5debc37a-5ed7-4056-8ad3-a537f191286820240328050211226naun:naunmdt@crossref.orgMDT DepositInternational Journal of Education and Information Technologies2074-131610.46300/9109http://www.naun.org/cms.action?id=3037312202431220241810.46300/9109.2024.18https://npublications.com/journals/educationinformation/2024.phpJavierBilbaoApplied Mathematics Department, University of the Basque Country, UPV/EHU SPAINEugenioBravoApplied Mathematics Department, University of the Basque Country, UPV/EHU SPAINOlatzGarcíaApplied Mathematics Department, University of the Basque Country, UPV/EHU SPAINCarolinaRebollarApplied Mathematics Department, University of the Basque Country, UPV/EHU SPAINMikko-JussiLaaksoUniversity of Turku, FINLANDHeidiKaartoUniversity of Turku, FINLANDDaraneeLehtonenUniversity of Turku, FINLANDMarikaParviainenUniversity of Turku, FINLANDAstaJankauskieneKlaipeda Gedminu Progymnasium, LITHUANIAArnoldPearsKTH Royal Institute of Technology, SWEDENIsmailGüvenAnkara University, TURKEYYaseminGulbaharAnkara University, TURKEYFatma ÖzdemirÖncülÖzkent Akbilek Middle School, TURKEYNilüfer TanYenigünÖzkent Akbilek Middle School, TURKEYZsuzsaPluhárEötvös Loránd University, HUNGARYPálSarmaságiEötvös Loránd University, HUNGARYValentinaDagieneVilnius University, LITHUANIAVaidaMasiulionyte-DagieneVilnius University, LITHUANIAComputational Thinking is part of the new curriculum in many countries and this new competence is often combined with Algebraic Thinking. Both types of thinking are part of the core of Mathematics and Computer Science. Algebraic Thinking is linked to acquiring the ability to represent and generalize patterns in any application area. Furthermore, the ability to communicate a mathematical argument, using the necessary language and symbolism, is a skill that is dependent on training in this type of thinking. Although Algebraic Thinking can be developed at different levels, and it is also developed at university levels, more and more countries see it as a basic mode of thought that should be encouraged from early childhood education. Algebraic Thinking has also a close relationship with Computational Thinking, and they are currently united in different situations, such as the international PISA student evaluation tests. We argue in this paper that this is a transversal competence that can be practiced in any subject and at any age. Sometimes combined with the process of teaching Mathematics. It is essential, in our opinion, to strengthen the inclusion of strategies that encourage students to reflect deeply on the concepts, theories, and applications they are learning, giving rise, among others, to number sense and abstraction. In this paper, we present the implementation of these two types of thinking, algebraic and computational, in the pre-university curriculum, particularly in Spain, within a European project. In this project, we seek to create more appropriate learning approaches for those who are often disadvantaged and help them to take advantage of Computational Thinking and Algebraic Thinking and, therefore, STEM knowledge, helping to a stronger and more equal society. We analyze its status and its relationship with the concepts taught in the different courses, although focusing on the subject of Mathematics.3282024328202411192https://npublications.com/journals/educationinformation/2024/a042008-002(2024).pdf10.46300/9109.2024.18.2https://npublications.com/journals/educationinformation/2024/a042008-002(2024).pdf10.37394/232015.2020.16.75I. Mavlutova, K. Lesinskis, M. Liogys, J. Hermanis, Innovative Teaching Techniques for Entrepreneurship Education in the Era of Digitalisation, WSEAS Transactions on Environment and Development, 16(1), 2020, pp. 725-733, https://doi.org/10.37394/232015.2020.16.75. J.M. Wing, Computational thinking, Communications of the ACM, vol. 49, no. 3, 2006, pp. 33-35. 