Identifying Mathematical Connections in Model-Eliciting Activities: A Case Study with Pre-service Mathematics Teachers as Designers

Year 2023, Volume: 7 Issue: 4, 1093 - 1118, 23.10.2023

Murat Genç

https://doi.org/10.34056/aujef.1261714

Abstract

This paper aimed to explore mathematical connections that pre-service elementary mathematics teachers identified in model-eliciting activities that they designed. The study used a qualitative, in-depth exploratory case study approach conducted with a total of 42 undergraduate students selected using a purposive sampling method. Data were collected from mathematical modeling problems prepared by pre-service mathematics teachers and from written assignments in which pre-service teachers evaluated their problems in terms of mathematical connections. Data analysis utilized open coding to identify and label common patterns thematically. Results showed that most of the problems designed were consistent with the principles of the model-eliciting activities. A cross-case analysis of model-eliciting activities revealed that four types of mathematical connections were identified: (i) connections to real-world situations, (ii) connections between mathematical concepts, (iii) connections between different modes of representation, and (iv) connections to other disciplines. The mathematical connections identified in the modeling activities did not seem to be mutually exclusive, but rather supportive and sometimes overlapping. Pre-service mathematics teachers’ identification of mathematical connections in modeling problems reflects both their awareness of mathematical connections and their perception that the skills required for the mathematical modeling process are directly related to mathematical connection skills. Therefore, it is important that pre-service mathematics teachers have a comprehensive understanding of mathematical connections and believe that this is an essential element of the modeling process so that the various dimensions of mathematical connections, along with relevant mathematical, pedagogical, and curricular knowledge, can be effectively integrated into model-eliciting activities.

Keywords

Mathematical connections, model-eliciting activities, mathematical modeling, pre-service mathematics teachers

Model Oluşturma Etkinliklerinde Matematiksel İlişkilendirmelerin Belirlenmesi: Tasarımcı Olarak Matematik Öğretmen Adaylarıyla Bir Durum Çalışması

Abstract

Bu araştırmanın amacı, ilköğretim matematik öğretmen adaylarının tasarladıkları model oluşturma etkinliklerinde belirledikleri matematiksel ilişkilendirmeleri incelemektir. Amaçlı örnekleme yöntemine göre seçilen kırk iki lisans öğrencisiyle yürütülen çalışmada nitel araştırma desenlerinden keşfetmeye dayalı durum çalışması kullanılmıştır. Araştırmanın verileri matematik öğretmen adaylarının hazırladıkları matematiksel modelleme problemlerinden ve öğretmen adaylarının problemlerini matematiksel ilişkilendirmeler açısından değerlendirdikleri yazılı ödevlerden toplanmıştır. Çalışmanın veri analizi, ortak yaklaşımları tematik olarak belirlemek ve sınıflandırmak için açık kodlama kullanılarak yapılmıştır. Araştırmanın sonuçları tasarlanan problemlerin çoğunun model oluşturma etkinliklerinin prensipleri ile tutarlı olduğunu göstermiştir. Model oluşturma etkinliklerinin analizinden elde edilen veriler ise dört tür matematiksel ilişkilendirmenin belirlendiğini ortaya çıkarmıştır: (i) gerçek yaşam durumlarıyla ilişkilendirmeler, (ii) matematiksel kavramlar arasındaki ilişkilendirmeler, (iii) farklı temsil biçimleri arasındaki ilişkilendirmeler ve (iv) diğer disiplinlerle ilişkilendirmeler. Modelleme etkinliklerinde belirlenen bu matematiksel ilişkilendirmeler birbirini dışlayan değil aksine birbirini destekleyen ve bazen örtüşen niteliktedir. Matematik öğretmen adaylarının modelleme problemlerindeki matematiksel ilişkilendirmeleri belirlemeleri hem matematiksel ilişkilendirmelere yönelik farkındalıklarını hem de matematiksel modelleme süreci için gerekli olan becerilerin matematiksel ilişkilendirme becerileri ile doğrudan ilişkili olduğuna dair algılarını yansıtmaktadır. Bu nedenle, matematik öğretmen adaylarının matematiksel ilişkilendirmelere ilişkin kapsamlı bir anlayışa sahip olmaları ve bunun modelleme sürecinin temel bir unsuru olduğuna inanmaları matematiksel ilişkilendirmelerin çeşitli boyutlarının ilgili matematik, pedagojik ve müfredat bilgisi ile birlikte model oluşturma etkinliklerine etkili bir şekilde entegre edilebilmesi açısından önemlidir.

