A study on multiple representation and self-efficacy perception in systems of linear equations

References

• Abalı-Öztürk, Y., & Şahin, Ç. (2015). Matematiğe ilişkin akademik başarı, öz yeterlilik ve tutum arasındaki ilişkilerin belirlenmesi [Determining the relationships between academic achievement, self-efficacy and attitudes towards maths]. The Journal of Academic Social Science Studies, 31(1), 343–366. https://doi.org/10.9761/JASSS2621
   Google Scholar
• Adu-Gaymfi, K. (2007). Connections among representations: The nature of students’ coordinations on a linear function task [Unpublished doctoral dissertation]. Math, Science and Technology Education.
   Google Scholar
• Akyıldız, P. (2013). İlköğretim matematik öğretmen adaylarının lineer cebir dersine yönelik tutumları ve alan Dili becerilerinin incelenmesi [An inquiry into the attitudes of the prospective primary education math teachers towards linear algebra course and their field language skills] [Master's thesis]. Gazi University. Turkish Higher Education Council thesis repository (#333427). https://tez.yok.gov.tr/UlusalTezMerkezi/
   Google Scholar
• Arseven, A. (2016). Self-effıcacy: A concept analysıs. Journal of Turkish Studies, 11(19), 63–80. https://doi.org/10.7827/TurkishStudies.10001
   Google Scholar
• Aydın, E., & Delice, A. (2008). Ölçme ve değerlendirmeye kavram yanılgıları perspektifinden bir bakış [An overview of measurement and evaluation from the perspective of misconceptions]. In M. F. Özmantar, E. Bingölbali, & H. Akkoç (Eds.), Matematiksel kavram yanılgıları ve çözüm önerileri [Mathematical misconceptions and solution suggestions] (pp. 393–436). Pegem Akademi.
   Google Scholar
• Aydın, E., Delice, A., & Kardeş, D. (2011). Matematik öğretmen adaylarına yönelik lineer denklem sistemleri öz-yeterlik algısı ölçeği [Development of a scale measuring mathematics teacher candidates’ self efficacy perceptions in solving systems of linear equations]. Turkish Journal of Computer and Mathematics Education, 2(2), 160–182. https://dergipark.org.tr/en/pub/turkbilmat/issue/21564/231444
   Google Scholar
• Aydın, S. (2009). On linear algebra education. Inonu University Journal of The Faculty of Education, 10(1), 93–105.
   Google Scholar
• Baki, A. (1996). Matematik öğretiminde bilgisayar herşey midir [Is computer everything in mathematics teaching? Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, (12), 135–143. http://www.efdergi.hacettepe.edu.tr/cilt-sayi-12-yil-1996.html.
   Google Scholar
• Balcı, A. (2005). Açıklamalı Eğitim Yönetim terimler Sözlüğü [Annotated Educational Management terms dictionary]. Tek Ağaç.
   Google Scholar
• Bandura, A. (1986). Social foundations of thought and action: A social cognitive theory. Prentice–Hall.
   Google Scholar
• Bandura, A. (1997). Self-efficacy: The exercise of control. Freeman.
   Google Scholar
• Bandura, A. (2010). Self-efficacy. In I. B. Weiner, & W. E. Craighead (Eds.), The corsini encyclopedia of psychology (pp. 1–3). John Wiley & Sons Inc. https://doi.org/10.1002/9780470479216.corpsy0836
   Google Scholar
• Cassidy, S., & Eachus, P. (2002). Developing the computer self-efficacy (CSE) scale: Investigating the relationship between CSE, gender and experience with computers. Journal of Educational Computing Research, 26(2), 133–153. https://www.academia.edu/download/49373362/Development_of_the_Computer_User_Self-Ef20161005-27752-1vxm0k.pdf.
   Google Scholar
• Çilenti, K. (1988). Eğitim teknolojisi ve öğretim [Educational technology and teaching]. Yargıcı Matbaası.
