An Anthropological Analysis of the Knowledge on Graphics within Middle School Mathematics

Year 2018, Issue: 13, 95 - 119, 25.01.2018

Nazlı Akar Filiz Tuba Dikkartın Övez

Abstract

        The aim of this study
is to analyze the knowledge on graphics within middle school mathematics from
an anthropological perspective. The study, which was carried out in framework
of the Anthropological Theory of the Didactic, conducted a document analysis
with the purpose of determining the institutional qualities of middle school
mathematics. In this context, the study examined a variety of documents
including mathematics curriculums that are used in Elementary Mathematics
Special Teaching Methods institutions in addition to middle school mathematics
course books, books on mathematics instruction, and the notes taken by faculty
members. The data that were obtained from document analysis were analyzed with
ecological and praxeological approaches. Based on the ecological approach, the
study identified the qualities of institutional recognition by revealing the
habitat and function (niche) of the graphic knowledge in its institution, while
the praxeological approach revealed the mathematical organizations consisting
the types of graphic-related tasks in the institution, techniques, the technologies
that explain the technique, and the theories which explain and defend the
necessity of the technology. The study concluded that the use of graphics as a
goal, a tool, and both as goal and tool the institution was addressed to the
instruction of subjects (ratio and proportion, percentage, curves, equations
and inequalities, equation systems, functions, statistics, and probability) in
numbers and operations, algebra and data processing learning fields, for the
improvement of mathematics literacy, problem-solving, communication,
association, and psycho-motor skills. The research institution employed three
mathematical organizations (graphic reading and interpretation, graphic
creating, making appropriate conversions between graphics) including 11 types of
tasks in total.

Keywords

Anthropological Theory of the Didactic, ecological approach, graphic, praxeological approach

