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APOS Teorisine Yönelik Çalışmaların Bir Analizi

Year 2019, Volume: 8 Issue: 16, 242 - 251, 30.12.2019

Abstract

Bu çalışmada 2000-2019 yılları arasında yazılmış olan APOS (Action-Process-Object-Schema) (Eylem–Süreç– Nesne–Şema) teorisine yönelik bilimsel araştırmaları incelemek amaçlanmıştır. Araştırma betimsel nitelikte olup durum tespiti yapılmıştır. Alanyazın taraması yapılırken uluslararası alanda en çok taranan Web of Science, ERIC, EBSCO ve ULAKBİM veri tabanları tercih edilmiş, Bu veri tabanlarından 2000-2019 yıllarında ulaşılan çalışmalar araştırma kapsamına dâhil edilmiştir. Bu doğrultuda yapılan literatür çalışmasında on iki adet Türkçe ve yirmi dokuz adet yabancı araştırmaya ulaşılmıştır. Ulaşılan bu kırk bir araştırma doküman analizi yöntemiyle yayınlanan üniversite, ülke, yıl, örneklem grubu, örneklemin öğrenim seviyesi ve araştırma metodu kriterlerine göre incelenmiştir. Elde edilen bulgular frekanslar yardımıyla tablolaştırılarak okuyucuya sunulmuştur. Yapılan çalışma sonucunda Türkiye’de bu alanda on iki adet çalışma olduğu, çalışmaların yoğunlukla yurt dışında bulunduğu, yıllara göre çalışma sayılarının benzerlik gösterdiği, araştırmaların çoğunlukla üniversite öğrencileri üzerinde yapıldığı, sınıf düzeyine göre çalışma sayılarının benzerlik gösterdiği ve nitel çalışmaların nicel ve karma araştırmalara göre daha yoğunlukta olduğu sonuçlarına ulaşılmıştır. Çalışmada elde edilen bulgular çerçevesinde APOS teorisine ilişkin önerilerde bulunulmuştur.