Keywords

Matematiksel ilişkilendirmeler, model oluşturma etkinlikleri, matematiksel modelleme, matematik öğretmen adayları

References

• Abassian, A., Safi, F., Bush, S., & Bostic, J. (2020). Five different perspectives on mathematical modeling in mathematics education. Investigations in Mathematics Learning, 12(1), 53-65. https://doi.org/10.1080/19477503.2019.1595360
• Baki, A. (2014). Kuramdan uygulamaya matematik eğitimi [Mathematics education from theory to practice]. Harf Educational Publications.
• Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching. Who knows mathematics well enough to teach third grade, and how can we decide? American Educator, 29(3), 14-46. http://hdl.handle.net/2027.42/65072
• Barbosa, J. C. (2003). What is mathematical modelling? In S. J. Lamon, W. A. Parker, & S. K. Houston (Eds.), Mathematical modelling: A way of life. ICTMA11 (pp. 227-234). Horwood Publishing.
• Barmby, P., Harries, T., Higgins, S., & Suggate, J. (2009). The array representation and primary children’s understanding and reasoning in multiplication. Educational studies in mathematics, 70(3), 217-241. https://doi.org/10.1007/s10649-008-9145-1
• Bartels, B. (1995). Examining and promoting mathematical connections with concept mappings. Unpublished Doctorate Dissertation, University of Illinois.
• Bay-Williams, J. M., & Stokes Levine, A. (2017). The role of concepts and procedures in developing fluency. In D. Spangler & J. Wanko (Eds.) Enhancing professional practice with research behind principles to actions. NCTM.
• Bingölbali, E., & Coşkun, M. (2016). A proposed conceptual framework for enhancing the use of making connections skill in mathematics teaching. Education and Science, 41(183), 233-249. https://doi.org/10.15390/EB.2016.4764
• Blum, W., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of Mathematical Modelling and Application, 1(1), 45-58.
• Blum, W., & Leiβ, D. (2007). How do students and teachers deal with modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics: Proceedings from the Twelfth International Conference on the Teaching of Mathematical Modelling and Applications (pp. 222-231). Horwood Publishing.
• Blum, W., Galbraith, P. L., Henn, H.-W., & Niss, M. (2007). Modelling and applications in mathematics education. Springer. http://doi.org/10.1007/978-0-387-29822-1
• Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik, 38(2), 86-95. https://doi.org/10.1007/BF02655883
• Businskas, A. (2008). Conversations about connections: How secondary mathematics teachers conceptualize and contend with mathematical connections. Doctoral Dissertation, Simon Fraser University.
• Cai, J., & Ding, M. (2015). On mathematical understanding: Perspectives of experienced Chinese mathematics teachers. Journal of Mathematics Teachers Education, 18(5), 1-25. https://doi.org/10.1007/s10857-015-9325-8
• Carlson, M., & Rasmussen, C. (2008). Making the connection: Research and teaching in undergraduate mathematics education. Mathematical Association of America. https://doi.org/10.5948/UPO9780883859759
• Cohen, L., Manion, L., & Morrison, K. (2017). Research methods in education (8th ed.). Routledge-Falmer. https://doi.org/10.4324/9781315456539
• Cook, M. P. (2006). Visual representations in science education: The influence of prior knowledge and cognitive load theory on instructional design principles. Science Education, 90(6), 1073-1091. http://doi.org/10.1002/sce.20164
• Dede, Y., Akçakın, V., & Kaya, G. (2020). Matematiksel modelleme etkinliklerin öğretim ortamlarında uygulanması ve yansımaları [Application and reflections of mathematical modeling activities in teaching environments]. Y. Dede, M. F. Doğan & F. Aslan-Tutak (Ed.), Matematik eğitiminde etkinlikler ve uygulamaları [Activities and applications in mathematics education] içinde (ss. 269-289). Pegem Akademi.
