Assessing Conceptual Understanding In Mathematics: Using Derivative Function To Solve Connected Problems
Abstract
Open and distance education plays an important role in the actualization of cultural goals as well as in societal developments. This is an independent teaching and learning method for mathematics which forms the dynamic of scientific thinking. Distance education is an important alternative to traditional teaching applications. These contributions brought by technology enable students to participate actively in having access to information and questioning it. Such an application increases students’ motivation and teaches how mathematics can be used in daily life. Derivative is a mathematical concept which can be used in many areas of daily life. The aim of this study is to enable the concept of derivatives to be understood well by using the derivative function in the solution of various problems. It also aims at interpreting difficulties theoretically in the solution of problems and determining mistakes in terms of teaching methods. In this study, how various aspects of derivatives are understood is emphasized. These aspects concern the explanation of concepts and process, and also their application to certain concepts in physics. Students’ depth of understanding of derivatives was analyzed based on two aspects of understanding; theoretical analysis and contextual application. Follow-up interviews were conducted with five students. The results show that the students preferred to apply an algebraic symbolic aspect instead of using logical meanings of function and its derivative. In addition, in relation to how the graph of the derivative function affects the aspect of function, it was determined that the students displayed low performance.
Keywords
Mathematics Education, Learning, Teaching, Derivative, Solving Problems.
References
- Amit, M., and Vinner, S., (1990). Some misconceptions in calculus: Proceedings of the 14th International Conference for the Psychology of Mathematics Education, 1, 3-10.
- Amoah, V., and Laridon, P. (2004). Using multiple representations to assess students’ understanding of the derivative concept. Proceeding of the British Society for Research into Learning maths. 24(1), 1-6.
- Asiala, M., Cottrill, J., and Dubinsky, E. (1997). The Development of Students’ Graphical
- Understanding of the Derivative. Journal of Mathematical Behavior 16 (4) 399-431. Aspinwall L., Shaw, K., and Presmeg, N. (1997), Uncontrollable images:Graphical connections between a function and its derivative. 78th Annual Meeting of the Mathematical Association of
- America and the 101st Annual Meeting of the American Mathematics Society, San Francisco, California. Breidenbach, D., Dubinsky, E., Hawkes, J., and Nichols, D. (1992). Development of the process conception of function. Educational Studies in Mathematics, 23,247-285.
- Berry, J.S., and Nyman, M. N. (2003), Promoting students’ graphical understanding of the calculus. Journal of Mathematical Behavior, 22,481-497.
- Eisenberg,T. (1992). On the development of a sense for functions. In Guershon Harel and ED Dubinsky, The concept of function: Aspects of epistemology and pedagogy,
- MAA notes 25, 153-174. Washington, DC: Mathematical Association of America. Eisenberg ,T., and Dreyfus,T.(1991). On the reluctance to visualize in mathematics in W.
- Zimmermann and S.Cunningham (eds), Visualization in Teaching and Learning Mathematics, Mathematical Association of America, Washington,DC, pp 25-37. Ferrini-Mundy, J., and Lauten, D. (1994). ”Learning About Calculus Learning”. The Mathematics Teacher, 87, 2 February.
- Hallet, D. H, (1991). Visualization and calculus reform in W.Zimmermann and S.Cunningham