Primary School Teachers’ Views on the Use of Multiple Representations in Mathematics Lessons During the Distance Education Process
Yıl 2025,
Cilt: 11 Sayı: 3, 283 - 298, 31.12.2025
Yasemin Kirtenoğlu
,
Mehmet Koray Serin
,
Adem Yılmaz
Öz
The primary aim of this study is to examine primary school teachers’ views on the use of multiple representations in mathematics lessons during the distance education process by evaluating these views in relation to their practices in face-to-face instruction. Designed within the interpretative phenomenological research approach, the study involved 15 primary school teachers working in the province of Kastamonu, who were selected through convenience sampling. Data were collected through semi-structured interviews and analyzed using content analysis. The findings revealed that teachers had limited awareness of multiple representations, found it challenging to diversify representations on digital platforms, and expressed a need for supportive professional development in this area. It was also determined that teachers predominantly used representations for the purpose of concretization, while experiencing difficulties in processes involving the coordination and transformation between representations. Additionally, teachers perceived their use of multiple representations as more effective in face-to-face instruction. The study offers recommendations for the effective use of multiple representations in distance education and contributes to teacher education. In this context, it is recommended that teachers be supported through in-service training focused on both technology use and multiple representations, particularly to enable the pedagogically effective integration of digital representations.
Etik Beyan
This study is an original study and all stages of the study, including preparation, data collection, analysis and presentation of information, were conducted in accordance with the principles and rules of scientific ethics. We declare that we comply with ethical duties and responsibilities by accepting all terms and conditions of the Committee on Publication Ethics (COPE). In the event that a situation contrary to this statement we have made regarding the study is detected, we declare that we agree to all moral and legal consequences that may arise.
Kaynakça
-
Ainsworth, S. (1996). The functions of multiple representations. Computers & Education, 33(2–3), 131–152. https://doi.org/10.1016/0360-1315(94)00029-X
-
Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183–198. https://doi.org/10.1016/j.learninstruc.2006.03.001
-
Ainsworth, S., Bibby, P., & Wood, D. (2002). Examining the effects of different multiple representational systems in learning primary mathematics. Journal of the Learning Sciences, 11(1), 25–61. https://doi.org/10.1207/S15327809JLS1101_2
-
Ainsworth, S., & Van Labeke, N. (2004). Multiple forms of dynamic representation. Learning and Instruction, 14(3), 241–255. https://doi.org/10.1016/j.learninstruc.2004.06.002
-
Alabdulaziz, M.S. (2021). COVID-19 and the use of digital technology in mathematics education. Educ Inf Technol. 26, 7609–7633. https://doi.org/10.1007/s10639-021-10602-3
-
Atasoy, M. & Yigitcan Nayır, Ö. (2019). Students’ opinions regarding the use of educational and ınformation network video modules in math courses. International Journal of Science and Education, 2(1), 24-37.
-
Ayyildiz, H. & Cansiz Aktas, M. (2022) Tendencies of representation studies in mathematics education in Turkey: A thematic content analysis, Cumhuriyet International Journal of Education, 11(1), 127-144.
-
Baroroh, U., & Mardiyana, L. F. (2021). Student mathematical representation ability in their learning habits during the Covid-19 pandemic. Proceedings of the Second Asia Pacific International Conference on Industrial Engineering and Operations Management, Surakarta, Indonesia.
-
Bengtsson, M. (2016). How to plan and perform a qualitative study using content analysis. NursingPlus Open, 2, 8–14. https://doi.org/10.1016/j.npls.2016.01.001
-
Bicer, A. (2021). Multiple representations and mathematical creativity. Thinking Skills and Creativity, 42, 1–17. https://doi.org/10.1016/j.tsc.2021.100960.
-
Božić, R., Peics, H., & Milenković, A. (2023). Multiple representations of functions in the frame of distance learning. Mathematics and Informatics, LXVI(4). https://doi.org/10.53656/math2023-4-3-mul
-
Bozkurt, A., & Sharma, R. C. (2020). Emergency remote teaching in a time of global crisis due to CoronaVirus pandemic. Asian Journal of Distance Education, 15(1), 1–6.
-
Borba, M. C. (2021). The future of mathematics education since COVID-19: Humans-with-media or humans-with-non-living-things. Educational Studies in Mathematics, 108(1), 385–400. https://doi.org/10.1007/s10649-021-10043-2
-
CCSSI. (2010). Common Core State Standards for Mathematics. National Governors Association Center for Best Practices & Council of Chief State School Officers.
