International Association of Educators   |  ISSN: 1949-4270   |  e-ISSN: 1949-4289

Original article | Educational Policy Analysis and Strategic Research 2022, Vol. 17(1) 295-311

Examination of Mathematical Errors and Mistakes in Calculus Course

Davut Köğce

pp. 295 - 311   |  DOI: https://doi.org/10.29329/epasr.2022.248.15   |  Manu. Number: MANU-2108-11-0002.R1

Published online: March 01, 2022  |   Number of Views: 61  |  Number of Download: 319


Abstract

This study was conducted to identify mathematical errors and mistakes made by preservice elementary mathematics teachers in the calculus course. To that end, the document analysis method of qualitative research models was used in the research. The sample of the research included a total of 75 preservice teachers who were attending the Department of Elementary Mathematics Education in the Faculty of Education at a public university and taking the calculus I course during the fall term of 2016-2017 academic year. Accordingly, written documents including the participant preservice teachers’ papers of interim exams, practice exams, and general exams constituted the data source. The exam papers were scanned with a scanner and transformed into the electronic environment. A content analysis was performed with the data by using MAXQDA 12 qualitative data analysis program, and “data coding” of data analysis techniques was utilized. It was concluded that the preservice teachers made procedural and conceptual errors and mistakes, mathematical errors and mistakes such as recalling generalizations incompletely or incorrectly. Some recommendations were made in light of these results.

Keywords: Preservice mathematics teachers, Calculus course, Mathematical errors, Mathematical mistakes


How to Cite this Article?

APA 6th edition
Kogce, D. (2022). Examination of Mathematical Errors and Mistakes in Calculus Course . Educational Policy Analysis and Strategic Research, 17(1), 295-311. doi: 10.29329/epasr.2022.248.15

Harvard
Kogce, D. (2022). Examination of Mathematical Errors and Mistakes in Calculus Course . Educational Policy Analysis and Strategic Research, 17(1), pp. 295-311.

Chicago 16th edition
Kogce, Davut (2022). "Examination of Mathematical Errors and Mistakes in Calculus Course ". Educational Policy Analysis and Strategic Research 17 (1):295-311. doi:10.29329/epasr.2022.248.15.

