A Glimpse into Infinity in Mathematics Education: A Descriptive Content Analysis Study

Ümranay Kuşçu; Serkan Narlı

doi:10.53444/deubefd.1826380

TR EN

Öz

Matematik Eğitiminde Sonsuzluğa Bir Bakış: Bir Betimsel İçerik Analiz Çalışması

Öz

Bu araştırmanın amacı, eğitimde sonsuzluk kavramı ile ilgili yapılmış araştırmaların eğilimlerini betimsel içerik analizi yöntemi ile ortaya koymaktır. Bu amaçla, çeşitli veri tabanları taranarak 1956-2024 yılları arasında gerçekleştirilen 224 çalışma analiz edilmiştir. Çalışmalar; yayın yılları, yayın türü, araştırma yöntemi, örneklem özellikleri, veri toplama araçları ve araştırma sonuçları açısından incelenmiştir. Bulgular; en fazla çalışmanın 2006-2010 yılları arasında yapıldığını ve nitel araştırma yöntemlerinin çoğunluğu oluşturduğunu ortaya koymuştur. Örneklem dağılımına bakıldığında, üniversite öğrencilerinin en sık çalışılan grup olduğu görülmüştür. Amaçları doğrultusunda, teorik bilgi sunmayı hedefleyen çalışmaların baskın olduğu, buna karşın sonsuzluk kavramının öğretimine odaklanan araştırmaların sınırlı kaldığı belirlenmiştir. Analiz ayrıca, öğrenenlerin formal eğitim öncesinde ve sonrasında farklı şemalar geliştirdiğini ve önceki öğrenmelerin ileri matematiksel konularda epistemolojik bir engel teşkil edebileceğini göstermiştir. Bu çalışma, erken yaş gruplarına yönelik araştırmalardaki önemli bir boşluğu ortaya koyarak ve deneysel çalışma ihtiyacını vurgulayarak literatüre katkı sağlamaktadır. Sonuç olarak, gelecek araştırmaların, formal tanımlar tanıtılmadan önce sezgisel anlayışı geliştirmek amacıyla sonsuzluk kavramının ilkokul ve ortaokul öğretim programlarına entegre edilmesine odaklanması önerilmektedir.

Anahtar Kelimeler

Betimsel içerik analizi, gerçek sonsuzluk, potansiyel sonsuzluk, sonsuzluk algısı.

A Glimpse into Infinity in Mathematics Education: A Descriptive Content Analysis Study

Öz

The purpose of this study is to examine trends in research regarding the concept of infinity in education using a descriptive content analysis method. To this end, 224 studies conducted between 1956 and 2024 were analyzed by scanning various databases. The studies were examined in terms of publication year, type, research method, sample characteristics, data collection tools, and research outcomes. The findings revealed that the highest number of studies was conducted between 2006 and 2010, and qualitative research methods constituted the majority. Regarding sample distribution, university students were the most frequently studied group. In terms of purpose, studies aimed at providing theoretical information were predominant, whereas research focusing on teaching the concept of infinity was limited. The analysis also indicated that learners develop different schemas before and after formal education, and prior learning can act as an epistemological obstacle in advanced mathematical topics. This study contributes to the literature by revealing a significant gap in research regarding early age groups and highlighting the need for experimental studies. Consequently, it is recommended that future research focus on integrating the concept of infinity into primary and middle school curricula to foster intuitive understanding before formal definitions are introduced.

Anahtar Kelimeler

Descriptive content analysis, actual ınfinity, potential ınfinity, perception of ınfinity.

