Ethnomathematical research and drama in education techniques: developing a dialogue in a geometry class of 10th grade students
Palavras-chave:
Ethnomathematics, Geometrical Notions, WebQuest, Drama-in-Education, Third Space, ??????????????, ??????????? ???????, ‘????????? ????? ???? ??????????’, ??????/????????? ?????Resumo
Abstract
Ethnomathematical research, together with digital technologies (WebQuest) and Drama-in-Education (DiE) techniques, can create a fruitful learning environment in a mathematics classroom—a hybrid/third space—enabling increased student participation and higher levels of cognitive engagement. This article examines how ethnomathematical ideas processed within the experiential environment established by the Drama-in-Education techniques challenged students’ conceptions of the nature of mathematics, the ways in which students engaged with mathematics learning using mind and body, and the ‘dialogue’ that was developed between the Discourse situated in a particular practice and the classroom Discourse of mathematics teaching. The analysis focuses on an interdisciplinary project based on an ethnomathematical study of a designing tradition carried out by the researchers themselves, involving a search for informal mathematics and the connections with context and culture; 10th grade students in a public school in Athens were introduced to the mathematics content via an original WebQuest based on this previous ethnomathematical study; Geometry content was further introduced and mediated using the Drama-in-Education (DiE) techniques. Students contributed in an unfolding dialogue between formal and informal knowledge, renegotiating both mathematical concepts and their perception of mathematics as a discipline.
Key words:
Περίληψη
Η εθνομαθηματική έρευνα, σε συνδυασμό με ψηφιακές τεχνολογίες και τεχνικές δραματικής τέχνης, μπορούν να δημιουργήσουν ένα γόνιμο περιβάλλον στην τάξη των μαθηματικών—έναν υβριδικό χώρο—ενθαρρύνοντας μεγαλύτερη συμμετοχικότητα των μαθητών. Στην εργασία αυτή, εξετάζεται πώς οι εθνομαθηματικές ιδέες και ο βιωματικός χαρακτήρας των Τεχνικών του Δράματος στην Εκπαίδευση ‘προκαλούν’: την αντίληψη των μαθητών για τη φύση των μαθηματικών, τον τρόπο που οι μαθητές εμπλέκονται στη μάθηση των μαθηματικών χρησιμοποιώντας σώμα και μυαλό, καθώς και το διάλογο που αναπτύσσεται ανάμεσα στο Λόγο το συνδεδεμένο με συγκεκριμένες πρακτικές και το Λόγο της σχολικής τάξης. Αναλύεται ένα διαθεματικό πρότζεκτ βασισμένο σε εθνογραφική έρευνα σχετικά με μια σχεδιαστική παράδοση —:μελέτη των άτυπων μαθηματικών και της σύνδεσής του με την κουλτούρα και το πλαίσιο— και στην εφαρμογή ενός WebQuest σε μαθητές 1ης Λυκείου σε ένα δημόσιο σχολείο της Αθήνα, με τις τεχνικές της ΔΤΕ να διαμεσολαβούν τη διδασκαλία της γεωμετρίας. Δημιουργώντας ένα τέτοιο περιβάλλον οι μαθητές είχαν τη ευκαιρία να συμβάλλουν σε έναν διάλογο που αναπτύχθηκε ανάμεσα σε τυπική και άτυπη γνώση και να επαναδιαπραγματευτούν μαθηματικές έννοιες, καθώς και την αντίληψή τους για τη φύση των μαθηματικών.
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Referências
Abreu, G. (1998). Reflecting on Mathematics Learning in and out-of-School, from a Cultural psychology Perspective. Proceedings of 22nd Conference of PME, Stellenbosch, South Africa.
Alkistis, Κ. (2000). Drama in Education. Athens: Ellinika Grammata.
Alkistis, Κ. (1998). The book of Dramatization. Athens: Ellinika Grammata.
Andersen, C. (2004). Learning in ‗As-If‘ Worlds: Cognition in Drama in Education. Theory Into Practice , 43( 4), 281-286.