• Deniz, Ö., & Uygur-Kabael, T. (2017). Students mathematization process of the concept of slope within the realistic mathematics education. Hacettepe University Journal of Education, 32(1), 123-142. https://doi.org/10.16986/HUJE.2016018796
• Dolores-Flores, C., Rivera-López, M. I., & García-García, J. (2019). Exploring mathematical connections of pre-university students through tasks involving rates of change. International Journal of Mathematical Education in Science and Technology, 50(3), 369-389. https://doi.org/10.1080/0020739X.2018.1507050
• Dreher, A. (2015). Dealing with multiple representations in the mathematics classroom - Teachers’ knowledge, views, and their noticing. Doctoral Dissertation, Pädagogische Hochschule Ludwigsburg.
• Dreyfus, T., Hershkowitz, R., & Schwarz, B. B. (2015). The nested epistemic actions model for Abstraction in Context: Theory as methodological tool and methodological tool as theory. In A. Bikner-Ahsbahs, C. Knipping, & N. Presmeg (Eds.), Approaches to qualitative research in mathematics education (pp. 185-217). Springer.
• Eisenhart, M., Borko, H., Underhill, R., Brown, C., Jones, D., & Agard, P. (1993). Conceptual knowledge falls through the Cracks: Complexities of learning to teach mathematics for understanding. Journal for Research in Mathematics Education, 24(1), 8-40. https://doi.org/10.2307/749384
• Eli, J. A, Mohr-Schroeder, M. J., & Lee, C. W. (2013). Mathematical connections and their relationship to mathematics knowledge for teaching geometry. School Science and Mathematics, 113(3), 120-134. https://doi.org/10.1111/ssm.12009
• Eli, J. A., Mohr-Schroeder, M. J., & Lee, C. W. (2011). Exploring mathematical connections of prospective middle-grades teachers through card-sorting tasks. Mathematics Education Research Journal, 23(3), 297-319. https://doi.org/10.1007/s13394-011-0017-0
• Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., & Baş, S. (2014). Mathematical modeling in mathematics education: Basic concepts and approaches. Educational Sciences: Theory and Practice, 14(4), 1621-1627. https://doi.org/10.12738/estp.2014.4.2039
• Fennema, E., & Romberg, T. A. (1999). Mathematics classrooms that promote understanding. Routledge.
• Flores, A., Park, J., & Bernhardt, S. A. (2018). Interactive technology to foster creativity in future mathematics teachers. In V. Freiman & J. L. Tassel (Eds.), Creativity and technology in mathematics education (pp. 149-180). Springer.
• Freudenthal, H. (1973). Mathematics as an educational task. D. Riedel Publishing Company.
• Fung, D. (2017). A Connected Curriculum for Higher Education. UCL Press.
• Galbraith, P. (2012). Models of modelling: genres, purposes or perspectives. Journal of Mathematical Modeling and Application, 1(5), 3-16.
• García-García, J., & Dolores-Flores, C. (2018). Intra-mathematical connections made by high school students in performing Calculus tasks. International Journal of Mathematical Education in Science and Technology, 49(2), 227-252. https://doi.org/10.1080/0020739X.2017.1355994
• García-García, J., & Dolores-Flores, C. (2019). Pre-university students’ mathematical connections when sketching the graph of derivative and antiderivative functions. Mathematics Education Research Journal, 33(1), 1-22. https://doi.org/10.1007/s13394-019-00286-x
• García-García, J., & Dolores-Flores, F. (2020). Exploring pre-university students’ mathematical connections when solving Calculus application problems. International Journal of Mathematical Education in Science and Technology, 52(6), 912-936. https://doi.org/10.1080/0020739X.2020.1729429
