Levels of Elementary Mathematics Teacher Candidates Determination Levels of Image Sets of Functions in $R^2$ and $R^3$

Purpose: This study aimed to reveal the relationship between elementary school mathematics teacher candidates' determination levels of image sets of functions in $R^2$ and $R^3$. Design/Methodology/Approach: This study was conducted with 49 elementary mathematics teacher candidates and the correlation design from quantitative approaches was used. For the given purpose, the data were collected by 2D and 3D tests. The 2D test was used to reveal the students' level of determining the image sets of the functions in $R^2$ and the 3D test was used to reveal that in $R^3$. In the data collection process, the graphics of the questions in 2D and 3D tests drawn with the support of GeoGebra were presented to the students together with the tests. Correlation analysis was used to compare the levels of students in determining image sets of functions in $R^2$ and $R^3$. Findings: According to findings, it was found that there was a high level, positive, and significant relationship between the students' levels of determining the image sets of the functions in $R^2$ and $R^3$. Another conclusion about the study was that the students were more successful in determining the image sets of functions in $R^3$ than in $R^2$. This is thought to be a result of the dynamic feature of the GeoGebra software. Highlights: It was observed that the GeoGebra program was important in determining the image set of a function, especially in $R^3$. For this reason it is thought that using activities designed with the GeoGebra program in related lessons can be effective in teaching two-variable functions.

İlköğretim Matematik Öğretmeni Adaylarının $R^2$ ve $R^3$ ’teki Fonksiyonların Görüntü Kümelerini Belirleme Düzeyleri

Çalışmanın amacı: Bu çalışmanın amacı ilköğretim matematik öğretmeni adaylarının $R^2$ ve $R^3$' teki fonksiyonların görüntü kümelerini belirleme düzeyleri arasındaki ilişkinin ortaya konmasıdır. Materyal ve Yöntem: Nicel yaklaşımlardan korelasyon deseninin kullanıldığı bu çalışma 49 ilköğretim matematik öğretmen adayıyla yürütülmüştür. Çalışmanın amacı doğrultusunda veriler, 2D ve 3D testi ile toplanmıştır. 2D testi öğrencilerin $R^2$’deki, 3D testi ise öğrencilerin $R^3$’teki fonksiyonların görüntü kümelerini belirleyebilme düzeylerini ortaya koymak için kullanılmıştır. Veri toplama sürecinde 2D ve 3D testindeki soruların GeoGebra desteğiyle çizilmiş grafikleri, testlerle birlikte öğrencilere sunulmuştur. Öğrencilerin $R^2$ ve $R^3$’teki fonksiyonların görüntü kümelerini belirleme düzeylerini karşılaştırmak için korelasyon analizi kullanılmıştır. Bulgular: Elde edilen bulgulara göre öğrencilerin $R^2$ ve $R^3$’teki fonksiyonların görüntü kümelerini belirleme düzeyleri arasında yüksek düzey, pozitif yönlü ve anlamlı bir ilişki olduğu bulunmuştur. Çalışmaya dair bir diğer sonuç ise öğrencilerin $R^3$’teki fonksiyonların görüntü kümelerini belirlemede $R^2$’den daha başarılı olduklarıdır. GeoGebra programının dinamik özelliğinin bu sonucu doğurduğu düşünülmektedir. Önemli Vurgular: GeoGebra programının, özellikle $R^3$’teki bir fonksiyonun görüntü kümesini belirleme sürecinde etkili olduğu görülmüştür. Bu nedenle iki değişkenli fonksiyonların öğretiminde, GeoGebra programıyla tasarlanmış etkinliklerin ilgili derslerde kullanılmasının etkili olabileceği düşünülmektedir.

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ers, T., Davis, G., Dubinsky, E., & Lewin, P. (1988). Computer experiences in learning composition of functions. Journal for Research in Mathematics Education, 19(3), 246-259.

Baki, A. (2001). Bilişim teknolojisi ışığı altında matematik eğitiminin değerlendirilmesi, Milli Eğitim Dergisi, 149.

Baki, A. (2008). Kuramdan uygulamaya matematik eğitimi (4. Basım). Ankara: Harf Eğitim Yayıncılığı.

Becker, A. B. (1991). The Concept Of Function: Misconceptions And Remediation At The College Level, Unpublished Doctoral Dissertation, Illinois State University, Illinois, USA.

Bell, C. J. (2001). Conceptual Understanding Of Functions İn A Multi-Representational Learning Environment, Unpublished Doctoral Dissertation, The University of Texas at Austin, Texas.

