SavedAdd your journal

Journals / Bartın Üniversitesi Eğitim Fakültesi Dergisi / 2026 / Issue: 4

Examining the Pedagogical Content Knowledge of Mathematics Teacher Candidates on Cone Subject Regarding Students’ Mistakes

Matematik Öğretmen Adaylarının Koni Hakkındaki Pedagojik Alan Bilgilerinin Öğrenci Hataları Açısından İncelenmesi

Feyza Aliustaoğlu(KASTAMONU UNIVERSITY)0000-0001-9262-5216
Abdulkadir Tuna(KASTAMONU UNIVERSITY)0000-0003-3553-7513
Pages
—
Publication Date
2026-08-17
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

On the other hand, some mathematics teacher candidates provided explanations about the teaching process but did not provide full details, whereas a small number offered sufficient explanations.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Purpose: This research aims to examine the pedagogical content knowledge of fourth-grade mathematics teacher candidates regarding the concept of the cone, based on knowledge of student understanding and knowledge of instructional strategies.
📊
Key Findings & Data:Method: The study sample consists of 51 fourth-grade mathematics teacher candidates.
💡
Conclusion & Impact:On the other hand, some mathematics teacher candidates provided explanations about the teaching process but did not provide full details, whereas a small number offered sufficient explanations.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Pedagogical content knowledge · knowledge of student understanding · knowledge of instructional strategies

Abstract

Purpose: This research aims to examine the pedagogical content knowledge of fourth-grade mathematics teacher candidates regarding the concept of the cone, based on knowledge of student understanding and knowledge of instructional strategies. Method: The study sample consists of 51 fourth-grade mathematics teacher candidates. The Pedagogical Content Knowledge Test and semi-structured interviews were used as data collection tools. The test was administered to 51 mathematics teacher candidates, and interviews were conducted with six of them. Findings: The study revealed that the mathematics teacher candidates had deficiencies in both knowledge of student understanding and knowledge of instructional strategies. In terms of knowledge of student understanding, it was observed that some mathematics teacher candidates did not include cone types other than the right circular cone in the cone group, did not consider the hierarchical relationship between cones and pyramids, and had incomplete knowledge regarding the open form and area-volume formulas of a cone. Due to these deficiencies, some mathematics teacher candidates were unable to correctly identify students' mistakes regarding the open and closed states of a cone. From the perspective of the knowledge of instructional strategies, some mathematics teacher candidates either omitted the teaching process because they believed it was not a mistake or designed a standard teaching process. On the other hand, some mathematics teacher candidates provided explanations about the teaching process but did not provide full details, whereas a small number offered sufficient explanations.

Özet

Amaç: Bu araştırmanın amacı, dördüncü sınıf matematik öğretmeni adaylarının koni kavramına ilişkin pedagojik alan bilgilerini öğrenci anlama bilgisi ve öğretim stratejileri bilgisi bileşenleri kapsamında incelemektir. Yöntem: Araştırmanın örneklemini 51 dördüncü sınıf matematik öğretmen adayı oluşturmaktadır. Veri toplama aracı olarak Pedagojik Alan Bilgisi Testi ve yarı yapılandırılmış görüşmeler kullanılmıştır. Test 51 öğretmen adayına uygulanmış, ardından 6 öğretmen adayı ile görüşmeler yapılmıştır . Bulgular: Araştırma sonucunda öğretmen adaylarının koninin kapalı ve açık halleri ile alan ve hacim formülleri ile ilgili hem öğrencileri anlama bilgisi hem de öğretim stratejileri bilgisi açısından eksiklikleri olduğu belirlenmiştir. Öğrencileri anlama bilgisi açısından bazı öğretmen adaylarının; dik dairesel koni dışındaki koni türlerini koni grubuna dâhil etmediği, koni ile piramit arasındaki hiyerarşik ilişkiyi dikkate almadığı ve koninin açılımı ile alan-hacim formüllerine ilişkin eksik bilgilere sahip olduğu görülmüştür. Bu eksiklikler nedeniyle öğretmen adaylarının bazıları, öğrencilerin koninin açık ve kapalı hâllerine yönelik hatalarını doğru biçimde tespit edememiştir. Bu durumların dışında hatayı kısmen doğru tespit eden ya da doğru tespit edenler de bulunmaktadır. Öğretim stratejileri bilgisi açısından bakıldığında ise hata olmadığını düşündüğü için öğretim sürecine yer vermeyen ya da genel-geçer öğretim süreci tasarlayan öğretmen adayları olmuştur. Diğer taraftan bazı öğretmen adayları öğretim süreci ile ilgili bazı açıklamalara yer vermiş ancak süreci tüm detayları ile açıklamamış; az sayıda da olsa bazıları ise yeterli öğretim sürecine yer vermiştir.

