- Abdullah, N., Zakaria, E., & Halim, L. (2012). The effect of a thinking strategy approach through visual representation on achievement and conceptual understanding in solving mathematical word problems. Asian Social Science, 8(16), 30-37. http://dx.doi.org/10.5539/ass.v8n16p30 [Google Scholar]
- Adu-Gyamfi, K. (2003). External multiple representations in mathematics teaching [Unpublished master’s tesis]. Raleigh: North Carolina State University. [Google Scholar]
- Adu-Gyamfi, K. (2007). Connections among representations: The nature of students’ coordinations on a linear function task [Unpublished doctoral dissertation]. North Carolina State University. [Google Scholar]
- Ahmad, A., Tarmizi, R. A., & Nawawi, M. (2010). Visual representations in mathematical word problem solving among form four students in Malacca. Procedia - Social and Behavioral Sciences, 8, 356-361. https://doi.org/10.1016/j.sbspro.2010.12.050 [Google Scholar] [Crossref]
- Ainstworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 183-198. https://doi.org/10.1016/j.learninstruc.2006.03.001 [Google Scholar] [Crossref]
- Ainsworth, S. E., Bibby, P. A., & Wood, D. J. (1997). Information technology and multiple representations: new opportunities–new problems. Journal of Information Technology for Teacher Education, 6(1), 93-105. https://doi.org/10.1080/14759399700200006 [Google Scholar] [Crossref]
- Akkan, Y. (2009). İlköğretim öğrencilerinin aritmetikten cebire geçiş süreçlerinin incelenmesi [Unpublished doctoral dissertation]. Karadeniz Technical University, Trabzon, Turkey. [Google Scholar]
- Akkuş Çıkla, O. (2004). The effects of multiple representations-based instruction on seventh grade students’ algebra performance, attitude toward mathematics, and representatıon preference [Unpublished doctoral dissertation]. Middle East Technical University, Ankara, Turkey. [Google Scholar]
- Akkuş Çıkla, O., & Çakıroğlu, E. (2006). Seventh grade students' use of multiple representations in pattern related algebra tasks. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 31(31), 13-24. Retrieved from https://dergipark.org.tr/en/pub/hunefd/issue/7807/102391 [Google Scholar]
- Altun, M. (2011). Eğitim fakülteleri ve lise matematik öğretmenleri için liselerde matematik öğretimi. Bursa: Aktüel Alfa Akademi [Google Scholar]
- Bal, A. P. (2014). The examination of representations used by classroom teacher candidates in solving mathematical problems. Educational Sciences: Theory & Practice, 14(6). 2349-2365. https://doi.org/10.12738/estp.2014.6.2189 [Google Scholar] [Crossref]
- Carraher, D. W., Martinez, M. V., & Schliemann, A. D. (2008). Early algebra and mathematical generalization. ZDM, Mathematics Education, 40(1), 3-22. [Google Scholar]
- Cetin, H., & Ertekin, E. (2011). The Relationship between Eighth Grade Primary School Students' Proportional Reasoning Skills and Success in Solving Equations. International Journal of Instruction, 4(1), 47-62. [Google Scholar]
- Çetin, H., & Aydın, S. (2019). The Effect of Multiple Representation Based Instruction on Mathematical Achievement: A Meta-Analysis. International Journal of Educational Research Review, 5(1), 26-36. [Google Scholar]
- Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications. [Google Scholar]
- Çağdaşer, B. T. (2008). Cebir öğrenme alanının yapılandırmacı yaklaşımla öğretiminin 6. sınıf öğrencilerinin cebirsel düşünme düzeyleri üzerindeki etkisi [Unpublished master’s thesis]. Uludag University, Bursa, Turkey. [Google Scholar]
- Dede, Y. & Argün, Z. (2003). Cebir, öğrencilere niçin zor gelmektedir?.Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 180-185. [Google Scholar]
- Dibbs, R. A., Hott, B. L., Martin, A., Raymond, L., & Kline, T. (2020). Combining like terms: A qualitative meta-synthesis of Algebra I interventions in mathematics and special education. International Journal of Education in Mathematics, Science and Technology (IJEMST), 8(3), 219-232. [Google Scholar]
- Dreher, A., & Kuntze, S. (2015). Teachers facing the dilemma of multiple representations being aid and obstacle for learning: evaluations of tasks and theme-specific. Journal für Mathematik-Didaktik, 36(1), 23-44. https://doi.org/10.1007/s13138-014-0068-3 [Google Scholar] [Crossref]
- Duncan, A. G. (2010). Teachers’ views on dynamically linked multiple representations, pedagogical practices and students’ understanding of mathematics using TI-N spire in Scottish secondary schools. ZDM Mathematics Education, 42, 763-774. doi:10.1007/s11858-010-0273-6. https://doi.org/10.1007/s11414-013-9386-3 [Google Scholar] [Crossref]
