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Öğrenci Matematiğini Araştırmada Öğretim Deneyi Yöntemi: Kuramsal Temeller ve Örnek Bir Uygulamadan Yansımalar

Year 2019, Volume: 7 Issue: 2, 792 - 825, 30.04.2019

Abstract

Bu çalışmada günümüzün matematik eğitimi araştırmalarında yaygın olarak kullanılan öğretim
deneyi yönteminin kuramsal temelleri, tarihsel gelişimi ve farklı türdeki öğretim deneylerinin
özellikleri açıklanmıştır. İlk kez 1960’lı yıllarda Sovyet Sosyalist Cumhuriyetler Birliği’nde
kullanılan öğretim deneyinin 1976’dan sonra ABD’de “yapılandırmacı öğretim deneyi”; 1990’lı yıllar
içerisinde ise “sınıf öğretim deneyi” isimlerinde yeni türlerinin oluşturulduğu bilinmektedir. Sovyet
öğretim deneylerinde öğrencilerin hedeflenen matematiksel kazanımları elde etmelerinde öğretmenin
müdahaleci desteklerini içeren uygun öğrenme ortamlarının hazırlanması ön plandayken,
yapılandırmacı öğretim deneyinde bir veya birkaç öğrencinin ön bilgisine dayanan uygun öğrenme
ortamlarının hazırlanması ve öğrenme süreçlerinin modellenmesi odaktadır. Sınıf öğretim deneyinde
ise öğrenmenin bireysel boyutunun yanında sosyal boyutu da ele alınmakta ve matematiksel bilginin
sınıf normları ve sosyal etkileşimler bağlamında nasıl yapılandırıldığı incelenmektedir. Öğretim
deneyinin temel unsurları keşfedici öğretim, öğretim bölümleri, klinik görüşmeler, geriye dönük
kavramsal analizler ve öğrenci matematiğine ilişkin yaşayan modeller olarak tanımlanırken, söz
konusu unsurlar örnek bir öğretim deneyinden yazarın edindiği deneyimlerle birlikte açıklanmaktadır.

