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Journals / Batı Anadolu Eğitim Bilimleri Dergisi / 2025 / Cilt: 16 Sayı: 3

Examining Mathematics Teachers’ Noticing Student Thinking on Pattern Generalization

Matematik Öğretmenlerinin Örüntü Genellemeleri ile ilgili Öğrenci Düşüncelerine Yönelik Farkındalıklarının İncelenmesi

Hatice Çetin Argaç(TC MİLLİ EĞİTİM BAKANLIĞI AFYON)0009-0008-4186-8275
Makbule Gözde Didiş Kabar(Tokat Gaziosmanpaşa Üniversitesi, Eğitim Fakültesi, Matematik ve Fen Bilimleri Eğitimi Bölümü)0000-0003-4202-2323
Pages
4800–4831
Publication Date
2025-12-27
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The findings revealed that three of the five teachers were able to analyze students' thinking to a certain level, while two of them were incapable of interpreting students' thoughts.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This study aims to examine the extent to which five mathematics teachers can notice student thinking about patterns in terms of attending to student thinking and interpreting student thinking and strategies.
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Key Findings & Data:The participants of this study were carried out with five mathematics teachers working in different public schools in Karaman.
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Conclusion & Impact:The findings revealed that three of the five teachers were able to analyze students' thinking to a certain level, while two of them were incapable of interpreting students' thoughts.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Ortaokul matematik öğretmenleri · fark etme · örüntüler

Abstract

This study aims to examine the extent to which five mathematics teachers can notice student thinking about patterns in terms of attending to student thinking and interpreting student thinking and strategies. The participants of this study were carried out with five mathematics teachers working in different public schools in Karaman. The data were collected through semi-structured one-on-one interviews with five mathematics teachers based on student solution papers and videos containing student thinking about pattern tasks. The study's findings displayed that the all teachers could recognize different details in students' thinking about patterns, but their noticing skills were at various levels. At the same time, teachers' ability to pay attention to the details in students' thinking about patterns was better than their ability to interpret. The findings revealed that three of the five teachers were able to analyze students' thinking to a certain level, while two of them were incapable of interpreting students' thoughts. The findings of this study suggest that teachers should be supported through professional development training to make sense of the strategies and thoughts that students reveal about patterns and to reflect in detail on how students understand them.

Özet

Bu araştırmanın amacı beş matematik öğretmeninin örüntülerle ilgili öğrenci düşüncelerini fark edebilme yeterliklerini öğrenci düşüncelerine dikkat etme ve öğrenci düşüncelerini yorumlama açısından incelemektir. Bu araştırmanın katılımcıları Karaman’da farklı devlet okullarında görev yapan beş matematik öğretmenidir. Nitel araştırma desenlerinden durum çalışması olarak tasarlanan bu araştırmanın verileri, beş matematik öğretmeni ile örüntü görevlerine yönelik öğrenci düşüncelerini içeren öğrenci çözüm kağıtları ve videoları üzerinden yapılmış yarı yapılandırılmış birebir görüşmeler aracılığıyla toplanmıştır. Araştırmanın bulguları öğretmenlerin öğrencilerin çözümlerinde ortaya çıkan düşüncelerin çeşitli ayrıntılarını fark edebildiklerini, ancak dikkat etme yeterliklerinin birbirlerinden farklı düzeylerde olduğunu ortaya koymuştur. Aynı zamanda öğretmenlerin öğrencilerin örüntülerle ilgili düşüncelerindeki ayrıntılara dikkat etme yeterliklerinin yorumlama yeterliklerinden daha iyi olduğunu göstermiştir. Bulgular araştırmaya katılan beş öğretmenden üçünün öğrenci düşüncelerini belli bir düzeye kadar yorumlayabildiklerini, fakat ikisinin öğrencilerin fark edebildikleri düşüncelerini yorumlama konusunda eksik olduklarını ortaya koymuştur. Bu araştırmanın bulguları öğretmenlerin öğrencilerin örüntülerle ilgili ortaya koydukları stratejileri ve düşünceleri anlamlandırarak öğrencilerin nasıl anladığını detaylı olarak yansıtabilmeleri için mesleki gelişim eğitimleri aracılığıyla sağlanan ortamlarda desteklenmelerini önermektedir.