Kaynakça

Adıgüzel, N. (2013). Preservice elementary mathematics teachers' and eighth grade students' knowledge and misconceptions about irrational numbers [İlköğretim matematik öğretmen adayları ve 8. sınıf öğrencilerinin irrasyonel sayılar ile ilgili bilgileri ve bu konudaki kavram yanılgıları] [Master’s thesis, University Name]. Council of Higher Education Thesis Center. (In Turkish)
Akyol, F. M. (2023). Saving the Cat in the Land of Numbers and the Queen: A comparative analysis of the content of two children's mathematics books [Sayılar diyarındaki kedi ve kraliçeyi kurtarmak: İki çocuk matematik kitabının içeriğinin karşılaştırmalı analizi] [Master’s thesis, University Name]. Council of Higher Education Thesis Center. (In Turkish)
Allen, G. D. (2000). The history of infinity. Texas A&M University.
Altun, N. (2009). An alternative approach to teaching limits [Limit öğretimine alternatif bir yaklaşım] [Master’s thesis, University Name]. Council of Higher Education Thesis Center. (In Turkish)
Apkarian, N., Tabach, M., Dreyfus, T. et al. The Sierpinski smoothie: blending area and perimeter. Educ. Stud. Math. 101, 19–34 (2019). https://doi.org/10.1007/s10649-019-09889-4
Aşık, S. (2010). Investigation of undefined and indeterminate concepts in the context of teachers' and preservice teachers' views and performances: Operations with 0, 1, and ∞ [Tanımsızlık ve belirsizlik kavramlarının öğretmen ve öğretmen adaylarının görüş ve performansları bağlamında incelenmesi: 0, 1 ve ∞ ile yapılan işlemler] [Master’s thesis, University Name]. Council of Higher Education Thesis Center. (In Turkish)
Avitan, S. (2010). Development of intuitive perceptions of children about the concept of infinity [Çocukların sonsuzluk kavramına ilişkin sezgisel algılarının geliştirilmesi] (Publication No. 28750362) [Doctoral dissertation, University Name]. ProQuest Dissertations & Theses Global. (In Turkish)
Aztekin, S. (2008). Investigation of structured concepts of infinity in students of different age groups [Farklı yaş gruplarındaki öğrencilerde yapılanmış sonsuzluk kavramlarının araştırılması] [Doctoral dissertation, Gazi University]. Council of Higher Education Thesis Center. (In Turkish)
Barahmand, A. (2017). The boundary between finite and infinite states through the concept of limits of sequences. International Journal of Science and Mathematics Education, 15(3), 569–585. https://doi.org/10.1007/s10763-015-9697-3
Barahmand, A. (2021). Exploring students’ consistency in their notions: the case of comparing infinite series. International Journal of Mathematical Education in Science and Technology, 52:7, 1049–1062, DOI: 10.1080/0020739X.2020.1736350