Andersen, C. (2002). Thinking as and thinking about: Cognitive and metacognitive processes in drama. In Bjørn Rasmussen & Anna-Lena Østern (Eds.), Playing betwixt and between: The IDEA Dialogues 2001. Oslo, Landslaget: Drama I Skolen.
Annarella, L. A. (1992a). Creative Drama in The Classroom. (ERIC Document Reproduction Service ED391206).
Annarella, L. A. (1992b). Encouraging Creativity and Imagination in the Classroom. (ERIC Document Reproduction Service ED434380).
Appelbaum, P. (2004). Mathematics Education. In Joe Kincheloe& Danny Weil (Eds), Critical Thinking and Learning: An Encyclopedia for Parents and Teachers. Greenwood: ABC-CLIO Press. Online available: http://gargoyle.arcadia.edu/appelbaum/encyc.htm
Appelbaum, P., & Clark, S. (2001). Science! Fun? A critical analysis of design/content/evaluation. Journal of Curriculum Studies, 33(5), 583-600.
Appelbaum, P., & Stathopoulou, C. (2015). Critical Issues in Culture and Mathematics Learning. Chapter to be included in the Handbook of International Research in Mathematics Education, edited by Lyn English and David Kirshner, pp. 744-798
Ascher, M. & Ascher, R. (1981). Code of the Quipu, University of Michigan Press.
Ascher, M. (1991). Ethnomathematics: A multicultural view of mathematical ideas. NewYork: Chapma and Hal.
Bailin, S. (1998). Critical thinking and drama education. Research in Drama Education, 3 (2). 145- 153.
Basu, S. J., & Barton, A. C. (2007). Developing a sustained interest in science among urban minority youth. Journal of Research in Science Teaching, 44(3), 466-489.
Barton, A. C., & Tan, E. (2009). Funds of knowledge and discourses and hybrid space. Journal of Research in Science Teaching, 46(1), 50-73.
Bishop, A. J. (1988a). Mathematics education in its cultural context. Educational Studies in Mathematics, 19, 179-191.
Bishop, A. J. (1988b). Mathematical Enculturation: A Cultural Perspective in Mathematics Education. Dordrecht: D. Reidel Publishing Company.
Bolton, G. (1985). Changes in thinking about drama in education. Theory into Practice, 24 (3),151- 157.
Burchum, J., Russell, C., Likes, W., Adymy, C., Britt, T., Driscoll, C., Graff, C., Jacob, S., & Cowan, P., (2007). Confronting Challenges in Online Teaching: The WebQuest Solution. MERLOT Journal of Online Learning and Teaching, 3(1). pp. 40-57.
Carraher, T. N., Carraher, D. W., & Schliemann,A . D. (1985). Mathematicsin the streets and in schools. British Journal of Developmental Psychology, 3, 21-29.
Catterall, J. S. (2007). Enhancing peer conflict resolution skills through drama: an experimental study. Research in Drama Education: The Journal of Applied Theatre and Performance, 12(2), 163-178.
Chronaki, A. (1990). An investigation of the potentiality of using drama in the teaching of mathematics in secondary school, Unpublished Master Dissertation, University of Bath.
D'Ambrosio, U. (2007a). Ethnomathematics: Perspectives. North American Study Group on Ethnomathematics News 2(1), 2-3.
D‘Ambrosio, U. (2007b). Preface Proceedings.10th International Congress of Mathematics Education, Discussion Group 15: Ethnomathematics, Tipografia Editrice Pisana, Pisa.
D‘Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics , 5(1), 44-48. (Reprinted in Powell & Frankenstein, 1997)
De La Roche, E. (1993). Drama, critical thinking and social issue (ERIC Document Reproduction Service ED379172).
Dodge, B. (1997). Some thoughts about WebQuests. The WebQuest Page. Retrieved April 22, 2006, from http://webquest.sdsu.edu/about_webquests.html
Duatepe, A. (2004). The effects of Drama based instruction on seventh grade students’ Geometry achievement, Van Hiele geometric thinking levels, attitude toward Mathematics and Geometry. PhDThesis submitted to the Graduate School of Natural and Applied Sciences 0f Middle East Technical University.
