Stochastic Case Problems for the Secondary Classroom with Reliability Theory

  • Usha Kotelawala
Conference paper
Part of the International Perspectives on the Teaching and Learning of Mathematical Modelling book series (IPTL, volume 1)


Basic models of reliability theory can provide relevant and motivating problems for secondary students as they develop skill and understanding in probability and algebra. This paper introduces the stochastic measurement of a system’s reliability. It then presents problems which can be used in secondary mathematics classrooms discussing the prerequisite mathematics and the variation in the types of problems which can be posed within the framework of reliability theory. This includes providing an example of an open-ended project with an assessment rubric. Finally, it summarizes the mathematical residue as a rationale for secondary teachers to consider incorporating interesting applied stochastic problems within their curricula.


Parallel Component Reliability Theory Minimal Path Secondary Student Secondary Teacher 
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  1. Barlow, R. E., (2002, June). Mathematical reliability theory: From the beginning to the present time. Invited paper at the Third International Conference on Mathematical Methods in Reliability, Trondheim, Norway.Google Scholar
  2. Barlow, R. E., & Proshan, F. (1965). Mathematical theory of reliability. New York: Wiley.Google Scholar
  3. Birnbaum, Z. W., Esary, J. D., & Saunders, S. C. (1961). Multi-component systems and structures and their reliability. Technometrics, 3(1), 55–77.CrossRefGoogle Scholar
  4. Blum, W., et al. (2002). ICMI study 14: Applications and modelling in mathematics education—Discussion document. Educational Studies in Mathematics, 51(1/2), 149–171.CrossRefGoogle Scholar
  5. Hillier, F. S., & Lieberman, G. J. Introduction to operations Research, 9th Edition. New York: McGraw-Hill.Google Scholar
  6. Kaiser, G., & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. Zentralblatt für Didaktik der Mathematik, 38(2), 196–208.CrossRefGoogle Scholar
  7. Kececioglu, D. (2002). Reliability and life testing handbook. Lancaster: DEStech Publications, Inc.Google Scholar
  8. Lesh, R. A., & Kelly, A. E. (2000). Multi-tiered teaching experiments. In R. A. Lesh & A. Kelly (Eds.), Handbook of research design in mathematics and science education (pp. 197–231). Mahwah: Lawrence Erlbaum Associates.Google Scholar
  9. Maaß, K. (2006). What are modelling competencies? Zentralblatt für Didaktik der Mathematik, 38(1), 113–142.CrossRefGoogle Scholar
  10. Mousoulides, N. G. (2009). Mathematical modeling for elementary and secondary school teachers. In A. Kontakos (Ed.), Research and theories in teacher education. Rhodes: University of the Aegean.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Graduate School of EducationFordham UniversityNew YorkUSA

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