🔖

Cite This Article

Aliustaoğlu, F., Tuna, A. (2026). Examining the Pedagogical Content Knowledge of Mathematics Teacher Candidates on Cone Subject Regarding Students’ Mistakes. Bartın Üniversitesi Eğitim Fakültesi Dergisi, Issue: 4. https://doi.org/10.14686/buefad.1847345

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (69)

  1. Akayuure, P. (2021). Preservice teachers’ content knowledge and learning obstacles in shape and space. Asian Research Journal of Mathematics, 17(7), 49-60.
  2. Aksu, Z. (2019). Pre-Service mathematics teachers' pedagogical content knowledge regarding student mistakes on the subject of circle. International Journal of Evaluation and Research in Education, 8(3), 440-445. http://doi.org/10.11591/ijere.v8i3.20250
  3. Alkış Küçükaydın, M., & Gökbulut, Y. (2013). Misconceptions of prospective primary teachers regarding the definition and unfolding process of geometric objects. International Journal of Education, 2(1), 102-125.
  4. Altaylı, D., Konyalıoğlu, A., Hızarcı, S., & Kaplan, A. (2014). The investigation of pre-service elementary mathematics teachers' pedagogical content knowledge on three dimensional objects. Middle Eastern & African Journal of Educational Research, 10(1), 4-24.
  5. An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge ofmiddle school, mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7(2),145–172.
  6. Aziiza, Y. F., & Juandi, D. (2021, March). Student’s learning obstacle on understanding the concept of prism surface area. In Journal of Physics: Conference Series (Vol. 1806, No. 1, p. 012115). IOP Publishing.
  7. Baki, M. (2013). Mathematical knowledge and instructional explanations of prospective primary teachers regarding division. Education and Science, 38(167), 300-311.
  8. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407.
  9. Battista, M. T., & Clements, D. H. (1996). Students' understanding of three-dimensional rectangular arrays of cubes. Journal for Research in Mathematics Education, 27(3), 258-292. https://doi.org/10.5951/jresematheduc.27.3.0258
  10. Bohara, P. S. (2024). Teachers' practices on using CRA approach in teaching grade ten mathematics. AMC Journal (Dhangadhi), 5(1), 25-32. https://doi.org/10.3126/amcjd.v5i1.69116
  11. Bozkurt, A., & Koç, Y. (2012). Investigating first year elementary mathematics teacher education students’ knowledge of prism. Educational Sciences: Theory & Practice, 12(4), 2949-2952.
  12. Cooksey, R., & McDonald, G. (2011). Surviving and thriving in postgraduate research, Prahran, VIC, Tilde University Press.
  13. Cunningham, R. F., & Roberts, A. (2010). Reducing the mismatch of geometry concept definitions and concept images held by pre-service teachers. Issues in the Undergraduate Mathematics Preparation of School Teachers, 1, 1-17.
  14. Çakmak, Z., Konyalıoğlu, A. C., & Işık, A. (2014). The investigation of pre-service elementary mathematics teachers’ content knowledge on three dimensional objects. Middle Eastern and African Journal of Educational Research, 8, 28-44.
  15. Erdem, E., & Man, S. (2023). Middle school mathematics teachers’ concept definitions of geometric objects: Concept definitions of geometric objects. International Journal for Mathematics Teaching and Learning, 24(2), 20-37. https://doi.org/10.4256/ijmtl.v24i2.404
  16. Erlandson, D. A. (2012). Naturalistic evaluation. In Secolsky, C. & Denison, B. (Eds.), Handbook on measurement, assessment, and evaluation in higher education. (p. 483-499). Routledge.
  17. Ertekin, E., Yazici, E., & Delice, A. (2014). Investigation of primary mathematics student teachers’ concept images: Cylinder and cone. International Journal of Mathematical Education in Science and Technology, 45(4), 566-588. https://doi.org/10.1080/0020739X.2013.868537
  18. Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147-164). Macmillian.
  19. Fernandez, C. (2005). Lesson study: A means for elementary teachers to develop the knowledge of mathematics needed for reform-minded teaching?, Mathematical Thinking and Learning, 7(4), 265–289. https://doi.org/10.1207/s15327833mtl0704_1
  20. Fujita, T., & Jones, K. (2007). Learners’ understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1), 3–20. https://doi.org/10.1080/14794800008520167
  21. Gilligan, K. A., Thomas, M. S., & Farran, E. K. (2020). First demonstration of effective spatial training for near transfer to spatial performance and far transfer to a range of mathematics skills at 8 years. Developmental Science, 23(4), e12909. https://doi.org/10.1111/desc.12909
  22. Gökkurt, B., & Soylu, Y. (2016). Examination of middle school mathematics teachers’ pedagogical content knowledge: The sample of cone. Elementary Education Online, 15(3), 946- 973.
