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Öğrencilerin “Geometrik Yer” Kavrayışlarının Analizi

Year 2016, Volume: 10 Issue: 2, 186 - 209, 30.12.2016
https://doi.org/10.17522/balikesirnef.277491

Abstract

Bu araştırmada kBk modelini kullanarak “geometrik yer” kavramı ile ilgili öğrenci kavrayışlarını
ortaya çıkarmak amaçlanmıştır. Bu amaç için İç Anadolu bölgesinde yer alan bir
büyükşehirdeki özel dershanede kursa devam eden ve araştırmaya gönüllü olarak
katılan 12 tane 10. sınıf öğrencisi ikişerli olarak gruplandırılmış ve
öğrencilerden bir çalışma yaprağındaki “geometrik yer” kavramı ile ilgili 5
tane soruyu cevaplamaları istenmiştir. İlk önce bu sorular temel alınarak
araştırmacılar tarafından kBk modeli yoluyla “geometrik yer” kavramının
kavramsal yapısı ortaya çıkarılmıştır. Daha sonra öğrencilerin bu sorulara
verdikleri cevaplar kullanılarak, “geometrik yer” kavramı ile ilgili
kavrayışlar analiz edilmiştir. Son olarak bu analizler karşılaştırılmış ve
yorumlanmıştır. Yapılan bu karşılaşmada, öğrencilerin sahip olduğu “geometrik
yer” ile ilgili kavrayışlarının sezgisel olduğu, öğrencilerin uygun olamayan
kavrayışlara sahip oldukları ve bu kavrayışlarını irdelemeksizin kullandıkları
sonucuna varılmıştır. Bu araştırmada amaç “geometrik yer” kavramını incelemek
olmasına rağmen, “grafik” kavramı ile ilgili ilginç sonuçlar ile de
karşılaşılmıştır.

