The Korea Society Of Educational Studies In Mathematics

Current Issue

Journal of Educational Research in Mathematics - Vol. 30 , No. 2

[ Article ]
Journal of Educational Research in Mathematics - Vol. 29, No. 1, pp.93-112
Abbreviation: JERM
ISSN: 2288-7733 (Print) 2288-8357 (Online)
Print publication date 28 Feb 2019
Received 09 Jan 2019 Reviewed 02 Feb 2019 Accepted 02 Feb 2019

An Analysis and a Suggestion about Narrative of 'the Relation between Definite Integral and Sum of Series' in 2015-Revised <Calculus> : From the Perspective of Connecting with <MathematicsⅡ>
Lee, Gi Don*
*Teacher, Kyeongin High School, South Korea (

Correspondence to : Teacher, Kyeongin High School, South Korea,


In the 2015-Revised mathematics curriculum the definite integral concept described as ‘the difference of two values of the function given by an indefinite integral’ and ‘the area between a curve and x-axis’ is dealt in <MathematicsⅡ> and the definite integral concept depicted as ‘the limit of a Riemann sum’ is presented in <Calculus> officially following <MathematicsⅡ> in the learning sequence, which is absolutely different from the previous curricula. In this paper, I analyzed the narrative structure of ‘the relation between definite integral and sum of series’ in <Calculus> which introduces ‘the limit of a Riemann sum’ as compared with the definite integral concept as ‘the area between a curve and x-axis’ etc. with the perspective of connecting with <MathematicsⅡ> in mind. In regards to the defects revealed by this analysis, I suggested concrete expressions in the textbook <Calculus> and curriculum document, respectively to make a more profound connection with <MathematicsⅡ> through the support of the new concept learning experience from the previous learning experience and to lead to dealing with ‘the relation between definite integral and sum of series’ mainly focused on the definite integral concept depicted as ‘the area between a curve and x -axis’.

Keywords: Narrative Structure about Definite Integral, 2015-Revised Mathematics Curriculum, Calculus, MathematicsⅡ, Connectivity

1. Bressoud, D. M. (2011). Historical reflections on teaching the fundamental theorem of integral calculus. The American Mathematical Monthly, 118(2), 99-115.
2. Heo, H. D.(2006). Understanding and epistemological obstacles of the formula for the area of a rectangle. Unpublished Mater thesis. Seoul National University.
3. Hong, G. J.(2008). An educational study on Archimedes’ mathematics. Unpublished doctoral dissertation. Seoul National University.
4. Iitaka, S., & Matsumoto, Y.(2012). MathⅢ. Tokyo: Tokyo Shoseki.
5. Joung, Y. J., & Lee, K. H.(2009a). A study on the fundamental theorem of calculus: focused on the relation between the area under time-velocity graph and distance. Journal of Educational Research in Mathematics, 19(1), 123-142.
6. Joung, Y. J., & Lee, K. H.(2009b). A study on the relationship between indefinite integral and definite integral. School Mathematics, 11(2), 301-316.
7. Jun, I., Kim, W., Nam, M., Lee, H., & Lee, E. (2015). A International Comparison Study on the Concept of Calculus in High School,. Research Report 2015_R7. Korea Foundation for the Advancement of Science & Creativity.
8. KOFAC(2015). A Study on the development of Mathematics curriculum under the 2015- Revised Curriculum. Research Report BD15120005. Ministry of Education.
9. Lee, G. D.(2014). An educational application of mathematics narrative. Unpublished doctoral dissertation. Seoul National University.
10. Lee, G. D.(2018). A proposal of the mathematical lesson where concepts are introduced according to students’ questioning, and an exploration of the possibilities of that method. Journal of Education Science, 20(1), 123-153.
11. Oberg, T. (2000). An investigation of undergraduate calculus student's conceptual understanding of the definite integral. Doctoral dissertation, University of Montana, Missoula, MT.
12. Orton, A. (1983). Students’ understanding of integration. Educational Studies in Mathematics, 14(1), 1-18.
13. Park, J. H., Park, M. S., & Kwon, O. N.(2018). An analysis of the introduction and application of definite integral in <MathematicsⅡ> textbook developed under the 2015-Revised Curriculum. The Mathematical Education, 57(2), 157-177.
14. Shin, B. M.(2008). An analysis of the concept on measuration by parts and definite integral. Journal of the Korean School Mathematics Society, 11(3), 421-438.
15. Shin, B. M.(2009). High School Students’ Understanding of Definite Integral. School Mathematics, 11(1), 93-110.
16. Shin, S. J., & Cho, W. Y.(2018). An alternatives of the definition of definite Integral in <MathematicsⅡ> textbook under 2015-Revised Curriculum. School Mathematics, 20,(4), 723-741.