Berry S. J., & Nyman A. M. (2003). Promoting students’ graphical understanding of the calculus. Journal of Mathematical Behavior, 22, 481–497.

Biber, A. Ç., & Argün, Z. (2015). Matematik öğretmen adaylarının tek ve iki değişkenli fonksiyonlarda limit konusunda sahip oldukları kavram bilgileri arasındaki ilişkilerin incelenmesi. Bartın Üniversitesi Eğitim Fakültesi Dergisi, 4(2), 501-515.

Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö.E., Karadeniz, Ş., & Demirel, F. (2011). Bilimsel araştırma yöntemleri (8. Baskı). Ankara: Pegem Akademi.

Cooney, T. J., Beckmann, S., & Lloyd, G. M. (2010). Developing essential understandings of functions for teaching mathematics in grades 9–12. Reston, VA: National Council of Teachers of Mathematics.

Darmadi, D. (2011). Imagery students in learning real analysis (ase study at IKIP PGRI madiun). Paper Presented at the National Seminar of UNY, Jogjakarta, Indonesia.

Darmadi, D. (2015). Visual Thinking Stdudent Profiles of Prospective Teachers of Mathematics in Understanding The Formal Definition Based On Gender Differences. Dissertation, UNESA, Surabaya.

DeMarois, P., & Tall, D. (1996). Facets and Layers of The Function Concept, Proceedings of PME 20 (Vol. 2, pp 297-304): Valencia.

DeMarois, P. (1996). Beginning Algebra Students’ İmages Of The Function Concept, Proceedings of the Twenty-Second Annual Conference of the American Mathematical Association of Two-Year Colleges, Long Beach, CA.

Eisenberg, T. (1992). On the development of a sense for functions. In G. Harel and E. Dubinsky (Eds.), The Concept Of Function: Aspects Of Epistemology And Pedagogy, Mathematical Association of America, 153-174.

Elia, I., & Spyrou, P. (2006). How students conceive function: a triarchic conceptual-semiotic model of the understanding of a complex concept.TMME, 3(2), 256-272.

Fest, A., Hiob, M., & Hoffkamp, A. (2011). An interactive learning activity for the formation of the concept of function based on representation transfer. The Electronic Journal of Mathematics and Technology, 5(2), 69–176.

Guncaga, J., & Majherova, J. (2012). GeoGebra as a motivational tool for teaching and learning in Slovakia. North American GeoGebra Journal, 1(1), 45-48.

Güveli, E., & Güveli, H. (2002). Lise 1 fonksiyonlar konsunda web tabanlı örnek bir öğretim materyali. V. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, Ankara, 866-872. Retrieved from http://infobank.fedu.metu.edu.tr/ufbmek-5/b_kitabi/PDF/Matematik/Poster/t195.pdfon 20.01.2020.

Harel, G., & Dubinsky, E. (1992). The concept of function: Aspects of epistemology and pedagogy. Washington, DC: Mathematical Association of America.

Hohenwarter, M., Preiner, J., & Yi, T. (2007). Incorporating GeoGebra into Teaching Mathematics at the College Level. The International Conference for Technology in Collegiate Mathematics, Washington DC, USA.

Hollar, J. C., & Norwood, K. (1999). The effects of a graphing-approach intermediate algebra curriculum on students’ understanding function. Journal for Research In Mathematics Education, 30, 220-226.

Johari, A. (1998). Effects Of İnductive Multimedia Programs On Creation Of Linear Function And Variable Conceptualization, Unpublished Doctoral Dissertation, Arizona State University, Arizona.

Kabael, T. (2011). Tek değişkenli fonksiyonların iki değişkenli fonksiyonlara genellenmesi, fonksiyon makinesi ve APOS. Kuram ve Uygulamada Eğitim Bilimleri, 11(1), 465-499.

Kalchman, M. (2001). Using A Neo-Piagetian Framework For Learning And Teaching Mathematical Functions, Unpublished Doctoral Thesis, University of Toronto, Toronto, Canada.

Kleiner, I. (1989). Evolution of the function concept: a brief survey. The College Mathematics Journal, 20(4), 282-300.

LeVeque, J. R. (2003). The development of the function concept in students in freshman precalculus, Unpublished Doctoral Dissertation, Morgan State University, Baltimore, USA.

Mackie, D. (2002). Using computer algebra to encourage a deep learning approach to calculus, 2nd International Conference on the Teaching of Mathematics, Hersonissos, Crete, Greece. Retrieved from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.647.193 &rep=rep1&type=pdf on 20.01.2020.

Mai, T., & Meyer, A. (2018). Sketching Functions As A Digital Task With Automated Feedback. 1st International STACK conference, Friedrich-Alexander-Universität Erlangen-Nürnberg: Fürth, Germany.