References

• Altun, M. (2016). Teaching mathematics in secondary schools (5th, 6th, 7th and 8th graders) (16th Edition). Bursa: Aktüel.
• American Statistical Association. (1915). Joint committee on standards for graphic presentation. Publications of the American Statistical Association, 14(112), 790-797.
• Artigue, M., & Winsløw, C. (2010). International comparativestudies on mathematics education: A view point from the anthropological theory of didactics. Recherches en Didactiques des Mathématiques, 30(1), 47-82.
• Baykul, Y. (2014). Teaching mathematics in secondary schools (2nd Edition). Ankara: Pegem.
• Bertin. J. (1967). Semiologie graphique: Les diagrammes-les reseaux-les cartes. The Hague: Mouton.
• Bilen, O. (2017). Secondary school mathematics textbook 7. Ankara: Gizem Publishing, ISBN: 978-975-7000-79-2.
• Bosch, M., & Gascón, J. (2006). Twenty-five years of the didactic transposition. ICMI Bulletin, 58, 51-65.
• Brousseau, G. (2002). Theory of didactical situations in mathematics. N. Balacheff, M. Cooper, R. Sutherland, & V. Warfield (Eds. & Trans.). Dordrecht, The Netherlands: Kluwer Academic.
• Cai, J., & Lester, F. K. (2005). Solution representations and pedagogical representations in Chinese and US classrooms. The Journal of Mathematical Behavior, 24(3), 221-237.
• Chevallard, Y. (1991). La transposition didactique – du savoir savant au savoir enseigné (first edition, 1985). Grenoble: La Pensée Sauvage.
• Chevallard, Y. (1992). A theoretical approach to curricula. Journal fuer Mathematik-Didaktik, 13(2-3), 215-230.
• Chevallard, Y., & Sensevy, G. (2014). Anthropological approaches in mathematics education, French perspectives. In Encyclopedia of Mathematics Education (pp. 38-43). Springer Netherlands.
• Chevallard, Y., Bosch, M., & Kim, S. (2015). What is a theory according to the anthropological theory of the didactic?. In CERME 9-Ninth Congress of the European Society for Research in Mathematics Education (pp. 2614-2620).
• Cırıtcı, H., Gönen, İ., Kavas, D., Özarslan, M., Pekcan, N. & Şahin, M. (2017). Secondary school mathematics textbook 5. İstanbul: Bilnet.
• Cleveland, W. S., & McGill, R. (1984). Graphical perception: Theory, experimentation, and application to the development of graphical methods. Journal of the American statistical association, 79(387), 531-554.
• Cohen, D. K., McLaughlin, M., & Talbert, J. (1993). Teaching for understanding: Challenges for practice, research and policy.
• Duval, R. (1999). Representation, Vision and Visualization: Cognitive Functions in Mathematical Thinking. Basic Issues for Learning (ERIC Documentation Reproduction Service No. ED 466 379).
• Ersoy, Y. (2006). Innovations in primary education mathematics curriculum-I: Objective, content and achievements. İlköğretim Online, 5(1), 30-44.
• Friel, S. N., Curcio, F. R., & Bright, G. W. (2001). Making sense of graphs: Critical factors influencing comprehension and instructional implications. Journal for Research in Mathematics Education, 124-158.
• Güven, D. (2017). Ortaokul matematik 6. Ankara: Mega.
• Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics, 65-97.
• Higher Education Board (2017). Primary School Mathematics Teaching Undergraduate Program. Higher Education Board. Ankara. Retrieved from http://www.yok.gov.tr/documents/10279/49665/ilkogretim_matematik/cca48fad-63d7-4b70-898c-dd2eb7afbaf5 on 10.07.2017.
• Kaput, J. J. (1987). Representation systems and mathematics. Problems of Representation in the Teaching and Learning of Mathematics, 19-26.
• Long, B. L. (Ed.). (2000). International Environmental Issues and the OECD 1950-2000: An historical perspective. OECD Publishing.
• MoNE, (2013). Secondary School Mathematics Course 5, 6, 7 and 8 Curriculum. Board of Education and Training Committee. Ankara. Retrieved from: http://ttkb.meb.gov.tr/program2.aspx on 24.03.2017.
• MoNE, (2017). Mathematics Course Curriculum (Elementary and Secondary Schools 1, 2, 3, 4, 5, 6, 7 and 8 Graders). Board of Education and Training Committee. Ankara. Retrieved from: http://mufredat.meb.gov.tr/ProgramDetay.aspx?PID=191 on 04.01.2018.
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage. National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.
• Pinker, S. (1990). A theory of graph comprehension. Artificial intelligence and the future of testing, 73-126.
• Roth, W. M., & Bowen, G. M. (2003). When are graphs worth ten thousand words? An expert-expert study. Cognition and Instruction, 21(4), 429-473.
• Sağlam-Arslan, A. (2004). Les équations différentielles en mathématiques et en physique: Etude des conditions de leur enseignement et caractérisation des rapports personnels des étudiants de première année d’université à cet objet de savoir, Thèse de doctorat, Université Joseph Fourier, Grenoble.
• Schultz, J. E., & Waters, M. S. (2000). Why representations?. The Mathematics Teacher, 93(6), 448-453.
• Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77(1), 20-26.
• Skiersko, A. (1991). Textbook selection and evaluation, in M. Celce-Murcia (ed.), Teac¬hing English as a Second or Foreign Language, Boston, Heinle & Heinle, pp. 432-453.
• Therer, J. (1992). Nouveaux concepts en didactique des Sciences, Bulletin de la Société géographique de Liège, 28.
• Thomas, G. B., Weir, M. D., & Hass, J. (2012). Thomas Kalkülüs. (M. Bayram, Trans.). İstanbul: Pearson. Üstündağ-Pektaş, Y. (2017). Secondary school mathematics 8th grade textbook. Ankara: Öğün.
• Van de Walle, J. A., & Karp, K. S. Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7th Edition) United State: Pearson Education.
• Vergnaud, G. (1990). 'Epistemology and psychology of mathematics education.', in J. Kilpatrick and P. Nesher (ed.) Mathematics and Cognition: A Research Synthesis by the International Group for the Psychology of Mathematics Education, Cambridge: Cambridge University Press, 14-30.
• Winn, W. (1991). Learning from maps and diagrams. Educational Psychology Review, 3(3), 211-247.
• Winsløw, C. (2011). Anthropological theory of didactic phenomena: some examples and principles of its use in the study of mathematics education. Un Panorama de TAD, CRM Docume, 117-138.
• Yıldırım, A., & Şimşek, H. (2013) Qualitative research methods in the social sciences (9th Edition). Ankara: Seçkin.