   Google Scholar
• Delice, A., Aydın, E., & Kardeş-Birinci, D. (2014). An investigation of pre-service mathematics teachers’ performances on systems of linear equations with in the context of self-efficacy levels. International Journal of Educational Studies in Mathematics, 1(2), 19–33. https://dergipark.org.tr/en/download/article-file/397450. https://doi.org/10.17278/ijesim.2014.02.002
   Google Scholar
• Delice, A., & Sevimli, E. (2010). Öğretmen adaylarının çoklu temsil kullanma becerilerinin problem çözme başarıları yönüyle incelenmesi: Belirli integral örneği [An investigation of the pre-services teachers’ ability of using multiple representations in problem-solving success: The case of definite integral]. Kuram ve Uygulamada Eğitim Bilimleri, 10(1), 111–149.
   Google Scholar
• Delice, A., & Sevimli, E. (2016). Matematik Eğitiminde Çoklu Temsiller [Multiple representations in mathematics education]. In E. Bingölbali, S. Arslan, & İÖ Zembat (Eds.), Matematik Eğitiminde Teoriler [Theories in mathematics education] (pp. 519–537). Pegem Akademi.
   Google Scholar
• Dogan, H. (2018). Differing instructional modalities and cognitive structures: Linear algebra. Linear Algebra and its Applications, 542, 464–483. https://doi.org/10.1016/j.laa.2017.07.007
   Web of Science ®Google Scholar
• Duman, B., & Yakar, A. (2017). Öğretime yönelik duyuşsal farkındalık ölçeği [The scale of affective awareness towards ınstruction]. Cumhuriyet International Journal of Education, 6(1), 200–229. https://dergipark.org.tr/en/download/article-file/314401. https://doi.org/10.30703/cije.321453
   Google Scholar
• Ertekin, E., Solak, S., & Yazıcı, E. (2010). The effects of formalism on teacher trainees’ algebraic and geometric interpretation of the notions of linear dependency/independency. International Journal of Mathematical Education in Science and Technology, 41(8), 1015–1035. https://doi.org/10.1080/0020739X.2010.500689
   Google Scholar
• Girard, N. R. (2002). Students’ representational approaches to solving calculus problems: Examining the role of graphing calculators [Unpublished doctoral dissertation]. University of Pittsburg.
   Google Scholar
• Goldin, G. A. (1998). Representational systems, learning, and problem solving in mathematics. The Journal of Mathematical Behavior, 17(2), 137–165. https://doi.org/10.1016/S0364-0213(99)80056-1
   Google Scholar
• Goldin, G. A., & Kaput, J. J. (1996). A joint perspective on the idea of representation in learning and doing mathematics. In L. P. Steffe, P. Nesher, P. Cobb, G. A. Goldin & B. Greer (Eds.), Theories of mathematical learning (pp. 397–430). Lawrence Erlbaum Associates.
   Google Scholar
• Haddad, M. (1999). Difficulties in the learning and teaching of linear algebra–a personal experience [Unpublished Master Dissertation]. Concordia University. Montreal.
   Google Scholar
• Harel, G. (1989). Learning and teaching linear algebra: Difficulties and an alternative approach to visualizing concepts and processes. Focus on Learning Problems in Mathematics, 11(2), 139–148.
   Google Scholar
• Harel, G. (2000). Three principles of learning and teaching mathematics. In J. L. Dorier (Ed.), On the teaching of linear algebra (pp. 177–189). Springer.
   Google Scholar
• Harel, G. (2017). The learning and teaching of linear algebra: Observations and generalizations. The Journal of Mathematical Behavior, 46, 69–95. https://doi.org/10.1016/j.jmathb.2017.02.007
   Web of Science ®Google Scholar
• Hiebert, J., & Carpenter, T. P. (1992). Learning and teaching with understanding. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 65–100). Reston.
   Google Scholar
• Hillel, J., & Sierpinska, A. (1994, July 29-August 3). On one persistent mistake in linear algebra, Proceedings of the 18th International Conference on the Psychology of Mathematics Education, Lisbon, Portugal, (vol. 1, pp. 65–72).