Barak, B. (2007). Determination of misconceptions about the concept of limit [Limit konusundaki kavram yanılgılarının belirlenmesi] [Master’s thesis, Gazi University]. Council of Higher Education Thesis Center. (In Turkish)
Bartolini Bussi, M. (1989). ‘Evaluation of teaching sequences that include individual and collective activities’, Proc. of the First Italian-German Bilateral Symposium on Didactics of Mathematics, Pavia, pp. 285–308.
Boero, P., Douek, N., & Garuti, R. (2003). Children’s conceptions of infinity of numbers in a fifth-grade classroom discussion context. Paper session presented at the meeting of Proceedings of PME27, Honolulu, ABD.
Bozkuş, F. (2014). Middle school students' conceptions of infinity [Ortaokul öğrencilerinin sonsuzluk kavrayışları] [Master’s thesis, Dokuz Eylül University]. Council of Higher Education Thesis Center. (In Turkish)
Bozkuş, F., Toluk Uçar, Z., & Çetin, İ. (2015). Middle school students' conceptions of infinity [Ortaokul öğrencilerinin sonsuzluğu kavrayışları]. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 6(3), 506–531. https://doi.org/10.16949/turcomat.53890 (In Turkish)
Cohen M., Manion L., Morrison K., Research Methods in Education, 6th ed., Routledge, London, New York, 2007.
Cordeiro, P. (1988). Playing with Infinity in the Sixth Grade. Language Arts, 65(6), 557–566. http://www.jstor.org/stable/41411424
Cottrill, J., Dubinsky, E., Nichols, D., Schwinngendorf, K., Thomas, K., & Vidakovic, D. (1996). Understanding the Limit concept: Beginning with a coordinated process schema. Journal of Mathematical Behavior, 15, 17–192.
Çalık, M., & Sözbilir, M. (2014). Parameters of content analysis [İçerik analizinin parametreleri]. Education and Science [Eğitim ve Bilim], 39(174), 33–38. (In Turkish)
Çalık, M., Ünal, S., Coştu, B., & Karataş, F. Ö. (2008). Trends in Turkish science education. Essays in Education, Special Edition, 23–45.
Çelik, D., & Akşan, E. (2013). Prospective mathematics teachers' understandings of the concepts of infinity, uncertainty, and undefined [Matematik öğretmeni adaylarının sonsuzluk, belirsizlik ve tanımsızlık kavramlarına ilişkin anlamaları]. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 7(1), 166–190. (In Turkish)
Deihl, S., & Markinson, M. P. (2019). Connecting the Tangent Function to Cardinality: A Method for Introducing Set Theory to High School Students. Journal of Mathematics Education at Teachers College, 10(2), 1–7. https://doi.org/10.7916/jmetc.v10i2.4190
Dinçer, S. (2018). Content analysis in educational science research: Meta-analysis, meta-synthesis, descriptive content analysis [Eğitim bilimleri araştırmalarında içerik analizi: Meta-analiz, meta-sentez, betimsel içerik analizi]. Bartın University Journal of Faculty of Education, 7(1), 176–190. https://doi.org/10.17556/erj.339616 (In Turkish)
Dubinsky, E., Weller, K., McDonald, M. A., & Brown, A. (2005). Some historical issues and paradoxes regarding the concept of infinity: An Apos-Based analysis: Part 1. Educational Studies in Mathematics, 58 (3), 335–359.
Dubinsky, E., Weller, K., McDonald, M. A., & Brown, A. (2005). Some historical issues and paradoxes regarding the concept of infinity: An APOS-based analysis - Part 2. Educational Studies in Mathematics, 60, 253–266.
Ely, R. (2011). Envisioning the infinite by projecting finite properties. Journal of Mathematical Behavior, 30, 1–18. https://doi.org/10.1016/j.jmathb.2010.12.001
Ergene, Ö. (2021). The concept of infinity and mathematics curriculum from the perspective of preservice teachers [Öğretmen adayları gözünden sonsuzluk kavramı ve matematik dersi öğretim programı]. Van Yüzüncü Yıl University Journal of Education Faculty, 18(2), 123–151. https://doi.org/10.33711/yyuefd.998263 (In Turkish)
Esposito, J. N. (1960). Infinite, finite, infinity. The Mathematics Teacher, 53(5), 395–397. http://www.jstor.org/stable/27956192
Falk, R. (2010). The Infinite Challenge: Levels of Conceiving the Endlessness of Numbers. Cognition and Instruction, 28(1), 1–38. http://www.jstor.org/stable/27806340
Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Springer,10(1), 3–40.
Fischbein, E. (2001). Tacit models and infinity. Educational Studies in Mathematics, 48(2-3), 309–329.
Fischbein, E., & Schnarch, D. (1997). The Evolution with Age of Probabilistic, Intuitively Based Misconceptions. Journal for Research in Mathematics Education, 28(1), 96–105. https://doi.org/10.2307/749665
Fischbein, E., Tirosh, D. & Hess, P. (1979). The intuition of infinity. Educational Studies in Mathematics, 10(1), 30–40.
Fischbein, E., Tirosh, D. & Melamed, U. (1981). Is it possible to measure the intuitive acceptance of a mathematical statement?. Educational Studies in Mathematics, 12(4), 491–512.
