Review Article
BibTex RIS Cite

Systematic review of studies on mathematical thinking

Year 2025, Volume: 15 Issue: ISRIS 2025, 826 - 845, 31.07.2025

Müberra Gök , Meral Cansiz Aktas

Abstract

Mathematical thinking has an important place in mathematics education. It is important to provide students with mathematical thinking skills so that they can be raised not only as individuals who memorize formulas, but also as individuals who question, interpret and think, and to understand that mathematics is a product of thought. In this context, the purpose of this study was to map the articles on mathematical thinking published between 1990-2021 in the Web of Science database using the bibliometric analysis method and to investigate the research trends. As a result of the search made with the phrase "mathematical thinking" in the Web of Science database; 668 articles published in English between January 1990 and December 2021 in the field of mathematics education were included in the research. The research revealed a consistent increase in the number of studies on mathematical thinking over the years examined.In addition, the most frequently used keywords in the studies examined were mathematics, noticing, mathematics education, student mathematical thinking, problem solving, advanced mathematical thinking, teacher education, teacher knowledge, reasoning, evaluation, teacher candidate education, technology, mathematics teaching, fractions, task design, cognitive demand, and reflection. Country-based analysis revealed that the United States, Australia, and Turkey produced the highest number of articles. The bibliometric analysis of the articles on mathematical thinking revealed a four-cluster structure formed according to the relationships of the keywords reflecting the articles. These sets are; recognition, development, advanced mathematical thinking and technology.

