İlköğretim Matematik Öğretmeni Adaylarına Yönelik Matematik Dilinin Öğretimi Öz Yeterlik Ölçeğinin Geliştirilmesi
Year 2025,
Issue: 65, 139 - 159, 19.09.2025
Erdem Çekmez
,
Mustafa Güler
,
Taha Ertuğrul Kuzu
Abstract
Bu araştırmada ilköğretim matematik öğretmeni adaylarının matematik dilini öğretmeye ilişkin öz yeterliklerini belirlemek için bir ölçeğin geliştirilmesi amaçlanmıştır. Araştırmanın katılımcılarını 14 üniversitenin ilgili programının son yarıyılında öğrenim gören 419 öğretmen adayı oluşturmaktadır. Ölçeğin ne düzeyde geçerli ve güvenilir ölçme gerçekleştirdiği madde uyum istatistikleri, benimsenen kategori yapısının işlevselliği, kişilere ve maddelere yönelik güvenirlik ve ayırt edicilik indeksleri, örneklemi hedefleme yeterliği, maddelerin oluşturduğu hiyerarşi, maddelerin yanlılık gösterme durumu, tek boyutluluk ve yerel bağımsızlık bileşenleri açısından incelenmiştir. Verilerin analizi, Rasch ölçme teorisi çerçevesinde derecelendirme ölçeği modeli temelinde Winsteps® yazılımı aracılığıyla gerçekleştirilmiştir. Bulgular kategori yapısının işlevsel olduğunu, madde uyum istatistiklerinin literatürde önerilen aralıkta bulunduğunu, tek boyutluluk ve yerel bağımsızlık kıstaslarının sağlandığını, kişilere ve maddelere ilişkin güvenirlik ve ayırt edicilik indekslerinin uygun olduğunu, maddelerin yanlılık göstermediğini ortaya koymuştur. Bununla birlikte ölçeğin örneklemi hedefleme hususunda orta düzey isabetsizlik sergilediği belirlenmiştir. Sonuç olarak ölçek makul düzeyde geçerli ve güvenilir bir ölçüm gerçekleştirmekte olup ileriki araştırmalarda kullanılabilir.
Ethical Statement
Bu araştırma, Trabzon Üniversitesi Sosyal ve Beşeri Bilimler Bilimsel Araştırma ve Yayın Etiği Kurulunun 24.04.2024 tarihli E-81614018-050.04-2400019593 sayılı kararı ile alınan izinle yürütülmüştür.
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Araujo, Z. d., Roberts, S. A., Willey, C., & Zahner, W. (2018). English learners in K–12 mathematics education: A review of the literature. Review of Educational Research, 88(6), 879-919. https://doi.org/10.3102/0034654318798093
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Çekmez, E., Tuti, G., & Terzi, S. Y. (2023). Investigation of the psychometric properties of a mathematics anxiety test for 3rd and 4th grade primary school students. Anadolu University Journal of Education Faculty, 7(4), 819-841. https://doi.org/10.34056/aujef.1254390
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Erath, K., Prediger, S., Quasthoff, U. Μ., & Heller, V. (2018). Discourse competence as important part of academic language proficiency in mathematics classrooms: The case of explaining to learn and learning to explain. Educational Studies in Mathematics, 99(2), 161 179. https://doi.org/10.1007/s10649-018-9830-7
-
Fan, J., & Bond T. (2019). Applying Rasch measurement in language assessment: Unidimensionality and local independence. In V. Aryadoust & M. Raquel (Eds.), Quantitative data analysis for language assessment: Fundamental techniques (pp.83 102). Routledge. https://doi.org/10.4324/9781315187815
-
Gökmen, A.D.Y., & Ulusoy, M. (2022). The role of vocabulary knowledge and comprehension skills on retelling skills: Different path analysis tests. Pamukkale University Journal of Education, 56, 372-400. https://doi.org/10.9779.pauefd.1026827.
