An investigation on the thinking structures and proof-writing levels of future mathematics teachers

Elif Aksan Kilicaslan

doi:10.29333/pr/13682

Full Text (PDF)

Elif Aksan Kilicaslan ¹ ^*

More Detail

¹ Department of Mathematics Education, Fatih Faculty of Education, Trabzon University, Trabzon, TÜRKİYE^* Corresponding Author

Abstract

In this study, it is aimed to reveal what kind of relationship exists between prospective teachers’ thinking structures and their level of writing proofs. This study was carried out as a case study. The study was carried out with 82 prospective teachers enrolled in the Department of Secondary School Mathematics Teaching of a state university located in the Eastern Black Sea Region of Turkey. The first data collection is the mathematical processing instrument developed by Presmeg (1986). The second data collection was developed by the researcher and consists of five proofs that are also covered in the curriculum about the geometric shapes circle and circular region. As a result, when the thinking structures of the participants are examined, it can be understood that harmonic thinking is the most common thinking type among the study participants. When the proof-writing levels in this study are looked at, it becomes obvious that most of the prospective teachers are weak in terms of this skill. In this study, the participants’ proof-writing levels and thinking structures were found to be correlated.

Keywords

mathematical processing instrument
proof-writing levels
prospective mathematics teachers
circle and circular region