References

  • Ackermann, E. (1995). Construction and transference of meaning through form. In L. P. Steffe & J. Gale (Eds.), Constructivism in education (pp. 341–354). Hillsdale, NJ: Lawrence Erlbaum.
  • Arievitch, I. M., & Haenen, J. P. P. (2005). Connecting sociocultural theory and educational practice: Galperin’s approach. Educational Psychologist, 40(3), 155-165.
  • Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practices in Cabri environments. Zentralblatt für Didaktik der Mathematik, 34(3), 66–72.
  • Aşık, G. ve Yılmaz, Z. (2017). Design-based research and teaching experiment methods in mathematics education: Differences and similarities. Journal of Theory and Practice in Education, 13(2), 343– 367.
  • Baccaglini-Frank, A. (2010). Conjecturing in dynamic geometry: A model for conjecture generation through maintaining dragging. Unpublished Doctoral Dissertation, Durham: University of New Hampshire.
  • Blumer, H. (1969). Symbolic interactionism: Perspective and method. Berkeley: University of California Press.
  • Cobb, P. (1989). Experimental, cognitive and anthropological perspectives in mathematics education. For the Learning of Mathematics. 9(2), 32–43.
  • Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 307–333). Mahwah. NJ: Erlbaum.
  • Cobb, P., & Bauersfeld, H. (Eds.), (1995). The emergence of mathematical meaning: Interaction in classroom cultures. Hillsdale, NJ: Lawrance Erlbaum.
  • Cobb, P., Jackson, K., & Dunlap, C. (2017). Conducting design studies to investigate and support mathematics students’ and teachers’ learning. In J. Cai (Ed.), First compendium for research in mathematics education (pp. 208–233). Reston, VA: National Council of Teachers of Mathematics.
  • Cobb, P. & Steffe, L. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14(2), 83–94.
  • Cobb, P. (2011). Part I Radical constructivism: Chapter 2: Introduction. In E. Yackel, Gravemeijer & A. Sfard (Eds.). A journey in mathematics education research: Insights from the work of Paul Cobb (pp. 9– 17). Mathematics Education Library 48, Netherlands: Springer.
  • Cobb, P., & Steffe, L. (2011). The constructivist researcher as teacher and model builder. In E. Yackel, Gravemeijer & A. Sfard (Eds.), A journey in mathematics education research: Insights from the work of Paul Cobb (pp. 19–30). Mathematics Education Library 48, Netherlands: Springer.
  • Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175–190.
  • Cobb, P., Yackel, E., & Wood, T. (1989). Young children’s emotional acts while engaged mathematical problem solving. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 117–148). New York: Springer-Verlag.
  • Czarnocha, B., & Maj, B. (2008). A teaching experiment. In B. Czarnocha (Ed.), Handbook of mathematics teaching research -a tool for teachers- researchers (pp. 47–58). Poland: University of Reszów.
  • Davydov, V. V. (1975). The psychological characteristics of the “prenumerical” period of mathematics instruction. In L. P. Steffe (Ed.), Soviet studies in the psychology of learning and teaching mathematics (Vol. 7). Stanford, CA: School Mathematics Study Group.
  • Elstak, I. R. (2007). College students’ understanding of rational exponents: A teaching experiment, Unpublished Doctoral Dissertation, Columbus: The Ohio State University.
  • Engelhardt, P. V., Corpuz, E. G., Ozimek, D. J., & Rebello, N. S. (2004, September). The teaching experimentwhat it is and what it isn't. ın 2003 Physics education research conference (Vol. 720, pp. 157–160).
  • Erickson, F. (1986). Qualitative methods in research on teaching. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd ed.) (pp. 119–161). New York: Macmillan.
  • Ginsburg, H. P. (1981). The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques. For the Learning of Mathematics, 1(3), 4–11.
  • Ginsburg, H. P. (1997). Entering the child’s mind: The clinical ınterview in psychological research and practice. Cambridge, UK: Cambridge University Press.
  • Goldin, G. A. (1997). Observing mathematical problem solving through task-based interviews. Journal for Research in Mathematics Education. Monograph, 9, 40–177.
  • Harel, G. & Sowder, L. (1998). Students’ proof schemes: results from exploratory studies. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education (pp. 234–283). Providence, RI: American Mathematical Society.
  • Hackenberg, A. J. (2010). Students’ reasoning with reversible multiplicative relationships. Cognition and Instruction, 28(4), 383–432.
  • Kantowski, M. G. (1977). Processes involved in mathematical problem solving. Journal for Research in Mathematics Education, 8, 163–186.
  • Komorek, M., & Duit, R. (2004). The teaching experiment as a powerful method to develop and evaluate teaching and learning sequences in the domain of non-linear systems. International Journal of Science Education, 25, 619–633.
  • Laborde, C. (1993). The computer as part of the learning environment: The case of geometry. In C. Keitel & K. Ruthven (Eds.), Learning through computers: Mathematics and educational technology (pp. 48–67). Berlin, Germany: Springer.
  • Leung, A. (2008). Dragging in a dynamic geometry environment through the lens of variation. International Journal of Computer for Mathematical Learning, 13, 135–157.
  • Leung, A. (2015). Discernment and reasoning in dynamic geometry environments. In S. J. Cho (Ed.), Selected regular lectures from the 12th ınternational congress on mathematical education (pp. 551–569). Switzerland: Springer.
  • Menchinskaya, N. A. (1969a). Fifty years of Soviet instructional psychology. In J. Kilpatrick & I. Wirszup (Eds.), Soviet studies in the psychology of learning and teaching mathematics, Vol. 1, (pp. 3–18). Stanford, CA: School Mathematics Study Group.
  • Menchinskaya, N. A. (1969b). The psychology of mastering concepts: Fundemental problems and methods of research. In J. Kilpatrick & I. Wirszup (Eds.), Soviet studies in the psychology of learning and teaching mathematics, Vol.1, (pp. 75–92). Stanford, CA: School Mathematics Study Group.
  • Mertler, C. A. (2012). Action research: Improving schools and empowering school educators (3rd ed.). Thousand Oaks, CA: Sage.
  • Milli Eğitim Bakanlığı (2009). İlköğretim matematik dersi 6 – 8. sınıflar öğretim programı. Ankara: Talim Terbiye Kurulu.
  • Milli Eğitim Bakanlığı (2013). Ortaokul matematik dersi 5 – 8. sınıflar öğretim programı. Ankara: Talim Terbiye Kurulu.
  • Mohan, L., & Anderson, C. W. (2009, June). Teaching experiments and the carbon cycle learning progression. Paper presented at the Learning Progressions in Science (LeaPS) Conference, Iowa City, IA.
  • Peirce, C. S. (1960). Collected papers. Cambridge, MA: Harvard University Press.
  • Piaget, J. (1952). The child’s conception of number. London: Routledge and Kegan Paul.
  • Piaget, J. (1964). Part I: Cognitive development in children: Piaget development and learning. Journal of Research in Science Teaching, 2(3), 176–186.
  • Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructive perspective. Journal of Research in Mathematics Education, 26(2), 114–145.
  • Steffe, L. P. (1991). The constructivist teaching experiment: Illustrations and implications. In E. Von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 177–194). New York: Kluwer Academic Publishers.
  • Steffe, L. P., Hirstein, J. & Spikes, C. (1976). Quantitative comparison and class inclusion as readiness variables for learning first grade arithmetic content. Technical Report No. 9. Project for Mathematical Development of Children, Tallahassee FL.
  • Steffe, L. P., & Olive, J. (2010). Children’s fractional knowledge. New York, NY. Springer.
  • Steffe, L. P. & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh, & A. E. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 267–307). Hillsdale: Erlbaum.
  • Steffe, L. P., & Ulrich, C. (2014). The constructivist teaching experiment. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 102–109). Springer, Berlin.
  • Stolzenberg, G. (1984). Can an inquiry into the foundations of mathematics tell us anything interesting about mind? In P. Watzlawick (Ed.), The ınvented reality (pp. 257–308). New York: W. W. Norton & Company.
  • Thompson, P. (1979). The constructivist teaching experiment in mathematics education research. Paper presented at the Annual Meeting of the National Council of Teachers of Mathematics, Boston, MA.
  • Thompson, P. W. (1982). Were lions to speak, we wouldn't understand. Journal of Mathematical Behavior, 3(2), 147–165.
  • Thompson, P. W. (2000). Radical constructivism: Reflections and directions. In L. P. Steffe & P. W. Thompson (Eds.), Radical constructivism in action: Building on the pioneering work of ernst von glasersfeld (pp. 412–448). London: Falmer Press.
  • Uygan, C. (2016). Ortaokul öğrencilerinin zihnin geometrik alışkanlıklarının kazanımına yönelik dinamik geometri yazılımındaki öğrenme süreçleri. Yayımlanmamış Doktora Tezi, Anadolu Üniversitesi, Eskişehir.
  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). İlkokul ve Ortaokul Matematiği Gelişimsel Yaklaşımla Öğretim. S. Durmuş (Çev. Ed.). Ankara: Nobel Akademik Yayıncılık.
  • van Hiele, P. M. (1984), A child’s thought and geometry. In D. Fuys, D. Geddes & R.W. Tischler (Eds.) (1959/1985) English translation of selected writings of Dina van Hiele Geldof and Pierre M. van Hiele, (pp. 243–252). Brooklyn: Brooklyn College.
  • von Glasersfeld, E. v. (1995). Radical constructivism: A Way of knowing and learning. London: Falmer Press.
  • Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.
  • Yıldırım, C. (2007). Matematiksel düşünme (13. Basım). İstanbul: Remzi Kitabevi.
  • Zazkis, R. & Hazzan, O. (1999). Interviewing in mathematics education research: Choosing the questions. Journal of Mathematical Behavior, 17(4), 429–439.