Martínez-Planell, R., & Trigueros Gaisman, M. (2012). Students' understanding of the general notion of a function of two variables. Educational Studies in Mathematics, 81, 365-384.

Martinez-Planell, R., & Trigueros-Gaisman, M. (2009). Students’ ideas on functions of two-variables: domain, range and representations. Proceedings of PME-NA, Georgia State University, Atlanta (Georgia), 23-26 September, 73-80.

McMillan, J. H., & Schumacher, S. (2006). Research in education: Evidence-based inquiry (6th Edition). Boston: Pearson.

Nagel, E. A. (1994). Effects of Graphing Calculators on College AlgebraStudents' Understanding of Functions and Graphs, Master, San Diego State University, USA.

National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. Reston, VA: Author. National Governors Association Center for Best Practices, Council of Chief

State School Officers (2010). Common core state standards in mathematics. Washington, DC: Author.

O’Callaghan, B. R. (1998). Computer-Intensive algebra and students’ conceptual knowledge of functions, Journal for Research in Mathematics Education, 29(1), 21-40.

Özkaya, M., & İşleyen, T. (2012). Fonksiyonlarla ilgili bazı kavram yanılgıları. Çankırı Karatekin Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 3(1), 1-32.

Patterson, N., D. & Norwood, K. S. (2004). A case study of teacher beliefs on students’ beliefs about multiple representations. International Journal Of Science And Mathematics Education, 2, 5–23.

Rider, R. L. (2004). The effect of multi-representational methods on students’ knowledge of function concepts in developmental college mathematics, Unpublished Doctoral Dissertation, North Carolina State University, North Carolina, USA.

Saidah, E. (2000). The role of the graphing calculator in teaching and learning of the function: observations in a mathematics classroom, Unpublished Master Dissertation, Concordia University, Montreal, Quebec, Canada.

Sajka, M. (2003). A secondary school student’s understanding of the concept of function – a case study, Educational Studies in Mathematics, 53, 229-254.

Schwarz, B., & Hershkowitz, R. (1999). Prototypes: brakes or levers in learning the function concept? The role of computer tools. Journal for Research in Mathematics Education, 30(4), 362-389.

Selden, A., & Selden, J. (1992). Research perspectives on conceptions of function: summary and overview. In G. Harel and E. Dubinsky (Eds.), The Concept Of Function: Aspects Of Epistemology And Pedagogy (pp.1-16). West LaFayette, IN: Mathematical Association of America.

Sierpinska, A. (1992). On understanding the notion of function’, in G. Harel and E. Dubinsky (Eds.), The Concept of Function: Aspects of Epistemology and Pedagogy, Mathematical Association of America, United States, pp. 25-58.

Şefik, Ö. (2017). Öğrencilerin İki Değişkenli Fonksiyon Kavramını Anlamalarının Apos Teorisi ile Analizi. Yayımlanmamış Yüksek lisans tezi, Hacettepe Üniversitesi Eğitim Bilimleri Enstitüsü: Ankara.

Taylor, J. A. (2013). Translation of Function: A Study of Dynamic Mathematical Software and Its Effects on Students Understanding of Translation of Function. Master Thesis, Science and Mathematics Teaching Center, University of Wyoming, USA.

Trigueros, M., & Martínez-Planell, R. (2010). Geometrical representations in the learning of two-variable functions. Educational Studies in Mathematics, 73(1), 3–19.

Urhan, S., Kuh, G., Günal, İ., & Arkün Kocadere, S. (2018). Sample Activities in Teaching Functions through ICT Support. ERPA International Congresses on Education, İstanbul Üniverstesi: İstanbul, Turkey.

Weber, E., & Thompson, P. W. (2014). Students' images of two-variable functions and their graphs. Educational Studies in Mathematics, 87(1), 67-85.

Wilson, M. R., & Krapfl, C. M. (1994). The impact of graphics calculators on students’ understanding of function. Journal of Computers in Mathematics and Science Teaching 13(3), 252-264.

Yerushalmy, M. (1997). Designing representations: reasoning about functions of two variables. Journal for Research in Mathematics Education, 28(4), 431-466.

Yerushalmy, M. (2000). Problem solving strategies and mathematical resources: a longitudinal view on problem solving in a function based approach to algebra, Educational Studies in Mathematics, 43, 125–147.

Zukhrufurrohmah, Z. (2018). Using technology to find the graph characteristic of quadratic function. Advances in Social Science, Education and Humanities Research (ASSEHR), 160, 251-255.