   Google Scholar
• Kaplan, T. (2011). Lineer denklem sistemleri ve uygulama alanları [Linear equation systems and their applications] [Master's thesis]. Atatürk University. Turkish Higher Education Council thesis repository (#299752). https://tez.yok.gov.tr/UlusalTezMerkezi/
   Google Scholar
• Kardeş, D. (2010). Matematik öğretmen adaylarının lineer denklem sistemleri çözüm süreçlerinin öz-yeterlik algısı ve çoklu temsil bağlamında incelenmesi [An investigation of the processes of pre-services mathematics teachers? Solving systems of linear equations within the context of self-efficacy and multiple representations] [Master's thesis]. Marmara University. Turkish Higher Education Council thesis repository (#264144). https://tez.yok.gov.tr/UlusalTezMerkezi/
   Google Scholar
• Konyalıoğlu, A. C., İpek, A. S., & Işık, A. (2003). On the teaching linear algebra at the university level: The role of visualization in the teaching vector spaces. Research in Mathematical Education, 7(1), 59–67. https://www.koreascience.or.kr/article/JAKO200311921733962.pdf
   Google Scholar
• Köroğlu, H., & Yeşildere, S. (2004). İlköğretim yedinci sınıf matematik dersi tamsayılar ünitesinde çoklu zeka teorisi tabanlı öğretimin öğrenci başarısına etkisi [Learner achievement effect of the multiple intelligences theory based teaching in the unit of whole numbers at the primary education seventh grade mathematics course]. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 24(2), 25–41. https://dergipark.org.tr/en/download/article-file/77316.
   Google Scholar
• Mallet, D. G. (2007). Multiple representations for systems of linear equations via the computer algebra system Maple. International Electronic Journal of Mathematics Education, 2(1), 16–32. https://doi.org/10.29333/iejme/173
   Google Scholar
• Malpass, J. R., O'Neil, H. F., & Hocevar, D. (1999). Self-regulation, goal orientation, self-efficacy, worry, and high-stakesmath achievement for mathematically gifted high school students. Roeper Review, 21(4), 281–288. https://doi.org/10.1080/02783199909553976
   Google Scholar
• National Council of Teachers of Mathematics [NCTM]. (2000). Principals and standards for school mathematics. NCTM.
   Google Scholar
• Oktaç, A. (2008). Ortaöğretim düzeyinde lineer cebir ile ilgili kavram yanılgıları [Misconceptions about linear algebra at secondary level]. In M. F. Özmantar, E. Bingölbali, & H. Akkoç (Eds.), Matematiksel Kavram Yanılgıları ve Çözüm Önerileri [Mathematical misconceptions and solution suggestions] (pp. 329–358). Pegem.
   Google Scholar
• Oktaç, A. (2018). Conceptions about system of linear equations and solution. In S. Stewart, C. Andrews-Larson, A. Berman & M. Zandieh (Eds.), Challenges and strategies in teaching linear algebra (pp. 71–101). Springer.
   Google Scholar
• Pajares, F. (1996). Self-efficacy beliefs in academic settings. Review of Educational Research, 66(4), 543–578. https://doi.org/10.3102/00346543066004543
   Web of Science ®Google Scholar
• Panasuk, R. M., & Beyranevand, M. L. (2010). Algebra students’ ability to recognize multiple representations and achievement. International Journal for Mathematics Teaching & Learning. https://www.cimt.org.uk/journal/
   Google Scholar
• Schultz, J. E., & Waters, M. S. (2000). Why representations? Mathematics Teacher, 93(6), 448–453. https://doi.org/10.5951/MT.93.6.0448
   Google Scholar
• Sevimli, E. (2009). Matematik öğretmen adaylarının belirli integral konusundaki temsil tercihlerinin uzamsal yetenek ve akademik başarı bağlamında incelenmesi [Consideration of pre-services mathematics teachers? preferences of representation in terms of definite integral within the context of certain spatial abilities and academic achievement] [Master's thesis]. Marmara University. Turkish Higher Education Council thesis repository (#250855). https://tez.yok.gov.tr/UlusalTezMerkezi/
   Google Scholar
• Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77(1), 20–26. http://www.davidtall.com/skemp/pdfs/instrumental-relational.pdf.
