Preservice middle school mathematics teachers’ strategy repertoire in proportional problem solving Muhammet Arican, Lieven Verschaffel, Wim Van Dooren Research in Mathematics Education, 2025 This study examined 91 preservice mathematics teachers’ strategy repertoire that they referred to when solving one direct and one inverse proportion missing-value word problems. When encouraged to provide multiple solutions, the preservice teachers exhibited the ability to solve the two problems using more than one strategy. However, they used a significantly greater number of strategies for solving the direct than for the inverse proportion problem. The most frequently used strategies for the two problems were the cross-multiplication and across-multiplication, respectively, and many of the preservice teachers also used these two strategies as their first strategy. On the other hand, the number of strategies applied by the preservice teachers did not differ significantly according to their first choice of strategies. A key finding of this study was that the preservice teachers possessing less common strategies in their repertoire had a significantly larger strategy repertoire than those who had more common strategies.
A diagnostic comparison of Spanish and Turkish middle school students’ proportional reasoning Sergio Martínez-Juste, Muhammet Arıcan, J. M. Muñoz-Escolano, A. Oller-Marcén Asian Journal for Mathematics Education, 2023 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.
Investigating Preservice Mathematics Teachers’ Definitions, Formulas, and Graphs of Directly and Inversely Proportional Relationships Muhammet Arıcan, Yasemin Kiymaz Mathematics Enthusiast, 2022 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.
Turkish-addressed social sciences citation index articles: What does the big picture tell us? Yusuf Ziya Olpak, Muhammet Arican International Journal of Educational Research Open, 2021 This study investigates articles in the SSCI written in the English language and published in the ‘Education & Educational Research’ area between 1980 and 2019. In the study, bibliometric methods were used to detect the number of SSCI articles published worldwide, and also the articles with a Turkish author address entered, meaning at least one author provided Turkey as their location. In addition, analysis was conducted according to various variables (e.g., research areas, publication year, number of authors, and source titles). The bibliometric data were obtained from the Web of Science Core Collection database. With regards to the ‘Education & Educational Research’ area, the analysis indicated the dominance of English-speaking countries in terms of the number of SSCI-indexed articles and those that had been cited the most. This finding appears to be affected by the majority of journals indexed in SSCI only accepting articles written in the English language. In terms of the number of SSCI articles published in the area of ‘Education & Educational Research’, Turkey was shown to be ranked seventh worldwide. Within Turkey, the number of SSCI articles for the ‘Education & Educational Research’ area ranked second, after ‘Business & Economics’. In comparison to the overall worldwide trend, the study's findings suggest that Turkish researchers have a tendency towards publishing their articles in mainly Turkey-originated journals with low impact factors. Factors that may affect this tendency and the potential implications of these findings are discussed, together with the limitations of the study and suggestions for further research.
Investigating preservice middle school mathematics teachers' competencies in statistics and probability in terms of various variables Okan KUZU, Muhammet ARICAN Journal of Measurement and Evaluation in Education and Psychology, 2020 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 International Journal of Research in Education and Science, 2019