Friedlander, A. (2009). Stories about Never-Ending Sums. Mathematics Teaching in the Middle School, 15(5), 274–280. Retrieved Jan 27, 2025, from https://doi.org/10.5951/MTMS.15.5.0274
Genç, F. (2021). Secondary school teachers' perceptions of infinity [Ortaöğretim öğretmenlerinin sonsuzluk algıları] [Unpublished master’s thesis]. Balıkesir University. (In Turkish)
Giaquinto, M. (1994). Epistemology of visual thinking in elementary real analysis. British Journal for the Philosophy of Science, 45(3), 789–813. https://doi.org/10.1093/bjps/45.3.789
Gökçe, O. (2006). Content analysis: Theoretical and practical information [İçerik analizi kuramsal ve pratik bilgiler] (1st ed.). Siyasal Kitabevi. (In Turkish)
Göktepe Yıldız, S., & Göktepe Körpeoğlu, S. (2018). Exploring pre-service mathematics teachers’ understandings of countability and infinity in WebQuest based learning environment. European Journal of Education Studies, 5(1), 94–120. https://doi.org/10.5281/zenodo.1403724
Güven, B., & Karataş, İ. (2004). Comparison of infinite sets: Methods used by students [Sonsuz kümelerin karşılaştırılması: Öğrencilerin kullandıkları yöntemler]. Dokuz Eylül University Journal of Buca Faculty of Education, 15, 65–73. (In Turkish)
Hewitt, D., & A 2-year Mathematics PGCE Group. (1995). Infinity and Arithmetic Progressions. Mathematics in School, 24(3), 34–35. http://www.jstor.org/stable/30228207
Homaeinejad, M., Barahmand, A., & Seif, A. (2021). The relationship between notions of infinity and strategies used to compare enumerable infinite sets. International Journal of Mathematical Education in Science and Technology, 53(12), 3307–3325. https://doi.org/10.1080/0020739X.2021.1941362
İşleyen, T. (2013). Secondary school students' perceptions of infinity [Ortaöğretim öğrencilerinin sonsuzluk algıları]. Kastamonu University Kastamonu Education Journal, 21(3), 1235–1252. (In Turkish)
Jayarajah, K., Saat, R.M. & Rauf, R.A.A. (2014). A review of science, technology, engineering & mathematics (STEM) education research from 1999–2013: A Malaysian perspective. Eurasia Journal of Mathematics, Science & Technology Education, 10(3), 155-163 DOI: 10.12973/eurasia. 2014.1072a.
Jirotkova, D. & Littler, G. (2004). Insight into pupils ’understanding of infinity in a geometrical context. Paper session presented at the meeting of Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Bergen, Norway.
Jirotkova, D., & Littler, G. (2003). Student's concept of ınfinity in the context of a simple geometrical construct. International Group for the Psychology of Mathematics Education, 3, 126–132.
Kadıoğlu, E., & Kamali, M. (2009). General mathematics [Genel matematik] (4th ed.). Kültür Eğitim Vakfı Publishing. (In Turkish)
Kanbolat, O. (2010). Epistemological obstacles related to some mathematical concepts [Bazı matematiksel kavramlarla ilgili epistemolojik engeller] [Master’s thesis, Atatürk University]. Council of Higher Education Thesis Center. (In Turkish)
Khasawneh A. A. (2020). Analysis of infinity conceptions in mathematics among graduate, undergraduate, and secondary Jordanian students. Psychology and Education. 57(2), 84–90.
Kim, D., Sfard, A., & Ferrini-Mundy, J. (2010). Students’ colloquial and mathematical discourses on infinity and limit. In Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 161-168). Belo Horizonte, Brazil: PME.
Kolar, V. M. & Cadez, T. H. (2012). Analysis of factors influencing the understanding of the concept of infinity. Educational Studies in Mathematics, 80(3), 389–412.
Lin, T. C., Lin, T. J. & Tsai, C. C. (2014). Research trends in science education from 2008 to 2012: A systematic content analysis of publications in selected journals. International Journal of Science Education, 36(8), 1346-1372.
Lune, H., & Berg, B. L. (2017). Qualitative research methods for the social sciences. Pearson.
Mamolo, A. M. (2009). Glimpses of infinity: intuitions, paradoxes, and cognitive leaps. Yayınlanmış Doktora Tezi, Canada, British Columbia: Simon Fraser University.
Mamolo, A. ve Zazkis, R. (2008). Paradoxes as a window to infinity. Research in Mathematics Education, 10 (2), 167-182.
Maria, K., Thanasia, M., Katerina, K., Constantinos, C. & George, P. (2009). Teachers ’perceptions about infinity: a process or an object? Proceedings of CERME 6 (28 January-1 February, Lyon, France, pp. 1771-1780).
Martin, W. G. & Wheeler, M. M. (1987), ‘Infinity concepts among preservice elementary school teachers’, Proceedings of the 11th Conference of the International Group for the Psychology of Mathematics Education, France, pp. 362–368.
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage.
Ministry of National Education [MEB]. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar).
