Problem solving

Draft

Introduction

This article aims to address "problem solving" in education, i.e. how one make learners acquire problem-solving skills.

“Problem solving is generally regarded as the most important cognitive activity in everyday and professional contexts. Most people are required to and rewarded for solving problems. However, learning to solve problems is too seldom required informal educational settings, in part, because our understanding of its processes is limited.” (Jonassen, 2000).

Jonassen also states that problem solving is not “sufficiently acknowledged or articulated in the instructional design literature” (p.63). But he also mentioned that problem-solving is at the center of practice in contemporary learning theory: “Contemporary conceptions of student-centered learning environments, such as open-ended learning environments (Hannafin, Hall, Land, & Hill, 1994; Land & Hannafin, 1996) , goal-based scenarios (Schank, Fano, Bell, & Jona, 1993/1994) , and even problem-based learning (Barrows, 1985; Barrows & Tamblyn, 1980) focus on problem-solving outcomes. They recommend instructional strategies, such as authentic cases, simulations, modeling, coaching, and scaffolding, to support their implicit problem-solving outcomes, but they inadequately analyze or explicate the nature of the problems to be solved” (Jonassen, 2000a).

The anatomy of problem solving

There are many definitions of problem solving both in psychology and related fields and computational sciences.

In a computational perspective, in order to solve a problem, a problem-solver has to perform a certain number of internal and external operations. Each domain of action has in principle a certain number of known operators, i.e. generic actions that can be applied to a certain class of mental or physical objects. An operation is thus defined as concrete realization (application) of an operator. An operator is generally more abstract and more general than one of its possible operation instantiation. Each object that can form a problem is a potential domain of action that can be in different states. Such a state is defined by several sub-states that we can called facts. We can call the set of facts that describe a problem a description. Thus technically speaking, problem solving means transforming states by applying operators to the facts, where a fact can be a mental object or a physical object, and an operation a mental or physical process. This potential domain of action can be call problem-domain.

The selection and use of operators is driven by heuristics at various levels that we will not introduce here for the moment.

Jonassen problem types

In his 2000 article on Toward a Design Theory of Problem Solving, Jonassen identifies a number of problem-solving types: (a) logical,(b) algorithmic, (c) story, (d) rule-using, (e) decision making, (0 troubleshooting, (g) diagnosis-solution, (h) strategic performance, (i) case analysis, (j) design, and (k) dilemma. In a 2011 article , Jonassen lists (a) story problems, (b) rule-using/rule induction problems, (c) decision-making problems, (d) troubleshooting problems, (e) strategic performance problems, (f) policy problems, (g) design problems, and (h) dilemmas.

He also summarized these problem typologies as five abstract types as presented in the taxonomy of meaningful learning article. Problems are not the same and each type requires different educational designs.

Each problem solving type was caracterized by a number of attribues:

• learning activity
• inputs
• success criteria
• context
• structuredness
• abstractness

Problem type	Learning activity	Inputs	Success criteria	Context	Structuredness	Abstractness
Logical	logical control and manipulation of limited variables; solve puzzle
Algorithmic	procedural sequence of manipulations; algorithmic process applied to similar sets of variables; Calculating or producing correct answer
Story	disambiguate variables; select and apply algorithm to produce correct answer using prescribed method
Rule-using	procedural process constrained by rules; select and apply rules to produce system- constrained answers or products
Decision making	identifying benefits and limitations; weighting options; selecting alternative and justifying
Trouble shooting	examine system; run tests; evaluate results; hypo- thesize and confirm fault states using strategies (re- place, serial elimination, space split)
Diagnosis- solution	troubleshoot system faults; select and evaluate treatment options and monitor; apply problem schemas
Strategic performance	applying tactics to meet strategy in real-time, complex performance maintaining situational awareness
Case analysis	solution identification, alternative actions, argue position
Design	acting on goals to produce artifact; problem structuring & articulation
Dilemmas	reconciling complex, non- predictive, vexing decision with no solution; perspectives irreconcil- able