Keywords

Bibliometric Analysis Mathematical Thinking Mathematics Education

References

  • Akcay, A. O., & Boston, M. D. (2018). Preservice mathematics teachers’ effective use of technology: Analyzing the cognitive demands of technology-based instructional activities. In Educating prospective secondary mathematics teachers (pp. 143–166). Springer. https://doi.org/10.1007/978-3-319-90179-4_7
  • Alkan, H., & Bukova Güzel, E. (2005). Öğretmen adaylarında matematiksel düşünmenin gelişimi. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 25(3), 221-236.
  • Altun, M. (2018). Ortaokullarda (5, 6, 7, 8. sınıflarda) matematik öğretimi (12. baskı). Aktüel Yayınları.
  • Amador, J. M. (2017). Preservice teachers’ video simulations and subsequent noticing: A practice-based method to prepare mathematics teachers. Research in Mathematics Education, 19(3), 217-235.
  • Arslan, S., & Yıldız, M. (2010). 11. sınıf öğrencilerinin matematiksel düşünme becerileri. Eğitim ve Bilim, 35(156), 143-154.
  • Bayazıt, Y., & Osmanoğlu, A. (2017). The effect of problem solving instruction on mathematical thinking. Pedagogika-Pedagogy, 89(1), 80-89.
  • Baykul, Y. (2009). İlköğretimde matematik öğretimi (6-8. sınıflar). Pegem Akademi Yayıncılık.
  • Benton, L., Kalas, I., Saunders, P., Hoyles, C., & Noss, R. (2018). Beyond jam sandwiches and cups of tea: An exploration of primary pupils' algorithm evaluation strategies. Journal of Computer Assisted Learning, 34, 590-601. https://doi.org/10.1111/jcal.12266
  • Bloom, I. (2007). Extended analyses: Promoting mathematical inquiry with preservice mathematics teachers. Journal of Mathematics Teacher Education, 10(4), 399-403.
  • Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2017). Bilimsel araştırma yöntemleri. Ankara: Pegem Akademi Yayıncılık.
  • Carter, I. S. W., & Amador, J. (2015). Lexical and indexical conversational components that mediate professional noticing during lesson study. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1339-1361.
  • Clarke, D., Clarke, B., & Roche, A. (2011). Building teachers’ expertise in understanding, assessing and developing children’s mathematical thinking: The power of task-based, one-to-one assessment interviews. ZDM Mathematics Education, 43, 901-913. https://doi.org/10.1007/s11858-011-0345-2
  • Cooke, B. D., & Buchholz, D. (2005). Mathematical communication in the classroom: A teacher makes a difference. Early Childhood Education Journal, 32(6), 365-369.
  • Coşkun, S. D., Sitrava, R. T., & Bostan, M. I. (2021). Pre-service elementary teachers’ noticing expertise of students’ mathematical thinking: The case of fractions. International Journal of Mathematical Education in Science and Technology, 1-18.
  • Cui, Z., & Ng, O. L. (2021). The interplay between mathematical and computational thinking in primary school students’ mathematical problem-solving within a programming environment. Journal of Educational Computing Research, 59(5), 988-1012.
  • Dickerson, D. S., & Damien, J. P. (2016). An examination of college mathematics majors’ understandings of their own written definitions. The Journal of Mathematical Behavior, 41, 1-9. DOI:10.1016/j.jmathb.2015.11.001
  • Dickerson, D. S., & Doerr, H. M. (2014). High school mathematics teachers’ perspectives on the purposes of mathematical proof in school mathematics. Mathematics Education Research Journal, 26, 711-733. https://doi.org/10.1007/s13394-013-0091-6
  • Dreyfus, T. (1991). Advanced mathematical thinking processes. In D. Tall (Ed.), Advanced mathematical thinking (pp. xx-xx). Kluwer Academic Publishers.
  • Drijvers, P., Kodde-Buitenhuis, H., & Doorman, M. (2019). Assessing mathematical thinking as part of curriculum reform in the Netherlands. Educational Studies in Mathematics, 102(3), 435-456.
  • Duran, N. (2005). Matematiksel düşünme becerilerine ilişkin bir araştırma [Yüksek lisans tezi, Hacettepe Üniversitesi Sosyal Bilimler Enstitüsü].
  • El-Demerdash, M., Mercat, C., Trgalova, J., Essonnier, N., & Lealdino Filho, P. (2016). Design and evaluation of digital resources to enhance creative mathematical thinking in a biomathematics context. Bulletin of the IEEE Technical Committee on Learning Technology, 18(1), 6-9.
  • Engelbrecht, J. (2010). Adding structure to the transition process to advanced mathematical activity. International Journal of Mathematical Education in Science and Technology, 41(2), 143-154. DOI: 10.1080/00207390903391890
  • Estrella, S., Zakaryan, D., Olfos, R., & Espinoza, G. (2020). How teachers learn to maintain the cognitive demand of tasks through Lesson Study. Journal of Mathematics Teacher Education, 23(3), 293-310.
  • Fernández, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through on-line discussions. ZDM Mathematics Education, 44, 747-759. https://doi.org/10.1007/s11858-012-0425-y
  • Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teacher’s noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1), 441-468.
  • Fisher, K., Hirsh-Pasek, K., & Golinkoff, R. M. (2012). Fostering mathematical thinking through playful learning. In E. Reese & S. P. Segate (Eds.), Contemporary debates on child development and education (pp. 81-92). Routledge.
  • Fisher, M. H., Thomas, J., Schack, E. O., Jong, C., & Tassell, J. (2018). Noticing numeracy now! Examining changes in preservice teachers’ noticing, knowledge, and attitudes. Mathematics Education Research Journal, 30(2), 209-232.
  • Fouze, A., & Amit, M. (2017). Development of mathematical thinking through integration of ethnomathematic folklore game in math instruction. Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 617-630. 10.12973/ejmste/80626
  • Fraivillig, J. L., Murphy, L. A., & Fuson, K. C. (1999). Advancing children’s mathematical thinking in everyday mathematics classrooms. Journal for Research in Mathematics Education, 30(2), 148-170. https://doi.org/10.2307/749608 Franke, M. L., & Carey, D. A. (1997). Young children's perceptions of mathematics in problem-solving environments. Journal for Research in Mathematics Education, 28(1), 8-25.
  • Gavin, M. K., Casa, T. M., Adelson, J. L., & Firmender, J. M. (2013). The impact of challenging geometry and measurement units on the achievement of grade 2 students. Journal for Research in Mathematics Education, 44(3), 478-509.
  • Ginsburg, H. P. (2016). Helping early childhood educators to understand and assess young children’s mathematical minds. ZDM, 48(7), 941-946.
  • Gökçe, S., & Güner, P. (2021). Forty years of mathematics education: 1980-2019. International Journal of Education in Mathematics, Science and Technology, 9(3), 514-539.
  • Gökçe, S., & Güner, P. (2022). Dynamics of GeoGebra ecosystem in mathematics education. Education and Information Technologies, 27(4), 5301-5323.
  • Guba, E. G., & Lincoln, Y. S. (1982). Epistemological and methodological bases of naturalistic inquiry. ECTJ, 30(4), 233-252.
