Problem Solving and Engineering Education

Posted on August 2, 2010

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Author:  Sanjay Goel, http://in.linkedin.com/in/sgoel

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In its most simplistic interpretation, a problem is something that cannot be solved in a single, obvious step. Here are some interesting definitions of problem and problem solving:

Pérez et al. –   problem is a situation for which there isn’t an evident solution.

Perales –    problem is any situation that produces, on one hand, a certain degree of uncertainty and, on the other, behavior in search of a solution.

Gagné   – problem solving is a process where the apprentice/learner discovers a combination of rules previously learned that he/she can apply to reach a solution for a new problematic situation.

Nickols’ typology of problem solving approaches

Nickols opines that what characterizes a problem is uncertainty about action, having a goal and not knowing how to achieve it. Problem solving depends upon cognitive processes of problem anticipation and identification, problem understanding, problem definition, problem formulation, problem representation, generations of alternatives, decision making and planning, implementation and integration, monitoring, evaluation, improvisation, and solution communication.  

Nickols proposed a typology of problem solving approaches. A repair approach is required to put things back the way they were, improvement approach is required to improve upon existing arrangements, and engineering approach is suitable for creating new, far superior arrangements. The repair approach starts from symptoms and focuses on causes/corrective measures through fault isolation. The improvement approach starts from existing systems/arrangements and focuses on constraints/modifications through structural analysis. The engineering approach starts from the required results and focuses on required design through structural design.

Jonassen proposed a taxonomy of problems based on variations in problem types and representations. The problem types vary in a three dimensional continuous space of three factors: structured-ness, complexity, and degree of domain specificity. The first among these is structured-ness, varying from extremely well-structured to absolutely ill-structured in a continuum, as discussed above. The second factor is complexity that depends upon a number of issues, functions, variables, and also interactions and degree of uncertainty of behavior of these.  The third factor is degree of domain specificity.  

Based on the cognitive task analysis of various kinds of problems, Jonassen  identified eleven different kinds of problems –

(i) logical problems,

(ii) algorithmic problems,

(iii) story problems,

(iv) rule using problems,

(v) decision making problems,

(vi) troubleshooting problems,

(vii) diagnostic-solution problems,

(viii) strategic-tactical performance,

(ix) situated case problems,

(x) design problems, and

(xi) dilemmas.

It may be noted that as per his classification, algorithmic problems imply direct application of known algorithms.

Jonassen  and Linda S. Gottfredson   have consolidated earlier research on problem solving and highlighted the distinctions between academic and practical problems. These differences are given below:

Academic Problems

Real life practical problems

1. Tend to be formulated by other people2. Well-defined or well-structured

3.  Tend to be complete. Presented with all the parameters and constraints. Usually consist of a well-defined initial state, a known goal state, and a constrained set of logical operators.

4.   Typically posses only a single answer

5.  Tend to encourage single method of obtaining a correct answer

6.  Require application of a finite number of concepts, rules, and principles

7.  Divorced from ordinary experience

8.  Tend to be of little or no intrinsic interest

1.  Require (re)formulation.2.   Ill-defined or ill-structured

3.   Require information seeking. One or more elements of the ill-defined problem are unknown or not known with certainty. The goals of real-life practical problems are usually vaguely defined with unstated constraints.

4.   Usually possess multiple acceptable solutions.

5.      Allow multiple paths to solution.

6.  Present uncertainty about useful and usable concepts, rules, and principles as well. Further, in case of ill-defined problems, the relationships between concepts, rules, and principles may be inconsistent between cases. 

7.   Embedded in and require prior experience. This requires the problem solver of ill-structured problem to distinguish important from irrelevant, and construct a problem space for generating solutions.

8.      Require motivation and personal involvement

Real-life ill-defined problems are not constrained by the content domain, may require the integration of several content domains, their solutions are not predictable or convergent, possess multiple criteria for evaluating solutions, and no explicit means for determining appropriate action. They require the solver to express personal opinion or belief, make judgments, and also defend them. Earlier it was believed that experiences with well-defined problem solving easily transferred to solving ill-defined problems. However, research in problem solving has demonstrated that performance on well-defined problems is not correlated with performance on ill-defined problems.  

16 Habits of Mind, Costa and Kallick

Costa and Kallick  have identified the following sixteen characteristics of what intelligent people do when they are confronted with problems, the resolution to which is not immediately apparent:

(i) persisting,

(ii) managing impulsivity,

(iii) listening to others with understanding and empathy,

(iv) thinking flexibly,

(v) thinking about our thinking (meta-cognition),

(vi) striving for accuracy and precision,

(vii) questioning and posing problems,

(viii) applying past knowledge to new situations

(ix) thinking and communicating with clarity and precision,

(x) gathering data through all senses,

(xi) creating, imagining, and innovating,

(xii) responding with wonderment and awe,

(xiii) taking responsible risks,

(xiv) finding humor,

(xv) thinking interdependently, and

(xvi) learning continuously

In the light of the above discussion, it is important for the education managers and educators, and even students to ponder over few key questions– 

1. Is it good  for majority of academic research to remain intellectually disengaged  from the industry and society?

2. Are education  systems and approaches sufficiently engaging the students (at all levels, i.e., undergrads, master’s, and doctoral) with real, uncertain, complex, and inter-disciplinary problem situations? 

3.  Do engineering faculty members ‘seriously’  interact with the professional engineers in the industy   and/or society to expand  their perspectives?

4.   Should something be done to address these gaps?  What steps can help?  Can we start taking the initial steps in our own courses and departments?

References:

1.  David H. Jonassen, Toward a design theory of problem solving, Educational Technology Research and Development, Volume 48, Number 4, Springer Boston, pp 63-85, December, 2000.

2.   Fred Nickols, Four Tips for “Beefing Up” Your Problem Solving Tool Box – Part One, April 2009, retrieved on January 30th, 2010 from http://blog.smartdraw.com/archive/2009/04/21/four-tips-for-beefing-up-your-problem-solving-tool-box-part-one.aspx.

3.   A.L.Costa and B. Kallick,  Discovering and Exploring Habits of Mind,  Association for Supervision and Curriculum Development (ASCD),  2000.

4.   .

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Keywords: Software Engineering Education, Computing Education, Computer Science Education, Engineering Education, Information Technology Education, Information Systems Education, College Education, Higher Education, Professional Education

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also check http://in.linkedin.com/in/sgoel

 

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