References

  • Açıl, E. (2015). Investigation of abstraction processes for equation concept of middle school 3rd grade students: APOS theory. Unpublished Doctoral Thesis, Atatürk University, Institute of Educational Sciences, Erzurum.
  • Alacacı, C. (2017). Subject-Oriented Pedagogical Field Knowledge for Mathematics. 3rd TURKISH Computer and Math Education Symposium 17 - 19 May 2017 Afyon “Mathematics and Democracy” Abstracts.
  • Asiala, M., Cottrill, J., Dubinsky, E. & Schwingendorf, E.K. (1997). The development of students’ graphical understanding of the derivative. The Journal of Mathematical Behavior, 16(4), 399-431.
  • Asiala, M., Dubinsky, E., Mathews, D.M., Morics, S. & Oktac, A. (1997). Development of students’ understanding of cosets, normality, and quotient groups. The Journal of Mathematical Behavior, 16(3), 241-309.
  • Baker, W.J., Czarnocha, B., Dias, O. & Doyle, K. (2012). Kennis procedural and conceptual knowledge: adults reviewing fractions. Alm International Journal, 7(2), 39-65.
  • Baki, A. & Güç, F.A. (2014). Ninth grade students’ misconceptions about cyclic decimal representation. Turkish Journal of Computer and Mathematics Education, 5(2), 176-206.
  • Barak, B. (2007). Determination of misconceptions about limit. Unpublished Master's Thesis. Balıkesir University, Institute of Natural and Applied Sciences, Balıkesir.
  • Bergsten, C. (2008). On the influence of theory on research in mathematics education: the case of teaching and learning limits of functions. ZDM Mathematics Education, 40(1), 189-199.
  • Çetin, H. (2009). A study on the relation between proportional reasoning skills and the successes of solving equation of elementary school secondary stage students. Published Master Thesis, Selçuk University, Institute of Natural and Applied Sciences, Konya.
  • Deniz, Ö. & Kabael, T. (2014). Examining the process of forming gradient of 8th grade students in the APOS theoretical framework. Education and Science, 42(192), 139-172.
  • Dubinsky, E. (1991). Constructive aspects of reflective abstraction in advanced mathematics; Epistomological Foundations of Mathematical Experience. New York: Springer-Verlag, 160-187.
  • Dubinsky, E. & McDonald, M.A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. In D. Holton (Ed.), The Teaching and Learning of Mathematics at University Level: An ICME Study (pp. 275-282). The Netherlands: Kluwer Academic Publishers.
  • Dubınsky, E., Weller, K., Mcdonald, M.A. & Brown, A. (2005). Some hıstorıcal issues and paradoxes regardıng the concept of infınıty: an APOS-based analysıs: part 1. Educational Studies in Mathematics, 58(3), 335–359.
  • Dubinsky, E. (2010). The APOS theory of learning mathematics: Pedagogical applications and results. Eighteenth Annual Meeting of the Southern African Association for Research in Mathematics, Paper presented at Science and Technology Education, Durban, South Africa.
  • Engelbrecht, J., Harding, A. & Potgieter, M. (2005). Undergraduate students’ performance and confidence in procedural and conceptual mathematics. International Journal of Mathematical Education in Science and Technology, 36(7), 701-712.
  • Gueudet, G. (2008). Investigating the secondary-tertiary transitio. Educatıon Study in Math, 67(1), 237-254.
  • Gürbüz, M.K. (2018). Investigation of the process of forming ratio-proportion concepts under activity based learning approach of seventh grade students. Unpublished Master Thesis, Eskisehir Osmangazi University Institute of Educational Sciences, Eskisehir.
  • Kabaca, T. (2006). The effect of computer algebra systems on teaching the concept of limit. Unpublished PhD Thesis, Gazi University Institute of Educational Sciences, Ankara.
  • Kabael, T. (2011). Generalization of functions of one variable to functions of two variables, function machine and APOS. Educational Sciences in Theory and Practice, 11(1), 484-499.
  • Kabael, T. (2015). Analysis II Students Forming Polar Functions. Necatibey Faculty of Education Journal of Electronic Science and Mathematics Education, 9(1), 246-274.
  • Karasar, N. (2012). Scientific Research Method. Ankara: Nobel Publishing.