Teaching Experiment Methodology for Investigating Students’ Mathematics: Theoretical Foundations and Reflections from an Exemplary Application

Year 2019, Volume: 7 Issue: 2, 792 - 825, 30.04.2019

Abstract

In this study theoretical foundations and historical changes of the teaching experiment
method, commonly conducted in the current mathematics education researches, and the features of the
various teaching experiment types are explained. The teaching experiment method, first conducted in
the Union of Soviet Socialist Republics in 1960s, was then divided to various types like constructivist
teaching experiment emerging after 1976 and classroom teaching experiment developing in 1990s in
the USA. In the Soviet type teaching experiment, it is aimed to design learning environments in which
the teacher intervenes the students’ learning processes with intent to obtain prior certain learning
achievements stated. The constructivist teaching experiment focuses on the design of learning
environments which are appropriate with one or more students’ preknowledge and possible
alternative learning processes and also aims to model their learning trajectories. In the classroom
teaching experiment, in addition to individual psychological factors, social factors are also considered
and it is investigated how students’ mathematical knowledge is constructed within classroom norms
and social interactions. While the main elements of the teaching experiments are exploratory teaching,
teaching episodes, clinical interviews, retrospective conceptual analysis and living models of the
students’ mathematics, in this study the aforementioned elements are explained with relation to the
writer’s experiences gained from an exemplary teaching experiment.