-
Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed.). Sage.
-
Creswell, J. W. (2013). Qualitative inquiry and research design: Choosing among five approaches (3rd ed.). Sage.
-
Cullen, C. J., Hertel, J. T., & Nickels, M. (2020). The roles of technology in mathematics education. The Educational Forum, 84(2), 166–178. https://doi.org/10.1080/00131725.2020.1698683
-
Debrenti, E. (2015). Visual representations in mathematics teaching: An experiment with students. Acta Didactica Napocensia, 8(1), 19–25.
-
Delice, A., & Sevimli, E. (2016). Matematik eğitiminde çoklu temsiller. E. Bingölbali, S. Arslan, & İ.Ö. Zembat (Ed.), Matematik eğitiminde teoriler (ss. 519-537). Ankara: Pegem Akademi Yayıncılık.
-
Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88(1), 89–114. https://doi.org/10.1007/s10649-014-9577-8
-
Eroğlu, D., & Tanışlı, D. (2021). Tahmini öğrenme yollarının uygulanması sürecinde matematik öğretmenlerinin çoklu temsil kullanımlarının gelişimi. Cumhuriyet Uluslararası Eğitim Dergisi, 10(1), 299-329. https://doi.org/10.30703/cije.718210
-
Friesen, M. E., & Kuntze, S. (2020). The role of professional knowledge for teachers’ analysing of classroom situations regarding the use of multiple representations. Research in Mathematics Education, 22(2), 117–134. https://doi.org/10.1080/14794802.2019.1710555
-
Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11, 199–219. https://doi.org/10.1007/s10857-007-9070-8
-
Goldin, G., & Kaput, J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In L. Steffe & P. Nesher (Eds.), Theories of Mathematical Learning (pp. 397–430). Lawrence Erlbaum.
-
Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. C. Cuoco (Ed.), The roles of representation in school mathematics: 2001 yearbook (Vol. 63rd Yearbook, pp. 1–23). NCTM.
-
Greno, P., & Hall, M. (1997). Mathematical representations: Problems and perspectives. Mathematics Teaching in the Middle School, 3(2), 114–120.
-
Heddens, J. W., & Speer, W. R. (1997). Today's mathematics: Concepts and classroom methods for elementary school teachers (8th ed.). Merrill.
-
Heinze, A., Star, J. R., & Verschaffel, L. (2009). Flexible and adaptive use of representations in mathematics. ZDM, 41, 535–540. https://doi.org/10.1007/s11858-009-0190-1
-
Hidayat R, Zainuddin Z, & Mazlan NH. (2024). The relationship between technological pedagogical content knowledge and belief among preservice mathematics teachers. Acta Physiol (Oxf), 249, 104432. https://doi.org/10.1016/j.actpsy.2024.104432.
-
Huang, X., Lai, M.Y. & Huang, R. (2022). Teachers’ changes when addressing the challenges in unexpected migration to online mathematics teaching during the COVID-19 pandemic: a case study in Shanghai. ZDM Mathematics Education, 54, 359–372. https://doi.org/10.1007/s11858-022-01378-y
-
Huinker, D. (2015). Representation. In B. M. Steele (Ed.), Mathematics teaching practices in action (pp. 63–78). National Council of Teachers of Mathematics.
-
Hwang, W. Y., Su, J. H., Huang, Y. M., & Dong, J. J. (2009). A study of multi-representation of geometry problem solving with Virtual Manipulatives and Whiteboard system. Educational Technology and Society, 12(3), 229–247. http://www.jstor.org/stable/jeductechsoci.12.3.229
-
Karabey, B., & Erdoğan, A. (2023). K12 beceriler çerçevesi Türkiye bütüncül modeli matematik alan becerileri. Milli Eğitim Dergisi, 52(1), 971-996. https://doi.org/10.37669/milliegitim.1309180
-
Krippendorff, K. (2018). Content analysis: An introduction to its methodology. Sage publications.
-
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33–40). Lawrence Erlbaum.
-
Lesh, R., & Doerr, H. M. (2003). Using representations as a central focus of mathematics teacher preparation. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: A models and modeling perspective on mathematics problem solving, learning, and teaching (pp. 33–59). Lawrence Erlbaum.
-
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. sage.