-
Gürefe, N. (2018). Mathematical language skills of mathematics prospective teachers. Universal Journal of Educational Research, 6(4), 661-671. https://doi.org/10.13189/ujer.2018.060410
-
Gray, V. (2004). The language of mathematics: A functional definition and development of an intrument to measure teacher perceived self-efficacy [Doctoral dissertation, Oregon State University]. http://hdl.handle.net/1957/31694
-
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-
Kabael, T., & Yayan, B. (2017). Effect of self-evaluation on pre-service mathematics teachers’ self-efficacy in language of mathematics. Anadolu Journal of Educational Sciences International, 7(1), 1-34. https://doi.org/10.18039/ajesi.292575
-
Kuzu, T. (2023). Multilingual meaning making – An explorative study of German-Turkish learners’ translanguaging processes regarding the part-whole-concept. Journal für Mathematik-Didaktik, 44(4), 325-353. https://doi.org/10.1007/s13138-023-00219-z
-
Kuzu, T., & Ratzke, C. (2024). Explanatory videos in the context of learning processes: An interdisciplinary interpretative interaction analysis of production and reflection processes. Journal of Pedagogical Research, 8(2), 227-259. https://doi.org/10.33902/JPR.202426555
-
Linacre, J. M. (2002). Optimizing rating scale category effectiveness. Journal of Applied Measurement, 3(1), 85-106.
-
Linacre, J. M. (2022). A user quide to Winsteps Ministep Rasch model computer programs. https://www.winsteps.com/a/Winsteps-Manual.pdf
-
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Millî Eğitim Bakanlığı [Ministry of National Education]. (2018b). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı [Secondary education mathematics curriculum (Grades 9, 10, 11, and 12)]. Millî Eğitim Bakanlığı.
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Moleko, M. M. (2021). Teachers’ perspectives on addressing linguistic factors affecting visualization of mathematics word problems. Eurasia Journal of Mathematics, Science and Technology Education, 17(11), em2029. https://doi.org/10.29333/ejmste/11248
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Development of the Mathematical Language Teaching Self-Efficacy Scale for Pre-service Elementary Mathematics Teachers
Year 2025,
Issue: 65, 139 - 159, 19.09.2025
Erdem Çekmez
,
Mustafa Güler
,
Taha Ertuğrul Kuzu
Abstract
This study aimed to develop a scale to determine the self-efficacy of pre-service primary mathematics teachers regarding teaching the language of mathematics. The participants of the research consisted of 419 teacher candidates studying in the final semester of the relevant program at 14 universities. The extent to which the scale provides valid and reliable measurement was examined in terms of item fit statistics, the functionality of the adopted category structure, reliability and discrimination indices for persons and items, sample targeting adequacy, the hierarchy formed by the items, item bias status, unidimensionality, and local independence components. Data analysis was conducted using Winsteps® software based on the rating scale model within the framework of Rasch measurement theory. The findings revealed that the category structure was functional, item fit statistics were within the ranges suggested in the literature, the criteria for unidimensionality and local independence were met, the reliability and discrimination indices for persons and items were appropriate, and the items did not exhibit bias. However, it was determined that the scale demonstrated a moderate level of mistargeting concerning the sample. Consequently, the scale provides reasonably valid and reliable measurement and can be utilized in future research.
Ethical Statement
This study was carried out with the approval of the Scientific Research and Publication Ethics Committee of Trabzon University for Social and Human Sciences, granted by the decision dated 24.04.2024 and numbered E-81614018-050.04-2400019593.
References
-
Açıl, E., & Zeybek, Z. (2017). Students’ ability to use and understand mathematical language with their teacher’s ability to notice the ways of how students use mathematical language? Pamukkale University Journal of Education, 42, 87-107.
-
Adler, J. (1999). The dilemma of transparency: Seeing and seeing through talk in the mathematics classroom. Journal for Research in Mathematics Education, 30(1), 47 64. https://doi.org/10.2307/749629
-
Akcan, F. (2023). The effect of the online supportive learning tool developed for digital security proficiency in social studies course on students' self-efficacy perceptions (Publication No: 776088) [Doctoral dissertation, Gazi University]. Council of Higher Education Thesis Center.
-
Andrich, D. (1996). A hyperbolic cosine latent trait model for unfolding polytomous responses: Reconciling Thurstone and Likert methodologies. British Journal of Mathematical and Statistical Psychology, 49, 347-365. https://doi.org/10.1111/j.2044-8317.1996.tb01093.x
-
Araujo, Z. d., Roberts, S. A., Willey, C., & Zahner, W. (2018). English learners in K–12 mathematics education: A review of the literature. Review of Educational Research, 88(6), 879-919. https://doi.org/10.3102/0034654318798093
-
Baber, R. L. (2011). The language of mathematics: Utilizing math in practice. John Wiley & Sons.