Monaghan, J. (1986). Adolescents' understanding of limits and infinity [Doctoral dissertation, University of Warwick]. Warwick University Repository.
Monaghan, J.D. (2001). Young People’s Ideas of Infinity. Educational Studies in Mathematics, 48(2-3), 239–257.
Moreno, L.E. & Waldegg, G. (1991). The conceptual evolution of actual infinity. Educational Studies in Mathematics, 22(3), 211 – 231.
Na, G., & Lee, E. (2006). Mathemamatıcally Gıfted Students’conceptıon of Infınıty. International Group For The Psychology Of Mathematics Education, 412.
Narlı, S. (2005). Evaluation of the effects of traditional and active learning methods on success in teaching numerical equivalence using a developed achievement test [Geliştirilen başarı testi ile geleneksel ve aktif öğrenme yöntemlerinin sayısal denklik konusu öğretiminde başarıya etkisinin değerlendirilmesi] [Unpublished doctoral dissertation]. Dokuz Eylül University. (In Turkish)
Narlı, S., & Başer, N. (2008). Cantor's set theory and teaching prospective teachers. International Journal of Environmental & Science Education, 3(2), 99-107.
Narlı, S., & Narlı, P. (2012). Determination of primary school students' perceptions and misconceptions of infinity in the light of infinite number sets [Sonsuz sayı kümeleri ışığında ilköğretim öğrencilerinin sonsuzluk algı ve yanılgılarının belirlenmesi]. Dokuz Eylül University Journal of Buca Faculty of Education, (33), 122–133. (In Turkish)
National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.
Núñez, R. (1994). Cognitive development and infinity in the small: paradoxes and consensus. Proceedings of the Sixteenth Annual Conference of the Cognitive Science Society. Hillsdale, NJ: Lawrence Erlbaum Associates.
Oflaz, G., & Polat, K. (2022). Determining the epistemological obstacles regarding the concepts of infinity, undefined and uncertainty [Sonsuzluk, tanımsızlık ve belirsizlik kavramlarına ilişkin epistemolojik engellerinin belirlenmesi]. Cumhuriyet International Journal of Education, 11(2), 301–320. https://doi.org/10.30703/cije.993425 (In Turkish)
Özmantar, F. (2010). The concept of infinity: Historical development, student difficulties and suggestions for solutions [Sonsuzluk kavramı: Tarihsel gelişimi, öğrenci zorlukları ve çözüm önerileri]. In M. F. Özmantar, E. Bingölbali, & H. Akkoç (Eds.), Mathematical misconceptions and suggestions for solutions [Matematiksel kavram yanılgıları ve çözüm önerileri] (2nd ed., pp. 151–180). Pegem Akademi. (In Turkish)
Pala, O. (2020). Investigation of the dynamics of proof image in the context of equivalence of infinite sets [İspat imajının dinamiklerinin sonsuz kümelerin denkliği bağlamında incelenmesi] [Doctoral dissertation, Dokuz Eylül University]. Council of Higher Education Thesis Center. (In Turkish)
Pala, O., & Narlı, S. (2018). Pre-service mathematics teachers’ proving approaches and difficulties regarding the equivalence of infinite sets [Matematik öğretmeni adaylarının sonsuz kümelerin denkliği ile ilgili ispatlama yaklaşımları ve yaşadıkları güçlükler]. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 9(3), 449–475. https://doi.org/10.16949/turcomat.337191 (In Turkish)
Pehkonen, E., Hannula, M. S., Maijala, H., & Soro, R. (2006). Infinity of numbers: How students understand it. In Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 345-352). Prague, Czech Republic: PME.
Petty, J. A. (1996). The role of reflective abstraction in the conceptualization of infinity and infinite processes (Order No. 9725604). Available from ProQuest Dissertations & Theses Global. (304262191). https://www.proquest.com/dissertations-theses/role-reflective-abstraction-conceptualization/docview/304262191/se-2
Sacristan, A. I. (1997). Windows on the Infinite: Creating Meanings in a Logo-Based Microworld. Yayınlanmış Doktora tezi, UK: University of London, Institute of Education.
Sacristán, A.I. & Noss, R. (2008). Computational Construction as a Means to Coordinate Representations of Infinity. Int. J. Comput. Math. Learn. 13, 47–70. https://doi.org/10.1007/s10758-008-9127-5
Sbaraglı, S. (2006). Primary school teachers ’beliefs and change of beliefs on mathematical infinity. Mediterranean Journal for Research in Mathematics Education, 5(2), 49–76.
Sevda Göktepe Yildiz & Seda Göktepe Körpeoğlu. (2018). Explorıng Pre-Servıce Mathematıcs Teachers' Understandıngs Of Countabılıty And Infınıty In a Webquest-Based Learnıng Envıronment. European Journal of Education Studies, 5(1). https://doi.org/10.5281/zenodo.1403724
Sierpińska, A. (1987). Humanities students and epistemological obstacles related to limits. Educational Studies in Mathematics, 18(4), 371-397.
Singer, F. M., & Voica, C. (2008). Between perception and intuition: Learning about infinity. The Journal of Mathematical Behavior, 27(3), 188–205.
