Semiotic Examination of Algebra Teaching Process in the Context of Gestures

Yıl 2023, , 1065 - 1092, 23.10.2023

Şahin Danişman , Dilek Tanışlı

https://doi.org/10.34056/aujef.1346962

Öz

This research aims to examine the gestures used by teachers and students in the algebra learning-teaching process and the purpose of these signs. The participants of this case study are 25 eigth graders and their mathematics teacher. The data were collected through video recordings and clinical interviews. Deductive analysis was used to analyze the data, while synchronic and diachronic analyses were utilized to analyze the signs in terms of semiotics. Findings revealed that the teacher used a bunch of iconic, metaphoric, deictic, and beat gestures during the algebra teaching process. The meaning of the iconic gestures that resulted in the study can be listed as centering and itemization, illustration of a table, constant term, preceding element, decrease, separation, base and power, rectangle and side, length, and vertical-horizontal. On the other hand, the metaphorical gestures attribute holding, equality, moving the term from one side to the other, numbers or letters, equality, distributing and hiding. The deictic gestures imply pointing out boards with fingers, board markers or hands, and indicating students and notebooks with fingers, while the beat gestures refer to lowering the hands from top to bottom, waving the fist up and down and moving the hand back and forth. It is seen that the teacher aims to strengthen her expression and support students' mathematical understanding through the gestures she uses.

Anahtar Kelimeler

Semiotics, gesture, algebra, mathematics instruction

Destekleyen Kurum

Anadolu Üniversitesi Bilimsel Araştırma Projeleri Birimi

Proje Numarası

1803E072

Teşekkür

We would like to express our sincere thanks for their support to Anadolu University Scientific Research Projects Commission.

Cebir Öğretim Sürecinin Jestler Bağlamında Göstergebilimsel Olarak İncelenmesi

Öz

Bu araştırma, öğretmen ve öğrencilerin cebir öğrenme-öğretme sürecinde kullandıkları jestleri ve bu işaretlerin kullanım amacını incelemeyi amaçlamaktadır. Durum çalışması desenindeki bu çalışmanın katılımcıları, 25 sekizinci sınıf öğrencisi ve onların matematik öğretmenidir. Veriler video kayıtları ve klinik görüşmeler yoluyla toplanmıştır. Verilerin analizinde tümdengelimli analiz, göstergelerin göstergebilimsel açıdan analizinde ise eşzamanlı ve artzamanlı analizlerden yararlanılmıştır. Bulgular, öğretmenin cebir öğretimi sürecinde bir dizi ikonik, metaforik, işaret ve vurgu jestlerini kullandığını ortaya koymuştur. Çalışmada ortaya çıkan ikonik jestlerin anlamı, ortalama ve maddeleştirme, tablo gösterimi, sabit terim, önceki öğe, eksiltme, ayırma, taban ve kuvvet, dikdörtgen ve kenar, uzunluk ve dikey-yatay olarak sıralanabilir. Öte yandan metaforik jestler, tutma, eşitlik, terimi bir taraftan diğer tarafa taşıma, sayılar veya harfler, eşitlik, dağıtma ve gizleme gibi nitelikler taşımaktadır. İşaret jestleri tahtayı parmakla, tahta kalemiyle veya ellerle gösterme, öğrencileri ve defterleri parmakla gösterme anlamı taşırken, vurgu jestleri söylemlere vurgu anlamı katmak için elleri yukarıdan aşağıya indirmeyi, yumruğu yukarı ve aşağı sallamayı ve eli ileri geri hareket ettirmeyi içermektedir. Öğretmenin, kullandığı jestler aracılığıyla anlatımını güçlendirmeyi ve öğrencilerin matematiksel anlayışlarını desteklemeyi amaçladığı görülmektedir.