-
Bali-Çalikoğlu, G. (2002). Language in mathematics teaching scale. Hacettepe University Journal of Education, 23, 57-61.
-
Bandura, A. (1977). Self-efficacy: Toward a unifying theory of behavioral change. Psychological Review, 84(2), 191-215. https://doi.org/10.1037/0033-295X.84.2.191
-
Bandura, A. (1997). Self-efficacy: The exercise of control. W. H. Freeman and Company.
-
Barton, B. (2008). The language of mathematics: Telling mathematical tales. Springer. https://doi.org/10.1007/978-0-387-72859-9
-
Barwell, R. (2016). Formal and informal mathematical discourses: Bakhtin and Vygotsky, dialogue and dialectic. Educational Studies in Mathematics, 92(3), 331-345. https://doi.org/10.1007/s10649-015-9641-z
-
Bond, T. G., & Fox, C. M. (2007). Applying the Rasch model: Fundamental measurement in the human sciences (2nd ed.). Lawrence Erlbaum Associates.
-
Bond, T. G., Yan, Z., & Heene, M. (2021). Applying the Rasch model: Fundamental measurement in the human sciences (4th ed.). Routledge
-
Boone, W. J. (2020). Rasch basics for the novice. In M. S. Khine (Ed.), Rasch measurement: Applications in quantitative educational research (pp. 9-30). Springer. https://doi.org/10.1007/978-981-15-1800-3
-
Boone, W. J., & Staver, J. R. (2020). Advances in Rasch analysis in the human sciences. Springer. https://doi.org/10.1007/978-3-030-43420-5
-
Boone, W. J., Staver, J. R., & Yale, M. S. (2014). Rasch analysis in the human sciences. Springer. https://doi.org/10.1007/978-94-007-6857-4_4
-
Burns, M. (2006). Marilyn Burns on the language of math. Instructor, 115(7), 41-43.
-
Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, Ö., Karadeniz, Ş., & Demirel, F. (2019). Bilimsel araştırma yöntemleri [Scientific research methods]. Pegem Akademi
-
Carlson, M., Wilcox, R., Chou, C.-P., Chang, M., Yang, F., Blanchard, J., … & Clark, F. (2011). Psychometric properties of reverse-scored items on the CES-D in a sample of ethnically diverse older adults. Psychological Assessment, 23(2), 582-562. https://doi.org/10.1037/a0022484
-
Çekmez, E., Tuti, G., & Terzi, S. Y. (2023). Investigation of the psychometric properties of a mathematics anxiety test for 3rd and 4th grade primary school students. Anadolu University Journal of Education Faculty, 7(4), 819-841. https://doi.org/10.34056/aujef.1254390
-
Çepni, S. (2007). Araştırma ve proje çalışmalarına giriş [Introduction to research and project studies]. Celepler Matbaacılık.
-
Duncan, P. W., Bode, R. K., Lai, S. M., & Perera, S. (2003). Rasch analysis of a new stroke-specific outcome scale: The stroke impact scale. Archives of Physical Medicine and Rehabilitation, 84(7), 950-963. https://doi.org/10.1016/S0003-9993(03)00035-2
-
Durkin, K., & Shire, B. (1991). Lexical ambiguity in mathematical contexts. In K. Durkin & B. Shire (Eds.), Language in mathematical education (pp. 71-84). Open University Press.
-
Erath, K., Prediger, S., Quasthoff, U. Μ., & Heller, V. (2018). Discourse competence as important part of academic language proficiency in mathematics classrooms: The case of explaining to learn and learning to explain. Educational Studies in Mathematics, 99(2), 161 179. https://doi.org/10.1007/s10649-018-9830-7
-
Fan, J., & Bond T. (2019). Applying Rasch measurement in language assessment: Unidimensionality and local independence. In V. Aryadoust & M. Raquel (Eds.), Quantitative data analysis for language assessment: Fundamental techniques (pp.83 102). Routledge. https://doi.org/10.4324/9781315187815
-
Gökmen, A.D.Y., & Ulusoy, M. (2022). The role of vocabulary knowledge and comprehension skills on retelling skills: Different path analysis tests. Pamukkale University Journal of Education, 56, 372-400. https://doi.org/10.9779.pauefd.1026827.