Singer, M. & Voica, C. (2003). Perception of infinity: Does it really help in problem solving?. The Mathematics Education into the 21st Century Project Proceedings of the International Conference.
Singer, M. & Voica, C. (2007). Children’s Perceptions of Infinity: Could They Be Structured?. Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education, Working Group 3-506, (22-26 February, Larnaca, Cyprus, pp. 506-515).
Suri, H. & Clarke, D. (2009). Advancements in research synthesis methods: From a methodologically inclusive perspective. Review of Educational Research, 79(1), 395–430.
Tall, D. (1977). Conflicts and catastrophes in the learning of mathematics. Mathematical education for teaching, 2(4), 2-18.
Tall, D. (1980). Mathematical intuition, with special reference to limiting processes. In Proceedings of the Fourth International Conference for the Psychology of Mathematics Education (pp. 170-176). Berkeley, CA.
Tall, D. (1981). Intuitions of Infinity. Mathematics in School, 10, 30-33.
Tall, D. O. (1991). Advanced Mathematical Thinking (editor), Kluwer: Dordrecht.
Tall, D. O. & Schwarzenberger, R. L. (1978). Conflicts in the learning of real numbers and limits. Mathematics Teaching, 82, 44-49.
Tall, D. O. & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational studies in mathematics, 12(2), 151-169.
Tall, D. O. & Tirosh, D. (2001). Infinity–The never-ending struggle. Educational studies in Mathematics, 48(2), 129-136.
Tall, D.O. (2001). Natural and formal infinities. Educational Studies in Mathematics, 48(2-3), 199-238.
Tirosh, D. (1991). The Role of Students' Intuitions of Infinity in Teaching the Cantorian Theory. In D. Tall, Advanced Mathematical Thinking (pp. 201–214). The Netherlands: Kluwer Academic Publishers.
Tirosh, D. (1999). Finite and infinite sets: definitions and intuitions. International Journal of Mathematical Education in Science and Technology, 30(3), 341–349. https://doi.org/10.1080/002073999287879
Tirosh, D. & Tsamir, P. (2006). Conceptual Change in mathematics learning: The case of infinite sets. In Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 159–161). Prague, Czech Republic: PME.
Tirosh, D., & Tsamir, P. (1996). The role of representations in students’ intuitive thinking about infinity. International Journal of Mathematical Education in Science and Technology, 27(1), 33–40. https://doi.org/10.1080/0020739960270105
Tsamir, P. (1999). The Transition from Comparing Finite Sets to Comparing Infinite Sets: Teaching Prospective Teachers. Educational Studies in Mathematics, 38, 209– 234.
Tsamir, P. (2001). When The Same'is not perceived as such: The case of infinite sets. Educational Studies in Mathematics, 48(2-3), 289–307.
Tsamir, P. & Dreyfus, T. (2002). Comparing infinite sets—a process of abstraction: The case of Ben. The Journal of Mathematical Behavior, 21(1), 1–23.
Tsamir, P. & Tirosh, D. (1999). Consistency and representations: The case of actual infinity. Journal for Research in Mathematics Education, 30(2), 213–219.
Tsamir, P., & Tirosh, D. (1999). Consistency and Representations: The Case of Actual Infinity. Journal for Research in Mathematics Education, 30(2), 213–219. https://doi.org/10.2307/749611
Ültay, E., Akyurt, H., & Ültay, N. (2021). Descriptive content analysis in social sciences [Sosyal bilimlerde betimsel içerik analizi]. IBAD Journal of Social Sciences, (10), 188–201. https://doi.org/10.21733/ibad.863116 (In Turkish)
Ünan, Z., & Doğan, M. (2011). Finite and countable infinite sets and a modeling of uncountable infinite sets [Sonlu ve sayılabilir sonsuz kümeler ve sayılamayan sonsuz kümelerin bir modellemesi]. Education Sciences, 6(2), 1938–1950. (In Turkish)
Wijeratne, C., & Zazkis, R. (2016). Exploring conceptions of infinity via super-tasks: A case of Thomson’s Lamp and Green Alien. Journal of Mathematical Behavior, 41, 1–17. https://doi.org/10.1016/j.jmathb.2015.11.002
Williams, S. R. (2001). Predications of the limit concept: An application of repertory grids. Journal for Research in Mathematics Education, 32(4), 341–367. https://doi.org/10.2307/749699
Yıldırım, A., & Şimşek, H. (2006). Qualitative research methods in the social sciences [Sosyal bilimlerde nitel araştırma yöntemleri] (5th ed.). Seçkin Publishing. (In Turkish)
Yıldırım, A., & Şimşek, H. (2011). Qualitative research methods in the social sciences [Sosyal bilimlerde nitel araştırma yöntemleri] (8th ed.). Seçkin Publishing. (In Turkish)
Yıldırım, K., & Keşan, C. (2017). Middle school students' views on the ellipsis and the concept of infinity [Ortaokul öğrencilerinin üç nokta ve sonsuzluk kavramına ilişkin görüşleri]. Black Sea Journal of Social Sciences, 9(16), 47–69. (In Turkish)