Anahtar Kelimeler

Göstergebilim, jest, cebir, matematik öğretimi

Proje Numarası

1803E072

Kaynakça

• Akçakoca, T. (2018). The investigation of secondary school students' embodied cognitions of some mathematical concepts through gestures. Unpublished master’s thesis, Institute of Educational Sciences, Gazi University.
• Akıncı, M. (2014). The investigation of the pre-service mathematics teachers' gestures of some geometric concepts. Unpublished doctoral disertation, Institute of Educational Sciences, Gazi University.
• Aktaş, F. N. & Argün, Z. (2018). Examination of mathematical values in classroom practices: a case study of secondary mathematics teachers. Education and Science, 43(193), 121-141.
• Aktaş, F. N. & Argün, Z. (2020). Görme engelli bireylerin matematiksel iletişim süreçlerinde matematiksel dil kullanımlarının incelenmesi: kabartma yazının rolü. Turkish Journal of Computer and Mathematics Education, 11(1), 128-156.
• Alibali, M. W., Nathan, M. J., & Fujimori, Y. (2011). Gestures in the mathematics classroom: What’s the point? In N. Stein and S. Raudenbush (Eds.), Developmental cognitive science goes to school (pp. 219–234). New York: Routledge, Taylor and Francis.
• Arzarello, F. (2006). Semiosis as a multimodal process. Revista Latinoamericana De Investigación En Matemática Educativa, Special Issue on Semiotics, Culture, and Mathematical Thinking, Special issue, 267-299.
• Arzarello F. & Edwards L. D. (2005). Gestures and the construction of mathematical meaning. In Chick, H. L. & Vincent, J. L. (Eds.). Proceedings of the 29th conference of the ınternational group for the psychology of mathematics education (Vol. 1, pp. 123-154). Melbourne: PME.
• Arzarello, F., Paola, D., Robutti, O., & Sabena, C. (2009). Gestures as semiotic resources in the mathematics classroom. Educational Studies in Mathematics, 70(2), 97-109.
• Balcı, S. (2022). Teaching transformation geometry with dynamic geometry software a view from semiotic mediation perspective. Unpublished master’s thesis, Institute of Educational Sciences, Anadolu University.
• Barab, S. A. & Duffy, T. M. (2000). From practice fields to communities of practice. In D. H. Jonassen & S. M. Land (Eds.), Theoretical foundations of learning environments (pp. 25-55). Lawrence Erlbaum Associates Publishers.
• Barthes, R. (1967/2012). Semiotic adventure (Trans. M. Rifat & S. Rifat). İstanbul: Yapı Kredi.
• Başkale, H. (2016). Determination of validity, reliability and sample size in qualitative studies. Journal of Nursing Effect, 9(1), 23-28.
• Bogdan, R., & Biklen, S. K. (1998). Qualitative research for education: An introduction to theories and methods. Boston: Allyn and Bacon.
• Bullock, J. O. (1994). Literacy in the language of mathematics. The American Mathematical Monthly, 101(8), 735-743.
• Cazden, C. B. and Beck, S. W. (2003). Classroom discourse. In (Eds. A. C. Graesser; M, A, Gernsbacher and S. R. Goldman), Handbook of discourse processes (pp.165-197). New Jersey: Lawrence Erlbaum Associates.
• Clement, J. (2000). Analysis of clinical interviews: Foundations and model viability. In Lesh, R. and Kelly, A., Handbook of research methodologies for science and mathematics education (pp. 341-385). Hillsdale, NJ: Lawrence Erlbaum.
• Cook, S. W. & Goldin-Meadow, S. (2006). The role of gesture in learning: Do children use their hands to change their minds? Journal of Cognition and Development, 7(2), 211-232.
• Cook, S. W., Duffy, R. G., & Fenn, K. M. (2013). Consolidation and transfer of learning after observing hand gesture. Child Development, 84, 863-1871.
• Cope, B. & Kalantzis, M. (1993). The powers of literacy: A genre approach to teaching writing. London: Routledge.
• Creswell, J. (2007). Qualitative inquiry and research design: Choosing among five approaches. Thousand Oaks, CA: Sage.
• Çetinbaş, M. (2022). An investigation of pre-service mathematics teachers' semiotic representations and modeling routes in a mathematical modeling activity. Unpublished master’s thesis, Institute of Educational Sciences, Middle East Technical University.
• Dede, Y. (2014). A comparison of Turkish and German mathematics teachers’ values: A gender perspective. Education and Science, 39(171), 180-198.
• Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61, 103-131.
• Eco, U. (1984). Semiotics and the philosophy of language. Bloomington: Indiana University Press.
• Edwards, L. (2009). Gestures and conceptual integration in mathematical talk. Educational Studies in Mathematics, 70(2), 127-141.
• Elden, M. (2009). Reklamcılık iletişim dizisi 1: Reklam ve reklamcılık. İstanbul: Say.
• Erkman-Akerson, F. (2005). Göstergebilime giriş. İstanbul: Multilingual.
• Guba E. G., & Lincoln Y. S. (1994). Competing paradigms in qualitative research. In Denzin N. K., Lincoln Y. S. (Eds.), Handbook of qualitative research (pp. 105–117). Thousand Oaks, CA: Sage.
• Gutiérrez, A. (1996). Visualization in 3-dimensional geometry: In search of a framework. In L. Puig and A. Guttierez (Eds.) Proceedings of the 20th conference of the international group for the psychology of mathematics education (pp. 3-19). Valencia: Universidad de Valencia.
• Günaydın, O. (2011). Investigation of solution processes of geometry and algebra problems in terms of visualization and semiotics. Unpublished master’s thesis, Institute of Educational Sciences, Marmara University.