-
Gürefe, N. (2018). Mathematical language skills of mathematics prospective teachers. Universal Journal of Educational Research, 6(4), 661-671. https://doi.org/10.13189/ujer.2018.060410
-
Gray, V. (2004). The language of mathematics: A functional definition and development of an intrument to measure teacher perceived self-efficacy [Doctoral dissertation, Oregon State University]. http://hdl.handle.net/1957/31694
-
Halliday, M. A. K. (1978). Language as social semiotic. Edward Arnold.
-
Kabael, T., & Yayan, B. (2017). Effect of self-evaluation on pre-service mathematics teachers’ self-efficacy in language of mathematics. Anadolu Journal of Educational Sciences International, 7(1), 1-34. https://doi.org/10.18039/ajesi.292575
-
Kuzu, T. (2023). Multilingual meaning making – An explorative study of German-Turkish learners’ translanguaging processes regarding the part-whole-concept. Journal für Mathematik-Didaktik, 44(4), 325-353. https://doi.org/10.1007/s13138-023-00219-z
-
Kuzu, T., & Ratzke, C. (2024). Explanatory videos in the context of learning processes: An interdisciplinary interpretative interaction analysis of production and reflection processes. Journal of Pedagogical Research, 8(2), 227-259. https://doi.org/10.33902/JPR.202426555
-
Linacre, J. M. (2002). Optimizing rating scale category effectiveness. Journal of Applied Measurement, 3(1), 85-106.
-
Linacre, J. M. (2022). A user quide to Winsteps Ministep Rasch model computer programs. https://www.winsteps.com/a/Winsteps-Manual.pdf
-
Millî Eğitim Bakanlığı [Ministry of National Education]. (2018a). Matematik dersi öğretim programı (İlkokul ve ortaokul 1,2,3,4,5,6,7, ve 8. sınıflar) [Mathematics curriculum (Primary and secondary school grades 1, 2, 3, 4, 5, 6, 7, and 8)]. Millî Eğitim Bakanlığı.
-
Millî Eğitim Bakanlığı [Ministry of National Education]. (2018b). Ortaöğretim matematik dersi (9, 10, 11 ve 12. sınıflar) öğretim programı [Secondary education mathematics curriculum (Grades 9, 10, 11, and 12)]. Millî Eğitim Bakanlığı.
-
Millî Eğitim Bakanlığı [Ministry of National Education]. (2024a). Ortaöğretim matematik dersi öğretim programı (Hazırlık, 9, 10, 11 ve 12. sınıflar) [Secondary Education Mathematics Curriculum (Preparatory, Grades 9, 10, 11, and 12)]. Millî Eğitim Bakanlığı.
-
Millî Eğitim Bakanlığı [Ministry of National Education]. (2024b). Ortaokul matematik dersi öğretim programı (5, 6, 7 ve 8. sınıflar) [Middle school mathematics curriculum (Grades 5, 6, 7, and 8)]. Millî Eğitim Bakanlığı.
-
Moleko, M. M. (2021). Teachers’ perspectives on addressing linguistic factors affecting visualization of mathematics word problems. Eurasia Journal of Mathematics, Science and Technology Education, 17(11), em2029. https://doi.org/10.29333/ejmste/11248
-
Moore, R. C. (1994). Making the transition to formal proof. Educational Studies in Mathematics, 27(3), 249-266. https://doi.org/10.1007/bf01273731
-
Morgan, C. (2020). Mathematical language. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 540-543). Springer. https://doi.org/10.1007/978-3-030-15789-0
-
Moschkovich, J. (2015). Academic literacy in mathematics for English learners. The Journal of Mathematical Behavior, 40, 43-62. https://doi.org/10.1016/j.jmathb.2015.01.005
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. NCTM.
-
Neumann, I., Neumann, K., & Nehm, R. (2011). Evaluating instrument quality in science education: Rasch-based analyses of nature of science test. International Journal of Science Education, 33(10), 1373-1405. https://doi.org/10.1080/09500693.2010.511297
-
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