Reasoning Skills in Mathematics Teaching: A Meta-Synthesis on Studies Conducted in Turkey

Yıl 2024, Cilt: 8 Sayı: 16, 45 - 86, 21.03.2024

Ali Tum

https://doi.org/10.31458/iejes.1389681

Öz

This research aims to analyze the results of studies conducted in Turkey on reasoning skills in mathematics teaching and to reveal what kind of trend there is in this field. Within the scope of this study, databases were searched with the keywords "reasoning"(muhakeme, akıl yürütme) and "reasoning skill" (Muhakeme becerisi, akıl yürütme becerisi), and the results were examined in accordance with the inclusion criteria regarding mathematics teaching. One hundred sixty-three studies were included. Each of the studies included in the meta-synthesis study was analyzed descriptively according to type, year, method, sample type and size, data collection tools, statistical analysis, learning field, keywords, reasoning type and purpose. In addition, the studies’ results were content analyzed and tabulated by coding the differences and similarities between them with a holistic approach. It has been determined that studies on the learning fields in the mathematics curriculum are mostly carried out in the field of learning numbers and operations in the secondary school mathematics curriculum. When evaluated in terms of reasoning types, almost half of the studies were conducted on mathematical reasoning. It has been observed that after mathematical reasoning, the most focus is on proportional reasoning. When the aims of the studies included in the research were examined, it was determined that the most focused ones were "examining the factors affecting reasoning skills", "measurement of reasoning skills" and "the effect of teaching practices on reasoning skills". In the studies examined, it was seen that there were 33 teaching practices whose effects on reasoning skills were examined.

Anahtar Kelimeler

Mathematics teaching, reasoning skill, meta-synthesis

Etik Beyan

Bu çalışmanın, özgün bir çalışma olduğunu; çalışmanın hazırlık, veri toplama, analiz ve bilgilerin sunumu olmak üzere tüm aşamalarından bilimsel etik ilke ve kurallarına uygun davrandığımı; bu çalışma kapsamında elde edilmeyen tüm veri ve bilgiler için kaynak gösterdiğimi ve bu kaynaklara kaynakçada yer verdiğimi; kullanılan verilerde herhangi bir değişiklik yapmadığımı kabul ederim. Ayrıca canlı bir varlıktan veri toplama süreci gerçekleştirilmediği için etik kurul iznine ihtiyaç duyulmamıştır.