   Google Scholar
• Smith, J., Lee, I., Zandieh, M., & Andrews-Larson, C. (2021). Two students’ conceptions of solutions to systems of linear equations. In S. S. Karunakaran & A. Higgins (Eds.), Proceedings of the research in undergraduate mathematics education [RUME Reports] (pp. 308–315). http://sigmaa.maa.org/rume/2021_RUME_Reports.pdf
   Google Scholar
• Tabachnick, B. T., & Fidell, L. S. (2006). Using multivariate statistics, international edition (5th ed.). Allynand Bacon.
   Google Scholar
• Tekay, T., & Doğan, M. (2015). İlköğretim 7. sınıf Öğrencilerinin Doğrusal Denklemlerin Grafikleri İle İlgili Soruları Çözme Becerilerinin Değerlendirilmesi [Evaluation of Primary School 7th Grade Students’ Skills in Solving Questions Related to Graphs of Linear Equations]. Matder Matematik Eğitimi Dergisi, 2(1), 1–9. https://dergipark.org.tr/en/download/article-file/109324.
   Google Scholar
• Tonbuloğlu, B., Aslan, D., Altun, S., & Aydın, H. (2013). Proje tabanlı öğrenmenin öğrencilerin bilişüstü becerileri ve öz-yeterlik algıları ile proje ürünleri üzerindeki etkisi [The impact of project based learning on students’ meta cognitive skills, perceptions of self-sufficiency and project outcomes]. Mustafa Kemal Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 10(23), 97–117. https://dergipark.org.tr/en/download/article-file/182917.
   Google Scholar
• Trigueros, M., Oktaç, A., & Manzanero, L. (2007, February 22–26). Understanding of systems of equations in linear algebra. Proceedings of the 5th Congress of the European Society for Research in Mathematics Education (pp. 2359–2368).
   Google Scholar
• Tuğran, Z. (2015). İşbirlikli Öğrenmenin Lise Öğrencilerinin Matematik Öz yeterlik Algısı ve Başarısı Üzerindeki Etkisi [The effects of cooperative learning on high school students perception of self - efficacy and mathematics achievement] [Master's thesis]. Çanakkale On sekiz Mart University. Turkish Higher Education Council thesis repository (#391267). https://tez.yok.gov.tr/UlusalTezMerkezi/
   Google Scholar
• Tuluk, G. (2014). Sınıf öğretmeni adaylarının nokta, çizgi, yüzey ve uzay bilgileri ve çoklu temsilleri [Pre-service classroom teachers’ knowledge on point, line, plane and space and their representation]. Kastamonu Eğitim Dergisi, 22(1), 361–384. https://dergipark.org.tr/tr/pub/kefdergi/issue/22603/241534.
   Google Scholar
• Turgut, M. (2010). Teknoloji Destekli Lineer Cebir Öğretiminin İlköğretim Matematik Öğretmen Adaylarının Uzamsal Yeteneklerine Etkisi [The effect of technology assisted linear algebra instruction on pre-service primary mathematics teachers? spatial ability] [Doctoral dissertation, Marmara University]. Turkish Higher Education Council thesis repository (#265541). https://tez.yok.gov.tr/UlusalTezMerkezi/
   Google Scholar
• Turgut, M., & Yılmaz, S. (2012). İlköğretim 7. ve 8. sınıf öğrencilerinin uzamsal yeteneklerinin incelenmesi [Investigation of 7th and 8th grade students’ spatial ability]. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 19, 69–79. https://dergipark.org.tr/en/download/article-file/786964.
   Google Scholar
• Wu, H. (2004). Computer aided teaching in linear algebra. The China Papers, 3 July, 100–102.
   Google Scholar
• Zandieh, M., & Andrews-Larson, C. (2019). Symbolizing while solving linear systems. ZDM Mathematics Education, 51(7), 1183–1197. https://doi.org/10.1007/s11858-019-01083-3
   Google Scholar