  • Güner, P., & Gökçe, S. (2021). Monitoring the nomological network of number sense studies. International Journal of Mathematical Education in Science and Technology, 52(4), 580-608.
  • Hallman-Thrasher, A. (2017). Prospective elementary teachers’ responses to unanticipated incorrect solutions to problem-solving tasks. Journal of Mathematics Teacher Education, 20(6), 519-555.
  • Hashemi, N., Abu, M. S., Kashefi, H., Mokhtar, M., & Rahimi, K. (2015). Designing learning strategy to improve undergraduate students’ problem solving in derivatives and integrals: A conceptual framework. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 227-238.
  • Henning, J. E., McKeny, T., Foley, G. D., & Balong, M. (2012). Mathematics discussions by design: Creating opportunities for purposeful participation. Journal of Mathematics Teacher Education, 15, 453-479.
  • Hino, K. (2007). Toward the problem-centered classroom: Trends in mathematical problem solving in Japan. ZDM, 39(5), 503-514.
  • Hitt, F., Saboya, M., & Cortés Zavala, C. (2016). An arithmetic-algebraic work space for the promotion of arithmetic and algebraic thinking: Triangular numbers. ZDM, 48(6), 775-791.
  • Huang, R., & Li, Y. (2012). What matters most: A comparison of expert and novice teachers' noticing of mathematics classroom events. School Science and Mathematics, 112, 420-432.
  • Hudson, B., Henderson, S., & Hudson, A. (2015). Developing mathematical thinking in the primary classroom: Liberating students and teachers as learners of mathematics. Journal of Curriculum Studies, 47(3), 374-398.
  • Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81-116.
  • Huscroft-Dâ, J. N., Higgins, K. N., & Crawford, L. L. (2014). A descriptive study examining the impact of digital writing environments on communication and mathematical reasoning for students with learning disabilities. Learning Disabilities: A Multidisciplinary Journal, 20(4), 177-188.
  • Inglis, M., & Alcock, L. (2012). Expert and novice approaches to reading mathematical proofs. Journal for Research in Mathematics Education, 43(4), 358-390.
  • Inglis, M., & Simpson, A. (2009). Conditional inference and advanced mathematical study: Further evidence. Educational Studies in Mathematics, 72(2), 185-198.
  • Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
  • Kallia, M., van Borkulo, S. P., Drijvers, P., Barendsen, E., & Tolboom, J. (2021). Characterising computational thinking in mathematics education: A literature-informed Delphi study. Research in Mathematics Education, 23(2), 159-187.
  • Kaur, H. (2020). Introducing the concept of angle to young children in a dynamic geometry environment. International Journal of Mathematical Education in Science and Technology, 51(2), 161-182.
  • Kieran, C. (2001). The mathematical discourse of 13-year-old partnered problem solving and its relation to the mathematics that emerges. Educational Studies in Mathematics, 46(1), 187-228.
  • Koichu, B. (2010). On the relationships between (relatively) advanced mathematical knowledge and (relatively) advanced problem-solving behaviours. International Journal of Mathematical Education in Science and Technology, 41(2), 257-275.
  • Krupa, E. E., Huey, M., Lesseig, K., Casey, S., & Monson, D. (2017). Investigating secondary preservice teacher noticing of students’ mathematical thinking. In E. Schack, M. Fisher, & J. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. xx–xx). Springer. https://doi.org/10.1007/978-3-319-46753-5_4
  • Leatham, K. R., Peterson, B. E., Stockero, S. L., & Van Zoest, L. R. (2015). Conceptualizing mathematically significant pedagogical opportunities to build on student thinking. Journal for Research in Mathematics Education, 46, 88-124.
  • Lee, H. S. (2005). Facilitating students’ problem solving in a technological context: Prospective teachers’ learning trajectory. Journal of Mathematics Teacher Education, 8, 223–254. https://doi.org/10.1007/s10857-005-2618-6
  • Lee, M. Y., & Cross Francis, D. (2018). Investigating the relationships among elementary teachers’ perceptions of the use of students’ thinking, their professional noticing skills, and their teaching practices. The Journal of Mathematical Behavior, 51, 118-128.
  • Lee, M. Y. (2019). The development of elementary pre-service teachers’ professional noticing of students’ thinking through adapted lesson study. Asia-Pacific Journal of Teacher Education, 47(4), 383-398.
  • Liu, P. H. (2003). The relationship of a problem-based calculus course and students' views of mathematical thinking [Unpublished doctoral dissertation]. Oregon State University.
  • Mewborn, D. S. (1999). Reflective thinking among preservice elementary mathematics teachers. Journal for Research in Mathematics Education, 30(3), 316-341.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage.
  • Milli Eğitim Bakanlığı. (2018). Matematik dersi öğretim programı. Milli Eğitim Bakanlığı. Nickels, M., & Cullen, C. J. (2017). Mathematical thinking and learning through robotics play for children with critical illness: The case of Amelia. Journal for Research in Mathematics Education, 48(1), 22-77.
  • Nickerson, S. D., Lamb, L., & LaRochelle, R. (2017). Challenges in measuring secondary mathematics teachers’ professional noticing of students’ mathematical thinking. In Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 381-398). Springer.
  • Norton, A., & Kastberg, S. (2012). Learning to pose cognitively demanding tasks through letter writing. Journal of Mathematics Teacher Education, 15(2), 109-130.
  • Oehrtman, M. (2009). Collapsing dimensions, physical limitation, and other student metaphors for limit concepts. Journal for Research in Mathematics Education, 40(4), 396-426.
  • Oers, B. V. (2002). Educational forms of initiation in mathematical culture. In Learning discourse (pp. 59-85). Springer.
  • Otten, S., Webel, C., & de Araujo, Z. (2017). Inspecting the foundations of claims about cognitive demand and student learning: A citation analysis of Stein and Lane (1996). The Journal of Mathematical Behavior, 45, 111-120.
  • Paterson, J., & Sneddon, J. (2011). Conversations about curriculum change: Mathematical thinking and team-based learning in a discrete mathematics course. International Journal of Mathematical Education in Science and Technology, 42(7), 879-889.
  • Pérez, A. (2018). A framework for computational thinking dispositions in mathematics education. Journal for Research in Mathematics Education, 49(4), 424-461.
  • Philipp, R. A., Ambrose, R., Lamb, L. L., Sowder, J. T., Schappelle, B. P., Sowder, L., ... & Chauvot, J. (2007). Effects of early field experiences on the mathematical content knowledge and beliefs of prospective elementary school teachers: An experimental study. Journal for Research in Mathematics Education, 38(5), 438-476.