• Gravemeijer, K. (1999). How emergent models may foster the constitution of formal mathematics. Mathematical Thinking and Learning, 1(2), 155-177. https://doi.org/10.1207/s15327833mtl0102_4
• Gravemeijer, K. (2002). Preamble: From models to modeling. In K. Gravemeijer, R. Lehrer, B. Oers, & L. Verschaffel (Eds.), Symbolizing, modeling and tool use in mathematics education (pp. 7-22). Kluwer Academic Publishers. https://doi.org/10.1007/978-94-017-3194-2_2
• Gravemeijer, K. (2007). Emergent modelling as a precursor to mathematical modelling. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education (pp. 137-144). Springer. https://doi.org/10.1007/978-0-387-29822-1_12
• Hennig, C. (2010). Mathematical models and reality: A constructivist perspective. Foundations of Science, 15(1), 29-48. https://doi.org/10.1007/s10699-009-9167-x
• Hıdıroğlu, Ç. N. (2023). Matematiği diğer disiplinlerle ilişkilendirme [Connecting mathematics with other disciplines]. H. Yavuz-Mumcu, A. Osmanoğlu & H. Korkmaz (Ed.), Matematik eğitiminde ilişkilendirme [Connection in mathematics education] içinde (ss. 167-202). Pegem Akademi.
• Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 65-97). Macmillan Publishing.
• Irvine, J. (2003). Educating teachers for diversity. Teachers College Press.
• Ji, E. L. (2012). Prospective elementary teachers’ perceptions of real-life connections reflected in posing and evaluating story problems. Journal of Mathematics Teacher Education, 15(6), 429-452. https://doi.org/10.1007/s10857-012-9220-5
• Julie, C., & Mudaly, V. (2007). Mathematical modelling of social issues in school mathematics in South Africa. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 503-510). Springer. https://doi.org/10.1007/978-0-387-29822-1_58
• Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. Zentralblatt für Didaktik der Mathematik, 38(3), 302-310. https://doi.org/10.1007/BF02652813
• Kaiser, G., Schwarz, B., & Buchholtz, N. (2011). Authentic modelling problems in mathematics education. In G. Kaiser, G. Stillman, W. Blum, & R. Borromeo Ferri (Eds.), Trends in teaching and learning of mathematical modelling (pp. 591-601). Springer. https://doi.org/10.1007/978-94-007-0910-2_57
• Kaput, J. J. (1998). Representations, inscriptions, descriptions and learning: A kaleidoscope of windows. The Journal of Mathematical Behavior, 17(2), 265-281. https://doi.org/10.1016/S0364-0213(99)80062-7
• Klosterman, P. (2018). Connecting new knowledge to old: Uncovering hidden premises in mathematical explanations. Australian Primary Mathematics Classroom, 23(2), 23-26.
• Korkmaz, H., & Kertil, M. (2023). Matematiği gerçek yaşamla ilişkilendirme [Connecting mathematics to real life]. H. Yavuz-Mumcu, A. Osmanoğlu & H. Korkmaz (Ed.), Matematik eğitiminde ilişkilendirme [Connection in mathematics education] içinde (ss. 127-148). Pegem Akademi.
• Lehrer, R., & Schauble, L. (2003). Origins and Evolution of Model-Based Reasoning in Mathematics and Science. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching (pp. 59-70). Lawrence Erlbaum. https://doi.org/10.4324/9781410607713
• Leikin, R., & Levav-Waynberg, A. (2007). Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks. Educational Studies in Mathematics, 66(3), 349-371. https://doi.org/10.1007/s10649-006-9071-z
• Lesh, R. A., & Doerr, H. M. (2003a). Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching. Lawrence Erlbaum. https://doi.org/10.4324/9781410607713
• Lesh, R., & Doerr, H. M. (2003b). In what ways does a models and modeling perspective move beyond constructivism. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning and teaching (pp. 519-556). Lawrence Erlbaum. https://doi.org/10.4324/9781410607713