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Cite This Article

Argaç, H. Ç., Kabar, M. G. D. (2025). Examining Mathematics Teachers’ Noticing Student Thinking on Pattern Generalization. Batı Anadolu Eğitim Bilimleri Dergisi, Cilt: 16 Sayı: 3, 4800–4831. https://doi.org/10.51460/baebd.1706164

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References (55)

  1. Altıntaş, Ş., ve Keskin, C. (2019). 7.sınıf matematik kitabı. Ekoyay.
  2. Amit, M., and Neria, D. (2008). “Rising to the challenge”: Using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM Mathematics Education, 40, 111–129. https://doi.org/10.1007/s11858-007-0069-5
  3. Ball, D. L., and Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In G. Sykes & L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–32). Jossey-Bass.
  4. Barnhart, T., and van Es, E. (2015). Studying teacher noticing: Examining the relationship among pre-service science teachers' ability to attend, analyze and respond to student thinking. Teaching and Teacher Education, 45, 83–93. https://doi.org/10.1016/j.tate.2014.09.005
  5. Bartell, T. G., Webel, C., Bowen, B., and Dyson, N. (2013). Prospective teacher learning: recognizing evidence of conceptual understanding. Journal of Mathematics Teacher Education, 16(1), 57–79. https://doi.org/10.1007/s10857-012-9205-4
  6. Bay-Williams, J. M. (2001). Principles and standards: What is algebra in elementary school. Teaching Children Mathematics, 8(4), 196–200. https://doi.org/10.5951/TCM.8.4.0196
  7. Blanton, M., Levi, L., Crites, T., and Dougherty, B. (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3–5. In B. J. Dougherty and R. M. Zbiek (Eds.), Essential Understanding Series. National Council of Teachers of Mathematics.
  8. Callejo, M. L., and Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309–333. https://doi.org/10.1007/s10857-016-9343-1
  9. Didis, M. G., Erbas, A. K., Cetinkaya, B., Cakiroglu, E., and Alacaci, C. (2016). Exploring prospective secondary mathematics teachers’ interpretation of student thinking through analysing students’ work in modelling. Mathematics Education Research Journal, 28(3), 349-378.
  10. Doğan-Coşkun, S. (2021). Sınıf öğretmeni adayları öğrencilerin yazılı çözümlerindeki cebirsel düşünme biçimlerini nasıl fark etmektedir? Journal of Qualitative Research in Education, 27, 103-124. doi:10.14689/enad.27.6.
  11. Doğan-Temur, Ö., ve Turgut, S. (2020). Sınıf öğretmenleri sayı ve şekil örüntülerini nasıl öğretiyorlar? İlkokul dördüncü sınıf örneği. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 20(1), 182–200. https://doi.org/10.17240/aibuefd.2020.20.52925-547220
  12. El Mouhayar, R. (2019). Exploring teachers’ attention to students’ responses in pattern generalization tasks. Journal of Mathematics Teacher Education, 22(6), 575–605. https://doi.org/10.1007/s10857-018-9406-6
  13. English, L. D., and Warren, E. A. (1998). Introducing the variable through pattern exploration. The Mathematics Teacher, 91, 166–170. https://doi.org/10.5951/MT.91.2.0166
  14. Fernández, C., Llinares, S., and Valls, J. (2013). Primary school teacher’s noticing of students’ mathematical thinking in problem solving. The Mathematics Enthusiast, 10(1), 441–468. https://doi.org/10.54870/1551-3440.1274
  15. Ferrini-Mundy, J., Lappan, G., and Phillips, E. (1997). Experiences with patterning. Teaching Children Mathematics, 3(6), 282–288. https://doi.org/10.5951/TCM.3.6.0282
  16. Girit-Yildiz, D. G., ve Akyuz, D. (2020). Mathematical knowledge of two middle school mathematics teachers in planning and teaching pattern generalization. İlkogretim Online, 19(4), 2098–2117. https://doi.org/10.17051/ilkonline.2020.763457
