Abstract

The purpose of this study is to implement an a-didactical activity relating to the acquisition of the triangle inequality, prepared within the framework of the Didactic Situations Theory (TDS), and to report the experiences of the students during the implementation process. The study employs a case study method based on a qualitative approach. Six seventh-grade students in a middle-low socioeconomic secondary school in the Marmara Region of Türkiye participated in the study. The researchers prepared an a-didactical activity in which students discovered triangle inequality. Data were collected through observation, video recording, and worksheets. A descriptive analysis was performed on the data obtained. As a result of the analysis, it was concluded that students completed the activity with the correct expressions by experiencing different phases of the a-didactical situation.

Keywords

References

• Aktaş, İ. (2019). Investigation on the effects of a-didactical milieu applications on problem solving process of middle school students [Unpublished master’s dissertation]. Marmara University, İstanbul.
• Angraini, L. M. (2021). Didactical design of mathematical reasoning in mathematical basic concepts of courses. Jurnal Nasional Pendidikan Matematika, 5(1), 1-12. https://doi.org/10.33603/jnpm.v5i1.3943
• Arslan, S., Baran, D., & Okumuş, S. (2011). Brousseau’s theory of didactical situations in mathematics and an application of a-didactical situations. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 5(1), 204-224.
• Arslan, S., Öztürk, M., Bilgin, A. K., & Taşkın, D. (2013). A-didactic situation applications for geometry lessons. Journal of Bayburt Education Faculty, 8(2), 1-12. https://doi.org/10.11114/jets.v6i11a.3811
• Atasay, M. (2018). Examining students' reflected game functions on mathematical games in an a-didactic milieu [Unpublished master’s dissertation]. Eskişehir Anadolu University, Eskişehir.
• Bal, R. (2021). The effect of realistic mathematics education on student achievement in factors and multiples and atti̇tudes towards mathematics [Unpublished master’s dissertation]. Hacettepe University, Ankara.
• Baştürk Şahin, B. N., Şahin, G., & Tapan Broutin, M. S. (2017). Teaching the concept of prime numbers regarding to the theory of didactical situations: An action research. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 11(2), 156-171.
• Berkant, H. G., & Yaren, R. (2020). The effect of realistic mathematics education on secondary school sixth grade students’ motivations in mathematics. Kahramanmaras Sutcu Imam University Journal of Social Sciences, 17(2), 543-571. https://doi.org/10.33437/ksusbd.555770
• Brousseau, G. (2002). Theory of didactical situations in mathematics: Didactique des mathématiques, 1970–1990 (N. Balacheff, M. Cooper, R. Sutherland, & V. Warfıeld, Trans.). Kluwer Academic Publishers. (Original work published 1997).
• Cantürk Günhan, S. (2006). An investigation on applicability of problem based learning in the mathematics lesson at the second stage in the elementary education [Unpublished doctoral dissertation]. Dokuz Eylül University, İzmir.
• Creswell, J. W. (2021). Nitel araştırma yöntemleri (Translation from the 3rd edition). Siyasal Kitapevi.
• Çepni, S. (2018). Araştırma ve proje çalışmalarına giriş [Introduction to research and project work]. Celepler Pub.
• Çiftci, O. (2018). The investigation of the technology supported cooperative learning environment designed for the prevention of learning difficulties in triangles [Unpublished master’s thesis]. Atatürk University, Erzurum.
• Ercan, N. Ö. (2020). Proof schemes used by 7 th grade students on geometry subjects in an a-didactic environment [Unpublished master’s thesis]. Kastamonu University.
• Erdoğan, A. (2016). Didaktik durumlar teorisi [Theory of didactical situations]. In E. Bingölbali, S. Arslan, & Zembat, İ. Ö. (Eds.), Matematik eğitiminde teoriler [Theories in eathematics education] (pp. 413-430). Pegem.
• Erdoğan, A., Gök, M., & Bozkır, M. (2014). Teaching proportion concept within an a-didactical milieu. Gazi University Journal of Gazi Education Faculty, 34(3), 535-562. https://doi.org/10.17152/gefad.87231
• Erdoğan, A., & Özdemir Erdoğan, E. (2013). Involving primary school students in mathematical processes through theory of didactical situations. Ahi Evran University Journal of Kırşehir Education Faculty, 14(1), 17-34.
• Erenkuş, M., & Eren Savaşkan, D. (2019). Ortaokul ve imam hatip ortaokulu matematik 8. sınıf ders kitabı [8th grade mathematics textbook for secondary school and imam hatip secondary school]. Koza Pub.
• Ergan, S. (2020). Examination on teaching processes of the subject of triangles in classes prepared via a-didactical teaching situation [Unpublished master’s dissertation]. Zonguldak Bülent Ecevit University, Zonguldak.
• Erümit, A. K., Arslan, S., & Fiş Erümit, S. (2012). Solution process in the a-didactic environment of the mathematics problem. Journal of Research in Education and Teaching, 1(4), 75-81.
• Fosnot, C. T. (2013). Constructivism: Theory, perspectives, and practice. Teachers College Press.
• Gök, M., & Erdoğan, A. (2017). Non-routine mathematical problem solving in classroom environment: an example based upon theory of didactical situations. Yüzüncü Yıl University Journal of Education, 14(1), 140-181. https://doi.org/10.23891/yyuni.2017.6
• Güneş, K., & Tapan Broutin, M. S. (2017). Teaching pythagoras theorem to eighth grade students in an a-didactic environment. Academy Journal of Educational Sciences, 1(1), 11-22. https://doi.org/10.31805/acjes.340364
• Laborde, C. (2007). Towards theoretical foundations of mathematics education. ZDM Mathematics Education, 39(1-2), 137-144. https://doi.org/10.1007/s11858-006-0015-y
• Özer, S. (2019). Realistic mathematics education designed with constructivist approach; access, learning persistence and impact on student opinions [Unpublished master’s dissertation]. Marmara University.
• Perkins, D. (1999). The many faces of constructivism. Educational Leadership, 57(3), 6-11.
• Rachmiati, W., Helnanelis, H., & Juhji, J. (2020). Utilization of literature based math in developing didactic designs for students' mathematical understanding in the decimal concept. Al Ibtida: Jurnal Pendidikan Guru MI, 7(2), 148-165. https://doi.org/10.24235/al.ibtida.snj.v7i2.4935
• Saydam, G. (2009). Elementary teachers views and attitudes towards applying constructivist approach in education [Unpublished master’s dissertation]. Adnan Menderes University, Aydın.
• Türnüklü, E. (2009). Some obstacles on the way of constructing triangular inequality. Education and Science, 34(152), 174-181.
• Warfield, V. M. (2016). Invitation to didactique. Springer.
• Yavuz, İ., Arslan, S., & Kepçeoğlu, İ. (2011). Didactic contract and its reflection to education: the case of table of values. International Journal of Human Sciences, 8(1), 385-409.
• Yenil, T. (2020). The correction of 6th-grade students' misconceptions on decimal notation with digital concept cartoons designed according to the 5E model [Unpublished master’s dissertation]. Bartın University.
• Yıldırım, A., & Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in social sciences]. Seçkin.
• Yurtyapan, M. İ., Tapan Broutın, M. S., & Kaleli Yılmaz, G. (2020). An action research aligned with the REACT+G teaching approach: “Thales’ Intercept Theorem”. Journal of Computer and Education Research, 8(15), 241-273. https://doi.org/10.18009/jcer.684808

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.