  • Piggott, J. (2004, January). Developing a framework for mathematical enrichment. Paper presented at the Symposium on Critical Thinking in Teaching and Learning, University of West Indies, St. Augustine, Trinidad.
  • Radu, I., & Weber, K. (2011). Refinements in mathematics undergraduate students’ reasoning on completed infinite iterative processes. Educational Studies in Mathematics, 78(2), 165-182. http://www.jstor.org/stable/41486160
  • Roth McDuffie, A., Foote, M. Q., Bolson, C., Turner, E. E., Aguirre, J. M., Bartell, T. G., Drake, C., & Land, T. (2014). Using video analysis to support prospective K-8 teachers' noticing of students' multiple mathematical knowledge bases. Journal of Mathematics Teacher Education, 17(3), 245–270. https://doi.org/10.1007/s10857-013-9257-0
  • Rowlett, P. (2015). Developing strategic and mathematical thinking via game play: Programming to investigate a risky strategy for Quarto. The Mathematics Enthusiast, 12(1), 55-61.
  • Rowlett, P., Webster, K., Bradshaw, N. A., & Hind, J. (2019). Evaluation of the maths arcade initiative at five UK universities. The Mathematics Enthusiast, 16(1), 451-460.
  • Ryken, A. E. (2009). Multiple representations as sites for teacher reflection about mathematics learning. Journal of Mathematics Teacher Education, 12(5), 347-364. Samo, D. D., Darhim, D., & Kartasasmita, B. (2017). Developing contextual mathematical thinking learning model to enhance higher-order thinking ability for middle school students. International Education Studies, 10(2), 17-29.
  • Schoenfeld, A. H. (2017). Uses of video in understanding and improving mathematical thinking and teaching. Journal of Mathematics Teacher Education, 20, 415-432. https://doi.org/10.1007/s10857-017-9381-3
  • Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 34(1), 4-36.
  • Sherman, M. F., Cayton, C., Walkington, C., & Funsch, A. (2020). An analysis of secondary mathematics textbooks with regard to technology integration. Journal for Research in Mathematics Education, 51(3), 361-374.
  • Sleep, L., & Boerst, T. A. (2012). Preparing beginning teachers to elicit and interpret students' mathematical thinking. Teaching and Teacher Education, 28(7), 1038-1048.
  • Stewart, S., & Thomas, M. O. (2009). A framework for mathematical thinking: The case of linear algebra. International Journal of Mathematical Education in Science and Technology, 40(7), 951-961.
  • Stockero, S. L., Rupnow, R. L., & Pascoe, A. E. (2017). Learning to notice important student mathematical thinking in complex classroom interactions. Teaching and Teacher Education, 63, 384-395.
  • Superfine, A. C., Fisher, A., Bragelman, J., & Amador, J. M. (2017). Shifting perspectives on preservice teachers’ noticing of children’s mathematical thinking. In Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 409-426). Springer.
  • Superfine, A., Amador, J., & Bragelman, J. (2018). Facilitating video-based discussions to support prospective teacher noticing. The Journal of Mathematical Behavior, 54. https://doi.org/10.1016/j.jmathb.2018.11.002
  • Şencan, H. (2005). Sosyal ve davranışsal ölçümlerde güvenilirlik ve geçerlilik. Ankara: Seçkin Yayıncılık.
  • Şengül, S., Katrancı, Y., & Gerez-Cantimer, G. (2014). Metaphor perceptions of secondary school students about “mathematics teacher”. The Journal of Academic Social Science Studies, 25(1), 89-111.
  • Szydlik, J. E. (2000). Mathematical beliefs and conceptual understanding of the limit of a function. Journal for Research in Mathematics Education, 31(3), 258-276. https://doi.org/10.2307/749807
  • Tall, D. (1995). Cognitive growth in elementary and advanced mathematical thinking. In L. Meira & D. Carraher (Eds.), Proceedings of the 19th Meeting of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 61-75). Recife, Brasil: Universidade Federal de Pernambuco.
  • Tall, D. (2002). Advanced mathematical thinking. Kluwer Academic Publishers.
  • 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
  • Umay, A. (2003). Matematiksel muhakeme yeteneği. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24(3), 234-243.
  • Vacc, N. N., & Bright, G. W. (1999). Elementary preservice teachers' changing beliefs and instructional use of children's mathematical thinking. Journal for Research in Mathematics Education, 30(1), 89-110.
  • van Eck, N. J., & Waltman, L. (2011). VOSviewer manual: Manual for VOSviewer version 1.0.
  • van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24(2), 244-276.
  • van Oers, B. (2010). Emergent mathematical thinking in the context of play. Educational Studies in Mathematics, 74(1), 23-37.
  • Wager, A. A. (2014). Noticing children's participation: Insights into teacher positionality toward equitable mathematics pedagogy. Journal for Research in Mathematics Education, 45(3), 312-350.
  • Wager, A. A., & Parks, A. N. (2016). Assessing early number learning in play. ZDM, 48(7), 991-1002.
  • Weber, K. (2009). How syntactic reasoners can develop understanding, evaluate conjectures, and generate counterexamples in advanced mathematics. The Journal of Mathematical Behavior, 28(2-3), 200-208.
  • Weber, K., & Mejia-Ramos, J. P. (2011). Why and how mathematicians read proofs: An exploratory study. Educational Studies in Mathematics, 76(3), 329-344.
  • Williams, S. R. (2001). Predications of the limit concept: An application of repertory grids. Journal for Research in Mathematics Education, 32(4), 341-367.
  • Wilson, P. H., Lee, H. S., & Hollebrands, K. F. (2011). Understanding prospective mathematics teachers' processes for making sense of students' work with technology. Journal for Research in Mathematics Education, 42(1), 39-64.
  • Woods, T., Williams, G., & McNeal, B. (2006). Children's mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37(3), 222-255.
  • Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.
  • Yıldırım, C. (1988). Matematiksel düşünme. İstanbul: Remzi Kitabevi.
  • Yıldız, C. (2016). Comparing the mathematical thinking experiences of students at faculty of education and faculty of arts and sciences. TOJET: The Turkish Online Journal of Educational Technology-Special Issue for INTE 2016, 480-488.
  • Yilmaz, R., & Argun, Z. (2017). Role of visualization in mathematical abstraction: The case of congruence concept. International Journal of Education in Mathematics, Science and Technology, 6, 1-11.
  • Yoon, C., Thomas, M. O., & Dreyfus, T. (2011). Gestures and insight in advanced mathematical thinking. International Journal of Mathematical Education in Science and Technology, 42(7), 891-901.
  • Young-Loveridge, J. (2011). Assessing the mathematical thinking of young children in New Zealand: The initial school years. Early Child Development and Care, 181(2), 267-276.
  • Yuzawa, M., Bart, W. M., Yuzawa, M., & Junko, I. (2005). Young children's knowledge and strategies for comparing sizes. Early Childhood Research Quarterly, 20(2), 239-253.