- Dündar, S. (2015). Mathematics teacher-candidates’ performance in solving problems with different representation styles: the trigonometry example. Eurasia Journal of Mathematics, Science and Technology Education, 11(6), 1379-1397. https://doi.org/10.12973/eurasia.2015.1396a [Google Scholar] [Crossref]
- Durmuş, S., & Yaman, H. (2002). Mevcut teknolojilerin sunduğu çoklu temsil olanaklarının oluşturmacı yaklaşıma getireceği yenilikler: 5. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi, Orta Doğu Teknik Üniversitesi: Ankara. [Google Scholar]
- Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning. In F. Hitt & M. Santos (Eds.), Proceedings of the 21st Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. I, pp. 3–26). Cuernavaca: Mexico. [Google Scholar]
- Erbaş, A. K. (2005). Çoklu gösterimlerle problem çözme ve teknolojinin rolü. TOJET: The Turkish Online Journal of Educational Technology, 4(4), 88-92. [Google Scholar]
- Ersoy, Y. & Erbaş, K. (2005). Kassel projesi cebir testinde bir grup Türk öğrencinin genel başarısı ve öğrenme güçlükleri. İlköğretim Online, 4(1),18-39. [Google Scholar]
- Gagatsis, A., & Elia, I. (2004). The effects of different modes of representation on mathematical problem solving. International Group for the Psychology of Mathematics Education. Retrieved from https://files.eric.ed.gov/fulltext/ED489751.pdf [Google Scholar]
- Gilbert J. K. (2010). The role of visual representations in the learning and teaching of science: An introduction. Asia-Pacific Forum on Science Learning and Teaching, 11(1), 1-19. [Google Scholar]
- Goldin, G. A. (1998). Representations, learning and problem solving in mathematics. Journal of Mathematical Behavior, 17(2), 137-165. https://doi.org/10.1016/S0364-0213(99)80056-1 [Google Scholar] [Crossref]
- Goldin, G. A. (2004). Representations in school mathematics: a unifying research perspectives. In J. Kilpatrick, W. G. Martin ve D. Schifter (Ed.), A Research Companion to Principles and Standards for School Mathematics (pp. 275-285). Reston, VA: NCTM. [Google Scholar]
- Greenes, C. E., & Findell, C. R. (1998). Groundworks: Algebra Puzzles & Problems. Creative Publications. [Google Scholar]
- Gürbüz, R., & Şahin, S. (2015). 8. Sınıf öğrencilerinin çoklu temsiller arasındaki geçiş becerileri. Kastamonu Eğitim Dergisi, 23(4), 1869-1888. Retrieved from https://dergipark.org.tr/en/pub/kefdergi/issue/22597/241376 [Google Scholar]
- Herbert, K. & Brown, R. (1997). Patterns as tools for algebraic reasoning. Teachinkilpatrig Children Mathematics, 3, 340-345. https://doi.org/10.5951/TCM.3.6.0340 [Google Scholar] [Crossref]
- Herman, M. (2007). What students choose to do and have to say about use of multiple representations in college algebra. Journal of Computers in Mathematics and Science Teaching, 26(1), 27-54. Retrieved from https://www.learntechlib.org/primary/p/21086/. [Google Scholar]
- Hoyles, C., Noss, R., & Kaput, J. (2002). Developing new notations for a learnable mathematics in the computation alera. In Handbook of international research in mathematics education (pp. 63-88). Routledge. [Google Scholar]
- İpek, A. S., & Okumuş, S. (2012). İlköğretim matematik öğretmen adaylarının matematiksel problem çözmede kullandıkları temsiller. Gaziantep University Journal of Social Sciences, 11(3), 681-700. Retrieved from https://dergipark.org.tr/en/pub/jss/issue/24238/256948 [Google Scholar]
- İzgiol, D. (2014). Teknoloji destekli çoklu temsil temelli öğretimin öğrencilerin lineer cebir öğrenimine ve matematiğe yönelik tutumlarına etkisi [Unpublished master’s thesis]. Dokuz Eylul University, İzmir, Turkey. [Google Scholar]
- Kabael, U. T. & Tanışlı, D. (2010). Cebirsel düşünme sürecinde örüntüden fonksiyona öğretim. İlköğretim Online Dergisi, 9(1), 213-228. [Google Scholar]
- Kaf, Y. (2007). Matematikte model kullanımının 6. sınıf öğrencilerinin cebir erişilerine etkisi [Unpublished master’s thesis]. Hacettepe University, Ankara, Turkey. [Google Scholar]
- Kaput, J. J. (1998). Representations, inscripions, descriptions and learning: a kaleidoscope of windows. Journal of Mathematical Behavior,17(2), 265-281. [Google Scholar]
- Kaya, D. (2015). Çoklu temsil temelli öğretimin öğrencilerin cebirsel muhakeme becerilerine, cebirsel düşünme düzeylerine ve matematiğe yönelik tutumlarına etkisi üzerine bir inceleme [Unpublished doctoral dissertation]. Dokuz Eylul University, İzmir, Turkey. [Google Scholar]
- Kaya, D., Keşan, C., İzgiol, D., & Erkuş, Y. (2016). Yedinci sınıf öğrencilerinin cebirsel muhakeme becerilerine yönelik başarı düzeyi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 7(1), 142-163. [Google Scholar]
- Kendal, M. (2002). Teaching and learning introductory differential calculus [Unpublished doctoral dissertation]. The University of Melbourne, Australia. [Google Scholar]