10.1787/13c8a22c-enOECD, PISA 2021 Mathematics Framework (draft). PISA, 2018. Retrieved from https://www.oecd.org/pisa/sitedocument/PISA-2021- mathematics-framework.pdf (Last Accessed Date: 2024/03/22) S. Wagner, C. Kieran (Eds.). Research issues in the learning and teaching of algebra (Vol. 4). Reston, VA: Lawrence Erlbaum Associates, 1989. Education for a Changing World, A NSW Government website – Education, Retrieved from https://education.nsw.gov.au/teaching-andlearning/education-for-a-changing-world.html (Last Accessed Date: 2024/03/20) 10.21125/inted.2021.0778J. Bilbao, E. Bravo, O. García, C. Rebollar, C. Varela, Computational Thinking as a New Cross-Curricular Competence, INTED2021 Proceedings, 2021, pp. 3748- 3754. Spanish Government, Official Curricula, General Mathematics (in Spanish: Currículo LOMLOE, Matemáticas generals), 2022. Retrieved from https://educagob.educacionyfp.gob.es/curriculo/curricul o-lomloe/menu-curriculosbasicos/bachillerato/materias/matematicasgenerales/desarrollo.html (Last Accessed Date: 2024/03/20) J. Kaput, M. Blanton, Student achievement in algebraic thinking: A comparison of third-graders’ performance on a state fourth-grade assessment. En R. Speiser, C. Maher, y C. Walter (Eds.), Proceedings of the 23rd Annual Meeting of the Qorth American Chapter of the Psychology of Mathematics Education, 1, 2001, pp. 99- 108. 10.1007/s10857-004-3350-3T.P. Carpenter, M.L. Franke, L. Levi, Thinking mathematically: integrating arithmetic and algebra in elementary school. Portsmouth: Heinemann, 2003. J. Mason, Inciting the student to use his natural ability to express generality: the Tunja sequences (in Spanish: Incitación al estudiante para que use su capacidad natural de expresar generalidad: las secuencias de Tunja), Revista EMA, 4(3), 1999, pp. 232-246. C. Kieran, Algebraic Thinking in the Early Grades: What Is It?, The Mathematics Educator, 18(1), 2004, pp. 139-151. National Council of Teachers of Mathematics, Principles and standards for school mathematics. Reston, 2000. Retrieved from https://www.nctm.org/standards2000/ (Last Accessed Date: 2024/03/22) 10.1080/10986065.2020.1779012K. Bråting, C. Kilhamn, Exploring the intersection of algebraic and computational thinking. Mathematical Thinking and Learning, 23(2), pp. 170–185, 2021. doi: 10.1080/10986065.2020.1779012 T. S. Barcelos, R. Muñoz-Soto, R. Villarroel, E. Merino, I. F. Silveira, Mathematics Learning through Computational Thinking Activities: A Systematic Literature Review. J. Univers. Comput. Sci., 24(7), 2018, pp. 815-845. 10.1007/s40751-016-0026-4C. Buteau, E. Muller, Assessment in Undergraduate Programming Based Mathematics Courses, Digital Experiences in Mathematics Education, Vol. 3, No. 2, 2017, pp. 97–114. https://doi.org/10.1007/s40751-016- 0026-4. 10.1007/978-3-319-52836-6_19A. Djurdjevic-Pahl, C. Pahl, I. Fronza, N. El Ioini, A Pathway into Computational Thinking in Primary Schools, In T.-T. Wu, R. Gennari, Y.-M. Huang, H. Xie & Y. Cao (Eds.), Emerging Technologies for Education (Vol. 10108). Cham: Springer International Publishing, 2017, pp. 165–175. https://doi.org/10.1007/978-3-319-52836-6_19. 10.1007/s10763-019-10003-6D. Pitta-Pantazi, M. Chimoni, C. Christou, Different Types of Algebraic Thinking: an Empirical Study Focusing on Middle School Students. International Journal of Science and Mathematics Education, 18(5), pp. 965–984, 2020. doi: 10.1007/s10763-019-10003-6. J.D. Godino, V. Font, Algebraic Reasoning and its Didactics for teachers (in Spanish: Razonamiento Algebraico y su Didáctica para maestros). Universidad de Granada, 2000. L. Radford, Algebraic thinking and the generalization of patterns: A semiotic perspective, PME-NA, 1, 2006, pp. 2-21. 10.14483/23448350.7753P.J. Rojas, R. Vergel, Generalization Processes and Algebraic Thinking (in Spanish: Procesos de Generalización y Pensamiento Algebraico), Revista científica, vol. 2, 2013, pp. 688-694. https://doi.org/10.14483/23448350.7753. S. Papert, An exploration in the space of Mathematics Education, International Journal of Computers for Mathematics, Vol. 1, No. 1, 1996, pp. 95-123. 10.1145/2999541.2999542M. Tedre, P.J. Denning, The long quest for computational thinking. In Proceedings of the 16th Koli Calling international conference on computing education research, 2016, pp. 120–129. https://doi.org/10.1145/2999541.2999542. A. Pears, Developing Computational Thinking, “Fad” or “Fundamental”? Constructivist Foundations, 14(3), 2019. 10.1109/fie49875.2021.9637416A. Pears, M. Tedre, T. Valtonen, H. Vartiainen, What Makes Computational Thinking so Troublesome? 2021 IEEE Frontiers in Education Conference (FIE), 2021, pp. 1–7. https://doi.org/10.1109/FIE49875.2021.9637416. 