References

  • Adams, W. M. (1866). Outlines of geometry; or, the motion of a point. Melborne: BiblioBazaar
  • Atallah, F. (2003). Mathematics through their eyes: Student conceptions of mathematics in everyday life. Unpublished doctoral dissertation, Concordia University, Canada.
  • Balacheff, N. (2000). A modeling challenge: untangling learners’ knowing, Journées Internationales d’Orsay sur les Sciences Cognitives: L’apprentissage, Paris. http://www-didactique.imag.fr/Balacheff/TextesDivers/JIOSC2000.html.
  • Balacheff, N., & Gaudin, N. (2002). Students conceptions: an introduction to a formal characterization, Cahier du laboratoire Leibniz 65, http://wwwleibniz.imag.fr/LesCahiers/Cahiers2002.html.
  • Balacheff, N., & Gaudin, N. (2003). ‘Baghera assessment project’ , In S. Soury-Lavergne (Ed.), Baghera Assessment Project: Designing an Hybrid and Emergent Educational Society. Les Cahiers du Laboratoire Leibniz, 81, Grenoble, Laboratorie Leibniz-IMAG.
  • Balacheff, N., & Gaudin, N. (2010). Modeling students’ conceptions: The case of function. Research in collegiate mathematics education, 7, 207–234.
  • Bishop, A. J. (2002). Critical challenges in researching cultural issues in mathematics education. Journal of Intercultural Studies in Education, 23(2), 119–131.
  • Breidenbach, D. , Dubinsky, E., Hawals, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 2, 247–285.
  • Brousseau G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic Publishers.
  • Brousseau, G., Brousseau, N., & Warfield, V. (2004). Rationals and decimals as required in the school curriculum. Part 1: Rationals as measurements. Journal of Mathematical Behavior, 23, 1–20.
  • Casey, J. (1888). A sequel to the first six books of the elements of Euclid, containing an easy introduction to modern geometry with numerous examples. Dublin: Hodges Figgis.
  • Cha, S., & Noss, R. (2002). Designing to exploit dynamic-geometric intuitions to make sense of functions and graphs, In A. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 209–216). Norwich, UK.
  • Chieu,V. M. & Herbst, P. (2011). Designing an intelligent teaching simulator for learning to teach by practicing. ZDM-The International Journal of Mathematics Education, 43, 105–117
  • Clement J., Mokros, J. R., & Schultz, K. (1986). Adolescents’ graphing skills: A descriptive analysis. The Annual Meeting of the American Educational Research Association, San Francisco.
  • Heath, T.L. (1961). Apollonius of Perga. Great Britain: Cambridge University.
  • Gorghiu, G., Păuna, N., & Gorghiu, L. M. (2009). Solving geometrical locus problems using dynamic interactive geometry applications. In A. Méndez-Vilas, A. Solano Martín, J.A. Mesa González. & J. Mesa González (Eds.), Research, Reflections and Innovations in Integrating ICT in Education (pp. 814–818). Badajoz, Spain: Formatex.
  • Greeno, J. G., & R. P. Hall., (1997). Practicing Representation: Learning with and about representational forms. Phi Delta Kappan, 78(5), 361–367.
  • Kaldrimidou M., & Tzakaki M., (2005). Theoretical issues in research of mathematics education: some considerations. In M. Bosch (Ed), The Fourth Congress of the European Society for Research in Mathematics Education (pp. 1244–1253). Sant Feliu de Guíxols, Spain
  • Maracci, M., (2003). Difficulties in vector space theory: A compared analysis in terms of conceptions and tacit models. In N.A. Pateman, B. J. Doherty, & J. Zilliox (Eds.). Proceedings of the 27th Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 229–236). Honolulu, Hawaii, USA.
  • Maracci, M. (2006). On students’ conceptions in vector space theory. In J. Novotná, H. Moraová, M. Krátká y N. Stehlíková (Eds.). Proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education (pp.129–136). Prague, Czech Republic.