  23. Gökkurt, B., Şahin, Ö., Soylu, Y., & Doğan, Y. (2015). Pre-service teachers’ pedagogical content knowledge regarding student mistakes on the subject of geometric shapes. Elementary Education Online, 14(1), 55-71. https://doi.org/10.17051/io.2015.55159
  24. Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. Teachers College Press.
  25. Guba, E. G., & Lincoln, Y. S. (1982). Epistemological and methodological bases of naturalistic inquiry. Educational Communication and Technology Journal, 30(4), 233-252.
  26. Haj-Yahya A. (2020). Do prototypical constructions and self-attributes of presented drawings affect the construction and validation of proofs? Mathematics Education Research Journal. 32(4), 685-718. https://doi.org/10.1007/s13394-019-00276-z
  27. Hartshorne, R. (2013). Geometry: Euclid and beyond. Springer.
  28. Hershkowitz, R. (1990). Psychological aspects of learning geometry. In P. Nesher & J. Kilpatrick (Eds.), Mathematics and Cognition (pp. 70-95). Cambridge University Press. https://doi.org/10.1017/CBO9781139013499.006
  29. Hussain, S., Anwer, M., Gul, N., Hussain, M., & Alwi, S. K. K. (2021). A comparative analysis of ınstructional strategies in middle-grade mathematics textbooks. International Journal of Innovation, Creativity and Change, 15(6), 129-147.
  30. Karakuş, F. (2018). Investigation of primary pre-service teachers’ concept images on cylinder and cone. Elementary Education Online, 17(2), 1033-1050.
  31. Karakuş, F., & Erşen, Z. B. (2021). Investigation of pre-service elementary mathematics teachers’ understanding on solids. REDIMAT – Journal of Research in Mathematics Education, 10(2), 175-212. https://doi.org/10.17583/redimat.2021.3638
  32. Koçak, M. & Soylu, Y. (2017). Analysis of pre-service mathematics teachers' teaching strategy knowledge of geometric formulas. Universal Journal of Educational Research, 5(3), 297-315. https://doi.org/10.13189/ujer.2017.050302
  33. Koçak, M., & Soylu, Y. (2018). Investigate of prospective mathematics teachers' teaching strategy knowledge in the context of the surface area and volume. International Journal of Educational Studies in Mathematics, 5(3), 78-97.
  34. Korkmaz, H. I., & Şahin, Ö. (2020). Preservice preschool teachers’ pedagogical content knowledge ongeometric shapes in terms of children’s mistakes. Journal of Research in Childhood Education, 34(3), 385-405. https://doi.org/10.1080/02568543.2019.1701150
  35. Kurniati, L., & Kusumawati, R. (2024). Junior high school mathematics subject matter in two different curriculum perspective. Journal of Medives: Journal of Mathematics Education IKIP Veteran Semarang, 8(1). 171 - 182. https://doi.org/10.31331/medivesveteran.v8i1.2725
  36. Marchis, I. (2012). Preservice primary school teachers’ elementary geometry knowledge. Acta Didactica Napocensia, 5(2), 33-40.
  37. Matitaputty, C., Nusantara, T., & Hidayanto, E. (2022). Examining the pedagogical content knowledge of ın-service mathematics teachers on the permutations and combinations in the context of student mistakes. Journal on Mathematics Education, 13(3), 393-414.
  38. Ministry of National Education [MoNE]. (2018a). Mathematics curriculum for primary and middle schools (Grades 1–8). Ministry of National Education.
  39. Ministry of National Education [MoNE]. (2018b). Secondary school mathematics curriculum (Grades 9–12). Ministry of National Education.
  40. Mcmillian, H. J. & Schumacher, S. (2010). Research in education. Pearson Education.
  41. Miles, M, B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. (2nd ed). Sage.
  42. Mjenda, M., Mutarutinya, V., & Owiti, D. (2023). Assessing the effectiveness of computer-aided instructional techniques in enhancing students’ 3d geometry spatial visualization skills among secondary school students in Tanzania. International Journal of Learning, Teaching and Educational Research, 22(6), 613-637.
  43. Monaghan, F. (2000). What difference does it make? Children’s views of the differences between some quadrilaterals. Educational Studies in Mathematics, 42(2), 179-196.
  44. National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. National Council of Teachers of Mathematics.
  45. National Research Council [NRC]. (2000). Inquiry and the national science education standards. National Academy Press.
  46. O' Hanlon, W. A. (2010). Characterizing the pedagogical content knowledge of pre-service secondary mathematics teachers (Publication No. 3485930) [Doctoral dissertation, Illinois State University]. ProQuest Dissertations & Theses Global.