-
Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054. https://doi.org/10.1111/j.1467-9620.2006.00684.x
-
MEB. (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara.
-
MEB. (2024). İlkokul matematik dersi öğretim programı. Ankara.
-
Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. Jossey-Bass.
-
NCTM. (2000). Principles and Standards for School Mathematics. National Council of Teachers of Mathematics.
-
Pape, S. J., & Tchoshanov, M. A. (2001). The role of representations in developing mathematical understanding. Theory into Practice, 40(2), 118–127.
-
Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. Sage publications.
-
Pierce, R., Stacey, K., Wander, R., & Ball, L. (2011). The design of lessons using mathematics analysis software to support multiple representations in secondary school mathematics. Technology, Pedagogy and Education, 20(1), 95–112. https://doi.org/10.1080/1475939X.2010.534869
-
Prain, V., & Waldrip, B. (2006). An Exploratory Study of Teachers’ and Students’ Use of Multi‐modal Representations of Concepts in Primary Science. International Journal of Science Education, 28(15), 1843–1866. https://doi.org/10.1080/09500690600718294
-
Prayitno, S., Lu’luilmaknunn, U., Sridana, N., & Subarinah, S. (2021, May). Analyzing the ability of mathematics students as prospective mathematics teachers on multiple mathematical representation. In 2nd Annual Conference on Education and Social Science (ACCESS 2020) (pp. 309-313). Atlantis Press.
-
Rau, M. A., Aleven, V., & Rummel, N. (2009). Intelligent tutoring systems with multiple representations and self-explanation prompts support learning of fractions. In V. Dimitrova, R. Mizoguchi, & B. du Boulay (Eds.), Proceedings of the 14th International Conference on Artificial Intelligence in Education, (pp. 441–448). IOS Press. https://doi.org/10.3233/978-1-60750-028-5-441
-
Rüzgar, M.E., Boyraz, S. & Sözcü İ. (2023). Eğitim bilimlerinde araştırma 101 (1. Baskı). Pegem Akademi.
Ryken, A.E. (2009). Multiple representations as sites for teacher reflection about mathematics learning. J Math Teacher Educ, 12, 347–364. https://doi.org/10.1007/s10857-009-9107-2
-
Satsangi, R., & Sigmon, S. D. (2023). Teaching multiplicative thinking with virtual representations to children with mathematics difficulty. Remedial and Special Education, 45(4), 216-229. https://doi.org/10.1177/07419325231206483
-
Sezgin, A. N. (2019). Çoklu temsillerle öğretimin 7. sınıf öğrencilerinin matematiksel anlama seviyelerine ve cebirsel problem çözme sürecine etkisinin incelenmesi (Yayınlanmamış yüksek lisans tezi). Marmara Üniversitesi, İstanbul.
-
Sezgin, S., & Fırat, M. (2020). Covid-19 pandemisinde uzaktan eğitime geçiş ve dijital uçurum tehlikesi. Açıköğretim Uygulamaları ve Araştırmaları Dergisi, 6(4), 37-54.
-
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
-
Skemp, R. R. (1978). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
-
Smith, J. A., Flowers, P., & Larkin, M. (2009). Interpretative phenomenological analysis: Theory, method and research. London, UK: Sage.
-
Şengül, S., & Mancoğlu Kaplan, E. (2024). Matematik öğretmenlerinin temsil kullanımlarının örüntü genelleme problemleri bağlamında video temelli olaylarla incelenmesi. Pearson Journal, 8(28), 1246–1268. https://doi.org/10.5281/zenodo.11582188
-
Türer, G., & Cantürk Günhan, B. (2022). Türkiye’de matematik eğitiminde çoklu temsiller ile ilgili yapılan çalışmaların incelenmesi. Fen Matematik Girişimcilik ve Teknoloji Eğitimi Dergisi, 5(3), 214-236.
-
Uslu, F., & Demir, E. (2023). Nitel bir veri toplama tekniği: Derinlemesine görüşme. Hacettepe Üniversitesi Edebiyat Fakültesi Dergisi, 40(1), 289-299. https://doi.org/10.32600/huefd.1184085
-
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2020). Elementary and middle school mathematics: Teaching developmentally (11th ed.). Pearson.
