng, S. J. (2015). A flowchart‐based intelligent tutoring system for improving problem‐solving skills of novice programmers. Journal of computer assisted learning, 31(4), 345-361. https://doi.org/10.1111/jcal.12099
Irawan, E., Rosjanuardi, R., and Prabawanto, S. (2024). Research trends of computational thinking in mathematics learning: A bibliometric analysis from 2009 to 2023. Eurasia Journal of Mathematics, Science and Technology Education, 20(3), em2417. https://doi.org/https://doi.org/10.29333/ejmste/14343
Iwamoto, T., & Matsumoto, S. (2019). Development of Web-Based Programming Learning Support System with Graph Drawing of Mathematics as a Learning Task. Proceedings - 2019 8th International Congress on Advanced Applied Informatics, IIAI-AAI 2019, 302–305. https://doi.org/10.1109/IIAI-AAI.2019.00067
Karaliopoulou, M., Apostolakis, I., & Kanidis, E. (2018). Perceptions of Informatics Teachers Regarding the Use of Block and Text Programming Environments. European Journal of Engineering and Technology Research. https://doi.org/10.24018/ejers.2018.0.cie.638
Maraza-Quispe, B., Sotelo-Jump, A. M., Alejandro-Oviedo, O. M., Quispe-Flores, L. M., Cari-Mogrovejo, L. H., Fernandez-Gambarini, W. C., & Cuadros-Paz, L. E. (2021). Towards the Development of Computational Thinking and Mathematical Logic through Scratch. International Journal Of Advanced Computer Science And Applications, 12(2), 332–338. https://dx.doi.org/10.14569/IJACSA.2021.0120242
Maryati, S., Lestarika, L., Idi, A., & Tri Samiha, Y. (2023). Madrasah as an Institution of Islamic Education and Social Change. Jurnal Konseling Pendidikan Islam, 4(2), 317–326. https://doi.org/10.32806/jkpi.v4i2.11
Miller, J. (2019). STEM education in the primary years to support mathematical thinking: using coding to identify mathematical structures and patterns. ZDM-MATHEMATICS EDUCATION, 51(6), 915–927. https://doi.org/10.1007/s11858-019-01096-y
Miterianifa, M., Ashadi, A., Saputro, S., & Suciati, S. (2021). Higher Order Thinking Skills in the 21st Century: Critical Thinking. https://doi.org/10.4108/eai.30-11-2020.2303766
Oluk, A., and Çakır, R. (2021). The Effect of Code. Org Activities on Computational Thinking and Algorithm Development Skills. Journal of Teacher Education and Lifelong Learning, 3(2), 32–40. https://doi.org/10.51535/tell.960476
Park, Y., & Shin, Y. (2022). Text Processing Education Using a Block-Based Programming Language. Ieee Access. https://doi.org/10.1109/access.2022.3227765
Papadakis, S., & Kalogiannakis, M. (2019). Evaluating a course for teaching advanced programming concepts with Scratch to preservice kindergarten teachers: A case study in Greece. In D. Farland-Smith (Ed.), Early childhood education. IntechOpen. https://doi.org/10.5772/intechopen.81714
Robins, A., Rountree, J., & Rountree, N. (2003). Learning and Teaching Programming: A Review and Discussion. Computer Science Education. https://doi.org/10.1076/csed.13.2.137.14200
Rodríguez-Martínez, J. A., González-Calero, J. A., and Sáez-López, J. M. (2020). Computational thinking and mathematics using Scratch: an experiment with sixth-grade students. Interactive Learning Environments, 28(3), 316–327. https://doi.org/10.1080/10494820.2019.1612448
Román-González, M., Pérez-González, J. C., & Jiménez-Fernández, C. (2017). Which cognitive abilities underlie computational thinking? Criterion validity of the Computational Thinking Test. Computers in human behavior, 72, 678-691. https://doi.org/10.1016/j.chb.2016.08.047
Selby, C., & Woollard, J. (2014). Refining an understanding of computational thinking. eprints.soton.ac.uk. https://eprints.soton.ac.uk/372410
Sentance, S, & Csizmadia, A. (2017). Computing in the curriculum: Challenges and strategies from a teacher’s perspective. In Education and Information Technologies. Springer. https://doi.org/10.1007/s10639-016-9482-0
Sentance, S, & Csizmadia, A. (2016). Computing in the Curriculum: Challenges and Strategies From a Teacher’s Perspective. Education and Information Technologies, 22(2), 469–495. https://doi.org/10.1007/s10639-016-9482-0
Seehorn, D., Carey, S., Fuschetto, B., Lee, I., Moix, D., O'Grady-Cunniff, D., & Verno, A. (2011). CSTA K--12 Computer Science Standards: Revised 2011. ACM.