  • Kusaeri, (2015). Terbentuknya konsepsi matematika pada diri anak dari perspektif teori reifikasi dan APOS. Journal Pendıdıkan Matematıka, 1(2), 101–105.
  • Maharaj, A. (2013). An APOS analysis of natural science students’ understanding of derivatives. South African Journal of Education, 33(1), 458-477.
  • Martin, W., Loch, S., Cooley, L., Dexter, S. & Vidakovic, D. (2010). Eıntegrating learning theories and application-based modules in teaching linear algebra. Linear Algebra and its Applications, 432(2010), 2089-2099.
  • Milli Eğitim Bakanlığı [MEB] (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar). Talim ve Terbiye Kurulu Başkanlığı, Ankara.
  • Moll, V.F., Trigueros, M., Badillo, E., & Rubio, N. (2016). Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educatıon Study in Math, 91(1), 107–122.
  • Murray, M.A. (2002). First-time calculus students discovering the product rule: functıon, notatıon and APOS theory. Unpublished Doctoral Thesis. University at Albany, New York.
  • Öksüz, R. (2018). Examining the process of forming fraction concept of 5th grade students in apos theoretical framework. Unpublished Master's Thesis. Eskişehir Osmangazi University Institute of Educational Sciences. Eskisehir.
  • Özmantar, M.F. & Monaghan, J. (2007). A dialectical approach to the formation of mathematical abstractions. Mathematics Education Research Journal, 19(2), 89-112.
  • Parraguez, M. & Oktaç, A. (2010). Construction of the vector space concept from the viewpoint of Apos theory. Linear Algebra and its Applications, 432(2010), 2112–2124.
  • Possani, E., Trigueros, M., Preciado, J.G. & Lozano, M.D. (2010). Use of models in linear algebra teaching. Linear Algebra and its Applications, 432(2010), 2125-2140.
  • Pradana, P. W., Kriswandani, Yunianta, T. N. H. (2016). Analisis Kemampuan Pemahaman Konsep Pada Materi Sistem Persamaan Linear Dua Variabel Berdasarkan Teori Apos Bagi Siswa Kelas Viii E Smp Negeri 2 Getasan. Program Studi Pendidikan Matematika Fakultas Keguruan dan Ilmu Pendidikan Universitas Kristen Satya Wacana Jl. Diponegoro No. 52-60 Salatiga, 50771 Jawa Tengah-Indonesia.
  • Salgadoa, H. & Trigueros, M. (2015). To teach eigenvalues and eigenvectors using model and APOS theory. Journal of Mathematical Behavior, 39(2015), 100-120.
  • Şefik, Ö. (2017). Analysis of students’ understanding of two variable function concept by apos theory. Published Master Thesis, Hacettepe University, Institute of Educational Sciences, Ankara.
  • Türnüklü, E. & Özcan, B.N. (2014). Relation between students' knowledge formation processes according to rbc theory in geometry and van hiele geometric thinking levels: case study. Mustafa Kemal University Journal of Institute of Social Sciences, 11(27), 295-316.
  • Trigueros, M. & Possani, E. (2013). Using an economics model for teaching linear. Algebra Linear Algebra and Applications, 438(2013), 1779-1792.
  • Trigueros, M. & Martínez, R. (2010). Planell geometrical representations in the learning of two-variable functions. Educ Study in Math, 73(1), 3-19.
  • Tzirias, W. (2011). APOS theory as a framework to study the conceptual stages of related rates problems. Unpublished Master’s Thesis, Concordia University, Institute of Educational Sciences, Canada.
  • Tzur, R. & Sımon, M. (2004). Dıstınguıshıng two stages of mathematıcs conceptual learnıng. International Journal of Science and Mathematics Education, 2(1), 287-304.
  • Urhan, S. & Dost, Ş. (2018). Analysis of pre-service mathematics teachers' understanding of derivative concept in the context of Apos theory. Published Master Thesis, Hacettepe University, Institute of Educational Sciences, Ankara.
  • Weller, K., Arnon, I., & Dubinsky, E. (2009). Preservice teachers’ understanding of the relation between a fraction or ınteger and ıts decimal expansion. Canadian Journal of Science Mathematics and Technology Education, 9(1), 5-28.
  • Yeşildere, S. & Türnüklü, E.B. (2008). Examination of the knowledge formation processes of eighth grade students according to their mathematical strengths. Uludağ University Faculty of Education Journal, 21(2), 485- 510.
  • Yıldım, A. & Şimşek, H. (2013). Qualitative research methods in social sciences. Ankara: Seçkin Publishing.