Dürdane, L. (2009). Drama and the enhancement of creativity: A review of research. In Christopher Crouch (Ed.) Subjectivity Creativity, and the Institution (pp.165-178). Florida, USA: Brown Walker Press.
Eglash, R. (1999). African Fractals: Modern computing and indigenous design. New Brunswick, NJ: Rutgers University Press.
Ersou, E. (2014). Polygons Teaching Through Creative Drama in Mathematics Teaching. American Journal of Educational Research, 2(6), 372-377.
Fawcett, H. (1938). The nature of proof (NCTM Yearbook) NY: Columbia University Teachers College Bureau of Publications.
Fleming M., Merell C., Tymms (2004). P., The impact of Drama on pupils‘ language, mathematics, and attitude in two primary schools. Research in Drama Education, 9(2), 177-197.
Fletcher, T. J. (1971). The teaching of Geometry. Present problems and future aims. Educational Studies in Mathematics, 3, 395-412.
Foster, M. and Foster, R. (2002). Numeracy all around: developing childrens‘ mathematics through role play and directed daily experience. In Cooper, H. and Sixsmith, C. (Ed.),Teaching across the early years 3-7, v.1, part 4 ( pp.189-195). October 2002, Routledge.
François, K. (2009). The role of Ethnomathematics within Mathematics Education. CERME6, Lyon, France.
Freudenthal, H. (1971). Geometry between the devil and the deep sea. Educational Studies in Mathematics, 3, 413-435.
Gadanidis, G., Gadanidis, J. M., Huang, A. (2005). Using Humor to Gain Mathematical Insight. Mathematics Teaching in the Middle School, 10 (5), 244-250 .
Gay, J., & Cole, M. (1967). The New Mathematics in an Old Culture. New York: Holt, Rienhart and Winston.
Gensrick, J. (1992) Drama in education : using ‘Mantle of the Expert’ in the teaching of mathematics. Thesis (M.A.)--University of Wisconsin--Madison Holden, 2002.
Gerdes, P. (2005). Lunda Symmetry where Geometry meets Art. The Visual Mind II, MIT Press, Boston, 335-348.
Gerdes, P. (1991). On mathematical elements in the Tchokwe drawing tradition. Discovery and Innovation, lournal of the African Academy of Sciences, 3(1), 29-36.
Gerdes, P. (1988). On culture, Geometrical thinking and Mathematics Education. Educational Studies in Mathematics, 19, 137-172.
Gerdes, P. (1986). How to recognize hidden geometrical thinking: A contribute to the development of anthropological mathematics. For the Learning of Mathematics, 6(2), 10-12/17.
Gerofsky, S. Gerofsky, S. (2009). Performance mathematics and democracy. Educational Insights 13(1), Special issue ―Performing the Sign‖. Available at http://einsights.ogpr.educ.ubc.ca/v13n01/toc.html
Harris, P. (1980). Measurement in tribal Aboriginal Communities. Northern Territory Department of Education, Australia.
Huizinga, J. (1949). Homo Ludens. London: Routledge and Kegan Paul.
Johnson, C. (2002). Drama and metacognition. Early Child Development and Care, 172 (6), 595-602.
Jones, K. (2011). The value of learning geometry with ICT: lessons from innovative educational research. In A. Oldknow, & C. Knights (Eds.), Mathematics Education with Digital Technology (pp. 39-45). London, GB: Continuum, (Education and Digital Technology).
Kayhan H. C. (2008). Effect of Creative Drama as a teaching method on Attitudes towards Mathematics. In proceedings of International congress of Drama/Theatre in Education, (pp. 277-278). Ankara (21-23 November).
Kayhan, H.C. (2004). Yaratici Dramanin Ilkögretim 3. Sinif Matematik Dersinde Ögrenmeye, Bilgilerin Kaliciligina ve Matematige Yönelik Tutumlara Etkisi. Yayinlanmamis Yüksek .Lisans Tezi Ankara.