Spencer, D., Mark, J., Reed, K., Goldenberg, P., Coleman, K., Chiappinelli, K., and Kolar, Z. (2023). Using Programming to Express Mathematical Ideas. Mathematics Teacher: Learning and Teaching PK-12, 116(5), 322–329. https://doi.org/https://doi.org/10.5951/MTLT.2022.0354
Stephen, J. S., & Rockinson-Szapkiw, A. J. (2021). A high-impact practice for online students: the use of a first-semester seminar course to promote self-regulation, self-direction, online learning self-efficacy. Smart Learning Environments, 8(1), 6. https://doi.org/https://doi.org/10.1186/s40561-021-00151-0
Tsarava, K., Moeller, K., Román-González, M., Golle, J., Leifheit, L., Butz, M. V., & Ninaus, M. (2022). A cognitive definition of computational thinking in primary education. Computers & Education, 179, 104425. https://doi.org/10.1016/j.compedu.2021.104425
Varela, C., Rebollar, C., Garcia, O., Bravo, E., & Bilbao, J. (2019). Skills in computational thinking of engineering students of the first school year. HELIYON, 5(11). https://doi.org/10.1016/j.heliyon.2019.e02820
Veerasamy, A. K., D’Souza, D., Lindén, R., & Laakso, M. (2018). Relationship Between Perceived Problem‐solving Skills and Academic Performance of Novice Learners in Introductory Programming Courses. Journal of Computer Assisted Learning, 35(2), 246–255. https://doi.org/10.1111/jcal.12326
Weintrop, D. (2015). Comparing Text-Based, Blocks-Based, and Hybrid Blocks/Text Programming Tools. https://doi.org/10.1145/2787622.2787752
Weintrop, D., & Wilensky, U. (2017). Comparing block-based and text-based programming in high school computer science classrooms. ACM Transactions on Computing Education (TOCE), 18(1), 1–25. https://doi.org/https://doi.org/10.1145/3089799
Witherspoon, E. B., Higashi, R. M., Schunn, C. D., Baehr, E. C., & Shoop, R. (2017). Developing Computational Thinking through a Virtual Robotics Programming Curriculum. ACM Transactions on Computing Education, 18(1). https://doi.org/10.1145/3104982
Xu, Z., Ritzhaupt, A. D., Tian, F., & Umapathy, K. (2019). Block-based versus text-based programming environments on novice student learning outcomes: a meta-analysis study. Computer Science Education, 29(2–3), 177–204. https://doi.org/10.1080/08993408.2019.1565233
Yadav, A., Gretter, S., Hambrusch, S., & Sands, P. (2016). Expanding computer science education in schools: understanding teacher experiences and challenges. Computer Science Education, 26(4), 235–254. https://doi.org/10.1080/08993408.2016.1257418
Ye, H., Liang, B., Ng, O. L., & Chai, C. S. (2023). Integration of computational thinking in K-12 mathematics education: A systematic review on CT-based mathematics instruction and student learning. International Journal of STEM Education, 10(1), 3. https://doi.org/10.1186/s40594-023-00396-w
Ye, H., Ng, O.-L., & Cui, Z. (2023). Conceptualizing Flexibility in Programming-Based Mathematical Problem-Solving. Journal of Educational Computing Research. https://doi.org/10.1177/07356331231209773
Yi, S., & Lee, Y.-J. (2018). An Educational System Design to Support Learning Transfer From Block-Based Programming Language to Text-Based Programming Language. International Journal on Advanced Science Engineering and Information Technology. https://doi.org/10.18517/ijaseit.8.4-2.5735
Yuana, R. A., Faisal, M., Pangestu, D., & Putri, Y. R. L. (2015). Math thematic learning through the introduction of basic science-based programming games virtual robot for high school students. Advanced Science Letters, 21(7), 2235–2238. https://doi.org/10.1166/asl.2015.6318
Zeng, Y., Yang, W., and Bautista, A. (2023). Teaching programming and computational thinking in early childhood education: a case study of content knowledge and pedagogical knowledge. Frontiers in Psychology, 14, 1252718. https://doi.org/10.3389/fpsyg.2023.1252718