Investigation of Middle School 8th Grade Students' Orientations to Mathematical Proof Schemas by Using Artificial Neural Network Model.

Although the general purpose in this research is to use the artificial neural network model in mathematics education, the main purpose is to show the relationship between students' tendency towards the types of mathematical proof and the learning styles they have by using the artificial neural network model. In addition, SOM-Ward clustering algorithm based on artificial intelligence was used to investigate the relationship between students' tendency towards the types of mathematical proof and the learning styles they have. In the qualitative data collection process, the criterion sampling method was used as the purposeful sampling. In the process of training the artificial neural network model, feed forward back propagation network structure was used. In the study, a lesson hour was given to the students to answer the open ended questions about the proposals and the learning style inventory. As a data collection tool, four questions from four different mathematical fields were asked for that students should be able to rank towards the proposition closest to them and that the reasons underlying the ranking formats were found. The learning styles of the students were tried to be predicted by taking advantage of the verbal expressions of the students. In addition, the results in the learning style inventory were combined with predictive learning styles. During the training of the artificial neural network model, placements that were ranked towards the proposition closest to students were used as input. Also predictive learning styles were used as output. As a result of the research, consistency between the results produced by the model and the predicted learning styles was observed sufficiently. It was seen that the students who placed the inductive proposals in the first place often had the learning style of accommodation. It was seen that the students who placed the perceptual proposals in the first place often had the learning style of assimilating. It was seen that the students who placed the perceptual proposals in the first place often had the learning style of assimilating. It was seen that some of the students who put the algebraic proposal in the first place had the learning style of assimilating and some of the students who put the algebraic proposal in the first place had the learning style of converging. Also it was seen that the students who placed the visual proposals in the first place often had the learning style of diverging. The proportion of girls was found to be higher than that of boys in the learning style of converging, as opposed to the students with other learning styles. Keywords: Artificial Neural Networks Model, Mathematics Education, Proof Schemas, Learning Styles. References Duran, M., Doruk, M., & Kaplan, A. (2017). An Examination of The Effectiveness of Argumentation-Based Probability Teaching on Middle School Students’ Achievements and Anxieties.  Egitimde Kuram ve Uygulama, 13(1), 55-87. Gencel, I. E. (2007). Kolb'un deneyimsel ogrenme kuramina dayali ogrenme stilleri envanteri-III'u Turkceye uyarlama calismasi. Harel, G., Sowder, L. (1998). Students’ proof shemes: Results from exploratory studies. Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for research in mathematics education, 396-428. Keles, E., & Cepni, S. (2006). Beyin ve ogrenme. Turk Fen Egitimi Dergisi, 3(2), 66-82. Kolb, D. A., Boyatzis, R. E., & Mainemelis, C. (2001). Experiential learning theory: Previous research and new directions. Perspectives on thinking, learning, and cognitive styles, 1(2001), 227-247. Lee, J. K. (2002). Philosophical perspectives on proof in mathematics education.  Philosophy of mathematics education journal ,  16 , 1-13. Liu, Y., & Manouchehri, A. (2013). Middle School Children's Mathematical Reasoning And Proving Schemes. Investigations in Mathematics Learning, 6(1). McLoughlin, C. (1999). The implications of the research literature on learning styles for the design of instructional material. Australasian Journal of Educational Technology, 15(3). Ozdemir O., Kazu I. Y. (2010). Bolumu–Elazig, F. U. E., & Bolumu–Elazig, B. Bilgisayar Destekli Bilgisayar Ogretiminde Yapay Zekâ Ile Ogrenme Ortami Sunmanin Ogrenci Basarisina Etkisi. Ozdemir, F., & Kaplan, A. (2014). Ogretmen Adaylarinin Ogrenme Stillerine Gore Matematiksel Ispat Hakkindaki Goruslerinin Incelenmesi. Amasya Universitesi Egitim Fakultesi Dergisi, 3(2), 410-429. Stylianou, D. A., Blanton, M. L., & Knuth, E. J. (Eds.). (2010). Teaching and learning proof across the grades: A K-16 perspective. Routledge.