• Lesh, R., & English, L. D. (2005). Trends in the evolution of models & modeling perspectives on mathematical learning and problem solving. Zentralblatt für Didaktik der Mathematik, 37(6), 487-489. https://doi.org/10.1007/BF02655857
• Lesh, R., & Zawojewski, J. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763-804). Information Age Publishing.
• Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought revealing activities for students and teachers. In A. Kelly & R. A. Lesh (Eds.), Handbook of Research Design in Mathematics and Science Education (pp. 591–645). Lawrence Erlbaum.
• Maaß, K. (2006). What are modelling competencies?. Zentralblatt für Didaktik der Mathematik, 38(2), 113-142. https://doi.org/10.1007/BF02655885
• Merriam, S. B., & Tisdell, E. J. (2015). Qualitative research: A guide to design and implementation (4th ed.). Jossey-Bass.
• Mhlolo, M. K., Venkat, H., & Schäfer, M. (2012). The nature and quality of the mathematical connections teachers make. Pythagoras, 33(1), 1-9. http://dx.doi.org/10.4102/pythagoras.v33i1.22
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis (2nd ed.). Sage Publications.
• National Council of Teachers of Mathematics. [NCTM]. (2000). Principles and standards for school mathematics. NCTM.
• National Council of Teachers of Mathematics. [NCTM]. (2014). Principles to actions: Ensuring mathematical success for all. NCTM.
• National Council of Teachers of Mathematics. [NCTM]. (2020a). Catalyzing Change in Middle School Mathematics: Initiating Critical Conversations. NCTM.
• National Council of Teachers of Mathematics. [NCTM]. (2020b). Standards for the preparation of middle level mathematics teachers. NCTM.
• National Research Council. (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, & B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. National Academy Press. https://doi.org/10.17226/9822
• Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3-32). Springer. https://doi.org/10.1007/978-0-387-29822-1_1
• Osmanoğlu, A. (2023). Kavramlar arası ilişkilendirme [Connection between concepts]. H. Yavuz-Mumcu, A. Osmanoğlu & H. Korkmaz (Ed.), Matematik eğitiminde ilişkilendirme [Connection in mathematics education] içinde (ss. 33-70). Pegem Akademi.
• Özgen, K. (2013). Self-efficacy beliefs in mathematical literacy and connections between mathematics and real world: The case of high school students. Journal of International Education Research, 9(4), 305-316. https://doi.org/10.19030/jier.v9i4.8082
• Özgen, K. (2016). A theoretical study on the mathematical connection. In W. Wu, M. T. Hebebci, & O. T. Öztürk (Eds.), International Conference on Research in Education and Science (pp. 220-230). ICRES Publishing. Retrieved from https://www.2016.icres.net/ICRES_Proceeding_Book.pdf?rnd=333040543
• Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. Sage Publications.
• Q. S. R. International (2012). NVivo qualitative data analysis software (Version 10) [Computer software]. QSR International Pty Ltd.
• Richland, L. E., Stigler, J. W., & Holyoak, K. J. (2012). Teaching the conceptual structure of mathematics. Educational Psychologist, 47(3), 189-203. https://doi.org/10.1080/00461520.2012.667065
• Rodríguez-Nieto, C. A, Rodríguez-Vásquez, F. M., & Moll, V. F. (2020). A new view about connections. The mathematical connections established by a teacher when teaching the derivative. International Journal of Mathematical Education in Science and Technology, 1-26. https://doi.org/10.1080/0020739X.2020.1799254
• Rodríguez-Nieto, C. A., Moll, V. F., Borji, V., & Rodríguez-Vásquez, F. M. (2021). Mathematical connections from a networking of theories between extended theory of mathematical connections and onto-semiotic approach. International Journal of Mathematical Education in Science and Technology, 1-27. https://doi.org/10.1080/0020739X.2021.1875071