References

  • Ackermann, E. (1995). Construction and transference of meaning through form. In L. P. Steffe & J. Gale (Eds.), Constructivism in education (pp. 341–354). Hillsdale, NJ: Lawrence Erlbaum.
  • Arievitch, I. M., & Haenen, J. P. P. (2005). Connecting sociocultural theory and educational practice: Galperin’s approach. Educational Psychologist, 40(3), 155-165.
  • Arzarello, F., Olivero, F., Paola, D., & Robutti, O. (2002). A cognitive analysis of dragging practices in Cabri environments. Zentralblatt für Didaktik der Mathematik, 34(3), 66–72.
  • Aşık, G. ve Yılmaz, Z. (2017). Design-based research and teaching experiment methods in mathematics education: Differences and similarities. Journal of Theory and Practice in Education, 13(2), 343– 367.
  • Baccaglini-Frank, A. (2010). Conjecturing in dynamic geometry: A model for conjecture generation through maintaining dragging. Unpublished Doctoral Dissertation, Durham: University of New Hampshire.
  • Blumer, H. (1969). Symbolic interactionism: Perspective and method. Berkeley: University of California Press.
  • Cobb, P. (1989). Experimental, cognitive and anthropological perspectives in mathematics education. For the Learning of Mathematics. 9(2), 32–43.
  • Cobb, P. (2000). Conducting teaching experiments in collaboration with teachers. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 307–333). Mahwah. NJ: Erlbaum.
  • Cobb, P., & Bauersfeld, H. (Eds.), (1995). The emergence of mathematical meaning: Interaction in classroom cultures. Hillsdale, NJ: Lawrance Erlbaum.
  • Cobb, P., Jackson, K., & Dunlap, C. (2017). Conducting design studies to investigate and support mathematics students’ and teachers’ learning. In J. Cai (Ed.), First compendium for research in mathematics education (pp. 208–233). Reston, VA: National Council of Teachers of Mathematics.
  • Cobb, P. & Steffe, L. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14(2), 83–94.
  • Cobb, P. (2011). Part I Radical constructivism: Chapter 2: Introduction. In E. Yackel, Gravemeijer & A. Sfard (Eds.). A journey in mathematics education research: Insights from the work of Paul Cobb (pp. 9– 17). Mathematics Education Library 48, Netherlands: Springer.
  • Cobb, P., & Steffe, L. (2011). The constructivist researcher as teacher and model builder. In E. Yackel, Gravemeijer & A. Sfard (Eds.), A journey in mathematics education research: Insights from the work of Paul Cobb (pp. 19–30). Mathematics Education Library 48, Netherlands: Springer.
  • Cobb, P., & Yackel, E. (1996). Constructivist, emergent, and sociocultural perspectives in the context of developmental research. Educational Psychologist, 31(3/4), 175–190.
  • Cobb, P., Yackel, E., & Wood, T. (1989). Young children’s emotional acts while engaged mathematical problem solving. In D. B. McLeod & V. M. Adams (Eds.), Affect and mathematical problem solving: A new perspective (pp. 117–148). New York: Springer-Verlag.
  • Czarnocha, B., & Maj, B. (2008). A teaching experiment. In B. Czarnocha (Ed.), Handbook of mathematics teaching research -a tool for teachers- researchers (pp. 47–58). Poland: University of Reszów.
  • Davydov, V. V. (1975). The psychological characteristics of the “prenumerical” period of mathematics instruction. In L. P. Steffe (Ed.), Soviet studies in the psychology of learning and teaching mathematics (Vol. 7). Stanford, CA: School Mathematics Study Group.
  • Elstak, I. R. (2007). College students’ understanding of rational exponents: A teaching experiment, Unpublished Doctoral Dissertation, Columbus: The Ohio State University.
  • Engelhardt, P. V., Corpuz, E. G., Ozimek, D. J., & Rebello, N. S. (2004, September). The teaching experimentwhat it is and what it isn't. ın 2003 Physics education research conference (Vol. 720, pp. 157–160).
  • Erickson, F. (1986). Qualitative methods in research on teaching. In M. C. Wittrock (Ed.), Handbook of research on teaching (3rd ed.) (pp. 119–161). New York: Macmillan.
  • Ginsburg, H. P. (1981). The clinical interview in psychological research on mathematical thinking: Aims, rationales, techniques. For the Learning of Mathematics, 1(3), 4–11.
  • Ginsburg, H. P. (1997). Entering the child’s mind: The clinical ınterview in psychological research and practice. Cambridge, UK: Cambridge University Press.
  • Goldin, G. A. (1997). Observing mathematical problem solving through task-based interviews. Journal for Research in Mathematics Education. Monograph, 9, 40–177.
  • Harel, G. & Sowder, L. (1998). Students’ proof schemes: results from exploratory studies. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education (pp. 234–283). Providence, RI: American Mathematical Society.
  • Hackenberg, A. J. (2010). Students’ reasoning with reversible multiplicative relationships. Cognition and Instruction, 28(4), 383–432.
  • Kantowski, M. G. (1977). Processes involved in mathematical problem solving. Journal for Research in Mathematics Education, 8, 163–186.
  • Komorek, M., & Duit, R. (2004). The teaching experiment as a powerful method to develop and evaluate teaching and learning sequences in the domain of non-linear systems. International Journal of Science Education, 25, 619–633.