  • Martínez-Planell R., Gonzalez, A. C., DiCristina G., & Acevedo, V. (2012). Students’ conception of infinite series. Educational Studies in Mathematics, 81, 235–249.
  • Mesa, V. (2004). Characterizing practices associated with functions in middle school textbooks: an empirical approach. Educational Studies in Mathematics, 56, 255–286.
  • Mesa, V. (2010). Strategies for controlling the work in mathematics textbooks for introductory calculus. Research in Collegiate Mathematics Education, 7, 235–265.
  • Miyakawa, T. (2004). Reflective symmetry in construction and proving. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the International Group for the Psychology of Mathematics Education (pp. 337–344). Bergen, Norway.
  • Modestou, M., & Gagatsis, A. (2013). A didactical situation for the enhancement of meta-analogical awareness. Journal of Mathematical Behavior, 32, 160– 172.
  • Nathan, M. J., & Bieda, K. N. (2006). What gesture and speech reveal about students’ interpretations of Cartesian graphs: Perceptions can bound thinking. Wisconsin Center for Education Research. (WCER Working Paper No. 2006-2).
  • Páez Murillo, R. E., &Vivier L. (2013). Teachers’ conceptions of tangent line. Journal of Mathematical Behavior, 32, 209– 229.
  • Parmar, R. S., & Signer, B. R. (2005). Sources of error in constructing and interpreting graphs: A study of fourth- and fifth-grade students with LD. Journal of Learning Disabilities, 38(3), 250–261.
  • Patton, M. Q. (2002). Qualitative research & evaluation methods. Thousand Oaks, CA: Sage.
  • Roth W., & Lee, Y. J. (2004). Interpreting unfamiliar graphs: A generative, activity theoretic model. Educational Studies in Mathematics, 57,265–290.
  • Selden, A., & Selden J. (1992). Research perspectives on conceptions of function: Summary and overview. In E. Dubinsky & G. Harel (Eds.). The Concept of Function: Aspects of Epistemology and Pedagogy. (pp. 1–16). MAA Notes 25: Mathematical Association of America.
  • Sfard, A. (1992). On the dual nature of mathematical conceptions: Reflections on process and objects on different sides of the same coin. Educational Studies in Mathematics, 22, 1–36.
  • Sierpinska, A. (1992). On understanding the notion of function. In E. Dubinsky & G. Harel (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy. (pp. 22–58). MAA Notes 25: Mathematical Association of America.
  • Skemp, R. R. (1986). The psychology of learning mathematics. (2nd ed.). Middlesex, England: Penguin Books.
  • Tayler, J. (1993). Some thoughts on locus - Its place in the 2 unit syllabus. Journal of the Mathematical Association of NS. November.
  • http://hsc.csu.edu.au/maths/teacher_resources/2384/prof_reading/journals/tayler/tayler.htm
  • Thompson, A. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In A. D. Grows (Ed.). Handbook of research on mathematics learning and teaching. (pp. 127–146). Macmillan, New York.
  • Vadcard, L., & Luengo, V. (2005). Interdisciplinary approach for the design of a learning environment.. In G. Richards (Ed.), Proceedings of World Conference on E-Learning in Corporate, Government, Healthcare, and Higher Education 2005 (pp. 2461-2468). Chesapeake, VA: AACE.
  • Vergaund, G. (1998). A comprehensive theory of representation for mathematics education. Journal of Mathematical Behavior, 17(2), 167–181.
  • Webber, C., Pesty S., & Balacheff, N. (2002). A multi-agent and emergent approach to learner modelling. In F. van Harmelen (Ed.). Proceedings of the 15th European Conference on Artificial Intelligence. Amsterdam: IOS Press.
  • Webber, C., & Pesty, S. (2002). Emergent Diagnosis via Coalition Formation. In F.J. Garijo, J.C. Riquelme, and M. Toro (Eds.). VIII Iberoamerican Conference on Artificial Intelligence (pp. 755–764) Seville, Spain.
  • Yıldırım, A. ve Şimşek, H. (2006). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayıncılık.