• Gürefe, N. (2015). The use of semi̇oti̇c resources on description process some geometric concepts of deaf students. Unpublished doctoral disertation, Institute of Educational Sciences, Gazi University.
• Halliday, M. A. K. (1996). Linguistics and literacy: A functional perspective. In R.Hasan & G. Williams (Eds.), Literacy in society (pp. 339-376). Harlow & NewYork: Longman.
• Hasan, R. (1995). The conception of context in text. In P. Fries & M. Gregory (Eds.), Discourse in society: Systemic functional perspectives (pp. 183-283). Norwood, NJ: Ablex.
• Herbert, S. (2012). Gesture types for functions. In J. Dindyal, L. P. Cheng and S. F. Ng (Eds.), Mathematics education: Expanding horizons (Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia) (pp. 322-328). Singapore: MERGA.
• Hostetter, A. B. (2011). When do gestures communicate? A meta-analysis. Psychological Bulletin, 137, 297-315.
• Lakoff, G. & Núñez, R. (2000). Where mathematics comes from: How the embodied mind brings mathematics into being. New York: Basic Books.
• McNeill, D. (1992). Hand and mind: What gestures reveal about thought. Chicago: University of Chicago Press.
• Merriam, S. B. (1998). Qualitative research and case study applications in education. San Francisco: Jossey-Bass Publishers.
• Nemirovsky, R. (2003). Three conjectures concerning the relationship between body activity and understanding mathematics. In N.A. Pateman, B.J. Dougherty, & J.T. Zilliox (Eds.), Proceedings of 27th conference of the ınternational group for the psychology of mathematics education (vol. 1, pp. 105–109). Honolulu, HI: University of Hawai’i.
• Novack, M. A. and Goldin-Meadow, S. (2015). Learning from gesture: How our hands change our minds. Educational Psychological Review, 27(3), 405-412.
• Novack, M. A. and Goldin-Meadow, S. (2016). Gesture as representational action: A paper about function. Psychological Bulletin Review, 24, 652-665.
• Núñez, R. (2000). Mathematical idea analysis: What embodied cognitive science can say about the human nature of mathematics. In T. Nakaora & M. Koyama (Eds.). Proceedings of PME24 (pp. 3-22). Hiroshima: Hiroshima University.
• Presmeg, N. C. (1992). Prototypes, metaphors, metonymies, and imaginative rationality in high school mathematics. Educational Studies in Mathematics, 23(6), 595-610.
• Presmeg, N. (2014). Mathematics at the center of distinct fields: A response to Michael and Ted. In M. N. Fried & T. Dreyfus (Eds.), Mathematics and mathematics education: Searching for common ground (pp. 45–53). Dordrecht: Springer.
• Radford, L. (2006). Algebraic thinking and the generalization of patterns: a semiotic perspective. In S. Alatorre, J. L. Cortina, M. Sáiz, A. Méndez (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (pp.2-21). Mérida: Universidad Pedagógica Nacional.
• Radford, L. (2010). Algebraic thinking from a cultural semiotic perspective. Research in Mathematics Education, 12(1), 1-19.
• Razfar, A. (2012). Discoursing mathematically: using discourse analysis to develop a sociocritical perspective of mathematics education. The Mathematics Educator, 22(1), 39-62.
• Rifat, M. (2013). XX. yüzyılda dilbilim ve göstergebilim kuramları I. İstanbul: Yapı Kredi Yayınları.
• Roth, W. M. & Lawless, D. (2002). Science, culture, and the emergence of language. Science Education, 86, 368–385.
• Rotman, B. (2006). Towards a semiotics of mathematics. In R. Hersh (Ed.), 18 Unconventional essays on teh natüre of mathematics (pp. 97-127). New York, NY: Springer.
• Saenz-Ludlow, A. & Kadunz, G. (2016). Constructing knowledge seen as a semiotic activity. In A. Saenz-Ludlow, & G. Kadunz (Eds.), Semiotics as a tool for learning mathematics: How to describe the construction, visualization, and communication of mathematical concepts (pp.1-21). Netherlands: Sense.
• Saldana, Johnny (2009). The coding manual for qualitative researchers. Thousand Oaks, California: Sage.
• Santi, G. (2010). Changes in meaning of mathematical objects due to semiotic transformations: a comparison between semiotic perspectives. Unpublished doctoral dissertation, University of Palermo.
• Sayın, Ö. (2014). Göstergebilim ve sosyoloji. Ankara: Anı Yayınevi.
• Seah, W. T., & Bishop, A. J. (2002). Values, mathematics and society: Making the connections. In C. Vale, J. Roumeliotis, & J. Horwood (Eds.), Valuing mathematics in society (pp. 105-113). Brunswick, Australia: Mathematical Association of Victoria.
• Sfard, A. (1998). Two metaphors for learning and the dangers of choosing just one. Educational Researcher, 27(2), 4-13.
• Sfard, A. (2001). There is more to discourse than meets the ears: Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46(1), 13-57.
• Streeck, J. (2008). Depicting by gesture. Gesture, 8(3), 285-301.
• Umay, A. (2002). Öteki matematik. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 23, 275-281.
• van Oers, B. (2000). The appropriation of mathematical symbols. A psychosemiotic approach to mathematics learning. In P. Cobb, E. Yackel & K. McClain (Eds.), Symbolizing and communicating in mathematics classrooms. Perspectives on discourse, tools, and instructional design (pp. 133-176 ). Mahwah: Erlbaum.
• Wertsch, J. V. (1998). Mind as action. Oxford: Oxford University Press.
• Yackel, E. & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458-477.
• Yıldırım, C. (1996). Matematiksel düşünme. İstanbul: Remzi.
• Yin, R. K. (2003). Case study research: design and methods. Thousand Oaks: Sage.