Matematiksel düşünme üzerine yapılan çalışmaların sistematik olarak incelenmesi

Year 2025, Volume: 15 Issue: ISRIS 2025, 826 - 845, 31.07.2025

Müberra Gök , Meral Cansiz Aktas

Abstract

Matematiksel düşünme, matematik eğitiminde önemli bir yere sahiptir. Öğrencilerin sadece formül ezberleyen bireyler olmayıp, sorgulayan, yorumlayan, düşünen bireyler olarak yetiştirilebilmesi, matematiğin bir düşünce ürünü olduğunun anlaşılabilmesi için öğrencilere matematiksel düşünme becerisi kazandırmak önem taşımaktadır.
Bu kapsamda çalışmanın amacı Web of Science veri tabanında 1990-2021 yılları arasında matematiksel düşünme üzerine yayınlanan makalelerin bibliyometrik analiz yöntemi kullanılarak haritalandırılması ve araştırma eğilimlerinin izlenmesi olarak belirlenmiştir. Web of Science veri tabanında “mathematical thinking” ifadesi ile yapılan tarama sonucunda; matematik eğitimi alanında Ocak1990 - Aralık 2021 tarihleri arasında İngilizce dilinde yayınlanan 668 adet makale araştırmaya dâhil edilmiştir.
Araştırmanın sonucunda belirlenen yıllar arasında matematiksel düşünme üzerine yapılan çalışma sayısının düzenli olarak artış gösterdiği belirlenmiştir. Ayrıca incelenen çalışmalarda en sık kullanılan anahtar kelimelerin matematik, fark etme, matematik eğitimi, öğrenci matematiksel düşünmesi, problem çözme, ileri matematiksel düşünme, öğretmen eğitimi, öğretmen bilgisi, akıl yürütme, değerlendirme, aday öğretmen eğitimi, teknoloji, matematik öğretimi, kesirler, görev tasarımı, bilişsel talep ve yansıtma olduğu görülmüştür. Ülkelere göre inceleme yapıldığında ABD, Avustralya ve Türkiye’nin en fazla makale üreten ülkeler olduğu fark edilmiştir. Matematiksel düşünme ile ilgili makalelerin bibliyometrik analizi makaleleri yansıtan anahtar kelimelerin birbirleriyle ilişkilerine göre oluşan dört kümeli bir yapıyı ortaya çıkarmıştır. Bu kümeler; fark etme, geliştirme, ileri matematiksel düşünme ve teknoloji olarak isimlendirilmiştir.
Matematiksel düşünmenin dinamiklerine yönelik olarak yapılan bu çalışmanın araştırmacıların, öğretmenlerin, öğrencilerin araştırmaya ihtiyaç duyulan alanlar hakkında fikir sahibi olmalarına ve bu doğrultuda planlamalar yapmalarına yardımcı olacağı düşünülmektedir.