Kaynakça

• Akdoğan, E. (2021). Investigation of postgraduate theses on mathematical thinking and mathematical reasoning in Turkey (Master’s Thesis). Retrieved from the Thesis Center of the Higher Education Institution. (Thesis Number: 684521)
• Aspfors, J.,& Fransson, G. (2015). Research on mentor education for mentors of newly qualified teachers: A qualitative meta-synthesis. Teaching and Teacher Education, 48, 75-86.
• Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi [Math education from theory to application]. Harf Eğitim Yayıncılığı.
• Bal-İncebacak, B., & Ersoy, E. (2016). Analysis of mathematical reasoning ability of the grade 7 students according to TIMSS. The Journal of International Social Research, 9 (46), 474-481.
• Barak, B. (2022). Investigation of graduate theses about mathematical reasoning in Turkey between 2007-2021. The Journal of International Education Science, 9(32), 236-266.
• Bragg, L. A., Herbert, S., & Davidson, A. (2018). Identifying, promoting, and assessing reasoning focused on analysing. Australian Primary Mathematics Classroom, 23(2), 3-7.
• Çoban, H., & Tezci, E. (2022). Mathematical Reasoning: Bibliometric Analysis of the Literature. OPUS Journal of Society Research, 19 (45) , 88-102 .https://doi.org/10.26466/opusjsr.1062867
• Erdem, E. (2015). The effect of enriched learning environment on mathematical reasoning and attitude (Doctoral Dissertation). Retrieved from the Thesis Center of the Higher Education Institution. (Thesis Number: 381651)
• Erdem, E., & Gürbüz, R. (2015). An analysis of seventh-grade students’ mathematical reasoning. Çukurova University Journual of Education Faculty, 44(1), 123-142.
• Erdem, E., & Soylu, Y. (2019). The effect of a learning environment designed using different teaching ways on mathematical reasoning and mathematics attitude. Kastamonu Education Journal, 27(3), 1273-1290. https://doi.org/10.24106/kefdergi.3056
• Ergün, Z., Tümoğlu, E., Şahin, D., &Kabataş-Memiş, E. (2023). Analysis of dissertations on scientific reasoning in Türkiye: A meta-synthesis study, E-International Journal of Educational Research, 14 (2), 102-119. https://doi.org/10.19160/e-ijer.1188680
• Ersanlı, E., Gencoglu, C., & Duran, V. (2018). A meta-synthesis study on investigations of dissertations on education regarding reasoning skills in Turkey. International Online Journal of Educational Sciences, 10(5), 222-243. https://doi.org/10.15345/iojes.2018.05.015
• Ersoy, E., Yıldız, İ., & Süleymanoğlu, E. (2017). A study upon the reasoning abilities of 5th graders. Turkish Studies, 12(17), 179-194.
• Ev-Çimen, E. (2008). A design of learning environment and related teacher activities to foster mathematical power of individuals in mathematics Education (Doctoral Dissertation). Retrieved from the Thesis Center of the Higher Education Institution. (Thesis Number: 220314).
• Fitriana, E. M., Musdi, E., and Anhar, A. (2018). Development of learning design based on realistic mathematics education. International Conferences on Educational, Social Sciences and Technology (pp.699-706), February 14th-15th 2018, Padang, Indonesia.
• Francisco, J. M. & Maher, C. A. (2005). Conditions for promoting reasoning in problem solving: Insights from a longitudinal study. Journal of Mathematical Behavior, 24, 361–372.
• Garfield, J.,& Ben-Zvi, D. (2009). Helping students develop statistical reasoning: implementing a statistical reasoning learning environment. Teaching Statistics, 31(3), 72-77.
• Gürbüz, R., Erdem, E., & Gülburnu, M. (2018). The relationship between mathematical reasoning and spatial ability of eighth grade students. Kastamonu Education Journual, 26(1), 255-260.
• Harms, T. J. (2003). Analysis of Minnesota students' mathematical literacy on TIMSS, NAEP, and MN BST. (Unpublished doctoral dissertation), The University of North Dakota.
• Herbert, S., Widjaja, W., Bragg, L. A., Loong, E., & Vale, C. (2016). Professional learning in mathematical reasoning: reflections of a primary teacher. In B. White, M. Chinnappan, & S. Trenholm (Eds.), Opening Up Mathematics Education Research: Proceedings of the 39th Annual Conference of the Mathematics Education Research Group of Australasia (pp. 279-286). Mathematics Education Research Group of Australasia.
• Kasmer, L. & Kim, O. K. (2011). Using prediction to promote mathematical understanding and reasoning. School Science and Mathematics, 111(1), 20-33.
• Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. National Academy Press.
• Kramarski, B. & Zoldan, S. (2008). Using errors as springboards for enhancing mathematical reasoning with three metacognitive approaches. The Journal of Educational Research, 102(2), 137-151. https://doi.org/10.3200/JOER.102.2.137-151