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik Eğitimi

Bölüm

Araştırma Makalesi

Yazarlar

Ümranay Kuşçu ^*
0009-0009-0715-1681
Türkiye

Serkan Narlı
0000-0001-8629-8722
Türkiye

Yayımlanma Tarihi

31 Mart 2026

Gönderilme Tarihi

18 Kasım 2025

Kabul Tarihi

11 Mart 2026

Yayımlandığı Sayı

Yıl 2026 Sayı: 67

DOI

https://doi.org/10.53444/deubefd.1826380

IZ

https://izlik.org/JA75BY24AN

APA

Kuşçu, Ü., & Narlı, S. (2026). A Glimpse into Infinity in Mathematics Education: A Descriptive Content Analysis Study. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, 67, 571-598. https://doi.org/10.53444/deubefd.1826380

AMA

1.Kuşçu Ü, Narlı S. A Glimpse into Infinity in Mathematics Education: A Descriptive Content Analysis Study. DEU BEF Dergi. 2026;(67):571-598. doi:10.53444/deubefd.1826380

Chicago

Kuşçu, Ümranay, ve Serkan Narlı. 2026. “A Glimpse into Infinity in Mathematics Education: A Descriptive Content Analysis Study”. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, sy 67: 571-98. https://doi.org/10.53444/deubefd.1826380.

EndNote

Kuşçu Ü, Narlı S (01 Mart 2026) A Glimpse into Infinity in Mathematics Education: A Descriptive Content Analysis Study. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi 67 571–598.

IEEE

[1]Ü. Kuşçu ve S. Narlı, “A Glimpse into Infinity in Mathematics Education: A Descriptive Content Analysis Study”, DEU BEF Dergi, sy 67, ss. 571–598, Mar. 2026, doi: 10.53444/deubefd.1826380.

ISNAD

Kuşçu, Ümranay - Narlı, Serkan. “A Glimpse into Infinity in Mathematics Education: A Descriptive Content Analysis Study”. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi. 67 (01 Mart 2026): 571-598. https://doi.org/10.53444/deubefd.1826380.

JAMA

1.Kuşçu Ü, Narlı S. A Glimpse into Infinity in Mathematics Education: A Descriptive Content Analysis Study. DEU BEF Dergi. 2026;:571–598.

MLA

Kuşçu, Ümranay, ve Serkan Narlı. “A Glimpse into Infinity in Mathematics Education: A Descriptive Content Analysis Study”. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, sy 67, Mart 2026, ss. 571-98, doi:10.53444/deubefd.1826380.

Vancouver

1.Ümranay Kuşçu, Serkan Narlı. A Glimpse into Infinity in Mathematics Education: A Descriptive Content Analysis Study. DEU BEF Dergi. 01 Mart 2026;(67):571-98. doi:10.53444/deubefd.1826380

Öz

Öz

Matematik Eğitiminde Sonsuzluğa Bir Bakış: Bir Betimsel İçerik Analiz Çalışması

Öz

Anahtar Kelimeler

A Glimpse into Infinity in Mathematics Education: A Descriptive Content Analysis Study

Öz

Anahtar Kelimeler

Kaynakça

Ayrıntılar

Birincil Dil

Konular

Bölüm

Yazarlar

Yayımlanma Tarihi

Gönderilme Tarihi

Kabul Tarihi

Yayımlandığı Sayı

DOI

IZ

Kaynak Göster