Kohn, A. (1993). Punished by rewards: The trouble with gold stars, incentive plans, A’s, praise, and other bribes. New York: Houghton Mifflin.
Kotarinou, P., Stathopoulou, C, (2015) Using Drama Techniques for Facilitating Democratic Access to Mathematical Ideas for all Learners. In U., Gellert, J., Gimenez Rodriguez, C., Hahn, S. Kafoussi, (Eds.) Educational Paths to Mathematics. A C.I.E.A.E.M. Sourcebook (pp.327-344). Springer.
Kotarinou, P., Stathopoulou, Ch. (2012). The History of 5th postulate: linking mathematics with other disciplines through Drama techniques. In proceedings of CERME8: Working Group 12:History in mathematics education (pp. 2010-2019). Antalya, Turkey, (6-10, February 2013).
Kotarinou, P., Stathopoulou Ch. (2008). Role –playing in Mathematics instruction, in proceedings of the 13th International congress of Drama/Theatre in Education, Ankara 21-23 November 2008, (pp. 108-118). Ankara, (21-22-23 November 2008).
Kotarinou, P. , Stathopoulou, Ch., Chronaki, A. (in press) Teaching no Euclidean Geometries through Drama in Education: Creativity for enhancing mathematics teaching . Mediterranean Journal for Research in Mathematics Education.
Kotarinou, P., Chronaki, A., Stathopoulou, C. (2010). Debating for ‗one measure for the world‘: Sensitive pendulum or heavy earth? In U. Gellert, E. Jablonka and C. Morgan (Eds.), Proceedings of Mathematics Education and Society 6th International Conference (pp. 322-329). Berlin: Freie Universität Berlin
Laborde, C., Kynigos, C., Hollebrands, K. and Strässer, R. (2006). Teaching and Learning Geometry with Technology. In A. Guitiérrez and P. Boero (Eds.) Handbook of research on the psychology of Mathematics Education: Past, Present and Future (pp. 275-304). Rotterdam: Sense Publishers.
Lancy, D. F. (1983). Cross-cultural Studies in Cognition and Mathematics. New York: Academic Press.
Lawrence, H. S. (2000). A Visit from Pythagoras--Using Costumes in the Classroom. Mathematics Teacher, 93(8), 652-55
Mayer, B. (2005). Game-based learning. Presentation, Retrieved 15-10-2014 from http://css.uni-graz.at/courses/TeLearn/SS05/Presentations/Game Based_Learning.pdf
Millroy, W. (1992). An Ethnographic Study of the Mathematical Ideas of a Group of Carpenters. Journal for Research in Mathematics Education, Monograph, no 5.
Moje, E. B., Ciechanowski, K. M., Kramer, K., Ellis, L., Carrillo, R., & Collazo, T. (2004). Working toward third space in content area literacy: An examination of everyday funds of knowledge and discourse. Reading Research Quarterly, 39, 38-72.
Mukhopadhyay, S. (2009). The decorative impulse: Ethnomathematics and Tlingit basketry. Zentralblatt für Didaktik der Mathematik, 41(1-2), 117–130.
Neelands, J. (1984). Making sense of Drama. A guide to Classroom Practice, Heinemann Educational Books.
November, A. (2012). Who owns the Learning? Preparing students for success in the digital age. Blooomington, IN: Solution Tree Press.
Omniewski, R. (1999). The Effects of an Arts Infusion Approach on the Mathematics Achievement of Second-Grade Students. Doctoral Dissertation, Kent State University, Dissertation Abstracts International, 60(05), 1389 A.
O‘ Neil, C. & Lambert, A. (1990). Drama Strucrures. Apractical Handbook for Teachers. Stanley Thornes (Publishers) Ltd.
Orey, D., & Rosa, M. (2007). Ethnomathematics and the teaching and learning mathematics from a multicultural perspective ICME 10, Proceeding F. Favilli, (Ed.), Ethnomathematics and Mathematics Education, Proceedings of the 10th International Congress of Mathematics Education, Discussion Group 15: Ethnomathematics, Tipografia Editrice Pisana, Pisa, pp. 139-140.
