Problem-Centered Approach in a Numerical Methods Course

This paper is an illustration of using a problem-centered approach in an undergraduate course in numerical methods. The problem used in the course was first encountered in a research project that related to the assembly procedure of the fulcrum of bascule bridges. It involved the study of the fulcrum assembly procedure where a trunnion cooled in a dry-ice/alcohol mixture for shrink fitting became stuck halfway in the hub before full insertion could take place. The solution of the problem and its implementation involved numerical solutions of mathematical procedures taught in a typical numerical methods course. The effect of the problem-centered approach in the classroom was quantitatively and qualitatively surveyed over a two-semester period. The results indicate very high student satisfaction in helping them: acquire basic knowledge and skills; reinforce information presented in class, reading assignments, and problem sets; learn to clearly formulate a specific problem and then work it through to completion; develop generic higher-order thinking and problem solving skills; and develop a sense of competence and confidence and see the relevance of the course material to their major.

Related Papers

A.K. Kaw, A.Yalcin, "Problem-Centered Approach in a Course in Numerical Methods", ASCE Journal of Professional Issues and Engineering Education, pp. 359-364, Vol. 134(4), 2008.

S. Garapati, L. Snyder, A. Kaw, "Comparing Two Procedures for Assembling Steel Fulcra in Simple-Trunnion Bascule Bridges", Bridge Structures, pp. 19-30, Vol 7(1), 2011.

C. Nguyen, A.K. Kaw, J. Paul, "Sensitivity Analysis of Cooling Methods and Geometric Parameters in Assembly Procedure of Bascule Bridge Fulcrums", The Journal of Strain Analysis for Engineering Design, pp.  337-349, Vol. 42, (2007).

N. Collier, A.K. Kaw, G.H. Besterfield, M. Rahman, "Benefits of Staged Cooling of Composite Cylinders in Shrink Fitting", The Journal of Strain Analysis for Engineering Design, pp. 349-361, Vol. 41 (5), (2006).

A.K. Kaw, G.H. Besterfield and S. Nichani, "Integrating a Research Problem in a Course in Applied Elasticity", International Journal of Mechanical Engineering Education, pp. 232-242, Vol. 32 (3), (2004). 

G.H. Besterfield, A.K. Kaw, S. Nichani, B. Ratnam, T. Cherukara, M. Denninger "Assembly Procedures of a Trunnion-Hub-Girder for Bascule Bridges",  Theoretical and Applied Fracture Mechanics, Vol 40, No 2, pp. 123-134, (2003).

G.H. Besterfield, S. Nichani, A.K. Kaw, T. Eason, "Full-Scale Testing of Trunnion-Hub-Girder Assemblies for Bascule Bridges", ASCE Journal of Bridge Engineering, Vol. 8, No 4., pp. (2003).