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General Problem Solver (A. Newell & H. Simon)

The General Problem Solver (GPS) was a theory of human problem solving stated in the form of a simulation program (Ernst & Newell, 1969; Newell & Simon, 1972). This program and the associated theoretical framework had a significant impact on the subsequent direction of cognitive psychology. It also introduced the use of productions as a method for specifying cognitive models.

The theoretical framework was information processing and attempted to explain all behavior as a function of memory operations, control processes and rules. The methodology for testing the theory involved developing a computer simulation and then comparing the results of the simulation with human behavior in a given task. Such comparisons also made use of protocol analysis (Ericsson & Simon, 1984) in which the verbal reports of a person solving a task are used as indicators of cognitive processes.

GPS was intended to provide a core set of processes that could be used to solve a variety of different types of problems. The critical step in solving a problem with GPS is the definition of the problem space in terms of the goal to be achieved and the transformation rules. Using a means-end-analysis approach, GPS would divide the overall goal into subgoals and attempt to solve each of those. Some of the basic solution rules include: (1) transform one object into another, (2) reduce the different between two objects, and (3) apply an operator to an object. One of the key elements need by GPS to solve problems was an operator-difference table that specified what transformations were possible.

Application

While GPS was intended to be a general problem-solver, it could only be applied to “well-defined” problems such as proving theorems in logic or geometry, word puzzles and chess.  However, GPS was the basis other theoretical work by Newell et al. such as  SOAR  and  GOMS . Newell (1990) provides a summary of how this work evolved.

Here is a trace of GPS solving the logic problem to transform L1= R*(-P => Q) into L2=(Q \/ P)*R (Newell & Simon, 1972, p420):

Goal 1: Transform L1 into LO Goal 2: Reduce difference between L1 and L0 Goal 3: Apply R1 to L1 Goal 4: Transform L1 into condition (R1) Produce L2: (-P => Q) *R Goal 5: Transform L2 into L0 Goal 6: Reduce difference between left(L2) and left(L0) Goal 7: Apply R5 to left(L2) Goal 8: Transform left(L2) into condition(R5) Goal 9: Reduce difference between left(L2) and condition(R5) Rejected: No easier than Goal 6 Goal 10: Apply R6 to left(L2) Goal 11: Transform left(L2) into condition(R5) Produce L3: (P \/ Q) *R Goal 12: Transform L3 into L0 Goal 13: Reduce difference between left(L3) and left(L0) Goal 14: Apply R1 to left(L3) Goal 15: Transform left(L3) into condition(R1) Produce L4: (Q \/ P)*R Goal 16: Transform L4 into L0 Identical, QED

• Problem-solving behavior involves means-ends-analysis, i.e., breaking a problem down into subcomponents (subgoals) and solving each of those.
• Ericsson, K. & Simon, H. (1984). Protocol Analysis. Cambridge, MA: MIT Press.
• Ernst, G. & Newell, A. (1969). GPS: A Case Study in Generality and Problem Solving. New York: Academic Press.
• Newell, A. (1990). Unified Theories of Cognition. Cambridge, MA: Harvard University Press.
• Newell, A. & Simon, H. (1972). Human Problem Solving. Englewood Cliffs, NJ: Prentice-Hall.

The Journal of Problem Solving

Home > Libraries > LIBRARIESPUBLISHING > PUPOAJ > JPS > Vol. 5 > Iss. 1 (2012)

The Problems with Problem Solving: Reflections on the Rise, Current Status, and Possible Future of a Cognitive Research Paradigm

Stellan Ohlsson , University of Illinois at Chicago Follow

The research paradigm invented by Allen Newell and Herbert A. Simon in the late 1950s dominated the study of problem solving for more than three decades. But in the early 1990s, problem solving ceased to drive research on complex cognition. As part of this decline, Newell and Simon’s most innovative research practices – especially their method for inducing subjects’ strategies from verbal protocols - were abandoned. In this essay, I summarize Newell and Simon’s theoretical and methodological innovations and explain why their strategy identification method did not become a standard research tool. I argue that the method lacked a systematic way to aggregate data, and that Newell and Simon’s search for general problem solving strategies failed. Paradoxically, the theoretical vision that led them to search elsewhere for general principles led researchers away from studies of complex problem solving. Newell and Simon’s main enduring contribution is the theory that people solve problems via heuristic search through a problem space. This theory remains the centerpiece of our understanding of how people solve unfamiliar problems, but it is seriously incomplete. In the early 1970s, Newell and Simon suggested that the field should focus on the question where problem spaces and search strategies come from. I propose a breakdown of this overarching question into five specific research questions. Principled answers to those questions would expand the theory of heuristic search into a more complete theory of human problem solving.