Keywords

Bibliyometrik Analiz Matematiksel Düşünme Matematik Eğitimi

References

  • Akcay, A. O., & Boston, M. D. (2018). Preservice mathematics teachers’ effective use of technology: Analyzing the cognitive demands of technology-based instructional activities. In Educating prospective secondary mathematics teachers (pp. 143–166). Springer. https://doi.org/10.1007/978-3-319-90179-4_7
  • Alkan, H., & Bukova Güzel, E. (2005). Öğretmen adaylarında matematiksel düşünmenin gelişimi. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 25(3), 221-236.
  • Altun, M. (2018). Ortaokullarda (5, 6, 7, 8. sınıflarda) matematik öğretimi (12. baskı). Aktüel Yayınları.
  • Amador, J. M. (2017). Preservice teachers’ video simulations and subsequent noticing: A practice-based method to prepare mathematics teachers. Research in Mathematics Education, 19(3), 217-235.
  • Arslan, S., & Yıldız, M. (2010). 11. sınıf öğrencilerinin matematiksel düşünme becerileri. Eğitim ve Bilim, 35(156), 143-154.
  • Bayazıt, Y., & Osmanoğlu, A. (2017). The effect of problem solving instruction on mathematical thinking. Pedagogika-Pedagogy, 89(1), 80-89.
  • Baykul, Y. (2009). İlköğretimde matematik öğretimi (6-8. sınıflar). Pegem Akademi Yayıncılık.
  • Benton, L., Kalas, I., Saunders, P., Hoyles, C., & Noss, R. (2018). Beyond jam sandwiches and cups of tea: An exploration of primary pupils' algorithm evaluation strategies. Journal of Computer Assisted Learning, 34, 590-601. https://doi.org/10.1111/jcal.12266
  • Bloom, I. (2007). Extended analyses: Promoting mathematical inquiry with preservice mathematics teachers. Journal of Mathematics Teacher Education, 10(4), 399-403.
  • Büyüköztürk, Ş., Çakmak, E. K., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2017). Bilimsel araştırma yöntemleri. Ankara: Pegem Akademi Yayıncılık.
  • Carter, I. S. W., & Amador, J. (2015). Lexical and indexical conversational components that mediate professional noticing during lesson study. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1339-1361.
  • Clarke, D., Clarke, B., & Roche, A. (2011). Building teachers’ expertise in understanding, assessing and developing children’s mathematical thinking: The power of task-based, one-to-one assessment interviews. ZDM Mathematics Education, 43, 901-913. https://doi.org/10.1007/s11858-011-0345-2
  • Cooke, B. D., & Buchholz, D. (2005). Mathematical communication in the classroom: A teacher makes a difference. Early Childhood Education Journal, 32(6), 365-369.
  • Coşkun, S. D., Sitrava, R. T., & Bostan, M. I. (2021). Pre-service elementary teachers’ noticing expertise of students’ mathematical thinking: The case of fractions. International Journal of Mathematical Education in Science and Technology, 1-18.
  • Cui, Z., & Ng, O. L. (2021). The interplay between mathematical and computational thinking in primary school students’ mathematical problem-solving within a programming environment. Journal of Educational Computing Research, 59(5), 988-1012.
  • Dickerson, D. S., & Damien, J. P. (2016). An examination of college mathematics majors’ understandings of their own written definitions. The Journal of Mathematical Behavior, 41, 1-9. DOI:10.1016/j.jmathb.2015.11.001
  • Dickerson, D. S., & Doerr, H. M. (2014). High school mathematics teachers’ perspectives on the purposes of mathematical proof in school mathematics. Mathematics Education Research Journal, 26, 711-733. https://doi.org/10.1007/s13394-013-0091-6
  • Dreyfus, T. (1991). Advanced mathematical thinking processes. In D. Tall (Ed.), Advanced mathematical thinking (pp. xx-xx). Kluwer Academic Publishers.
  • Drijvers, P., Kodde-Buitenhuis, H., & Doorman, M. (2019). Assessing mathematical thinking as part of curriculum reform in the Netherlands. Educational Studies in Mathematics, 102(3), 435-456.
  • Duran, N. (2005). Matematiksel düşünme becerilerine ilişkin bir araştırma [Yüksek lisans tezi, Hacettepe Üniversitesi Sosyal Bilimler Enstitüsü].
  • El-Demerdash, M., Mercat, C., Trgalova, J., Essonnier, N., & Lealdino Filho, P. (2016). Design and evaluation of digital resources to enhance creative mathematical thinking in a biomathematics context. Bulletin of the IEEE Technical Committee on Learning Technology, 18(1), 6-9.
  • Engelbrecht, J. (2010). Adding structure to the transition process to advanced mathematical activity. International Journal of Mathematical Education in Science and Technology, 41(2), 143-154. DOI: 10.1080/00207390903391890
  • Estrella, S., Zakaryan, D., Olfos, R., & Espinoza, G. (2020). How teachers learn to maintain the cognitive demand of tasks through Lesson Study. Journal of Mathematics Teacher Education, 23(3), 293-310.
  • Fernández, C., Llinares, S., & Valls, J. (2012). Learning to notice students’ mathematical thinking through on-line discussions. ZDM Mathematics Education, 44, 747-759. https://doi.org/10.1007/s11858-012-0425-y
  • Fernández, C., Llinares, S., & Valls, J. (2013). Primary school teacher’s noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1), 441-468.
  • Fisher, K., Hirsh-Pasek, K., & Golinkoff, R. M. (2012). Fostering mathematical thinking through playful learning. In E. Reese & S. P. Segate (Eds.), Contemporary debates on child development and education (pp. 81-92). Routledge.
  • Fisher, M. H., Thomas, J., Schack, E. O., Jong, C., & Tassell, J. (2018). Noticing numeracy now! Examining changes in preservice teachers’ noticing, knowledge, and attitudes. Mathematics Education Research Journal, 30(2), 209-232.
  • Fouze, A., & Amit, M. (2017). Development of mathematical thinking through integration of ethnomathematic folklore game in math instruction. Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 617-630. 10.12973/ejmste/80626
  • Fraivillig, J. L., Murphy, L. A., & Fuson, K. C. (1999). Advancing children’s mathematical thinking in everyday mathematics classrooms. Journal for Research in Mathematics Education, 30(2), 148-170. https://doi.org/10.2307/749608 Franke, M. L., & Carey, D. A. (1997). Young children's perceptions of mathematics in problem-solving environments. Journal for Research in Mathematics Education, 28(1), 8-25.
  • Gavin, M. K., Casa, T. M., Adelson, J. L., & Firmender, J. M. (2013). The impact of challenging geometry and measurement units on the achievement of grade 2 students. Journal for Research in Mathematics Education, 44(3), 478-509.
  • Ginsburg, H. P. (2016). Helping early childhood educators to understand and assess young children’s mathematical minds. ZDM, 48(7), 941-946.
  • Gökçe, S., & Güner, P. (2021). Forty years of mathematics education: 1980-2019. International Journal of Education in Mathematics, Science and Technology, 9(3), 514-539.
  • Gökçe, S., & Güner, P. (2022). Dynamics of GeoGebra ecosystem in mathematics education. Education and Information Technologies, 27(4), 5301-5323.
  • Guba, E. G., & Lincoln, Y. S. (1982). Epistemological and methodological bases of naturalistic inquiry. ECTJ, 30(4), 233-252.
  • Güner, P., & Gökçe, S. (2021). Monitoring the nomological network of number sense studies. International Journal of Mathematical Education in Science and Technology, 52(4), 580-608.
