Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The term “reliability” has meanings in common language and with slight variances in different regions of the world. For the purpose of this paper, the author is using the specific stochastic meaning initiated in Mathematical Theory of Reliability by Barlow and Proschan in 1965.
- 2.
The purpose of this paper is to demonstrate how an extracted type of problem from a field generally taught only in tertiary programs can be used to generate interesting and educationally useful problems. The methods demonstrated thus far only present a small portion of the beginning ideas of reliability theory. It is common for next steps to be consideration of minimal paths and minimal cuts to generate an algorithm for determining the reliability of a system. While this too may have potential with secondary students, it is outside the scope of this paper.
Methods which build the reliability function from minimal paths or minimal cuts can frequently be found in textbooks for Operations Research (Hillier and Lieberman 2010) and in the work of Birnbaum et al. (1961).
- 3.
This question could become an entry point into the varied methods of solution involving minimal paths and minimal cuts.
References
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.
Barlow, R. E., & Proshan, F. (1965). Mathematical theory of reliability. New York: Wiley.
Birnbaum, Z. W., Esary, J. D., & Saunders, S. C. (1961). Multi-component systems and structures and their reliability. Technometrics, 3(1), 55–77.
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.
Hillier, F. S., & Lieberman, G. J. Introduction to operations Research, 9th Edition. New York: McGraw-Hill.
Kaiser, G., & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. Zentralblatt für Didaktik der Mathematik, 38(2), 196–208.
Kececioglu, D. (2002). Reliability and life testing handbook. Lancaster: DEStech Publications, Inc.
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.
Maaß, K. (2006). What are modelling competencies? Zentralblatt für Didaktik der Mathematik, 38(1), 113–142.
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this paper
Cite this paper
Kotelawala, U. (2011). Stochastic Case Problems for the Secondary Classroom with Reliability Theory. In: Kaiser, G., Blum, W., Borromeo Ferri, R., Stillman, G. (eds) Trends in Teaching and Learning of Mathematical Modelling. International Perspectives on the Teaching and Learning of Mathematical Modelling, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0910-2_59
Download citation
DOI: https://doi.org/10.1007/978-94-007-0910-2_59
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0909-6
Online ISBN: 978-94-007-0910-2
eBook Packages: Humanities, Social Sciences and LawEducation (R0)