- Kılıç, Ç., & Özdaş, A. (2010). İlköğretim 5. sınıf öğrencilerinin kesirlerde karşılaştırma ve sıralama yapmayı gerektiren problemlerin çözümlerinde kullandıkları temsiller. Kastamonu Eğitim Dergisi, 18(2), 513-530. [Google Scholar]
- Kilpatrick, J., J. Swafford, J. & B. Findell. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. [Google Scholar]
- Kriegler, S. (2004). Just What is Algebraic Thinking?.http://www.match.ucla.edu/-kriegler/pub/algebrat.htlm, Erişim Tarihi: 07.03.2014. [Google Scholar]
- López-Ibáñez, M., Prasad, T. D., & Paechter, B. (2005). Optimal pump scheduling: Representation and multiple objectives. In Proceedings of the eighth International Conference on Computing and Control for the Water Industry, 1, 117-122. [Google Scholar]
- Mallet, D. G. (2007). Multiple representations for systems of linear equations via computer algebra system maple. International Electronic Journal of Mathematics Education. 2(1). 16-31. [Google Scholar]
- Mills, G. E., & Gay, L. R. (2016) Education research: Competencies for analysis and applications. London, England: Pearson Education. [Google Scholar]
- MoNE. (2009). İlköğretim matematik dersi 6-8. sınıflar öğretim programı ve kılavuzu. Ankara: MoNE. [Google Scholar]
- MoNE. (2017). İlköğretim matematik dersi 5-8. sınıflar öğretim programı ve kılavuzu. Ankara: MoNE. [Google Scholar]
- Nathan, J. M., & Koellner, K. (2007). A Framework for understanding and cultivating the transition from arithmetic to algebraic reasoning. Mathematical Thinking and Learning, 9(3), 179-192. [Google Scholar]
- National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: NCTM. [Google Scholar]
- National Council of Teachers of Mathematics [NCTM]. (2008). The role of technology in the teaching and learning of mathematics. Reston, VA: National Council of Teacher of Mathematics. [Google Scholar]
- Özgün Koca, S.A. (2004). The effects of multiple linked representations on students’ learning of linear relationships. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 26, 82-90. [Google Scholar]
- Pallant, J. (2001). SPSS Survival Manual: A Step by Step Guide to Data Analysis Using SPSS for Windows (Versions 10 and 11): SPSS Student Version 11.0 for Windows. Open University Press. [Google Scholar]
- Parkinson, A., & Redmond, J. A. (2002). Do cognitive styles affect learning performance in different computer media?. ACM SIGCSE Bulletin, 34(3), 39-43. [Google Scholar]
- Plano Clark, V. L., & Creswell, J. W. (2011). Designing and conducting mixed methods research. Sage Publications. [Google Scholar]
- Roschelle, J. M., Pea, R. D., Hoadley, C. M., Gordin, D. N., & Means, B. M. (2000). Changing how and what children learn in school with computer-based technologies. The future of children, 76-101. [Google Scholar]
- Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, meta-cognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for Research on Mathematics Teaching and Learning. New York: MacMillan. [Google Scholar]
- Seçer, İ. (2015). SPSS ve LISREL ile pratik veri analizi: Analiz ve raporlaştırma. Ankara: Anı Yayıncılık. [Google Scholar]
- Selling, S. K. (2016). Learning to represent, representing to learn. The Journal of Mathematical Behavior, 41, 191-209. [Google Scholar]
- Sevimli, E. (2009). Matematik öğretmen adaylarının belirli integral konusundaki temsil tercihlerinin uzamsal yetenek ve akademik başarı bağlamında incelenmesi (Unpublished master’s thesis). Marmara University, İstanbul, Turkey. [Google Scholar]
- Stylianou, D. A. (2002). On the interaction of visualization and analysis: the negotiation of a visual representation in expert problem solving. The Journal of Mathematical Behavior, 21(3), 303-317. [Google Scholar]
- TIMSS (2003). IEA’s TIMSS 2003 international report on achievement in the mathematics cognitive domains: Findings from a developmental project international association for the evaluation of educational achievement. TIMSS & PIRLS International Study Lynch School of Education, Boston College. [Google Scholar]
- Warren, E., & Cooper, T. J. (2009). Developing mathematics understanding and abstraction: The case of equivalence in the elementary years. Mathematics Education Research Journal, 21(2), 76-95. [Google Scholar]
- Yenilmez, K. & Avcu, T. (2009). Altıncı sınıf öğrencilerinin cebir öğrenme alanındaki başarı düzeyleri. Ahi Evran Üniversitesi Eğitim Fakültesi Dergisi, 10(2), 37-45. [Google Scholar]
- Yenilmez, K. & Teke, M. (2008). Yenilenen matematik programının öğrencilerin cebirsel düşünme düzeylerine etkisi. İnönü Üniversitesi Eğitim Fakültesi Dergisi, 9(15), 229-246. [Google Scholar]
|