  17. Girit-Yildiz, D., Osmanoglu, A., and Gundogdu Alayli, F. (2023). Providing a video-case-based professional development environment for prospective mathematics teachers to notice students’ misconceptions in measurement. Journal of Mathematics Teacher Education, 26(2), 179–209. https://doi.org/10.1007/s10857-021-09525-0
  18. Gökçe, R., ve Yeşildere-İmre, S. (2017). Cebirsel genelleme yapmayı destekleyen etkinliklerin 7. sınıf öğrencilerinin genelleme yapma becerilerini şekillendirmedeki rolü. Gaziantep Üniversitesi Sosyal Bilimler Dergisi, 16(1), 194–213. https://doi.org/10.21547/jss.281675
  19. Hargreaves, M., Shorrocks‐Taylor, D., and Threlfall, J. (1998). Children's strategies with number patterns. Educational Studies, 24(3), 315–331.
  20. Ivars, P., Fernández, C., and Llinares, S. (2020). A learning trajectory as a scaffold for pre-service teachers’ noticing of students’ mathematical understanding. International Journal of Science and Mathematics Education, 18(3), 529–548. https://doi.org/10.1007/s10763-019-09973-4
  21. Jacobs, V. R., Lamb, L. C., and Philipp, R. A. (2010). Professional noticing of children’s mathematical thinking. Journal for Research in Mathematics Education, 41(2), 169–202. https://doi.org/10.5951/jresematheduc.41.2.0169
  22. Jurdak, M. E., and El Mouhayar, R. R. (2014). Trends in the development of student level of reasoning in pattern generalization tasks across grade level. Educational Studies in Mathematics, 85, 75–92. https://doi.org/10.1007/s10649-013-9494-2
  23. Keskin-Oğan, A., ve Öztürk, S. (2019). 7. Sınıf matematik ders kitabı. Millî Eğitim Bakanlığı.
  24. Kılıç, S. D. (2019). Matematik öğretmen adaylarının, 6. Sınıf öğrencilerinin cebirsel örüntüleri genellemelerine ilişkin farkındalıkları. Kastamonu Eğitim Dergisi, 27(4), 1713-1728. https://doi.org/10.24106/kefdergi.3263
  25. Kocamaz, B., ve İkikardeş, N. Y. (2021). Örüntüler konusunda 7. sınıf öğrencilerinin karşılaştıkları zorlukların incelenmesi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 23(2), 831–849. https://doi.org/10.25092/baunfbed.868802
  26. Lannin, J. K. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and learning, 7(3), 231–258. https://doi.org/10.1207/s15327833mtl0703_3
  27. LaRochelle, R., Nickerson, S. D., Lamb, L. C., Hawthorne, C., Philipp, R. A., and Ross, D. L. (2019). Secondary practising teachers' professional noticing of students' thinking about pattern generalisation. Mathematics Teacher Education and Development, 21(1), 4–27.
  28. Lee, M. Y., and Lee, J. E. (2023). An analysis of elementary prospective teachers’ noticing of student pattern generalization strategies in mathematics. Journal of Mathematics Teacher Education, 26(2), 155–177. https://doi.org/10.1007/s10857-021-09520-5
  29. Markworth, K. A. (2010). Growing and growing: Promoting functional thinking with geometric growing patterns [Unpublished doctoral dissertation]. University of North Carolina at Chapel Hill. Available from ERIC (ED519354)
  30. Maula, N. F., Suryadi, D., and Jupri, A. (2024). Learning obstacles in the generalization process: In case number pattern topic. Research and Development in Education (RaDEn), 4(2), 964–976. https://doi.org/10.22219/raden.v4i1. 36342
  31. Millî Eğitim Bakanlığı [MEB]. (2018). Matematik dersi öğretim programı (İlkokul ve Ortaokul 1,2,3,4,5,6,7, ve 8. Sınıflar). MEB.
  32. Miles, M. B., and Huberman, A. M. (1994). Qualitative data analysis (second edition). SAGE.
  33. National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Author.
  34. Özel, Z. (2019). Investigation into prospective middle school mathematics teachers’ noticing of students’ algebraic thinking within the context of pattern generalization [Unpublished Master’s thesis]. Middle East Technical University.
  35. Pang, J., and Sunwoo, J. (2022). Design of a pattern and correspondence unit to foster functional thinking in an elementary mathematics textbook. ZDM Mathematics Education, 54, 1315–1331. https://doi.org/10.1007/s11858-022-01411-0