Recommended Citation

Ohlsson, Stellan (2012) "The Problems with Problem Solving: Reflections on the Rise, Current Status, and Possible Future of a Cognitive Research Paradigm," The Journal of Problem Solving : Vol. 5 : Iss. 1, Article 7. DOI: 10.7771/1932-6246.1144 Available at: https://docs.lib.purdue.edu/jps/vol5/iss1/7

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The Problems with Problem Solving: Reflections on the Rise, Current Status, and Possible Future of a Cognitive Research Paradigm

• October 2012
• The Journal of Problem Solving 5(1)

• University of Illinois at Chicago

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What is problem solving?

A problem arises when we need to overcome some obstacle in order to get from our current state to a desired state. Problem solving is the process that an organism implements in order to try to get from the current state to the desired state.

An historical review of approaches to problem solving

The behaviourist approach.

Behaviourist researchers argued that problem solving was a reproductive process; that is, organisms faced with a problem applied behaviour that had been successful on a previous occasion. Successful behaviour was itself believed to have been arrived at through a process of trial-and-error. In 1911 Edward Thorndike had developed his law of effect after observing cats discover how to escape from the cage into which he had placed them. This greatly influenced the behaviourist view of problem solving:

The Gestalt approach

By contrast, Gestalt psychologists argued that problem solving was a productive process. In particular, in the process of thinking about a problem individuals sometimes "restructured" their representation of the problem, leading to a flash of insight that enabled them to reach a solution. In The Mentality of Apes (1915) Wolfgang Köhler described a series of studies with apes in which the animals appeared to demonstrate insight in problem solving situations. A description of these studies, with photographs, can be found here .

The Gestalt psychologists described several aspects of thought that acted as barriers to successful problem solving. One of these was called the Einstellung effect , now more commonly referred to as mental set or entrenchment . This occurs when a problem solver becomes fixated on applying a strategy that has previously worked, but is less helpful for the current problem. Luchins (1942) reported a study in which people had to use three jugs of differing capacity (measured in cups) to measure out a required amount of water (given by the experimenter). Some people were given a series of "practice" trials prior to attempting the critical problems. These practice problems could be solved by filling Jug B, then tipping water from Jug B into Jug A until it is filled, and then twice using the remainging contents of Jug A to fill Jug C. Expressed as a formula, this is B - A - 2C. However, although this formula could be applied to the subsequent "critical" problems, these also had simpler solutions, such as A - C. People who had experienced the practice problems mostly tried to apply the more complex solution to these later problems, unlike people who had not experienced the earlier problems (who mostly found the simpler solutions).

Another barrier to problem solving is functional fixedness , whereby individuals fail to recognize that objects can be used for a purpose other than that they were designed for. Maier (1930) illustrated this with his two string problem .

For a real life example of overcoming fuctional fixedness, see: Overcoming functional fixedness: Apollo 13

Questions : What do you think of Köhler's claim that his apes had demonstrated insight? What proportion of Maier's participants spontaneously found the solution before getting any kind of hint? What did Maier do that led some people to get the correct solution? (these questions require some research)

The cognitive approach to problem solving

Problem space theory.

In 1972, Allen Newell and Herbert Simon published the book Human Problem Solving , in which they outlined their problem space theory of problem solving. In this theory, people solve problems by searching in a problem space . The problem space consists of the initial (current) state, the goal state, and all possible states in between. The actions that people take in order to move from one state to another are known as operators . Consider the eight puzzle . The problem space for the eight puzzle consists of the initial arrangement of tiles, the desired arrangement of tiles (normally 1, 2, 3….8), and all the possible arrangements that can be arrived at in between. However, problem spaces can be very large so the key issue is how people navigate their way through the possibilities, given their limited working memory capacities. In other words, how do they choose operators? For many problems we possess domain knowledge that helps us decide what to do. But for novel problems Newell and Simon proposed that operator selection is guided by cognitive short-cuts, known as heuristics . The simplest heuristic is repeat-state avoidance or backup avoidance 1 , whereby individuals prefer not to take an action that would take them back to a previous problem state. This is unhelpful when a person has taken an inappropriate action and actually needs to go back a step or more.

Another heuristic is difference reduction , or hill-climbing , whereby people take the action that leads to the biggest similarity between current state and goal state. Before reading further, see if you can solve the following problem:

In the hobbits and orcs problem the task instructions are as follows:

On one side of a river are three hobbits and three orcs. They have a boat on their side that is capable of carrying two creatures at a time across the river. The goal is to transport all six creatures across to the other side of the river. At no point on either side of the river can orcs outnumber hobbits (or the orcs would eat the outnumbered hobbits). The problem, then, is to find a method of transporting all six creatures across the river without the hobbits ever being outnumbered.

