Teaching and Learning of Continuous Functions and Continuous Random Variables

함수의 연속과 연속확률변수 개념에 대한 교수·학습적 고찰

  • Received : 2019.03.14
  • Accepted : 2019.05.15
  • Published : 2019.06.30


One of the reasons students have difficulty in studying probability is that they do not understand the meaning of mathematical terms precisely. One such term is a continuous random variable. Students tend not to think of the accurate definition of continuous random variables but to understand the definition of continuity of functions and the meaning of continuity in probability as equal. In this study, we try to explore the degree of pre-service teachers' understanding on the concept of continuation of functions and continuous random variables. To do this, the questionnaire items related to continuous random variables and continuity of functions were developed by experts and examined by pre-service teachers. Based on this, we make suggestions on implications for teaching and learning about continuous random variables.


  1. BAEK S. J., CHOI Y. G., A Historical Study on the Continuity of Function-Focusing on Aristotle's Concept of Continuity and the Arithmetization of Analysis-, Journal of Educational Research in Mathematics 27(4) (2017), 727-745.
  2. CHANG Y. S., Topology Basic Theory, Kyungmoonsa, 2013.
  3. CHOI J. S., YUN Y. S., HWANG H. J., A Study on Pre-Service Teachers' Understanding of Random Variable, School Mathematics 16(1) (2014), 19-37.
  4. HWANG S. G., YOON J. H., A Study on Teaching Continuous Probability Distribution in Terms of Mathematical Connection, School Mathematics13(3) (2011), 423-446.
  5. JEONG D. M., CHO S. J., Real Analysis Introduction, Kyungmoonsa, 2009.
  6. JOUNG Y. J., KIM J. H., (2013). An Historical Investigation of the Historical Developments of the Concept of Continuous Functions, Journal of Educational Research in Mathematics 23(4) (2013), 567-784.
  7. F. KACHAPOVA, L. KACHAPOV, Student's misconceptions about random variables, International Journal of Mathematical Education in Science and Technology 43(7) (2012), 963-971.
  8. KIM J. H., PARK K. S., Analysis on Definitions of Continuity Conveyed by School Mathematics and Academic Mathematics, Journal of Educational Research in Mathematics 27(3) (2017), 375-389.
  9. LEE K. S. et al, High school Calculus, Mirae N Co., Ltd, 2016.
  10. Ministry of Education, Ministry of Education Notice No. 2015-74 [Separate Book 8], Mathematics curriculum, 2015.
  11. D. MUMFORD, The dawning of the age of stochasticity, In V. I. ARNOLD, M. ATIYAH, P. D. LAX, B. MAZUR(Eds.) Mathematics: Frotiers and Perspectives, 2000(pp. 197-218). RI:AMS.
  12. PARK D. W., HONG S. S., SHIN M. Y., High School Textbook Definition and Students' Understanding of Continuity of Functions, Journal of the Korean School Mathematics 15(3) (2012), 453-456.
  13. PARK Y. H., A Study on the Intuitive Understanding Concept of Continuous Random Variable, School Mathematics 4(4) (2002), 677-688.
  14. SHIN Y. W., Basic probability theory, Kyungmoonsa, 2004.
  15. D. TALL, S. VINNER, Concept image and concept definition in mathematics with particular reference to limits and continuity, Educational Studies in Mathematics 12 (1981), 151-169.
  16. YU J. O., Understandable topology mathematics, Kyowoosa, 2006.