References
  1. Baki, M., & Çekmez, E. (2012). Prospective elementary mathematics teachers’ understandings about the formal definition of limit. Turkish Journal of Computer and Mathematics Education, 3(2), 81-98. [Google Scholar]
  2. Balcı, M. (2016). Matematik analiz 1.  Ankara: Palme Yayıncılık. [Google Scholar]
  3. Barak, B. (2007). Diagnosis of misconceptions about limit concept (Unpublished master’s thesis). Balıkesir University, Balıkesir. [Google Scholar]
  4. Brasell, H. M. & Rowe, M. B. (1993). Graphing skills among high school physics students. School Science and Mathematics, 93(2), 63-70. [Google Scholar]
  5. Çepni, S. (2012). Araştırma ve proje çalışmalarına giriş (6. Baskı). Trabzon: Celepler Matbaacılık.  [Google Scholar]
  6. Delice, A., & Sevimli, E. (2012). An investigating calculus students’ solution processes of integral volume problems in terms of thinking abilities. Marmara University Atatürk Education Faculty Journal of Educational Sciences, 36(36), 95-113. [Google Scholar]
  7. Demir, H. (2008). Teori ve temelleri ile analiz I (1. Baskı). Ankara: Pegem Akademik Yayıncılık. [Google Scholar]
  8. Dereli, A. B. (2015). The identification the errors and misconceptions of the elementary mathematics teacher candidates' related to the sequences and series (Unpublished master’s thesis). İnönü University, Malatya. [Google Scholar]
  9. Doruk, M., & Kaplan, A. (2018).  Pre-service mathematics teachers’ understanding of fundamental calculus definitions. İnönü University Journal of the Faculty of Education, 19(3), 117-140. doi: 10.17679/inuefd.298371 [Google Scholar] [Crossref] 
  10. Driver, R., & Easley, Y. (1978). Pupils and paradigms: a review of literature related to concept development in adolescent science students. Studies in Science Education, 5, 61-84. [Google Scholar]
  11. Gökçek, T., & Açıkyıldız, G. (2016). Preservice mathematics teachers’ errors related to derivative. Turkish Journal of Computer and Mathematics Education, 7(1), 112-141. doi: 10.16949/turcomat.14647  [Google Scholar] [Crossref] 
  12. Göktaş, H., & Erdoğan, A. (2016). Prospective mathematics teachers’ conceptual structure about continuity. Journal of Research in Education and Teaching, 5(3), 208-217.  [Google Scholar]
  13. Gür, H., & Barak, B. (2007). The erroneous derivative examples of eleventh grade students. Educational Sciences: Theory & Practice, 7(1), 453-480. [Google Scholar]
  14. Jones, K. (2000). The student experience of mathematical proof at university level. International Journal of Mathematical Education in Science and Technology, 31(1), 53-60. doi:10.1080/002073900287381  [Google Scholar] [Crossref] 
  15. Kabaca, T. (2011). Matematiğin deneysel gelişimi ve öğretimindeki uzantısı: analiz dersi örneği. Pamukkale University Journal of Education, 30(30), 173-177. [Google Scholar]
  16. Karasar, N. (2019). Bilimsel araştirma yöntemi: kavramlar, ilkeler ve teknikler (34. Baskı). Ankara: Nobel Yayın Dağıtım. [Google Scholar]
  17. Kertil, M. (2014). Pre-service elementary mathematics teachers' understanding of derivative through a model development unit (Unpublished doctoral dissertation). Middle East Technical University, Ankara. [Google Scholar]
  18. Koparan, T., Yıldız, C., Köğce, D., & Güven, B. (2010). The effect of conceptual change approach on 9th grade students’ achievement. Procedia Social and Behavioral Sciences, 2(2), 3926-3931. doi:10.1016/j.sbspro.2010.03.618  [Google Scholar] [Crossref] 
  19. Kramarski, B. (2004). Making sense of graphs: Does metacognitive instruction make a difference on students’ mathematical conceptions and altenative conceptions? Learning and Instruction, 14(6), 593-619. doi: 10.1016/j.learninstruc.2004.09.003 [Google Scholar] [Crossref] 
  20. Merriam, S. B. (1988). Case study research in education: a qualitative approach. San Francisco (C.A): Jossey-Bass.  [Google Scholar]
  21. Mevarech, Z. R. & Kramarsky, B. (1997). From verbal descriptions to graphic representations: Stability and change in students’ alternative conceptions. Educational Studies in Mathematics, 32, 229-263. doi:10.1023/A:1002965907987 [Google Scholar] [Crossref] 
  22. Miles, M. & Huberman, M. (1994). An expanded source book qualitative data analysis (2nd Ed.). Thousand Oaks (CA): Sage Publications. [Google Scholar]
  23. Özmantar, M. F., Bingölbali, E. & Akkoç, H. (2013). Matematiksel kavram yanılgıları ve çözüm önerileri. Ankara: Pegem Akademi Yayıncılık.  [Google Scholar]
  24. Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri. Ankara: Pegem Akademi. [Google Scholar]
  25. Sierpinska, A. (1992). On understanding the notion of function. In Harel. G. & Dubinsky, E. (Eds.), MAA Notes and Reports Series: 25-58. [Google Scholar]
  26. Sofronas, K. S., DeFranco, T.C., Vinsonhaler, C., Gorgievski, N., Schroeder, L., & Hamelin, C. (2011). What does it mean for a student to understand the first-year calculus? Perspectives of 24 experts. The Journal of Mathematical Behavior, 30(2), 131-148. doi:10.1016/j.jmathb.2011.02.001 [Google Scholar] [Crossref] 
  27. Tall, D. (1992). The transition to advanced mathematical thinking: functions, limits, infinity and proof. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning. New York: Macmillan. [Google Scholar]
  28. Ubuz, B.(1999). Genel matematikde calculus öğrenci hataları. Matematik Dünyası, 8, 9-11. [Google Scholar]
  29. Weber, K. (2001). Student difficulty in constructing proof: the need for strategic knowledge. Educational Studies in Mathematics, 48(1), 101–119. doi:10.1023/A:1015535614355 [Google Scholar] [Crossref] 
  30. Yıldırım, A. & Şimşek, H. (2018). Sosyal bilimlerde nitel araştirma yöntemleri (11. Baskı). Ankara: Seçkin Yayıncılık. [Google Scholar]
  31. Yıldız, C., Baki, A., Aydın, M., & Köğce, D. (2010). Development of materials in instruction of decimals according to constructivist approach. Procedia Social and Behavioral Sciences, 2(2), 3660-3665. doi: 10.1016/j.sbspro.2010.03.569  [Google Scholar] [Crossref] 
  32. Yıldız, C., Taşkın, D., Aydın, M., & Köğce, D. (2011). The effect of instructional materials on decimal fractions to the conceptual change. Procedia Social and Behavioral Sciences, 15, 899-903. doi:10.1016/j.sbspro.2011.03.208 [Google Scholar] [Crossref] 
  33. Yıldız, C., Taşkın, D., Köğce, D., & Aydın, M. (2011). The effect of instructional materials developed in relation to decimal fractions on success. Procedia Social and Behavioral Sciences, 15, 859-863. doi: 10.1016/j.sbspro.2011.03.199 [Google Scholar] [Crossref] 
  34. Yin, R. K. (1994). Case study research design and methods (2nd Ed.). Thousand Oaks (CA): Sage. [Google Scholar]
  35. Zandieh, M. J. (2000). A theoretical framework for analyzing student understanding of the concept of derivative. CBMS Issues in Mathematics: Research in Collegiate Mathematics Education, 4(8), 103-127. [Google Scholar]