The solution to this problem, together with an explanation of how difference reduction is often applied, can be found by clicking here .

A more sophisticated heuristic is means-ends analysis . Like difference reduction, the means-ends analysis heuristic looks for the action that will lead to the greatest reduction in difference between the current state and goal state, but also specifies what to do if that action cannot be taken. Means-ends analysis can be specified as follows 2 :

• Compare the current state with the goal state. If there is no difference between them, the problem is solved.
• If there is a difference between the current state and the goal state, set a goal to solve that difference. If there is more than one difference, set a goal to solve the largest difference.
• Select an operator that will solve the difference identified in Step 2.
• If the operator can be applied, apply it. If it cannot, set a new goal to reach a state that would allow the application of the operator.
• Return to Step 1 with the new goal set in Step 4.

The application of means-ends analysis can be illustrated with the Tower of Hanoi problem .

In 1957 Newell and Simon developed the General Problem Solver , a computer program that used means-ends analysis to find solutions to a range of well-defined problems - problems that have clear paths (if not easy ones) to a goal state. In their 1972 book on problem solving they reported the verbal protocols of participants engaged in problem solving, which showed a close match between the steps that they took and those taken by the General Problem Solver.

Acquiring operators

There are three ways in which operators can be acquired:

• Trial-and-error. As noted above, this formed the basis of the behaviourist account of problem solving.
• Direct instruction.
• Analogies. Analogies are examples from one domain (the source), whose elements can be used to aid problem solving in another domain (the target). However, novices often struggle to spot analogies, as described here .

Next: Problem solving and insight

The problems with problem solving: Reflections on the rise, current status, and possible future of a cognitive research paradigm

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Newell and Simon's problem-space theory

Review of the literature, 2.4. information-processing theory and the problem understanding task, 2.4.1. newell and simon's problem-space theory.

Newell and Simon's research into human problem solving, especially their seminal work, "Human problem solving" (1972), still remains a much quoted reference in contemporary information-processing theory and research (Dawson, 1998). Despite the age o f this theory, it was found with a few modifications to be a useful way of structuring thinking

in the area o f interviewer reasoning. The current debate between the classical and the connectionist views of information processing is beyond the scope of this thesis, however readers are referred to Dawson (1998) who provides an excellent coverage o f the issues involved.

Newell and Simon (1972) conducted a wide range of experiments under controlled laboratory conditions into how people (usually undergraduates), approached a range of three-dimensional puzzles, and in particular the Tower o f Hanoi problem. In the Tower o f Hanoi problem participants were presented with three vertical pegs in a row, the first of which had three disks piled on it in order of size; that is the largest disk was at the bottom, the next on top, and so on. The goal o f the problem was to have all the disks piled in the same order on the last peg. However, disks could only be moved in certain ways. Only one disk could be moved at a time, and a larger disk could not be placed on top o f a smaller disk (Eysenck & Keane, 1995, p.363).

Figure 2.2 presents the problem space o f legal moves for the Tower o f Hanoi problem which will be referred to in the discussions below. From Newell and Simon's perspective people went about solving problems by first exploring a range o f possible ways (paths) o f finding a solution. Puzzles, such as the Tower of Hanoi, begin with a point outside the problem space (or maze), and then progress through a series o f moves to the centre - the solution. To achieve the goal o f getting to the centre, the person comes across many junctions where they have to make decisions (e.g., go straight, turn left, and so on). Each of these alternative paths may branch again and again, with some leading to the centre and the solution, and some not. Different strategies can be employed to find one's way inside the problem space (e.g., mark where you have come from, initially take left turns, and so on). These strategies provide the person with a systematic way of searching the problem space, and selecting one path firom a range o f alternative paths to get closer to the solution.

Their findings suggested that the stmcture of a problem could be characterised by a set o f states, beginning with an initial problem state (e.g., standing outside the problem space), involving many intermediate states (e.g., moving through the problem space), and ending with a goal state (e.g., being at the centre of the problem space). People in their studies began with an initial state and "searched" through a space o f alternative mental

States until they reached a goal state. Each of these alternative states can also have alternatives. The number o f these alternatives increases greatly as one moves away from the initial state to the goal state.

