Why is Problem Representation So Important for Problem Solving?

We are constantly faced with problem solving situations at work and in daily life, which makes problem solving one of the most important skills that students can learn. In an economy that heavily relies on expert thinking and complex communication, the need to posses those deep learning skills, which consist of problem-solving, critical thinking, communication, collaboration and innovation, is essential. Schools have tried several approaches to address the need, most important of which are project-based learning (PBL),social media, and games. Each proven by research to be effective in improving learning, but neither has generated the learning outcomes that improves student ranking on the PISA test from its current average state to the top. In most of these approaches, the process of solving problems is not directly attempted. It is assumed that students will have to solve problems, as part of their engagement with these methods. However, the fact that in a deep learning study conducted by the American Institute for Research, students did not show improvement in complex problem solving, communication, and conceptual understanding, indicates that something is missing in our approach to problem solving.

Why has the field of education largely ignored how to learn to solve problems? One of the main reasons is because most contemporary research and theory in problem solving claims that problem solving skills are domain and context specific (Jonassen, 2004). That means that within a domain or a context, problems vary in terms of their structuredness, complexity and dynamicity. Christine M. Massey, one of the NRC committee members and the education director for the Institute for Research in Cognitive Science at the University of Pennsylvania, says that “it’s not the case that you can just practice up a set of generic skills and apply that in a certain area. You have to do it on top of a well-founded knowledge base. We really just don’t know how to get that cross-discipline deep transfer.”Schools don’t find it feasible to teach so many types of problems especially complex problems,which also explains why most common problems that students solve in schools are well-structured problems–consisting only of few variables compared to the multiple variables and factors that an ill-structured problem consists of.

Yet reality shows that ill-structured problems are more often encountered in everyday and professional practice and the need for people who can handle those types of problems is growing daily. One way of trying to tackle the complexities of problem solving is through the creation of mental representations of a problem. The way solvers represent or frame the problem to themselves is the key to problem solving. However, the more complex these problems are and due to the limitations of our brain, it is less likely that solvers can easily handle the challenge only by using their inner cognitive abilities. Considering that people are daily solving some very challenging and complex problems, it becomes clear that something else is at work here that had to be discovered.

In “Distributed Intelligence” Roy Pea urges that we do well to reconsider human cognition as distributed beyond the person proper to include other persons, symbolic media, the environment and artifacts (as cited in Perkins,1990). David Perkins has extended on this idea with his ‘Person-Plus’ entity, stating that “the surround –the immediate physical and social resources outside of the person–participate in cognition, not just as source of input and receiver of output, but as a vehicle of thought” and that “what is learned —lingers not just in the mind of the  learner, but in the arrangement of the surround as well; yet it is just as genuinely learning for all that.”

Including external representations as part of many cognitive tasks, such as concept mapping, graphic organizers for capturing patterns, narrative, compare contrast relationships, etc.,provide an immense support system for cognition. According to Jiajie Zhang, those “external representations are not simply inputs and stimuli to the internal mind; rather they are so intrinsic to many cognitive tasks that they guide, constrain, and even determine cognitive behavior.” Our thinking gets altered by them because much of the structure of the internal mind is a reflection of the structure of the external environment (Zhang,1997). By creating a well designed external representation we provide a surrogate short-term memory that supports learners in attaining the new concepts they are trying to learn.

Indeed, when we look at experienced problem solvers–individuals who have a well organized knowledge structure–we discover that the way they represent the problem space integrate not only content knowledge, but also higher level knowledge about problem solving strategies, explanations, styles of justifications, and inquiry characteristic of the domain. Skills they keep using while facing any problem solving situation. By constructing the problem space and actively manipulating and testing their model, it helps them interpret information about the problem, simulate the behavior of elements in the problem, and trigger particular solution processes.

As powerful and as intuitive as these external mental representations seem, very little attention was directed towards them by researchers and schools. Zhang admits that this may be simply because of a lack of suitable methodologies for studying external representations (Zhang,1997). As David Perkins says:“the best use of these physical support systems is an art. It is not so widely found. And conventional instruction does little to acquaint students with this art.”  These support systems exist in the form of word processors, concept maps, tables, graphic organizers, etc.,and students could benefit of the opportunities they afford. The problem is that we assume that because they are there,students will take advantage of them. While reality shows that most students miss some of the best uses of these support systems at their disposal (Perkins,1990). This is probably the reason why PBL,social media and game design are all based on the assumption that using them will naturally develop students problem solving skills. It may develop those skills in some cases,but it is not very clear why and it clearly does not generate the physical support system that students can always get back to when faced with problem solving situations.