  • Hallman-Thrasher, A. (2017). Prospective elementary teachers’ responses to unanticipated incorrect solutions to problem-solving tasks. Journal of Mathematics Teacher Education, 20(6), 519-555.
  • Hashemi, N., Abu, M. S., Kashefi, H., Mokhtar, M., & Rahimi, K. (2015). Designing learning strategy to improve undergraduate students’ problem solving in derivatives and integrals: A conceptual framework. Eurasia Journal of Mathematics, Science and Technology Education, 11(2), 227-238.
  • Henning, J. E., McKeny, T., Foley, G. D., & Balong, M. (2012). Mathematics discussions by design: Creating opportunities for purposeful participation. Journal of Mathematics Teacher Education, 15, 453-479.
  • Hino, K. (2007). Toward the problem-centered classroom: Trends in mathematical problem solving in Japan. ZDM, 39(5), 503-514.
  • Hitt, F., Saboya, M., & Cortés Zavala, C. (2016). An arithmetic-algebraic work space for the promotion of arithmetic and algebraic thinking: Triangular numbers. ZDM, 48(6), 775-791.
  • Huang, R., & Li, Y. (2012). What matters most: A comparison of expert and novice teachers' noticing of mathematics classroom events. School Science and Mathematics, 112, 420-432.
  • Hudson, B., Henderson, S., & Hudson, A. (2015). Developing mathematical thinking in the primary classroom: Liberating students and teachers as learners of mathematics. Journal of Curriculum Studies, 47(3), 374-398.
  • Hufferd-Ackles, K., Fuson, K. C., & Sherin, M. G. (2004). Describing levels and components of a math-talk learning community. Journal for Research in Mathematics Education, 35(2), 81-116.
  • Huscroft-Dâ, J. N., Higgins, K. N., & Crawford, L. L. (2014). A descriptive study examining the impact of digital writing environments on communication and mathematical reasoning for students with learning disabilities. Learning Disabilities: A Multidisciplinary Journal, 20(4), 177-188.
  • Inglis, M., & Alcock, L. (2012). Expert and novice approaches to reading mathematical proofs. Journal for Research in Mathematics Education, 43(4), 358-390.
  • Inglis, M., & Simpson, A. (2009). Conditional inference and advanced mathematical study: Further evidence. Educational Studies in Mathematics, 72(2), 185-198.
  • Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169-202.
  • Kallia, M., van Borkulo, S. P., Drijvers, P., Barendsen, E., & Tolboom, J. (2021). Characterising computational thinking in mathematics education: A literature-informed Delphi study. Research in Mathematics Education, 23(2), 159-187.
  • Kaur, H. (2020). Introducing the concept of angle to young children in a dynamic geometry environment. International Journal of Mathematical Education in Science and Technology, 51(2), 161-182.
  • Kieran, C. (2001). The mathematical discourse of 13-year-old partnered problem solving and its relation to the mathematics that emerges. Educational Studies in Mathematics, 46(1), 187-228.
  • Koichu, B. (2010). On the relationships between (relatively) advanced mathematical knowledge and (relatively) advanced problem-solving behaviours. International Journal of Mathematical Education in Science and Technology, 41(2), 257-275.
  • Krupa, E. E., Huey, M., Lesseig, K., Casey, S., & Monson, D. (2017). Investigating secondary preservice teacher noticing of students’ mathematical thinking. In E. Schack, M. Fisher, & J. Wilhelm (Eds.), Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. xx–xx). Springer. https://doi.org/10.1007/978-3-319-46753-5_4
  • Leatham, K. R., Peterson, B. E., Stockero, S. L., & Van Zoest, L. R. (2015). Conceptualizing mathematically significant pedagogical opportunities to build on student thinking. Journal for Research in Mathematics Education, 46, 88-124.
  • Lee, H. S. (2005). Facilitating students’ problem solving in a technological context: Prospective teachers’ learning trajectory. Journal of Mathematics Teacher Education, 8, 223–254. https://doi.org/10.1007/s10857-005-2618-6
  • Lee, M. Y., & Cross Francis, D. (2018). Investigating the relationships among elementary teachers’ perceptions of the use of students’ thinking, their professional noticing skills, and their teaching practices. The Journal of Mathematical Behavior, 51, 118-128.
  • Lee, M. Y. (2019). The development of elementary pre-service teachers’ professional noticing of students’ thinking through adapted lesson study. Asia-Pacific Journal of Teacher Education, 47(4), 383-398.
  • Liu, P. H. (2003). The relationship of a problem-based calculus course and students' views of mathematical thinking [Unpublished doctoral dissertation]. Oregon State University.
  • Mewborn, D. S. (1999). Reflective thinking among preservice elementary mathematics teachers. Journal for Research in Mathematics Education, 30(3), 316-341.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage.
  • Milli Eğitim Bakanlığı. (2018). Matematik dersi öğretim programı. Milli Eğitim Bakanlığı. Nickels, M., & Cullen, C. J. (2017). Mathematical thinking and learning through robotics play for children with critical illness: The case of Amelia. Journal for Research in Mathematics Education, 48(1), 22-77.
  • Nickerson, S. D., Lamb, L., & LaRochelle, R. (2017). Challenges in measuring secondary mathematics teachers’ professional noticing of students’ mathematical thinking. In Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 381-398). Springer.
  • Norton, A., & Kastberg, S. (2012). Learning to pose cognitively demanding tasks through letter writing. Journal of Mathematics Teacher Education, 15(2), 109-130.
  • Oehrtman, M. (2009). Collapsing dimensions, physical limitation, and other student metaphors for limit concepts. Journal for Research in Mathematics Education, 40(4), 396-426.
  • Oers, B. V. (2002). Educational forms of initiation in mathematical culture. In Learning discourse (pp. 59-85). Springer.
  • Otten, S., Webel, C., & de Araujo, Z. (2017). Inspecting the foundations of claims about cognitive demand and student learning: A citation analysis of Stein and Lane (1996). The Journal of Mathematical Behavior, 45, 111-120.
  • Paterson, J., & Sneddon, J. (2011). Conversations about curriculum change: Mathematical thinking and team-based learning in a discrete mathematics course. International Journal of Mathematical Education in Science and Technology, 42(7), 879-889.
  • Pérez, A. (2018). A framework for computational thinking dispositions in mathematics education. Journal for Research in Mathematics Education, 49(4), 424-461.
  • Philipp, R. A., Ambrose, R., Lamb, L. L., Sowder, J. T., Schappelle, B. P., Sowder, L., ... & Chauvot, J. (2007). Effects of early field experiences on the mathematical content knowledge and beliefs of prospective elementary school teachers: An experimental study. Journal for Research in Mathematics Education, 38(5), 438-476.
  • Piggott, J. (2004, January). Developing a framework for mathematical enrichment. Paper presented at the Symposium on Critical Thinking in Teaching and Learning, University of West Indies, St. Augustine, Trinidad.
  • Radu, I., & Weber, K. (2011). Refinements in mathematics undergraduate students’ reasoning on completed infinite iterative processes. Educational Studies in Mathematics, 78(2), 165-182. http://www.jstor.org/stable/41486160
