Examination of lecturers' content preferences in the teaching of integral: The case of curriculum revision

Year 2022, Volume: 12 Issue: 1, 188 - 205, 15.04.2022

Eyüp Sevimli

https://doi.org/10.19126/suje.1057851

Abstract

In this study, the content preferences of the lecturers were evaluated in the context of the revision made in the undergraduate mathematics teachers training program in Turkey in 2018. Within this scope, the theorems and examples preferred by the lecturers while teaching the integral subject were evaluated in the context of the shortened time with the revision of the analysis course curriculum. The participants of the study were eight lecturers from different universities. The qualitative data collection procedures were used via document analysis and interviews. The results of the study showed that the participants attached more importance to the pure content in the revised curriculum compared to the previous curriculum, and the time limitations caused a decrease in the applied content in particular. It has been determined that the content in the "Riemann sums" category remained important during the application of both curricula, but after the curriculum revision, the contents in the "Integrability" and "Applications of integral" categories are less placed in the lecture notes. Due to time limitations, some theorems and examples were not included in the teaching of the integral, and this may cause limited understanding for students. The reflections of lecturers' content preferences on student understanding are discussed within the relevant literature.

Keywords

integral, curriculum revision, theorems, examples

References

• Alcock, L. (2014). How to think about Analysis. UK: Oxford University Press.
• Apostol, T. M. (1974). Mathematical Analysis (2nd ed.). Reading: Addison-Wesley Publishing.
• Berg, B. L. (2001). Qualitative Research Methods for the Social Sciences. Boston: Allyn and Bacon.
• Bingolbali, E. & Ozmantar, M. F. (2009). Factors shaping mathematics lecturers’ service teaching in different departments. International Journal of Mathematical Education in Science and Technology, 40(5), 597-617. doi: 10.1080/00207390902912837
• Brannan, A. D. (2006). A first course in Mathematical Analysis. UK: Cambridge University Press.
• Bressoud, D. M. (2011). Historical reflections on teaching the Fundamental Theorem of Integral Calculus. The American Mathematical Monthly, 118(2), 99-115. doi: 10.4169/amer.math.monthly.118.02.099
• Chevallard, Y., & Bosch M. (2014). Didactic transposition in mathematics education. In: Lerman S. (Eds.), Encyclopedia of Mathematics Education. Dordrecht: Springer.
• Dernek, A. (2009). Analiz I (2nd ed.). Ankara: Nobel Yayıncılık.
• Ely, R. (2017). Definite integral registers using infinitesimals. Journal of Mathematical Behavior, 48, 152-167. doi: 10.1016/j.jmathb.2017.10.002
• Goerdt, L. S. (2007). The effect of emphasizing multiple representations on calculus students’ understanding of the derivative concept. Unpublished. EdD, The Universty of Minnesota: USA.
• Guba, E. G., & Lincoln, Y. S. (1994). Competing paradigms in qualitative research. In N. K. Denzin, & Y. S. Lincoln (Eds.), Handbook of qualitative research (pp. 105-117). London: Sage Publications.
• Güler, G. (2016). The difficulties experienced in teaching proof to prospective mathematics teachers: Academician views. Higher Education Studiess, 6, 145–158. doi: 10.5539/hes.v6n1p145
• Hughes Hallett, D. (2006). What have we learned from calculus reform? The road to conceptual understanding. MAA Notes, 69, 43-47. Retrieved from https://www.math.arizona.edu/~dhh/NOVA/calculus-conceptual-understanding.pdf
• Hughes-Hallett, D., Gleason, A. M., McCallum, W. G. et al. (2008). Calculus: Single variable (5th Edition). New York: Wiley. Jones, S. (2013). Understanding the integral: Students’ symbolic forms. Journal of Mathematical Behavior, 32, 122–141. doi: 10.1016/j.jmathb.2012.12.004
• Jones, S. R. (2015a). Areas, anti-derivatives, and adding up pieces: Definite integrals in pure mathematics and applied science contexts. Journal of Mathematical Behavior, 38, 9–28. doi: 10.1016/j.jmathb.2015.01.001
• Jones, S. R. (2015b). The prevalence of area-under-a-curve and antiderivative conceptions over Riemann sum-based conceptions in students’ explanations of definite integrals. International Journal of Mathematical Education in Science and Technology, 46(5), 721-736. doi: 10.1080/0020739X.2014.1001454
• Klymchuk, S., Zverkova, T., Gruenwald, N., & Sauerbier, G. (2010). University students’ difficulties in solving application problems in calculus: Student perspectives. Mathematics Education Research Journal, 22, 81–91. doi: 10.1007/BF03217567
• Kouropatov, A., & Dreyfus, T. (2013). Constructing the integral concept on the basis of the idea of accumulation: suggestion for a high school curriculum. International Journal of Mathematical Education in Science and Technology, 44(5), 641-651. doi: 10.1080/0020739X.2013.798875.
• Miles, M. B., & Huberman, A. M., (1994). Qualitative data analysis: An expanded sourcebook. Thousand Oaks: Sage Publications. Oberg, R. (2000). An investigation of under graudate calculus students understanding of the definite integral. Unpublished EdD., The Univesrty of Montana: USA.
• Orton, A. (1983). Student’s understanding of integration. Educational Studies in Mathematics, 14(1), 1-18. doi: 10.1007/BF00704699
• Sealey, V. (2014). A framework for characterizing student understanding of Riemann sums and definite integrals. Journal of Mathematical Behavior, 33(1), 230–245. doi: 10.1016/j.jmathb.2013.12.002
• Schröder, B. (2007). Mathematical analysis-A concise introduction. New Jersey: Wiley-Interscience.
• Sevimli, E. (2016). Evaluating views of lecturers on the consistency of teaching content with teaching approach: traditional versus reform calculus. International Journal of Mathematical Education in Science and Technology, 47(6), 877-896. doi: 10.1080/0020739X.2016.1142619
• Sevimli, E. (2018). Understanding students’ hierarchical thinking: a view from continuity, differentiability and integrability. Teaching Mathematics and its Applications: An International Journal of the IMA, 37(1), 1-16. doi: 10.1093/teamat/hrw028
• Sofronas, K.S., De Franco, 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, 131-148. doi: 10.1016/j.jmathb.2011.02.001
• Stewart, J. (2015). Calculus: Early transcendentals (8th ed.). Belmont, CA: Brooks/Cole.
• Tall, D. (1992). Students’ difficulties in calculus. In K-D. Graf, N. Malara, N. Zehavi, & J. Ziegenbalg (Eds.), Proceedings of Working Group 3 at ICME–7, Québec 1992 (pp. 13–28). Berlin: Freie Universität Berlin.
• Thomas, G. B., Weir, M. D., & Hass, J. (2013). Thomas’ calculus (13th ed.). Boston, MA: Pearson.
• Winslow, C. (2007). Didactics of mathematics: An epistemological approach to mathematics education. The Curriculum Journal, 18(4), 523-536. doi: 10.1080/09585170701687969
• Yin, R. K. (2009). Case study research: Design and methods (4th Ed.). Thousand Oaks: Sage Publications.
• YOK [Council of Higher Education in Turkey], (2018). İlköğretim matematik öğretmenliği lisans programı [Mathematics teacher training program]. Retrieved from https://www.yok.gov.tr/Documents/Kurumsal/egitim_ogretim_dairesi/ Yeni-Ogretmen-Yetistirme-Lisans-Programlari/Ilkogretim_Matematik_Lisans_Programi.pdf.