-
Van Manen, M. (2023). Phenomenology of practice: Meaning‐giving methods in phenomenological research and writing. NY: Routledge. https://doi.org/10.4324/9781003228073
-
Yanık, H. B. (2016). Matematik öğretiminde kavramsal anlamaya dayalı yaklaşımlar. İçinde E. Bingölbali, M. F. Özmantar & H. Akkoç (Eds.), Matematiksel kavram yanılgıları ve çözüm önerileri (pp. 17–40). Pegem Akademi.
-
Yavuz-Mumcu, H. (2023). Farklı temsiller arası ilişkilendirme. İçinde H. Yavuz Mumcu, A. Osmanoğlu, & H. Korkmaz (Eds.), Matematik eğitiminde ilişkilendirme (ss. 72-119). Pegem A.
-
Yıldırım, A., & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (9. baskı). Seçkin Yayıncılık.
-
Yilmaz, A., & Kostur, M. (2021). Rethinking principles of school mathematics during the COVID-19 Pandemic: A multiple-case study on higher education courses related to teaching mathematics. International Electronic Journal of Mathematics Education, 16(3), em0653. https://doi.org/10.29333/iejme/11103
-
Yuhasriati, Y., Johar, R., Khairunnisak, C., Rohaizati, U., Jupri, A., & Zubaidah, T. (2022). Students mathematical representation ability in learning algebraic expression using realistic mathematics education. Jurnal Didaktik Matematika, 9(1), 151-169.
Uzaktan Eğitim Sürecinde Sınıf Öğretmenlerinin Matematik Derslerinde Çoklu Temsil Kullanımına İlişkin Görüşleri
Yıl 2025,
Cilt: 11 Sayı: 3, 283 - 298, 31.12.2025
Yasemin Kirtenoğlu
,
Mehmet Koray Serin
,
Adem Yılmaz
Öz
Bu çalışmanın temel amacı, sınıf öğretmenlerinin uzaktan eğitim sürecinde matematik derslerindeki çoklu temsil kullanımlarına yönelik görüşlerini, yüz yüze eğitimdeki uygulamalarıyla birlikte değerlendirerek ortaya koymaktır. Nitel araştırma desenlerinden yorumlayıcı fenomenoloji yaklaşımına göre tasarlanan çalışmaya, Kastamonu ilinde görev yapan ve kolay ulaşılabilir durum örneklemesi ile belirlenen 15 sınıf öğretmeni katılmıştır. Veriler, yarı yapılandırılmış görüşmeler aracılığıyla toplanmış ve içerik analizi yöntemiyle çözümlenmiştir. Bulgular, öğretmenlerin çoklu temsile yönelik farkındalıklarının sınırlı olduğunu, dijital platformlarda temsilleri çeşitlendirmenin zorlayıcı bulunduğunu ve bu konuda destekleyici eğitimlere ihtiyaç duyduklarını ortaya koymuştur. Öğretmenlerin temsilleri daha çok somutlaştırma amacıyla kullandıkları, temsiller arası ilişkilendirme ve dönüşüm süreçlerinde ise güçlük yaşadıkları belirlenmiştir. Ayrıca öğretmenlerin yüz yüze eğitimde çoklu temsil uygulamalarını daha etkin buldukları belirlenmiştir. Çalışma, çoklu temsillerin uzaktan eğitimde etkili kullanımına ilişkin öneriler sunmakta ve öğretmen eğitimine katkı sağlamaktadır. Bu bağlamda, öğretmenlerin özellikle dijital temsilleri pedagojik olarak etkili biçimde bütünleştirebilmeleri için hem teknoloji hem de çoklu temsil temelli hizmet içi eğitimlerle desteklenmeleri önerilmektedir.
Etik Beyan
Bu çalışma, özgün bir çalışma olup; çalışmanın hazırlık, veri toplama, analiz ve bilgilerin sunumu olmak üzere tüm aşamalarından bilimsel etik ilke ve kurallarına uygun davranılmıştır. Committee on Publication Ethics (COPE)' in tüm şartlarını ve koşullarını kabul ederek etik görev ve sorumluluklara riayet ettiğimizi beyan ederiz. Çalışmayla ilgili yaptığımız bu beyana aykırı bir durumun saptanması durumunda, ortaya çıkacak tüm ahlaki ve hukuki sonuçlara razı olduğumuzu bildiririz.