• Kutluca, T., & Tum, A. (2021). The effect of enriched learning environments using different learning ways on mathematical reasoning skills and problem solving attitude. Cumhuriyet International Journal of Education, 10(1), 344-370. http://dx.doi.org/10.30703/cije.722191
• Kutluca, T., Tum, A. & Mut, A. (2020). Evaluation of Enriched Learning Environment in the Context of Mathematical Reasoning from the Perspective of the Students and their Teacher. Discourse and Communication for Sustainable Education, 11(2) 85-105.
• Mandacı-Şahin, S. (2007). Determining the mathematical power of 8th grade students (Doctoral Dissertation). Retrieved from the Thesis Center of the Higher Education Institution. (Thesis Number: 212030)
• Mason, J. (2001). Questions about mathematical reasoning and proof in schools. Opening address to QCA Conference, UK.
• Mercan, Z. (2021). Studies on early childhood reasoning skills in Turkey. Journal of Muallim Rıfat Faculty of Education, 3(2), 104-120.
• Ministry of National Education [MoNE]. (2015). Ortaokul matematik dersi (5,6,7 ve 8. Sınıflar) öğretim programı [Secondary School Mathematics Curriculum (Grade 5,6,7 and 8)]. Talim ve Terbiye Kurulu Başkanlığı.
• Ministry of National Education [MoNE]. (2018). Matematik dersi öğretim programı (İlkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar)[Primary and secondary school mathematics curriculum (Grade 1,2,3,4,5,6,7,8)]. Talim ve Terbiye Kurulu Başkanlığı.
• Mullis, I. V. S., Martin, M. O., Foy, P., Kelly, D. L., & Fishbein, B. (2020). TIMSS 2019 International Results in Mathematics and Science. Boston College, TIMSS & PIRLS International Study Center. Retrieved from https://timssandpirls.bc.edu/timss2019/international-results/
• Naksutthi, K. & Chidmongkol, S. (2017). Effect of organizing mathematics learning activities using proof mapping technique to write geometric proofs on geometric reasoning ability of eighth grade students. An Online Journal of Education, 12(2), 18-31.
• National Council of Teachers of Mathematics [NCTM] (1989). Curriculum and evaluation standards for school mathematics. Virginia
• National Council of Teachers of Mathematics [NCTM]. (2014). Principles to actions: Ensuring mathematics success for all. Reston, VA: National Council of Teachers of Mathematics.
• Niswah, U., & Qohar, A. (2020). Mathematical reasoning in mathematics learning on pyramid volume concepts. Malikussaleh Journal of Mathematics Learning (MJML), 3(1), 23-26.
• Pham, S. (2015). Teachers’ perceptions on the use of math manipulatives in elementary classroom. Master's Thesis, University of Toronto. Retrieved from https://tspace.library.utoronto.ca/bitstream/1807/68723/1/Pham_Son_H_201506_M T_MTRP.pdf
• Polat, S., & AY, O. (2016). Meta-synthesis: A Conceptual Analysis. Journal of Qualitative Research in Education, 4(2), 52-64. https://doi.org/10.14689/issn.2148-2624.1.4c2s3m
• Ross, K. A. (1998). Doing and proving: The place of algorithms and proof in school mathematics. The American Mathematical Monthly, 105(3), 252-255.
• Smith, P. L., & Ragan, T. J. (2005). Instructional design (3rd edition). John Wiley & Sons.
• Sukirwan, Darhim, & Herman, T. (2018). Analysis of students’ mathematical reasoning. Journal of Physics: Conference Series, 948, 012036.
• Toulmin, S., Rieke, R., &Janik, A. (1984). An introduction to reasoning. Macmillan Publishing Co.
• Tum, A. (2019). The effect of enriched learning environments on mathematical reasoning and problem solving attitude in the context of learning styles (Master’s Thesis). Retrieved from the Thesis Center of the Higher Education Institution. (Thesis Number: 583517)
• Türkoğlu, D., & Cihangir, A. (2017). A meta-synthesis study on algebraic thinking skill. Journal of Research in Education, Science and Technology, 2(2), 25-39.
• Uçar, R. (2022). A systematic reviewing study on proportional reasoning (Master’s Thesis). Retrieved from the Thesis Center of the Higher Education Institution. (Thesis Number: 772882)
• Umay, A. (2003). Mathematical reasoning ability. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 234-243.
• Umay, A., & Kaf, Y. (2005). A study on flawed reasoning in mathematics. Hacettepe University Journal of Education Faculty, 28(28), 188-195.
• Van De Walle, J., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics; Teaching developmentally (7th Ed.). Allyn & Bacon.
• Yankelewitz, D., Mueller, M., & Maher, C. A. (2010). A task that elicits reasoning: A dual analysis. The Journal of Mathematical Behavior, 29, 76-85.
• Yavuz-Mumcu, H. (2011). The interpretation of twelveth grade students ability of using mathematics (Doctoral Dissertation). Retrieved from the Thesis Center of the Higher Education Institution. (Thesis Number: 275480)