10.21125/edulearn.2016.2136S. Bocconi, A. Chioccariello, P. Kampylis, V. Dagiené, P. Wastiau, K. Engelhardt, J. Earp, M.A. Horvath, E. Jasutė, C. Malagoli, V. Masiulionytė-Dagienė, G. Stupurienė, Reviewing Computational Thinking in Compulsory Education. Inamorato dos Santos, A., Cachia, R., Giannoutsou, N. and Punie, Y. editor(s). Publications Office of the European Union, Luxembourg, 2022. doi: 10.2760/126955, JRC128347 10.15388/infedu.2021.21P.J. Denning, M. Tedre, Computational Thinking: A Disciplinary Perspective, Informatics in Education 20, no. 3, 2022, pp. 361-390. doi: 10.15388/infedu.2021.21 10.22364/bjmc.2017.5.4.05J. Bilbao, E. Bravo, O. Garcia, C. Varela, C. Rebollar, Assessment of Computational Thinking notions in Secondary School, Baltic J. Modern Computing, Vol. 5, No. 4, 2017, pp. 391-397. http://dx.doi.org/10.22364/bjmc.2017.5.4.05. Department for Education, National College for Teaching & Leadership: Initial teacher training census for the academic year 2015 to 2016, England. London: DfE, 2017. Retrieved from https://www.gov.uk/government/statistics/initialteacher-training-trainee-number-census-2015-to-2016 (Last Accessed Date: 2024/03/22) Department for Education: The national curriculum in England. London: DfE, 2013. Retrieved from https://www.gov.uk/government/publications/nationalcurriculum-in-england-primary-curriculum (Last Accessed Date: 2024/03/22) M. Bower, K. Falkner, Computational Thinking, the Notional Machine, Pre-service Teachers, and Research Opportunities. In ACE, 2015, pp. 37-46. 10.1007/978-3-030-97986-7_11P. Niemelä, A. Pears, V. Dagienė, M. Laanpere, Computational Thinking–Forces Shaping Curriculum and Policy in Finland, Sweden and the Baltic Countries. In Open Conference on Computers in Education, pp. 131-143, Springer, Cham. 2021. 10.1145/2713609.2713610L. Mannila, V. Dagiene, B. Demo, N. Grgurina, C. Mirolo, L. Rolandsson, A. Settle, Computational Thinking in K-9 Education. Proceedings of the Working Group Reports of 2014 on Innovation & Technology in Computer Science Education Conference, pp. 1–29, 2014. https://doi.org/10.1145/2713609.2713610. H. Isaksson Persson, Has Computational Thinking a Place in the Curriculum?. In PATT39: Pupils’ Attitudes Towards Technology, pp. 213-230, 2022. 10.1080/10986065.2020.1779012K. Bråting, C. Kilhamn, Exploring the intersection of algebraic and computational thinking, Mathematical Thinking and Learning, 23:2, 2021, pp. 170-185. doi: 10.1080/10986065.2020.1779012. OECD, Mathematics performance (PISA) (indicator), 2023. doi: 10.1787/04711c74-en. Retrieved from https://www.oecd-ilibrary.org/education/mathematicsperformance-pisa/indicator/english_04711c74-en (Last Accessed Date: 2024/03/22) 10.1016/j.heliyon.2021.e06135J. Bilbao, E. Bravo, O. García, C. Rebollar, C. Varela, Study to find out the perception that first year students in engineering have about the Computational Thinking skills, and to identify possible factors related to the ability of Abstraction, Heliyon, Vol. 7, Issue 2, e06135, 2021. doi.org/10.1016/j.heliyon.2021.e06135. Y. Punie, editor(s), C. Redecker, European Framework for the Digital Competence of Educators: DigCompEdu, EUR 28775 EN, Publications Office of the European Union, Luxembourg, 2017, ISBN: 978-92-79-73718-3 (print),978-92-79-73494-6 (pdf), doi:10.2760/178382 (print),10.2760/159770 (online), JRC107466. European Commission,EACEA,Eurydice, Informatics education at school in Europe. Eurydice report. Luxembourg: Publications Office of the European Union, 2022. doi: 10.2797/393964. 10.15388/infedu.2021.22V. Dagiene, J. Hromkovic, R. Lacher, Designing informatics curriculum for K-12 education: From Concepts to Implementations, Informatics in Education 20, no. 3, 2022, pp. 333-360. doi: 10.15388/infedu.2021.22. Royal Society: After the reboot: computing education in UK schools. London: The Royal Society, 2017. 10.1145/3230977.3230993L. Mannila, L.Å. Nordén, A. Pears, Digital Competence, Teacher Self-Efficacy, and Training Needs. Proceedings of the 2018 ACM Conference on International Computing Education Research, pp. 78– 85, 2018. https://doi.org/10.1145/3230977.3230993. 10.1080/08993408.2016.1257418Yadav, 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. 10.1145/2899415.2899460Martinez, M. C., Gomez, M. J., Moresi, M., & Benotti, L. (2016, July). Lessons learned on computer science teachers professional development. In Proceedings of the 2016 ACM conference on innovation and technology in computer science education (pp. 77-82). T. Oates, Why Textbooks Count: A policy paper. Cambridge: Cambridge Assessment, 2014. EU project TeaEdu4CT. https://www.fsf.vu.lt/mokslas/projektai/tarptautiniaiprojektai/erasmus/29-projektai/2720-future-teacherseducation-computational-thinking-and-steam (Last Accessed Date: 2024/03/20)