Kaynakça
-
Ainsworth, S. (1996). The functions of multiple representations. Computers & Education, 33(2–3), 131–152. https://doi.org/10.1016/0360-1315(94)00029-X
-
Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16(3), 183–198. https://doi.org/10.1016/j.learninstruc.2006.03.001
-
Ainsworth, S., Bibby, P., & Wood, D. (2002). Examining the effects of different multiple representational systems in learning primary mathematics. Journal of the Learning Sciences, 11(1), 25–61. https://doi.org/10.1207/S15327809JLS1101_2
-
Ainsworth, S., & Van Labeke, N. (2004). Multiple forms of dynamic representation. Learning and Instruction, 14(3), 241–255. https://doi.org/10.1016/j.learninstruc.2004.06.002
-
Alabdulaziz, M.S. (2021). COVID-19 and the use of digital technology in mathematics education. Educ Inf Technol. 26, 7609–7633. https://doi.org/10.1007/s10639-021-10602-3
-
Atasoy, M. & Yigitcan Nayır, Ö. (2019). Students’ opinions regarding the use of educational and ınformation network video modules in math courses. International Journal of Science and Education, 2(1), 24-37.
-
Ayyildiz, H. & Cansiz Aktas, M. (2022) Tendencies of representation studies in mathematics education in Turkey: A thematic content analysis, Cumhuriyet International Journal of Education, 11(1), 127-144.
-
Baroroh, U., & Mardiyana, L. F. (2021). Student mathematical representation ability in their learning habits during the Covid-19 pandemic. Proceedings of the Second Asia Pacific International Conference on Industrial Engineering and Operations Management, Surakarta, Indonesia.
-
Bengtsson, M. (2016). How to plan and perform a qualitative study using content analysis. NursingPlus Open, 2, 8–14. https://doi.org/10.1016/j.npls.2016.01.001
-
Bicer, A. (2021). Multiple representations and mathematical creativity. Thinking Skills and Creativity, 42, 1–17. https://doi.org/10.1016/j.tsc.2021.100960.
-
Božić, R., Peics, H., & Milenković, A. (2023). Multiple representations of functions in the frame of distance learning. Mathematics and Informatics, LXVI(4). https://doi.org/10.53656/math2023-4-3-mul
-
Bozkurt, A., & Sharma, R. C. (2020). Emergency remote teaching in a time of global crisis due to CoronaVirus pandemic. Asian Journal of Distance Education, 15(1), 1–6.
-
Borba, M. C. (2021). The future of mathematics education since COVID-19: Humans-with-media or humans-with-non-living-things. Educational Studies in Mathematics, 108(1), 385–400. https://doi.org/10.1007/s10649-021-10043-2
-
CCSSI. (2010). Common Core State Standards for Mathematics. National Governors Association Center for Best Practices & Council of Chief State School Officers.
-
Creswell, J. W. (2009). Research design: Qualitative, quantitative, and mixed methods approaches (3rd ed.). Sage.
-
Creswell, J. W. (2013). Qualitative inquiry and research design: Choosing among five approaches (3rd ed.). Sage.
-
Cullen, C. J., Hertel, J. T., & Nickels, M. (2020). The roles of technology in mathematics education. The Educational Forum, 84(2), 166–178. https://doi.org/10.1080/00131725.2020.1698683
-
Debrenti, E. (2015). Visual representations in mathematics teaching: An experiment with students. Acta Didactica Napocensia, 8(1), 19–25.
-
Delice, A., & Sevimli, E. (2016). Matematik eğitiminde çoklu temsiller. E. Bingölbali, S. Arslan, & İ.Ö. Zembat (Ed.), Matematik eğitiminde teoriler (ss. 519-537). Ankara: Pegem Akademi Yayıncılık.
-
Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88(1), 89–114. https://doi.org/10.1007/s10649-014-9577-8
-
Eroğlu, D., & Tanışlı, D. (2021). Tahmini öğrenme yollarının uygulanması sürecinde matematik öğretmenlerinin çoklu temsil kullanımlarının gelişimi. Cumhuriyet Uluslararası Eğitim Dergisi, 10(1), 299-329. https://doi.org/10.30703/cije.718210
-
Friesen, M. E., & Kuntze, S. (2020). The role of professional knowledge for teachers’ analysing of classroom situations regarding the use of multiple representations. Research in Mathematics Education, 22(2), 117–134. https://doi.org/10.1080/14794802.2019.1710555
-
Gainsburg, J. (2008). Real-world connections in secondary mathematics teaching. Journal of Mathematics Teacher Education, 11, 199–219. https://doi.org/10.1007/s10857-007-9070-8
-
Goldin, G., & Kaput, J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In L. Steffe & P. Nesher (Eds.), Theories of Mathematical Learning (pp. 397–430). Lawrence Erlbaum.