AN ANALYSIS OF THE STUDIES ON THE APOS THEORY

Year 2019, Volume: 8 Issue: 16, 242 - 251, 30.12.2019

Abstract

In this study, it is aimed to examine scientific researches about APOS (Action-Process-Object-Schema) theory written between 2000-2019. The research was descriptive and the situation was determined. While searching the literature, Web of Science, ERIC, EBSCO and ULAKBİM databases which are the most searched internationally were preferred. The studies reached from these databases in 2000-2019 were included in the research scope. In this respect, in the literature study, twelve Turkish and twenty-nine foreign researches were reached. Forty one of these researches were analyzed according to the criteria of university, country, year, sample group, education level of the sample and research method published by document analysis method. The findings were tabulated with the help of frequencies and presented to the reader. The studies result in Turkey, where twelve studies in this area, which abroad the intensity of the work, according to the year in which the similarity of the number of studies is made mostly on college students' research, the similarity of the number of working on the grade level and according to quantitative and mixed research of qualitative studies density was reached. In the framework of the findings obtained in the study, suggestions were made about the APOS theory.

References

  • Açıl, E. (2015). Investigation of abstraction processes for equation concept of middle school 3rd grade students: APOS theory. Unpublished Doctoral Thesis, Atatürk University, Institute of Educational Sciences, Erzurum.
  • Alacacı, C. (2017). Subject-Oriented Pedagogical Field Knowledge for Mathematics. 3rd TURKISH Computer and Math Education Symposium 17 - 19 May 2017 Afyon “Mathematics and Democracy” Abstracts.
  • Asiala, M., Cottrill, J., Dubinsky, E. & Schwingendorf, E.K. (1997). The development of students’ graphical understanding of the derivative. The Journal of Mathematical Behavior, 16(4), 399-431.
  • Asiala, M., Dubinsky, E., Mathews, D.M., Morics, S. & Oktac, A. (1997). Development of students’ understanding of cosets, normality, and quotient groups. The Journal of Mathematical Behavior, 16(3), 241-309.
  • Baker, W.J., Czarnocha, B., Dias, O. & Doyle, K. (2012). Kennis procedural and conceptual knowledge: adults reviewing fractions. Alm International Journal, 7(2), 39-65.
  • Baki, A. & Güç, F.A. (2014). Ninth grade students’ misconceptions about cyclic decimal representation. Turkish Journal of Computer and Mathematics Education, 5(2), 176-206.
  • Barak, B. (2007). Determination of misconceptions about limit. Unpublished Master's Thesis. Balıkesir University, Institute of Natural and Applied Sciences, Balıkesir.
  • Bergsten, C. (2008). On the influence of theory on research in mathematics education: the case of teaching and learning limits of functions. ZDM Mathematics Education, 40(1), 189-199.
  • Çetin, H. (2009). A study on the relation between proportional reasoning skills and the successes of solving equation of elementary school secondary stage students. Published Master Thesis, Selçuk University, Institute of Natural and Applied Sciences, Konya.
  • Deniz, Ö. & Kabael, T. (2014). Examining the process of forming gradient of 8th grade students in the APOS theoretical framework. Education and Science, 42(192), 139-172.
  • Dubinsky, E. (1991). Constructive aspects of reflective abstraction in advanced mathematics; Epistomological Foundations of Mathematical Experience. New York: Springer-Verlag, 160-187.
  • Dubinsky, E. & McDonald, M.A. (2001). APOS: A constructivist theory of learning in undergraduate mathematics education research. In D. Holton (Ed.), The Teaching and Learning of Mathematics at University Level: An ICME Study (pp. 275-282). The Netherlands: Kluwer Academic Publishers.
  • Dubınsky, E., Weller, K., Mcdonald, M.A. & Brown, A. (2005). Some hıstorıcal issues and paradoxes regardıng the concept of infınıty: an APOS-based analysıs: part 1. Educational Studies in Mathematics, 58(3), 335–359.
  • Dubinsky, E. (2010). The APOS theory of learning mathematics: Pedagogical applications and results. Eighteenth Annual Meeting of the Southern African Association for Research in Mathematics, Paper presented at Science and Technology Education, Durban, South Africa.
  • Engelbrecht, J., Harding, A. & Potgieter, M. (2005). Undergraduate students’ performance and confidence in procedural and conceptual mathematics. International Journal of Mathematical Education in Science and Technology, 36(7), 701-712.
  • Gueudet, G. (2008). Investigating the secondary-tertiary transitio. Educatıon Study in Math, 67(1), 237-254.
  • Gürbüz, M.K. (2018). Investigation of the process of forming ratio-proportion concepts under activity based learning approach of seventh grade students. Unpublished Master Thesis, Eskisehir Osmangazi University Institute of Educational Sciences, Eskisehir.
  • Kabaca, T. (2006). The effect of computer algebra systems on teaching the concept of limit. Unpublished PhD Thesis, Gazi University Institute of Educational Sciences, Ankara.