  • Laborde, C. (1993). The computer as part of the learning environment: The case of geometry. In C. Keitel & K. Ruthven (Eds.), Learning through computers: Mathematics and educational technology (pp. 48–67). Berlin, Germany: Springer.
  • Leung, A. (2008). Dragging in a dynamic geometry environment through the lens of variation. International Journal of Computer for Mathematical Learning, 13, 135–157.
  • Leung, A. (2015). Discernment and reasoning in dynamic geometry environments. In S. J. Cho (Ed.), Selected regular lectures from the 12th ınternational congress on mathematical education (pp. 551–569). Switzerland: Springer.
  • Menchinskaya, N. A. (1969a). Fifty years of Soviet instructional psychology. In J. Kilpatrick & I. Wirszup (Eds.), Soviet studies in the psychology of learning and teaching mathematics, Vol. 1, (pp. 3–18). Stanford, CA: School Mathematics Study Group.
  • Menchinskaya, N. A. (1969b). The psychology of mastering concepts: Fundemental problems and methods of research. In J. Kilpatrick & I. Wirszup (Eds.), Soviet studies in the psychology of learning and teaching mathematics, Vol.1, (pp. 75–92). Stanford, CA: School Mathematics Study Group.
  • Mertler, C. A. (2012). Action research: Improving schools and empowering school educators (3rd ed.). Thousand Oaks, CA: Sage.
  • Milli Eğitim Bakanlığı (2009). İlköğretim matematik dersi 6 – 8. sınıflar öğretim programı. Ankara: Talim Terbiye Kurulu.
  • Milli Eğitim Bakanlığı (2013). Ortaokul matematik dersi 5 – 8. sınıflar öğretim programı. Ankara: Talim Terbiye Kurulu.
  • Mohan, L., & Anderson, C. W. (2009, June). Teaching experiments and the carbon cycle learning progression. Paper presented at the Learning Progressions in Science (LeaPS) Conference, Iowa City, IA.
  • Peirce, C. S. (1960). Collected papers. Cambridge, MA: Harvard University Press.
  • Piaget, J. (1952). The child’s conception of number. London: Routledge and Kegan Paul.
  • Piaget, J. (1964). Part I: Cognitive development in children: Piaget development and learning. Journal of Research in Science Teaching, 2(3), 176–186.
  • Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructive perspective. Journal of Research in Mathematics Education, 26(2), 114–145.
  • Steffe, L. P. (1991). The constructivist teaching experiment: Illustrations and implications. In E. Von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 177–194). New York: Kluwer Academic Publishers.
  • Steffe, L. P., Hirstein, J. & Spikes, C. (1976). Quantitative comparison and class inclusion as readiness variables for learning first grade arithmetic content. Technical Report No. 9. Project for Mathematical Development of Children, Tallahassee FL.
  • Steffe, L. P., & Olive, J. (2010). Children’s fractional knowledge. New York, NY. Springer.
  • Steffe, L. P. & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh, & A. E. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 267–307). Hillsdale: Erlbaum.
  • Steffe, L. P., & Ulrich, C. (2014). The constructivist teaching experiment. In S. Lerman (Ed.), Encyclopedia of mathematics education (pp. 102–109). Springer, Berlin.
  • Stolzenberg, G. (1984). Can an inquiry into the foundations of mathematics tell us anything interesting about mind? In P. Watzlawick (Ed.), The ınvented reality (pp. 257–308). New York: W. W. Norton & Company.
  • Thompson, P. (1979). The constructivist teaching experiment in mathematics education research. Paper presented at the Annual Meeting of the National Council of Teachers of Mathematics, Boston, MA.
  • Thompson, P. W. (1982). Were lions to speak, we wouldn't understand. Journal of Mathematical Behavior, 3(2), 147–165.
  • Thompson, P. W. (2000). Radical constructivism: Reflections and directions. In L. P. Steffe & P. W. Thompson (Eds.), Radical constructivism in action: Building on the pioneering work of ernst von glasersfeld (pp. 412–448). London: Falmer Press.
  • Uygan, C. (2016). Ortaokul öğrencilerinin zihnin geometrik alışkanlıklarının kazanımına yönelik dinamik geometri yazılımındaki öğrenme süreçleri. Yayımlanmamış Doktora Tezi, Anadolu Üniversitesi, Eskişehir.
  • Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). İlkokul ve Ortaokul Matematiği Gelişimsel Yaklaşımla Öğretim. S. Durmuş (Çev. Ed.). Ankara: Nobel Akademik Yayıncılık.
  • van Hiele, P. M. (1984), A child’s thought and geometry. In D. Fuys, D. Geddes & R.W. Tischler (Eds.) (1959/1985) English translation of selected writings of Dina van Hiele Geldof and Pierre M. van Hiele, (pp. 243–252). Brooklyn: Brooklyn College.
  • von Glasersfeld, E. v. (1995). Radical constructivism: A Way of knowing and learning. London: Falmer Press.
  • Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.
  • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27, 458–477.
  • Yıldırım, C. (2007). Matematiksel düşünme (13. Basım). İstanbul: Remzi Kitabevi.
  • Zazkis, R. & Hazzan, O. (1999). Interviewing in mathematics education research: Choosing the questions. Journal of Mathematical Behavior, 17(4), 429–439.
There are 57 citations in total.