  47. Park, S., & Oliver, J. S. (2008). Revisiting the conceptualisation of pedagogical content knowledge (PCK): PCK as a conceptual to understand teachers as professionals. Research in Science Education, 38(3), 261-284. https://10.1007/s11165-007-9049-6
  48. Patton, M. Q. (2014). Qualitative research & evaluation methods: Integrating theory and practice. Sage Publications.
  49. Pittalis, M., Mousoulides, N., & Christou, C. (2010). Students’ 3D geometry thinking profiles, In. Durand-Guerrier., S. Soury-Lavergne & F. Arzarello (Eds.), Proceedings of CERME 6, (pp. 816-825), INRP.
  50. Putnam, R. T., Heaton, R. M., Prawat, R. S., & Remillard, J. (1992). Teaching mathematics for understanding: Discussing case studies of four fifth-grade teachers. The Elementary School Journal, 93(2), 213–228.
  51. Putra, Z. H., Afrillia, Y. M., & Tjoe, H. (2023). Prospective elementary teachers' informal mathematical proof using Geogebra: The case of 3D shapes. Journal on Mathematics Education, 14(3), 449-468. http://doi.org/10.22342/jme.v14i3.pp449-468
  52. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004
  53. Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-23. https://doi.org/10.17763/haer.57.1.j463w79r56455411
  54. Sieng, V., & Takuya, B. (2024). Analysis of geometry units in the mathematics curriculum of Cambodia from the perspective of coherence. Journal of Science and Education (JSE), 5(1), 197-213. https://doi.org/10.58905/jse.v5i1.335
  55. Smith, D. C., & Neale, D. C. (1989). The construction of subject matter knowledge in primary science teaching. Teaching and teacher Education, 5(1), 1-20. https://doi.org/10.1016/0742-051X(89)90015-2
  56. Sunzuma, G., & Maharaj, A. (2019). In-service teachers’ geometry content knowledge: Implications for how geometry is taught in teacher training institutions. International Electronic Journal of Mathematics Education, 14(3), 633-646. https://doi.org/10.29333/iejme/5776
  57. Şahin, Ö., Gökkurt, B., & Soylu, Y. (2016). Examining prospective mathematics teachers' pedagogical content knowledge on fractions in terms of students' mistakes. International Journal of Mathematical Education in Science and Technology, 47(4), 531-551. https://doi.org/10.1080/0020739X.2015.1092178
  58. Şener, A., Poçan, S., & Ergen, B. (2025). Enhancing geometry education through deep learning models: Addressing challenges in three-dimensional shape visualization. Turkish Journal of Nature and Science, 14(2), 247-258. https://doi.org/10.46810/tdfd.1639446
  59. Tekin Sitrava, R., & Işıksal Bostan, M. (2018). The nature of middle school mathematics teachers' pedagogical content knowledge: The case of the volume of prisms. Australian Mathematics Teacher, 74(1), 22-30.
  60. Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2015). Early-years teachers’ concept images and concept definitions: triangles, circles, and cylinders. ZDM, 47(3), 497-509. https://10.1007/s11858-014-0641-8
  61. Türnüklü, E., & Ergin, A. S. (2016). 8th year students’ definitions and figural recognitions of solids: Concept images. Elementary Education Online, 15(1), 40-52. https://doi.org/10.17051/io.2016.33489
  62. Van De Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2014). İlkokul ve ortaokul matematiği: Gelişimsel yaklaşımla öğretim. Nobel Akademik Yayıncılık.
  63. Watson, A., & Mason, J. (2002). Student‐generated examples in the learning of mathematics. Canadian Journal of Math, Science & Technology Education, 2(2), 237-249. https://doi.org/10.1080/14926150209556516
  64. Weigand, H. G., Hollebrands, K., & Maschietto, M. (2025). Geometry education at secondary level–a systematic literature review. ZDM–Mathematics Education, 1-15. https://doi.org/10.1007/s11858-025-01703-1
  65. Wilson, P.S. (1990). Inconsistent ideas related to definitions and examples. Focus on Learning Problems in Mathematics, 12(3&4), 31-47.
  66. Yetkin, E. (2003). Student difficulties in learning elementary mathematics. ERIC Digest, ERIC Clearinghouse for Science Mathematics and Environmental Education.
  67. Yi, M., Flores, R., & Wang, J. (2020). Examining the influence of van Hiele theory-based instructional activities on elementary preservice teachers’ geometry knowledge for teaching 2-D shapes. Teaching and Teacher Education, 91, 103038. https://doi.org/10.1016/j.tate.2020.103038
  68. Yıldızlı, H., & Sarı M.H. (2017). The investigation of primary teachers’ content knowledge on geometric objects. Uludağ University Faculty of Education Journal, 30(2), 601-636. https://doi.org/10.19171/uefad.368975
  69. Yunianto, W., Rully Charitas Indra, P., & Crisan, C. (2021). Indonesian mathematics teachers' knowledge of content of area and perimeter of rectangle. Journal on Mathematics Education, 12(2), 223-238. https://doi.org/10.22342/jme.12.2.13537.223-238