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"Well Defined" Problem Solving Made Easy!

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Well Defined Problems: The Early Years

Early Research into well defined problem solving was conducted by Gestalt Psychologists, their research involved placing a hungry cat into a box which had a leaver fitted, which once pressed would open the door, a bowl of food was placed within eyesight (and scent!) of the cat. To begin with the cat lashed wildly around, until by accident it knocked the leaver, thus getting its food. Once the association was made, the cat learned to simply press the leaver instantly, to receive food.

Behavioural psychologists interpreted these findings in behavioural terms. They argued that the cats behaviour was initially random, trial and error, until the correct behaviour was found, then this was simply re-produced. However, the Gestalt psychologists argued that there was more to it than this, they argued for the important of 'insight' and 'restructuring'


one conceptualisation of the problem solving process

one conceptualisation of the problem solving process

Exploring problem solving: The Research

Problem solving involves more than simply reproducing behaviour it involves insight.

Functional Fixedness: 9 dot and two strings puzzles...

This is demonstrated through the way that "functional fixedness"; that is the inability to re-conceptualise a problem, can hinder problem solving. In the 9 dot problem, the participants assumed they could not go out of the lines, thus they were unable to solve the problem, conformity to unwritten rules impeded their ability to problem solve.

Similarly in the "two strings" problem (A participant is place in a room with two strings hanging from the wall, asked to tie the ends together, only problem is, whilst holding one string, the other is out of reach, participant given a number of objects to help him/her) The participant was unable to re-conceptualise the 'screwdriver' and implement it as a pendulum once attached to one string. Aloowing it to be swung, and grabbed whilst holding the other string.

All in all the Gestalt psychologists deminstrated that prblem solving was more complex than simply a reproduction of learned responces. They introducded the helpful, but vague notions of 'insight' and 're-conceptualisation' They also left a corpus of experimental material to be studied.

Newall and Simon's "Problem Space Theory"

This theory was developed in 1972 and has been hugely influential. They used the analogy of trying to find the center of a maze as being akin to problem solving. They saw the objective structure of a problem as characterised by a set of states, and there is a whole range of possible states and paths through these states.

We start with the 'initial knoledge' state and pass through to the 'goal state' Heuristic methods or strategies are used to move form one state to the next. They also noted importantly that problem solving occurs within the context of a cognitive system which is constrained by working memory limits, and the time taken to retrieve information from Long Term Memory.

Heuristics, are general rules of thumb which can be applied to problems, but they may not always yield results. Algorithms systematically check all potential alternatives, it is time consuming but will always come up with an answer.

In problem solving, experimentation has shown that prior experience can help problem solving.  



Testing Problem Space Theory

Atwood et al tested problem space theory by using a means ends heuristic method opted for by the participants, however when this principal was needed to be violated to find the solution the participants found ti harder to complete the task. 

The theory combines predictive specificity and generalability, making it an attractive model.

When the 9 dot problem was revisited, (participant required to draw four lines through nine dots without taking pen from page) the researcher gave the participant the hint that you could draw outside the lines, (removing their 'unwarranted assumptions' about the rules.) Only 20% got it, even with this hint. Indicating that there is something more than menta fixedness responsible for the failure.

Subjects were found to need highly problem specific knoledge. In their eyes this undercut the notion of insight and fixation. However, other researchers have argued for the importance of insight in problem solving theory. Metcalf et al asked for participants metacognitions of insight in problem solving, and found that they had accurate metacognitions for trivia questions but no predictive metacognitions for the 'insight' problems.  

Evaluating Resrach on Puzzles

Problem space theory has remained undefeated since it was first proposed in the 1950s and has continued to develop encompassing more problem solving phenomena

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Newall and Simon's problem space teory makes a substantial contribution to cognitive psychology.

A fundemmental contribution of problem solving theory is that it contains a normatie theory of problem solving. For most of the puzzles we can count the shortest amount of moves it takes to achieve 'goal' state. Thus in a normative way it tells us what an ideal thinker should do, and then we can see how and why people deviate.

It provides an account of how people solve problems by heuristics, How the understanding of a problem can affect subsequent problem solving performance. It is generalisable and demonstrates theoretical unity.

However, there is questionable ecological validity to the puzzles. Puzzles contain the knoledge we need to solve them, everyday problems do not always.. Requirments in puzzle problems are clear, and the goal state is made apparent, this is also not the case in real life.

Problem space theory focuses on well defined problems, rather than ill defined  / creative problems. Which it should be extended to include. 


ed77burns from USA on November 28, 2010:

This hub proves to be very beneficial when an individual is in depression,this hub will work out for them and take out any individual out of it.

Anon (author) from UK on January 14, 2009:

wow thank you everyone, i really appreciate the comments.

Teresa, it's always the way isn't it, everything is so complex and layered, there is rarely a simple solve all solution, as much as we might wish there was sometimes!

Elkin,your job sounds very intersting, i'd love to hear more about it? I think there could be some really useful insights to gain from problem solving research


Bruce Elkin from Victoria, BC Canada on January 14, 2009:

Fascinating! I'm gonna re-read a couple or four times before I comment in depth. I make my living helping people shift from a focus on problems and solutions, to a focus on creating results that truly matter.

I differentiate (a la EF Shumacher) between "convergent" problems that have single solutions, and "divergent" challenges that can approach in multiple ways, and people come up with multiple answer. Ex. what's the best way to raise a child? There is no best way. But you can create a way that works well for you and your child.

But, lots to think about from this hub. I appreciate the stimulation. Thanks!

earnestshub from Melbourne Australia on January 14, 2009:

Very interesting hub well done! I like the graphics too.

Sheila from The Other Bangor on January 14, 2009:

I agree with your concluding statement, and have always had a problem with any attempt to produce some sort of "catch-all" approach to problem solving, when random circumstance may well take the place of fixed and predictable factors.

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