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

PEDAGOGICAL RES, Volume 8, Issue 4, October 2023, Article No: em0172

https://doi.org/10.29333/pr/13682

Online publication date: 13 Sep 2023

Article Views: 568

Article Downloads: 474

Open Access References How to cite this article

References

Alkan, H., & Bukova-Guzel, E. (2005). Öğretmen adaylarında matematiksel düşünmenin gelişimi [Development of mathematical thinking in teacher candidates]. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi [Journal of Gazi University Gazi Education Faculty], 25(3), 221-236.
Bell, A. W. (1976). A study of pupils’ proof-explanations in mathematical situations. Educational Studies in Mathematics, 7(1/2), 23-40. https://doi.org/10.1007/BF00144356
Büyüköztürk, Ş. (2006). Sosyal bilimler için veri analizi el kitabı [Manual of data analysis for social sciences](6. Edn.). Pegem.
Cepni, S. (2005). Araştırma ve proje çalışmalarına giriş [Introduction to research and project work]. Üçyol Kültür Merkezi [Üçyol Cultural Center].
Delice, A., & Sevimli, E. (2011). İntegral kavramının öğretiminde konu sıralamasının kavram imgeleri bağlamında incelenmesi; belirli ve belirsiz integraller [Examining the subject order in the context of concept images in the teaching of the concept of integral; definite and indefinite integrals]. Pamukkale Üniversitesi Eğitim Fakültesi Dergisi [Pamukkale University Faculty of Education Journal], 30(30), 51-62.
Delice, A., & Sevimli, E. (2012). Analiz dersi öğrencilerinin integral hacim hesabı problemlerindeki çözüm süreçlerinin düşünme yapısı farklılıkları bağlamında değerlendirilmesi [Evaluation of analysis course students’ solution processes in integral volume calculation problems in the context of thinking structure differences]. Marmara Üniversitesi Atatürk Eğitim Fakültesi Eğitim Bilimleri Dergisi [Marmara University Ataturk Faculty of Education Journal of Educational Sciences], 36(36), 95-113.
Dickerson, D. S. (2008). High school mathematics teachers’ understandings of the purposes of mathematical proof [PhD thesis, Syracuse University].
Dursun, S., 6 Coban, A. (2006). Geometri dersinin lise programları ve ÖSS soruları açısından değerlendirilmesi [Evaluation of geometry course in terms of high school programs and OSS questions]. C.Ü. Sosyal Bilimler Dergisi [C.U. Journal of Social Sciences], 30(2), 213-221.
Galindo-Morales, E. (1994). Visualization in the calculus class: Relationship between cognitive style, gender, and use of technology [Unpublished PhD thesis]. The Ohio State University.
Guven, B., Celik, D., & Karatas, V. I. (2005). High school students’ sufficiencies of doing mathematical proofs. Journal of Contemporary Education, 30, 319-332.
Kozhevnikov, M., Hegarty, M., & Mayer, R. E. (2002). Revising the visualizer-verbalizer dimension: Evidence for two types of visualizers. Cognition and Instruction, 20(1), 47-77. https://doi.org/10.1207/S1532690XCI2001_3
Krutetskii, V. (1976). Psychology of mathematical abilities in schoolchildren. The University of Chicago Press.
Lean, G., & Clements, M. A. (1981). Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12(3), 267-299. https://doi.org/10.1007/BF00311060
Lowrie, T., & Kay, R. (2001). Relationship between visual and nonvisual solution methods and difficulty in elementary mathematics. The Journal of Educational Research, 94(4), 248-255. https://doi.org/10.1080/00220670109598758
McCrone, S. M. S., & Martin, T. S. (2004). Assessing high school students’ understanding of geometric proof. Canadian Journal of Math, Science & Technology Education, 4(2), 223-242. https://doi.org/10.1080/14926150409556607
McGillicuddy-DeLisi, A. V., & Sigel, I. E. (1991). Family environments and children’s representational thinking. Advances in Reading/Language Research, 5, 63-90.
Morali, S., Ugurel, I., Turnuklu, E., & Yesildere, S. (2006). Matematik öğretmen adaylarının ispat yapmaya yönelik görüşleri [Opinions of pre-service mathematics teachers on proving]. Kastamonu Eğitim Dergisi [Kastamonu Journal of Education], 14(1), 147-160.
Ozdemir, F., & Ozdemir, H. (2018). Investigation of high school students’ opinions on constructing proof and skill perceptions on problem-solving. Journal of Academic Social Sciences, 6(71), 405-419.
Presmeg, N. C. (1986). Visualisation in high school mathematics. For the Learning of Mathematics, 6(3), 42-46.
Presmeg, N. C. (2006). Research on visualization in learning and teaching mathematics: Emergence from psychology. In Á. Gutiérrez, & P. Boero (Eds.), Handbook of research on the psychology of mathematics education (pp. 205-235). Brill. https://doi.org/10.1163/9789087901127_009
Senk, S. L. (1983). Proof-writing achievement and Van Hiele levels among secondary school geometry students [PhD thesis, The University of Chicago].
Sevgi, S., & Orman, F. (2022). Eighth grade students’ views about giving proof and their proof abilities in the geometry and measurement. International Journal of Mathematical Education in Science and Technology, 53(2), 467-490. https://doi.org/10.1080/0020739X.2020.1782493
Tasova, H. I. (2011). Matematik öğretmen adaylarının modelleme etkinlikleri ve performansı sürecinde düşünme ve görselleme becerilerinin incelenmesi [Examining the thinking and visualization skills of pre-service mathematics teachers during modeling activities and performance] [Doctoral dissertation, Marmara University].
Tekin, M., Ozmutlu, I., & Erhan, S. E. (2009). Özel yetenek sınavlarına katılan öğrencilerin karar verme ve düşünme stillerinin incelenmesi [Examining the decision-making and thinking styles of students who participated in special talent exams]. Beden Eğitimi ve Spor Bilimleri Dergisi [Journal of Physical Education and Sport Sciences], 11(3), 42-56.
Turan, A. O. (2011). 12. sınıf öğrencilerinin analitik geometrideki temsil geçişlerinin Krutetskii düşünme yapıları bağlamında Incelenmesi [Investigation of 12th grade students’ representation transitions in analytic geometry in the context of Krutetskii thinking structures] [Doctoral dissertation, Marmara University].
Ubuz, B. (1999). 10. ve 11. sınıf öğrencilerinin temel geometri konularındaki hataları ve kavram yanılgıları (10th and 11thgrade students errors and misconceptions on basic geometry) [Errors and misconceptions of 10th and 11th grade students on basic geometry subjects (10th and 11thgrade students errors and misconceptions on basic geometry)]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi [Journal of Hacettepe University Faculty of Education], 16-17, 95-104.
Umay, A. (2003). Matematiksel muhakeme yeteneği [Mathematical reasoning ability]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi [Journal of Hacettepe University Faculty of Education], 24(24), 234-243.
Varghese, T. (2009). Secondary-level student teachers’ conceptions of mathematical proof. IUMPST: The Journal, 1.
Waring, S. (2000). Can you prove it? Developing concepts of proof in primary and secondary schools. The Mathematical Association.

How to cite this article

APA

Aksan Kilicaslan, E. (2023). An investigation on the thinking structures and proof-writing levels of future mathematics teachers. Pedagogical Research, 8(4), em0172. https://doi.org/10.29333/pr/13682

Vancouver

Aksan Kilicaslan E. An investigation on the thinking structures and proof-writing levels of future mathematics teachers. PEDAGOGICAL RES. 2023;8(4):em0172. https://doi.org/10.29333/pr/13682

AMA

Aksan Kilicaslan E. An investigation on the thinking structures and proof-writing levels of future mathematics teachers. PEDAGOGICAL RES. 2023;8(4), em0172. https://doi.org/10.29333/pr/13682

Chicago

Aksan Kilicaslan, Elif. "An investigation on the thinking structures and proof-writing levels of future mathematics teachers". Pedagogical Research 2023 8 no. 4 (2023): em0172. https://doi.org/10.29333/pr/13682

Harvard

Aksan Kilicaslan, E. (2023). An investigation on the thinking structures and proof-writing levels of future mathematics teachers. Pedagogical Research, 8(4), em0172. https://doi.org/10.29333/pr/13682

MLA

Aksan Kilicaslan, Elif "An investigation on the thinking structures and proof-writing levels of future mathematics teachers". Pedagogical Research, vol. 8, no. 4, 2023, em0172. https://doi.org/10.29333/pr/13682