Analyzing Students’ Conceptions of “Geometric Locus”

Year 2016, Volume: 10 Issue: 2, 186 - 209, 30.12.2016
https://doi.org/10.17522/balikesirnef.277491

Abstract

In this paper we investigate students’ conceptions of “geometric locus” by using the cK¢ model. For this purpose, we formed 6 groups, each of which consisted of two 10th grade students, who were studying in a big city in the Central Anatolian region. We asked the participants 5 questions related to the “geometric locus” concept. In light of the literature, we firstly revealed the conceptual structure of “geometric locus”. Later, students’ conceptions about this concept have been analyzed by comparing students’ responses to these questions and conceptual structure of “geometric locus” concept. The analyses we have conducted with the data suggest that students’ conceptions were not convenient, moreover; they did not have exact conceptions about the core of concepts and they were not able to correctly explain each situation. Although the main focus was on the “geometric locus”, we have obtained interesting outcomes related to “graphic”.

References

  • Adams, W. M. (1866). Outlines of geometry; or, the motion of a point. Melborne: BiblioBazaar
  • Atallah, F. (2003). Mathematics through their eyes: Student conceptions of mathematics in everyday life. Unpublished doctoral dissertation, Concordia University, Canada.
  • Balacheff, N. (2000). A modeling challenge: untangling learners’ knowing, Journées Internationales d’Orsay sur les Sciences Cognitives: L’apprentissage, Paris. http://www-didactique.imag.fr/Balacheff/TextesDivers/JIOSC2000.html.
  • Balacheff, N., & Gaudin, N. (2002). Students conceptions: an introduction to a formal characterization, Cahier du laboratoire Leibniz 65, http://wwwleibniz.imag.fr/LesCahiers/Cahiers2002.html.
  • Balacheff, N., & Gaudin, N. (2003). ‘Baghera assessment project’ , In S. Soury-Lavergne (Ed.), Baghera Assessment Project: Designing an Hybrid and Emergent Educational Society. Les Cahiers du Laboratoire Leibniz, 81, Grenoble, Laboratorie Leibniz-IMAG.
  • Balacheff, N., & Gaudin, N. (2010). Modeling students’ conceptions: The case of function. Research in collegiate mathematics education, 7, 207–234.
  • Bishop, A. J. (2002). Critical challenges in researching cultural issues in mathematics education. Journal of Intercultural Studies in Education, 23(2), 119–131.
  • Breidenbach, D. , Dubinsky, E., Hawals, J., & Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 2, 247–285.
  • Brousseau G. (1997). Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic Publishers.
  • Brousseau, G., Brousseau, N., & Warfield, V. (2004). Rationals and decimals as required in the school curriculum. Part 1: Rationals as measurements. Journal of Mathematical Behavior, 23, 1–20.
  • Casey, J. (1888). A sequel to the first six books of the elements of Euclid, containing an easy introduction to modern geometry with numerous examples. Dublin: Hodges Figgis.
  • Cha, S., & Noss, R. (2002). Designing to exploit dynamic-geometric intuitions to make sense of functions and graphs, In A. Cockburn & E. Nardi (Eds.), Proceedings of the 26th Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 209–216). Norwich, UK.
  • Chieu,V. M. & Herbst, P. (2011). Designing an intelligent teaching simulator for learning to teach by practicing. ZDM-The International Journal of Mathematics Education, 43, 105–117
  • Clement J., Mokros, J. R., & Schultz, K. (1986). Adolescents’ graphing skills: A descriptive analysis. The Annual Meeting of the American Educational Research Association, San Francisco.
  • Heath, T.L. (1961). Apollonius of Perga. Great Britain: Cambridge University.
  • Gorghiu, G., Păuna, N., & Gorghiu, L. M. (2009). Solving geometrical locus problems using dynamic interactive geometry applications. In A. Méndez-Vilas, A. Solano Martín, J.A. Mesa González. & J. Mesa González (Eds.), Research, Reflections and Innovations in Integrating ICT in Education (pp. 814–818). Badajoz, Spain: Formatex.
  • Greeno, J. G., & R. P. Hall., (1997). Practicing Representation: Learning with and about representational forms. Phi Delta Kappan, 78(5), 361–367.
  • Kaldrimidou M., & Tzakaki M., (2005). Theoretical issues in research of mathematics education: some considerations. In M. Bosch (Ed), The Fourth Congress of the European Society for Research in Mathematics Education (pp. 1244–1253). Sant Feliu de Guíxols, Spain
  • Maracci, M., (2003). Difficulties in vector space theory: A compared analysis in terms of conceptions and tacit models. In N.A. Pateman, B. J. Doherty, & J. Zilliox (Eds.). Proceedings of the 27th Annual Conference of the International Group for the Psychology of Mathematics Education (pp. 229–236). Honolulu, Hawaii, USA.
