Muhammet Arican

@bogazici.edu.tr

Mathematics and Science Education
Boğaziçi University



           

https://researchid.co/marican

RESEARCH, TEACHING, or OTHER INTERESTS

Education

15

Scopus Publications

Scopus Publications

  • Preservice middle school mathematics teachers’ strategy repertoire in proportional problem solving
    Muhammet Arican, Lieven Verschaffel, and Wim Van Dooren
    Informa UK Limited



  • A diagnostic comparison of Spanish and Turkish middle school students’ proportional reasoning
    Sergio Martínez-Juste, Muhammet Arıcan, J. M. Muñoz-Escolano and A. Oller-Marcén

    This small-scale comparative study investigated Spanish and Turkish middle school students’ mastery of four core cognitive skills required for proportional reasoning using the log-linear cognitive diagnosis model. We compared students in the two samples for their proportional reasoning and provided a diagnostic assessment of their strengths and weaknesses. The study included 314 Spanish eighth grade and 282 Turkish seventh grade students. The students were administered a proportional reasoning test with 22 multiple-choice items. We found significant differences between the two samples in two of the cognitive skills. While the Spanish sample were better at understanding nonproportional relationships, the Turkish sample were better at understanding the concept of ratio. Furthermore, while the Spanish sample had a more dispersed distribution of students among different attribute profiles, the Turkish sample mostly consisted of either low-performing or high-performing students. To better understand the similarities and differences between the two samples, we compared students’ performance on some specific test items. The study shows how cognitive diagnostic models, which are not widely used in small-scale comparative studies, can be very useful in revealing similarities and differences between two samples that cannot be detected by traditional psychometric models.

  • Preservice middle school mathematics teachers’ strategy repertoire in proportional problem solving
    Muhammet Arican, Lieven Verschaffel, and Wim Van Dooren
    Informa UK Limited

  • Investigating Preservice Mathematics Teachers’ Definitions, Formulas, and Graphs of Directly and Inversely Proportional Relationships
    Muhammet Arıcan and Yasemin Kiymaz

    This study investigates 48 preservice middle school teachers’ formal textbook definitions, formulas, and graphs of the directly and inversely proportional relationships. The connections among these three types of representations and how preservice teachers’ representations differ according to the two relationships are also examined. The data of the study included the preservice teachers’ responses to a paper-and-pencil test with two items. An explanatory research design model was followed when developing this study. The study findings indicated the preservice teachers’ over-attention to the simultaneous increases and/or decreases when representing the directly and inversely proportional relationships. Only four preservice teachers stated in their definitions that the ratio was constant in the directly proportional relationship. Whereas none of them stated constant product in their inversely proportional definition. Although the preservice teachers were slightly better at writing the direct proportion formula than the inverse proportion formula, this difference was much greater in terms of drawing the direct and inverse proportion graphs. Sixty percent of the preservice teachers drew their inverse proportion graphs as linear with negative slopes. Moreover, the analysis showed that the preservice teachers’ definitions were not well-linked with their graphs and formulas. On the other hand, the preservice teachers who were better at providing correct formulas were also better at drawing the correct graphs. Implications for teaching and future study suggestions are discussed.




  • Investigating preservice middle school mathematics teachers' competencies in statistics and probability in terms of various variables
    Okan KUZU and Muhammet ARICAN
    Egitimde ve Psikolojide Olcme ve Degerlendirme Dergisi
    In this study, probabilities of preservice middle school mathematics teachers’ possession of four fundamental cognitive skills required for learning and teaching statistics and probability topics were examined by using the log-linear cognitive diagnostic model, which is one of the cognitive diagnostic models. Moreover, the probabilities of preservice teachers’ possession of these skills were investigated according to gender, university ranking, and grade level variables. Hence, it was examined whether there was a significant relationship between the probabilities of having each skill and these variables. A Statistical Reasoning Test, which was developed by Arican and Kuzu in 2019, measured preservice teachers’ possession of four critical skills was used in collecting the data. These four skills included representing and interpreting data, drawing inferences about populations based on samples, selecting and using appropriate statistical methods to analyze data, and understanding and applying basic concepts of probability. In the 2016-2017 academic year, the test was applied to 456 preservice teachers selected from four different universities in Turkey, and probabilities of their possession of each attribute were calculated. Later, the relationship between the preservice teachers’ test scores and gender was examined by using the Mann-Whitney U test, and the relationship between their test scores and ranking of the attended university and grade level were examined using the Kruskal Wallis-H test. Although probabilities of the preservice teachers’ possession of these four skills did not significantly differ according to gender, some significant differences were detected for university ranking and grade level variables.

  • Facilitating pre-service mathematics teachers’ understanding of directly and inversely proportional relationships using hands-on and real-world problems



  • Investigating the effects of peer instruction on preservice mathematics teachers’ achievements in statistics and probability
    Yusuf Ziya Olpak, Serdal Baltaci, and Muhammet Arican
    Springer Science and Business Media LLC


  • Preservice middle grades mathematics teachers’ strategies for solving geometric similarity problems
    Muhammet Arican, Oguz Koklu, Ibrahim Burak Olmez, and Serdal Baltaci
    ISTES Organization
    Proportional relationships and geometric similarity are two of the critical topics in school mathematics. Students and even teachers often struggle with recognizing the proportional relationships in geometric similarity problems. The purpose of this study was to investigate preservice middle-grades mathematics teachers’ (PSTs) strategies when solving geometric similarity problems. Furthermore, we also examined the influence of the problem characteristics on the PSTs’ solution strategies. The data for the present study came from 32 PSTs’ responses to a geometric similarity test consisting of five problems and individual semi-structured interviews with three of these PSTs. The results revealed that the PSTs used a limited number of strategies when solving the similarity problems and usually relied on the cross-multiplication strategy in their solutions. Only a few PSTs were able to explain proportional relationships between corresponding sides of the geometric figures in the given problems. The PSTs’ overreliance on the cross-multiplication strategy appeared to constrain their identification of proportional relationships. Based on the results of the present study, we propose the use of dilating perspective, a dynamic dilation-oriented method that promotes side-by-side comparison of similar figures in teaching geometric similarity.