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Journal of the Operational Research Society

, Volume 58, Issue 8, pp 983–995 | Cite as

How novices formulate models. Part I: qualitative insights and implications for teaching

  • S G PowellEmail author
  • T R Willemain
General Paper

Abstract

Teaching novices how to formulate mathematical models for ill-structured problems is a challenging task. Little is known about how novices approach ill-structured problems and how their performance differs from that of experts. We audiotaped 28 MBA students while they worked through four ill-structured modelling problems. The task in each problem was to begin to develop a model that could ultimately be used for forecasting or analysis of alternative courses of action. We analysed transcripts of these think-aloud protocols both quantitatively and qualitatively. We observed five behaviours that are not typical of experts and that limit the effectiveness of our subjects. These include: over-reliance on given numerical data, taking shortcuts to an answer, insufficient use of abstract variables and relationships, ineffective self-regulation, and overuse of brainstorming relative to structured problem solving. We conclude that an effective modelling pedagogy should teach how to: formulate models both in the presence and the absence of data, abstract variables and relationships, employ control strategies for self-regulation, and use structured problem-solving methods.

Keywords

modelling teaching problem solving 

Notes

Acknowledgements

We thank the Tuck MBA students who volunteered for this study. Special thanks also go to Professor Zeynep Aksehirli of the Tuck School of Business for conducting the exercises and helping to code the transcripts. Transcripts of the verbal protocols are available to interested researchers from the authors.

References

  1. Atman CJ and Bursic KM (1998). Verbal protocol analysis as a method to document engineering student design processes. J Eng Educ 87: 121–132.CrossRefGoogle Scholar
  2. Atman CJ, Chimka JR, Bursick KM and Nachtman HL (1999). A comparison of freshman and senior engineering design processes. Des Stud 20: 131–152.CrossRefGoogle Scholar
  3. Chi MTH, Feltovich PJ and Glaster R (1981). Categorization and representation of physics problems by experts and novices. Cogn Sci 5: 121–152.CrossRefGoogle Scholar
  4. Clement JJ (1998). Expert novice similarities and instruction using analogies. Int J Sci Educ 20: 1271–1286.CrossRefGoogle Scholar
  5. Crismond D (2001). Learning and using science ideas when doing investigate-and-redesign tasks: A study of naïve, novice, and expert designers doing constrained and scaffolded design work. J Res Sci Teach 38: 791–820.CrossRefGoogle Scholar
  6. Glaser R (1990). Expert knowledge and the thinking process. Chemtech 20: 394–397.Google Scholar
  7. Glaser R and Chi MTH (1988). Overview. In: Chi MTH, Glaser R and Farr M (eds). The Nature of Expertise, XV-XXVIII. Lawrence Erlbaum Associates: Hillsdale: NJ.Google Scholar
  8. Heyworth RM (1999). Procedural and conceptual knowledge of expert and novice students for the solving of a basic problem in chemistry. Int J Sci Educ 21: 195–211.CrossRefGoogle Scholar
  9. Morris MT (1967). On the art of modelling. Mngt Sci 13: B-707–B-717.CrossRefGoogle Scholar
  10. Pidd M (1996). Tools for Thinking. Wiley: Chichester, UK.Google Scholar
  11. Polya G (1945). How to Solve It. Princeton University Press: Princeton, NJ.Google Scholar
  12. Powell SG (1995a). Teaching the art of modelling to MBA students. Interfaces 25: 88–94.CrossRefGoogle Scholar
  13. Powell SG (1995b). Six key modelling heuristics. Interfaces 25: 114–125.CrossRefGoogle Scholar
  14. Powell SG (1998). The studio approach to teaching the craft of modelling. Ann Opns Res 82: 29–47.CrossRefGoogle Scholar
  15. Reitman W (1965). Cognition and Thought. Wiley: New York.Google Scholar
  16. Savelsbergh ER, DeJong T and Ferguson-Hessler MGM (2002). Situational knowledge in physics: The case of electrodynamics. J Res Sci Teach 39: 928–951.CrossRefGoogle Scholar
  17. Schoenfeld A (1985). Mathematical Problem Solving. Academic Press: New York, NY.Google Scholar
  18. Schoenfeld A (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In: Grouws D. (ed). Handbook for Research on Mathematics Teaching and Learning. MacMillan: New York: NY. pp 334–370.Google Scholar
  19. Schön DA (1983). The Reflective Practitioner. Jossey-Bass: San Francisco, CA.Google Scholar
  20. Schön DA (1987). Educating the Reflective Practitioner. Jossey-Bass: San Francisco, CA.Google Scholar
  21. Simon HA (1973). The structure of ill-structured problems. Artif Intell 4: 181–201.CrossRefGoogle Scholar
  22. Slotta JD, Chi MTH and Joram E (1995). Assessing students' misclassifications of physics concepts: An ontological basis for conceptual change. Cognition Instruct 13: 373–400.CrossRefGoogle Scholar
  23. Voss JF and Post TA (1988). On the solving of ill-structured problems. In: Chi MTH, Glaser R and Farr MJ (eds). The Nature of Expertise. Lawrence Erlbaum Associates: Hillsdale: NJ. pp 261–285.Google Scholar
  24. Willemain TR (1994). Insights on modelling from a dozen experts. Opns Res 42: 213–222.CrossRefGoogle Scholar
  25. Willemain TR (1995). Model formulation: What experts think about and when. Opns Res 43: 916–932.CrossRefGoogle Scholar
  26. Willemain TR and Powell SG (2007). How novices formulate models Part II: A quantitative description of behaviour. J Opl Res Soc (forthcoming, 2007).Google Scholar

Copyright information

© Palgrave Macmillan Ltd 2006

Authors and Affiliations

  1. 1.Dartmouth CollegeHanoverUSA
  2. 2.Rensselaer Polytechnic InstituteTroyUSA

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