-
Goldin, G., & Shteingold, N. (2001). Systems of representations and the development of mathematical concepts. In A. C. Cuoco (Ed.), The roles of representation in school mathematics: 2001 yearbook (Vol. 63rd Yearbook, pp. 1–23). NCTM.
-
Greno, P., & Hall, M. (1997). Mathematical representations: Problems and perspectives. Mathematics Teaching in the Middle School, 3(2), 114–120.
-
Heddens, J. W., & Speer, W. R. (1997). Today's mathematics: Concepts and classroom methods for elementary school teachers (8th ed.). Merrill.
-
Heinze, A., Star, J. R., & Verschaffel, L. (2009). Flexible and adaptive use of representations in mathematics. ZDM, 41, 535–540. https://doi.org/10.1007/s11858-009-0190-1
-
Hidayat R, Zainuddin Z, & Mazlan NH. (2024). The relationship between technological pedagogical content knowledge and belief among preservice mathematics teachers. Acta Physiol (Oxf), 249, 104432. https://doi.org/10.1016/j.actpsy.2024.104432.
-
Huang, X., Lai, M.Y. & Huang, R. (2022). Teachers’ changes when addressing the challenges in unexpected migration to online mathematics teaching during the COVID-19 pandemic: a case study in Shanghai. ZDM Mathematics Education, 54, 359–372. https://doi.org/10.1007/s11858-022-01378-y
-
Huinker, D. (2015). Representation. In B. M. Steele (Ed.), Mathematics teaching practices in action (pp. 63–78). National Council of Teachers of Mathematics.
-
Hwang, W. Y., Su, J. H., Huang, Y. M., & Dong, J. J. (2009). A study of multi-representation of geometry problem solving with Virtual Manipulatives and Whiteboard system. Educational Technology and Society, 12(3), 229–247. http://www.jstor.org/stable/jeductechsoci.12.3.229
-
Karabey, B., & Erdoğan, A. (2023). K12 beceriler çerçevesi Türkiye bütüncül modeli matematik alan becerileri. Milli Eğitim Dergisi, 52(1), 971-996. https://doi.org/10.37669/milliegitim.1309180
-
Krippendorff, K. (2018). Content analysis: An introduction to its methodology. Sage publications.
-
Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 33–40). Lawrence Erlbaum.
-
Lesh, R., & Doerr, H. M. (2003). Using representations as a central focus of mathematics teacher preparation. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: A models and modeling perspective on mathematics problem solving, learning, and teaching (pp. 33–59). Lawrence Erlbaum.
-
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. sage.
-
Mishra, P., & Koehler, M. J. (2006). Technological pedagogical content knowledge: A framework for teacher knowledge. Teachers College Record, 108(6), 1017–1054. https://doi.org/10.1111/j.1467-9620.2006.00684.x
-
MEB. (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara.
-
MEB. (2024). İlkokul matematik dersi öğretim programı. Ankara.
-
Merriam, S. B. (2009). Qualitative research: A guide to design and implementation. Jossey-Bass.
-
NCTM. (2000). Principles and Standards for School Mathematics. National Council of Teachers of Mathematics.
-
Pape, S. J., & Tchoshanov, M. A. (2001). The role of representations in developing mathematical understanding. Theory into Practice, 40(2), 118–127.
-
Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. Sage publications.
-
Pierce, R., Stacey, K., Wander, R., & Ball, L. (2011). The design of lessons using mathematics analysis software to support multiple representations in secondary school mathematics. Technology, Pedagogy and Education, 20(1), 95–112. https://doi.org/10.1080/1475939X.2010.534869
-
Prain, V., & Waldrip, B. (2006). An Exploratory Study of Teachers’ and Students’ Use of Multi‐modal Representations of Concepts in Primary Science. International Journal of Science Education, 28(15), 1843–1866. https://doi.org/10.1080/09500690600718294
-
Prayitno, S., Lu’luilmaknunn, U., Sridana, N., & Subarinah, S. (2021, May). Analyzing the ability of mathematics students as prospective mathematics teachers on multiple mathematical representation. In 2nd Annual Conference on Education and Social Science (ACCESS 2020) (pp. 309-313). Atlantis Press.