  36. Papic, M. (2007). Promoting repeating patterns with young children-more than just alternating colours!. Australian Primary Mathematics Classroom, 12(3), 8-13.
  37. Salman, S., ve Didiş-Kabar, M. G. (2024). Ortaokul matematik öğretmenlerinin 5. sınıf düzeyinde örüntüleri öğretim süreçleri. Trakya Eğitim Dergisi, 15(1), 201-247. https://doi.org/10.24315/tred.1456791
  38. Smith, E. (2008). Representational thinking as a framework for introducing functions in the elementary curriculum. In J. Kaput, D. Carraher and M. Blanton (Eds.), Algebra in the Early Grades. Lawrence Erlbaum Associates.
  39. Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20(2), 147–164.
  40. Stockero, S. L., Rupnow, R. L., and Pascoe, A. E. (2017). Learning to notice important student mathematical thinking in complex classroom interactions. Teaching and Teacher Education, 63, 384–395. https://doi.org/10.1016/j.tate.2017.01.006
  41. Store, J. C., Richardson, K. D., and Carter, T. S. (2016). Fostering understanding of variable with patterns. Teaching Children Mathematics, 22(7), 420–427.
  42. Stump, S. L. (2011). Patterns to develop algebraic reasoning. Teaching Children Mathematics, 17(7), 410–418. https://doi.org/10.5951/teacchilmath.17.7.0410
  43. Tanışlı, D. (2008). İlköğretim beşinci sınıf öğrencilerinin örüntülere ilişkin anlama ve kavrama biçimlerinin belirlenmesi [Yayımlanmamış Doktora Tezi]. Anadolu Üniversitesi.
  44. Tanışlı, D. (2011). Functional thinking ways in relation to linear function tables of elementary school students. The Journal of Mathematical Behavior, 30(3), 206–223. https://doi.org/10.1016/j.jmathb.2011.08.001
  45. Tanışlı, D., ve Köse, N. Y. (2011). Lineer şekil örüntülerine ilişkin genelleme stratejileri: Görsel ve sayısal ipuçlarının etkisi. Eğitim ve Bilim, 36 (160), 184–198.
  46. Ulusoy, F., and Çakıroğlu, E. (2021). Exploring prospective teachers’ noticing of students' understanding through micro-case videos. Journal of Mathematics Teacher Education, 24, 253–282. https://doi.org/10.1007/s10857-020-09457-1
  47. Ureña, J., Ramírez-Uclés, R., Cañadas, M. C., and Molina, M. (2024). Generalization strategies and representations used by final-year elementary school students. International Journal of Mathematical Education in Science and Technology, 55(1), 23-43. https://doi.org/10.1080/0020739X.2022.2058429
  48. van Es, E. A., and Sherin, M. G. (2008). Mathematics teachers’“learning to notice” in the context of a video club. Teaching and teacher education, 24(2), 244–276. https://doi.org/10.1016/j.tate.2006.11.005
  49. van Es, E. A., and Sherin, M. G. (2024). Expanding on prior conceptualizations of teacher noticing. ZDM–Mathematics Education, 53, 17–27. https://doi.org/10.1007/s11858-020-01211-4
  50. Walkoe, J. (2015). Exploring teacher noticing of student algebraic thinking in a video club. Journal of Mathematics Teacher Education, 18, 523–550. https://doi.org/10.1007/s10857-014-9289-0
  51. Warren, E., and Cooper, T. (2006). Using repeating patterns to explore functional thinking. Australian Primary Mathematics Classroom, 11(1), 9–14.
  52. Warren, E., Miller, J., and Cooper, T. J. (2013). Exploring young students’ functional thinking. PNA, 7(2), 75–84.
  53. Warshauer, H. K., Starkey, C., Herrera, C. A., and Smith, S. (2021). Developing prospective teachers’ noticing and notions of productive struggle with video analysis in a mathematics content course. Journal of Mathematics Teacher Education, 24, 89–121. https://doi.org/10.1007/s10857-019-09451-2
  54. Yıldırım, A., ve Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri (5. Baskı). Seçkin Yayıncılık.
  55. Yin, R. K. (2009). Case study research: design and methods (4th edition). Sage Publication