  • Kabael, T. (2011). Generalization of functions of one variable to functions of two variables, function machine and APOS. Educational Sciences in Theory and Practice, 11(1), 484-499.
  • Kabael, T. (2015). Analysis II Students Forming Polar Functions. Necatibey Faculty of Education Journal of Electronic Science and Mathematics Education, 9(1), 246-274.
  • Karasar, N. (2012). Scientific Research Method. Ankara: Nobel Publishing.
  • Kusaeri, (2015). Terbentuknya konsepsi matematika pada diri anak dari perspektif teori reifikasi dan APOS. Journal Pendıdıkan Matematıka, 1(2), 101–105.
  • Maharaj, A. (2013). An APOS analysis of natural science students’ understanding of derivatives. South African Journal of Education, 33(1), 458-477.
  • Martin, W., Loch, S., Cooley, L., Dexter, S. & Vidakovic, D. (2010). Eıntegrating learning theories and application-based modules in teaching linear algebra. Linear Algebra and its Applications, 432(2010), 2089-2099.
  • Milli Eğitim Bakanlığı [MEB] (2018). Matematik Dersi Öğretim Programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar). Talim ve Terbiye Kurulu Başkanlığı, Ankara.
  • Moll, V.F., Trigueros, M., Badillo, E., & Rubio, N. (2016). Mathematical objects through the lens of two different theoretical perspectives: APOS and OSA. Educatıon Study in Math, 91(1), 107–122.
  • Murray, M.A. (2002). First-time calculus students discovering the product rule: functıon, notatıon and APOS theory. Unpublished Doctoral Thesis. University at Albany, New York.
  • Öksüz, R. (2018). Examining the process of forming fraction concept of 5th grade students in apos theoretical framework. Unpublished Master's Thesis. Eskişehir Osmangazi University Institute of Educational Sciences. Eskisehir.
  • Özmantar, M.F. & Monaghan, J. (2007). A dialectical approach to the formation of mathematical abstractions. Mathematics Education Research Journal, 19(2), 89-112.
  • Parraguez, M. & Oktaç, A. (2010). Construction of the vector space concept from the viewpoint of Apos theory. Linear Algebra and its Applications, 432(2010), 2112–2124.
  • Possani, E., Trigueros, M., Preciado, J.G. & Lozano, M.D. (2010). Use of models in linear algebra teaching. Linear Algebra and its Applications, 432(2010), 2125-2140.
  • Pradana, P. W., Kriswandani, Yunianta, T. N. H. (2016). Analisis Kemampuan Pemahaman Konsep Pada Materi Sistem Persamaan Linear Dua Variabel Berdasarkan Teori Apos Bagi Siswa Kelas Viii E Smp Negeri 2 Getasan. Program Studi Pendidikan Matematika Fakultas Keguruan dan Ilmu Pendidikan Universitas Kristen Satya Wacana Jl. Diponegoro No. 52-60 Salatiga, 50771 Jawa Tengah-Indonesia.
  • Salgadoa, H. & Trigueros, M. (2015). To teach eigenvalues and eigenvectors using model and APOS theory. Journal of Mathematical Behavior, 39(2015), 100-120.
  • Şefik, Ö. (2017). Analysis of students’ understanding of two variable function concept by apos theory. Published Master Thesis, Hacettepe University, Institute of Educational Sciences, Ankara.
  • Türnüklü, E. & Özcan, B.N. (2014). Relation between students' knowledge formation processes according to rbc theory in geometry and van hiele geometric thinking levels: case study. Mustafa Kemal University Journal of Institute of Social Sciences, 11(27), 295-316.
  • Trigueros, M. & Possani, E. (2013). Using an economics model for teaching linear. Algebra Linear Algebra and Applications, 438(2013), 1779-1792.
  • Trigueros, M. & Martínez, R. (2010). Planell geometrical representations in the learning of two-variable functions. Educ Study in Math, 73(1), 3-19.
  • Tzirias, W. (2011). APOS theory as a framework to study the conceptual stages of related rates problems. Unpublished Master’s Thesis, Concordia University, Institute of Educational Sciences, Canada.
  • Tzur, R. & Sımon, M. (2004). Dıstınguıshıng two stages of mathematıcs conceptual learnıng. International Journal of Science and Mathematics Education, 2(1), 287-304.
  • Urhan, S. & Dost, Ş. (2018). Analysis of pre-service mathematics teachers' understanding of derivative concept in the context of Apos theory. Published Master Thesis, Hacettepe University, Institute of Educational Sciences, Ankara.
  • Weller, K., Arnon, I., & Dubinsky, E. (2009). Preservice teachers’ understanding of the relation between a fraction or ınteger and ıts decimal expansion. Canadian Journal of Science Mathematics and Technology Education, 9(1), 5-28.
  • Yeşildere, S. & Türnüklü, E.B. (2008). Examination of the knowledge formation processes of eighth grade students according to their mathematical strengths. Uludağ University Faculty of Education Journal, 21(2), 485- 510.
  • Yıldım, A. & Şimşek, H. (2013). Qualitative research methods in social sciences. Ankara: Seçkin Publishing.
There are 43 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Funda Bayraktar 0000-0001-8075-4811

Tayfun Tutak 0000-0002-0277-6377

Aziz İlhan 0000-0001-7049-5756

Publication Date December 30, 2019
Published in Issue Year 2019 Volume: 8 Issue: 16

Cite

APA Bayraktar, F., Tutak, T., & İlhan, A. (2019). AN ANALYSIS OF THE STUDIES ON THE APOS THEORY. Elektronik Eğitim Bilimleri Dergisi, 8(16), 242-251.