-
Rau, M. A., Aleven, V., & Rummel, N. (2009). Intelligent tutoring systems with multiple representations and self-explanation prompts support learning of fractions. In V. Dimitrova, R. Mizoguchi, & B. du Boulay (Eds.), Proceedings of the 14th International Conference on Artificial Intelligence in Education, (pp. 441–448). IOS Press. https://doi.org/10.3233/978-1-60750-028-5-441
-
Rüzgar, M.E., Boyraz, S. & Sözcü İ. (2023). Eğitim bilimlerinde araştırma 101 (1. Baskı). Pegem Akademi.
Ryken, A.E. (2009). Multiple representations as sites for teacher reflection about mathematics learning. J Math Teacher Educ, 12, 347–364. https://doi.org/10.1007/s10857-009-9107-2
-
Satsangi, R., & Sigmon, S. D. (2023). Teaching multiplicative thinking with virtual representations to children with mathematics difficulty. Remedial and Special Education, 45(4), 216-229. https://doi.org/10.1177/07419325231206483
-
Sezgin, A. N. (2019). Çoklu temsillerle öğretimin 7. sınıf öğrencilerinin matematiksel anlama seviyelerine ve cebirsel problem çözme sürecine etkisinin incelenmesi (Yayınlanmamış yüksek lisans tezi). Marmara Üniversitesi, İstanbul.
-
Sezgin, S., & Fırat, M. (2020). Covid-19 pandemisinde uzaktan eğitime geçiş ve dijital uçurum tehlikesi. Açıköğretim Uygulamaları ve Araştırmaları Dergisi, 6(4), 37-54.
-
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
-
Skemp, R. R. (1978). Relational understanding and instrumental understanding. Mathematics Teaching, 77, 20–26.
-
Smith, J. A., Flowers, P., & Larkin, M. (2009). Interpretative phenomenological analysis: Theory, method and research. London, UK: Sage.
-
Şengül, S., & Mancoğlu Kaplan, E. (2024). Matematik öğretmenlerinin temsil kullanımlarının örüntü genelleme problemleri bağlamında video temelli olaylarla incelenmesi. Pearson Journal, 8(28), 1246–1268. https://doi.org/10.5281/zenodo.11582188
-
Türer, G., & Cantürk Günhan, B. (2022). Türkiye’de matematik eğitiminde çoklu temsiller ile ilgili yapılan çalışmaların incelenmesi. Fen Matematik Girişimcilik ve Teknoloji Eğitimi Dergisi, 5(3), 214-236.
-
Uslu, F., & Demir, E. (2023). Nitel bir veri toplama tekniği: Derinlemesine görüşme. Hacettepe Üniversitesi Edebiyat Fakültesi Dergisi, 40(1), 289-299. https://doi.org/10.32600/huefd.1184085
-
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2020). Elementary and middle school mathematics: Teaching developmentally (11th ed.). Pearson.
-
Van Manen, M. (2023). Phenomenology of practice: Meaning‐giving methods in phenomenological research and writing. NY: Routledge. https://doi.org/10.4324/9781003228073
-
Yanık, H. B. (2016). Matematik öğretiminde kavramsal anlamaya dayalı yaklaşımlar. İçinde E. Bingölbali, M. F. Özmantar & H. Akkoç (Eds.), Matematiksel kavram yanılgıları ve çözüm önerileri (pp. 17–40). Pegem Akademi.
-
Yavuz-Mumcu, H. (2023). Farklı temsiller arası ilişkilendirme. İçinde H. Yavuz Mumcu, A. Osmanoğlu, & H. Korkmaz (Eds.), Matematik eğitiminde ilişkilendirme (ss. 72-119). Pegem A.
-
Yıldırım, A., & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri (9. baskı). Seçkin Yayıncılık.
-
Yilmaz, A., & Kostur, M. (2021). Rethinking principles of school mathematics during the COVID-19 Pandemic: A multiple-case study on higher education courses related to teaching mathematics. International Electronic Journal of Mathematics Education, 16(3), em0653. https://doi.org/10.29333/iejme/11103
-
Yuhasriati, Y., Johar, R., Khairunnisak, C., Rohaizati, U., Jupri, A., & Zubaidah, T. (2022). Students mathematical representation ability in learning algebraic expression using realistic mathematics education. Jurnal Didaktik Matematika, 9(1), 151-169.