Details

Primary Language Turkish
Journal Section Articles
Authors

Candaş Uygan 0000-0002-2224-5004

Publication Date April 30, 2019
Published in Issue Year 2019 Volume: 7 Issue: 2

Cite

APA Uygan, C. (2019). Öğrenci Matematiğini Araştırmada Öğretim Deneyi Yöntemi: Kuramsal Temeller ve Örnek Bir Uygulamadan Yansımalar. Eğitimde Nitel Araştırmalar Dergisi, 7(2), 792-825.
AMA Uygan C. Öğrenci Matematiğini Araştırmada Öğretim Deneyi Yöntemi: Kuramsal Temeller ve Örnek Bir Uygulamadan Yansımalar. Derginin Amacı ve Kapsamı. April 2019;7(2):792-825.
Chicago Uygan, Candaş. “Öğrenci Matematiğini Araştırmada Öğretim Deneyi Yöntemi: Kuramsal Temeller Ve Örnek Bir Uygulamadan Yansımalar”. Eğitimde Nitel Araştırmalar Dergisi 7, no. 2 (April 2019): 792-825.
EndNote Uygan C (April 1, 2019) Öğrenci Matematiğini Araştırmada Öğretim Deneyi Yöntemi: Kuramsal Temeller ve Örnek Bir Uygulamadan Yansımalar. Eğitimde Nitel Araştırmalar Dergisi 7 2 792–825.
IEEE C. Uygan, “Öğrenci Matematiğini Araştırmada Öğretim Deneyi Yöntemi: Kuramsal Temeller ve Örnek Bir Uygulamadan Yansımalar”, Derginin Amacı ve Kapsamı, vol. 7, no. 2, pp. 792–825, 2019.
ISNAD Uygan, Candaş. “Öğrenci Matematiğini Araştırmada Öğretim Deneyi Yöntemi: Kuramsal Temeller Ve Örnek Bir Uygulamadan Yansımalar”. Eğitimde Nitel Araştırmalar Dergisi 7/2 (April 2019), 792-825.
JAMA Uygan C. Öğrenci Matematiğini Araştırmada Öğretim Deneyi Yöntemi: Kuramsal Temeller ve Örnek Bir Uygulamadan Yansımalar. Derginin Amacı ve Kapsamı. 2019;7:792–825.
MLA Uygan, Candaş. “Öğrenci Matematiğini Araştırmada Öğretim Deneyi Yöntemi: Kuramsal Temeller Ve Örnek Bir Uygulamadan Yansımalar”. Eğitimde Nitel Araştırmalar Dergisi, vol. 7, no. 2, 2019, pp. 792-25.
Vancouver Uygan C. Öğrenci Matematiğini Araştırmada Öğretim Deneyi Yöntemi: Kuramsal Temeller ve Örnek Bir Uygulamadan Yansımalar. Derginin Amacı ve Kapsamı. 2019;7(2):792-825.