• Sawyer, A. (2008). Making connections: Promoting connectedness in early mathematics education. In M. Goos, R. Brown, & K. Makar (Eds.), Navigating currents and charting directions (Proceedings of the 31st annual conference of the Mathematics Education Research Group of Australasia, Vol. 2, (pp. 429-436). MERGA. Available: www.merga.net.au/documents/RP512008.pdf
• Silver, E. A., Mesa, V. M., Morris, K. A., Star, J. R., & Benken, B. M. (2009). Teaching mathematics for understanding: An analysis of lessons submitted by teachers seeking NBPTS certification. American Educational Research Journal, 46(2), 501-531. https://doi.org/10.3102/0002831208326559
• Skemp, R. (1987). The psychology of learning mathematics. Lawrence Erlbaum.
• Sokolowski, A. (2018). Scientific inquiry in mathematics-theory and practice: A STEM perspective. Berlin: Springer. https://doi.org/10.1007/978-3-319-89524-6
• Star, J. R., & Stylianides, G. J. (2013). Procedural and conceptual knowledge: Exploring the gap between knowledge type and knowledge quality. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 169-181. https://doi.org/10.1080/14926156.2013.784828
• Stylianides, A. J., & Stylianides, G. J. (2008). Studying the classroom implementation of tasks: High-level mathematical tasks embedded in ‘real-life’ contexts. Teaching and Teacher Education, 24(4), 859-875. https://doi.org/10.1016/j.tate.2007.11.015
• Suh, J. M., Matson, K., Birkhead, S., Green, S., Rossbach, M., Seshaiyer, P., & Jamieson, T. S. (2021). Elementary teachers’ enactment of the core practices in problem formulation through situational contexts in mathematical modeling. In J. M. Suh, M. H. Wickstrom, & L. D. English, (Eds), Exploring mathematical modeling with young learners (pp. 113-145). Springer. https://doi.org/10.1007/978-3-030-63900-6_6
• Tekin-Dede, A., & Bukova-Güzel, E. (2018). A Rubric Development Study for the Assessment of Modeling Skills. The Mathematics Educator, 27(2), 33-72.
• Treffers, A. (1987). Three dimensions. A model of goal and theory description in mathematics education: The Wiskobas Project. D. Riedel Publishing Company.
• Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2019). Elementary and middle school mathematics: Teaching developmentally (10th ed.). Pearson.
• Van den Heuvel-Panhuizen, M., & Wijers, M. (2005). Mathematics standards and curricula in the Netherlands. Zentralblatt für Didaktik der Mathematik, 37(4), 287-307. https://doi.org/10.1007/BF02655816
• Venkat, H., & Adler, J. (2012). Coherence and connections in teachers’ mathematical discourses in instruction. Pythagoras, 33(3), 1-8. http://dx.doi.org/10.4102/pythagoras.v33i3.188
• Weinberg, S. L. (2001). Is there a connection between fractions and division? Students’ inconsistent responses. Paper presented at the Annual Meeting of the American Educational Research Association 10-14 April 2001 (pp 1-43).
• Wright, N. (2018). Becoming an innovative learning environment: The making of a New Zealand secondary school. Springer. https://doi.org/10.1007/978-981-13-0764-5
• Yavuz-Mumcu, H. (2018). A theoretical examination of the mathematical connection skill: The case of the concept of derivative. Turkish Journal of Computer and Mathematics Education, 9(2), 211-248. https://doi.org/10.16949/turkbilmat.379891
• Yavuz-Mumcu, H. (2023). İlişkilendirme ve matematik eğitimindeki anlamı [Connection and its meaning in mathematics education]. H. Yavuz-Mumcu, A. Osmanoğlu & H. Korkmaz (Ed.), Matematik eğitiminde ilişkilendirme [Connection in mathematics education] içinde (ss. 1-32). Pegem Akademi.
• Yin, R. K. (2018). Case study research: Design and methods (6th ed.). Sage Publications.