Orey, D, & Rosa, M. (2006). Ethnomathematics: Cultural Assertions and Challenges Towards Pedagogical Action. Journal of Mathematics and Culture, 6(1) ISSN – 1558-5336.
Oswalt, W. H. (1976). An Anthropological Analysis of Food-getting Technology. New York: Wiley.
Pennington, E & Faux, G. (1999). ‘‘…No Royal Road to Geometry’’ A ten lesson project in Mathematics, History & Drama for year5 or 6, Education Initiatives, Cardew Farm, Dalston, Carlisle.
Pinxten, R. (1994). Anthropology in the mathematics classroom? In Lerman, S., editor, Cultural Perspectives on the Mathematics Classroom, pages 85–97. Kluwer Academic Publishers, Dordrecht.
Pompeu, G. Jr. (1992). Bringing Ethnomathematics into the school curriculum. (Unpublished Doctoral Dissertation). University of Cambridge, UK
Saab, J. (1987). The effects of creative Drama methods on mathematics achievement, attitudes and creativity. PhD Dissertation Education D., West Virginia University.
Scribner, S. (1974). Developmental aspects of categorized recall in a West African society. Cognitive Psychology, 6(4), 475-494
Somers, J. (2001). Drama in Education: what teachers and students do. Theater and Education, 1, 5-9.
Somers, J. (1994). Drama in the curriculum. London: Cassell.
Starr, L. (2005). Wire side chats: Meet Bernie Dodge: the Frank Lloyd Wright of learning environments!. Education World. Retrieved October 15, 2014, from http://www.educationworld.com/a_issues/chat/chat015.shtml
Saxe, G. B. (1988). Candy selling and math learning. Educational Researcher, 17(6), 14-21.
Stathopoulou, C. (2007). Traditional patterns in Pyrgi of Chios (Greece): Their Role in the Community and the Incorporated Mathematical Ideas. Nexus Network Journal, 9(1), 103-117.
Stathopoulou, C. (2006a). Symmetry and gold section: two mathematical ideas incorporated in the tradition of ‘Xysta’ (Pyrgi-Chios-Greece). Οpen presentation in Third International Conference on Ethnomathematics, Auckland, New Zealand.
Stathopoulou, C. (2006b). Exploring Informal mathematics of Craftsmen in the designing tradition of ‗xysta‘ at Pyrgi of Chios. For the Learning of Mathematics 26(3). pp. 9-16.
Stathopoulou, C.; Chronaki, A.; Kotarinou, P. (2013). Establishing the use of 'metre' as a measure unit: an interdisciplinary approach for teaching mathematics. Teaching Mathematics and Its Applications doi:10.1093/teamat/hrt016 , pp.1-17.
Stathopoulou, C., & Kotarinou, P. (2008). Using Ethnomathematical ideas for designing an interdisciplinary project through a WebQuest, ICME-11, Monterrey, Mexico.
Vithal, R. (1992). The Construct of Ethnomathematics and Implications for Curriculum Thinking in South Africa. (Mphil thesis). University of Cambridge.
Vithal, R., & Skovsmose, O. (1997). The end of innocence: A critique of Ethnomathematics. Educational Studies in Mathematics, 34(2), 134-157.
Wagner, B. (1999a). Dorothy Heathcote. Drama as a Learning Medium. Portsmouth: Heinemann.
Wagner, B. (1999b). Attitudes, Behavior and Moral reasoning In Betty Wagner (Ed.) Building Moral Communities Through Educational Drama. London: Alex Publishin Corporation
Wilburne, J., Napoli M., (2007). Integrating Literature and Mathematics: A mysterious connection. Mathematics Teaching in the Middle School, 13(3), 134-139.
Wooland, B. (1999). Teaching Drama in the public school. Athens: Hellinika Grammata.
Yassa, N. (1999). High School Students‘ Involvement in Creative Drama:The Effects on Social Interaction.
Research in Drama and Theatre in Education, 4 (1), 37-51.
Zaslavsky, C. (1973). Africa Counts. Boston: Prindle, Weber and Schmidt, Inc.
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