  • Maracci, M. (2006). On students’ conceptions in vector space theory. In J. Novotná, H. Moraová, M. Krátká y N. Stehlíková (Eds.). Proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education (pp.129–136). Prague, Czech Republic.
  • Martínez-Planell R., Gonzalez, A. C., DiCristina G., & Acevedo, V. (2012). Students’ conception of infinite series. Educational Studies in Mathematics, 81, 235–249.
  • Mesa, V. (2004). Characterizing practices associated with functions in middle school textbooks: an empirical approach. Educational Studies in Mathematics, 56, 255–286.
  • Mesa, V. (2010). Strategies for controlling the work in mathematics textbooks for introductory calculus. Research in Collegiate Mathematics Education, 7, 235–265.
  • Miyakawa, T. (2004). Reflective symmetry in construction and proving. In M. J. Høines & A. B. Fuglestad (Eds.), Proceedings of the 28th conference of the International Group for the Psychology of Mathematics Education (pp. 337–344). Bergen, Norway.
  • Modestou, M., & Gagatsis, A. (2013). A didactical situation for the enhancement of meta-analogical awareness. Journal of Mathematical Behavior, 32, 160– 172.
  • Nathan, M. J., & Bieda, K. N. (2006). What gesture and speech reveal about students’ interpretations of Cartesian graphs: Perceptions can bound thinking. Wisconsin Center for Education Research. (WCER Working Paper No. 2006-2).
  • Páez Murillo, R. E., &Vivier L. (2013). Teachers’ conceptions of tangent line. Journal of Mathematical Behavior, 32, 209– 229.
  • Parmar, R. S., & Signer, B. R. (2005). Sources of error in constructing and interpreting graphs: A study of fourth- and fifth-grade students with LD. Journal of Learning Disabilities, 38(3), 250–261.
  • Patton, M. Q. (2002). Qualitative research & evaluation methods. Thousand Oaks, CA: Sage.
  • Roth W., & Lee, Y. J. (2004). Interpreting unfamiliar graphs: A generative, activity theoretic model. Educational Studies in Mathematics, 57,265–290.
  • Selden, A., & Selden J. (1992). Research perspectives on conceptions of function: Summary and overview. In E. Dubinsky & G. Harel (Eds.). The Concept of Function: Aspects of Epistemology and Pedagogy. (pp. 1–16). MAA Notes 25: Mathematical Association of America.
  • Sfard, A. (1992). On the dual nature of mathematical conceptions: Reflections on process and objects on different sides of the same coin. Educational Studies in Mathematics, 22, 1–36.
  • Sierpinska, A. (1992). On understanding the notion of function. In E. Dubinsky & G. Harel (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy. (pp. 22–58). MAA Notes 25: Mathematical Association of America.
  • Skemp, R. R. (1986). The psychology of learning mathematics. (2nd ed.). Middlesex, England: Penguin Books.
  • Tayler, J. (1993). Some thoughts on locus - Its place in the 2 unit syllabus. Journal of the Mathematical Association of NS. November.
  • http://hsc.csu.edu.au/maths/teacher_resources/2384/prof_reading/journals/tayler/tayler.htm
  • Thompson, A. (1992). Teachers’ beliefs and conceptions: A synthesis of the research. In A. D. Grows (Ed.). Handbook of research on mathematics learning and teaching. (pp. 127–146). Macmillan, New York.
  • Vadcard, L., & Luengo, V. (2005). Interdisciplinary approach for the design of a learning environment.. In G. Richards (Ed.), Proceedings of World Conference on E-Learning in Corporate, Government, Healthcare, and Higher Education 2005 (pp. 2461-2468). Chesapeake, VA: AACE.
  • Vergaund, G. (1998). A comprehensive theory of representation for mathematics education. Journal of Mathematical Behavior, 17(2), 167–181.
  • Webber, C., Pesty S., & Balacheff, N. (2002). A multi-agent and emergent approach to learner modelling. In F. van Harmelen (Ed.). Proceedings of the 15th European Conference on Artificial Intelligence. Amsterdam: IOS Press.
  • Webber, C., & Pesty, S. (2002). Emergent Diagnosis via Coalition Formation. In F.J. Garijo, J.C. Riquelme, and M. Toro (Eds.). VIII Iberoamerican Conference on Artificial Intelligence (pp. 755–764) Seville, Spain.
  • Yıldırım, A. ve Şimşek, H. (2006). Sosyal Bilimlerde Nitel Araştırma Yöntemleri. Ankara: Seçkin Yayıncılık.
There are 42 citations in total.

Details

Journal Section Makaleler
Authors

Gönül Yazgan-sağ

Ziya Argün This is me

Publication Date December 30, 2016
Submission Date February 20, 2015
Published in Issue Year 2016 Volume: 10 Issue: 2

Cite

APA Yazgan-sağ, G., & Argün, Z. (2016). Analyzing Students’ Conceptions of “Geometric Locus”. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 10(2), 186-209. https://doi.org/10.17522/balikesirnef.277491