  • Roth McDuffie, A., Foote, M. Q., Bolson, C., Turner, E. E., Aguirre, J. M., Bartell, T. G., Drake, C., & Land, T. (2014). Using video analysis to support prospective K-8 teachers' noticing of students' multiple mathematical knowledge bases. Journal of Mathematics Teacher Education, 17(3), 245–270. https://doi.org/10.1007/s10857-013-9257-0
  • Rowlett, P. (2015). Developing strategic and mathematical thinking via game play: Programming to investigate a risky strategy for Quarto. The Mathematics Enthusiast, 12(1), 55-61.
  • Rowlett, P., Webster, K., Bradshaw, N. A., & Hind, J. (2019). Evaluation of the maths arcade initiative at five UK universities. The Mathematics Enthusiast, 16(1), 451-460.
  • Ryken, A. E. (2009). Multiple representations as sites for teacher reflection about mathematics learning. Journal of Mathematics Teacher Education, 12(5), 347-364. Samo, D. D., Darhim, D., & Kartasasmita, B. (2017). Developing contextual mathematical thinking learning model to enhance higher-order thinking ability for middle school students. International Education Studies, 10(2), 17-29.
  • Schoenfeld, A. H. (2017). Uses of video in understanding and improving mathematical thinking and teaching. Journal of Mathematics Teacher Education, 20, 415-432. https://doi.org/10.1007/s10857-017-9381-3
  • Selden, A., & Selden, J. (2003). Validations of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 34(1), 4-36.
  • Sherman, M. F., Cayton, C., Walkington, C., & Funsch, A. (2020). An analysis of secondary mathematics textbooks with regard to technology integration. Journal for Research in Mathematics Education, 51(3), 361-374.
  • Sleep, L., & Boerst, T. A. (2012). Preparing beginning teachers to elicit and interpret students' mathematical thinking. Teaching and Teacher Education, 28(7), 1038-1048.
  • Stewart, S., & Thomas, M. O. (2009). A framework for mathematical thinking: The case of linear algebra. International Journal of Mathematical Education in Science and Technology, 40(7), 951-961.
  • Stockero, S. L., Rupnow, R. L., & Pascoe, A. E. (2017). Learning to notice important student mathematical thinking in complex classroom interactions. Teaching and Teacher Education, 63, 384-395.
  • Superfine, A. C., Fisher, A., Bragelman, J., & Amador, J. M. (2017). Shifting perspectives on preservice teachers’ noticing of children’s mathematical thinking. In Teacher noticing: Bridging and broadening perspectives, contexts, and frameworks (pp. 409-426). Springer.
  • Superfine, A., Amador, J., & Bragelman, J. (2018). Facilitating video-based discussions to support prospective teacher noticing. The Journal of Mathematical Behavior, 54. https://doi.org/10.1016/j.jmathb.2018.11.002
  • Şencan, H. (2005). Sosyal ve davranışsal ölçümlerde güvenilirlik ve geçerlilik. Ankara: Seçkin Yayıncılık.
  • Şengül, S., Katrancı, Y., & Gerez-Cantimer, G. (2014). Metaphor perceptions of secondary school students about “mathematics teacher”. The Journal of Academic Social Science Studies, 25(1), 89-111.
  • Szydlik, J. E. (2000). Mathematical beliefs and conceptual understanding of the limit of a function. Journal for Research in Mathematics Education, 31(3), 258-276. https://doi.org/10.2307/749807
  • Tall, D. (1995). Cognitive growth in elementary and advanced mathematical thinking. In L. Meira & D. Carraher (Eds.), Proceedings of the 19th Meeting of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 61-75). Recife, Brasil: Universidade Federal de Pernambuco.
  • Tall, D. (2002). Advanced mathematical thinking. Kluwer Academic Publishers.
  • 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
  • Umay, A. (2003). Matematiksel muhakeme yeteneği. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24(3), 234-243.
  • Vacc, N. N., & Bright, G. W. (1999). Elementary preservice teachers' changing beliefs and instructional use of children's mathematical thinking. Journal for Research in Mathematics Education, 30(1), 89-110.
  • van Eck, N. J., & Waltman, L. (2011). VOSviewer manual: Manual for VOSviewer version 1.0.
  • van Es, E. A., & Sherin, M. G. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24(2), 244-276.
  • van Oers, B. (2010). Emergent mathematical thinking in the context of play. Educational Studies in Mathematics, 74(1), 23-37.
  • Wager, A. A. (2014). Noticing children's participation: Insights into teacher positionality toward equitable mathematics pedagogy. Journal for Research in Mathematics Education, 45(3), 312-350.
  • Wager, A. A., & Parks, A. N. (2016). Assessing early number learning in play. ZDM, 48(7), 991-1002.
  • Weber, K. (2009). How syntactic reasoners can develop understanding, evaluate conjectures, and generate counterexamples in advanced mathematics. The Journal of Mathematical Behavior, 28(2-3), 200-208.
  • Weber, K., & Mejia-Ramos, J. P. (2011). Why and how mathematicians read proofs: An exploratory study. Educational Studies in Mathematics, 76(3), 329-344.
  • Williams, S. R. (2001). Predications of the limit concept: An application of repertory grids. Journal for Research in Mathematics Education, 32(4), 341-367.
  • Wilson, P. H., Lee, H. S., & Hollebrands, K. F. (2011). Understanding prospective mathematics teachers' processes for making sense of students' work with technology. Journal for Research in Mathematics Education, 42(1), 39-64.
  • Woods, T., Williams, G., & McNeal, B. (2006). Children's mathematical thinking in different classroom cultures. Journal for Research in Mathematics Education, 37(3), 222-255.
  • Yıldırım, A., & Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.
  • Yıldırım, C. (1988). Matematiksel düşünme. İstanbul: Remzi Kitabevi.
  • Yıldız, C. (2016). Comparing the mathematical thinking experiences of students at faculty of education and faculty of arts and sciences. TOJET: The Turkish Online Journal of Educational Technology-Special Issue for INTE 2016, 480-488.
  • Yilmaz, R., & Argun, Z. (2017). Role of visualization in mathematical abstraction: The case of congruence concept. International Journal of Education in Mathematics, Science and Technology, 6, 1-11.
  • Yoon, C., Thomas, M. O., & Dreyfus, T. (2011). Gestures and insight in advanced mathematical thinking. International Journal of Mathematical Education in Science and Technology, 42(7), 891-901.
  • Young-Loveridge, J. (2011). Assessing the mathematical thinking of young children in New Zealand: The initial school years. Early Child Development and Care, 181(2), 267-276.
  • Yuzawa, M., Bart, W. M., Yuzawa, M., & Junko, I. (2005). Young children's knowledge and strategies for comparing sizes. Early Childhood Research Quarterly, 20(2), 239-253.
There are 107 citations in total.

Details

Primary Language English
Subjects Other Fields of Education (Other)
Journal Section REVIEW RESEARCH
Authors

Müberra Gök 0000-0003-0207-9632

Meral Cansiz Aktas 0000-0003-0425-9565

Publication Date July 31, 2025
Submission Date June 29, 2025
Acceptance Date July 10, 2025
Published in Issue Year 2025 Volume: 15 Issue: ISRIS 2025

Cite

APA Gök, M., & Cansiz Aktas, M. (2025). Systematic review of studies on mathematical thinking. Ordu Üniversitesi Sosyal Bilimler Enstitüsü Sosyal Bilimler Araştırmaları Dergisi, 15(ISRIS 2025), 826-845. https://doi.org/10.48146/odusobiad.1729711
 Download Cover Image

  Bilginin ışığında aydınlanmak dileğiyle....

 ODÜSOBİAD