In order for people to solve the Tower of Hanoi problem they have to employ a range of cognitive strategies to reduce the number of states which they have to pass through to reach the goal state. Newell and Simon describe such strategies as heuristics. A heuristic strategy is in essence a nonrigorous way of achieving a solution to a problem. While heuristic procedures often lead to solutions, they offer no guarantee o f doing so (Bruner, 1996). Heuristics are contrasted with algorithms, which are methods that produce a definite solution. For example, in the Tower of Hanoi problem, a person could check every state, by starting at the beginning and systematically checking every alternative state until the goal state were achieved. This procedure would take far too long to be efficient, but is guaranteed to solve the problem. Heuristics, on the other hand are "rules of thumb", that may not guarantee a solution to a given problem every time, but most o f the time, thus saving time and effort.

One of the most important heuristic principles proposed by Newell and Simon was means-ends analysis. It consists of three main steps: first, the person notes the difference between the initial state and the goal state, second, they create subgoals to reduce this observed difference, and third, they select an operator that will solve this subgoal. Moves from one state to another are achieved by the application o f "mental operators". As problems may have a large number o f alternative paths, people use strategies to move from the initial state to the goal state efficiently. Thus, people's conception of a problem (i.e. the nature of the initial state), and the knowledge they bring to it (the operators and strategies available to them), make contributions to their problem­ solving behaviour (Newell & Simon, 1972).

Newell and Simon's problem-space theory identifies the various hypothetical states, processes and strategies that people may use to go about solving problems, at least puzzle based problems. The theory also predicts the types o f constraints that will make solving problems difficult, for example, the constraint o f human working memory and the interaction between this and the types o f strategies people use to search it. From a theoretical perspective it provides a normative theory o f human problem solving. The

theory allows for the structure of the problem to be specified and the best solution to the problem to be defined. In puzzle-based research from the 1950s to the present day, it is possible to elaborate the problem space and identify the correct or best solution to the problem by tracing the shortest sequence of moves from the initial state to the goal state. It provides a normative model o f what an "expert" problem solver would do, and how and why people's behaviour diverges from that o f the "expert".

2.4.2. Sum m ary of Newell and Simon's problem-space theory

Newell and Simon's (1972) information-processing theory o f problem solving suggests that when people move from an initial problem state towards a solution state they form a mental representation of the problem, which in this thesis is called a problem map. Research on expert problem solvers (outlined in section 2.7 o f this chapter) shows that they acquire through experience mechanisms for internally representing the problem space. This internal model acts as a precondition for planning, reasoning, anticipating and controlling subsequent cognitive behaviour (Ericsson & Lehmann, 1996).

The problem map undergoes a series of transformations as the problem solver tries to move from the initial problem state to a solution state. These transitions are achieved by the problem solver employing a series of cognitive operations, or strategies, such as means-ends analysis (this is the strategy whereby the problem solver evaluates the difference between the initial problem and the solution state). In summary, Newell and Simon's theory suggests that:

1. Problems have a large number o f alternative paths from the initial problem state to the solution state.

2. The total number o f such states, as generated by mental operators, is called the 'basic problem' space.

3. People's problem-solving behaviour is seen as the production of knowledge states by using mental operators to move from the initial knowledge state to a goal knowledge state.

4. People use their knowledge and various heuristic methods (i.e. means-ends analysis) to search through the problem space to find an efficient path from the initial state to the goal state.

5. All o f these processes occur within the limitations o f the individual's cognitive system, that is their working memory and information processing limitations (i.e. sorting and retrieving information from long-term memory).

6. The contents of people's short-term memory are open to conscious reporting by the individual. This assumption guided much of their work in which they used think-aloud protocols. This is a method whereby individuals say out loud what is going through their minds as they solve problems. The researcher records responses which are analysed later (Eysenck & Keane, 1995, p.363).

• Context-constraints
• Newell and Simon's problem-space theory (You are here)
• THE HYPOTHESIS-TESTING FRAMEWORK TO GUIDE PROBLEM UNDERSTANDING
• THE CHARACTERISTICS OF EXPERT AND NOVICE PROBLEM SOLVERS
• ARGYRIS AND SCHON'S THEORY OF INTERPERSONAL EFFECTIVENESS
• ROBINSON AND HALLIDAY’S RESEARCH ON ACCESSIBLE REASONING
• Critique of model
• Section One (Interviewing)
• Interviewing
• LIMITATIONS OF STUDY ONE
• CONCLUSIONS
• RATIONALE FOR STUDY TWO
• General design and interviewing tasks
• Use o f accessible reasoning statements
• RATIONALE FOR STUDY TWO (A)
• Research questions and hypotheses for study two (a)

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Human Problem Solving Hardcover – February 5, 2019

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First published in 1972, this monumental work develops and defends the authors' information processing theory of human reasoning. Human reasoners, they argue, can be modeled as symbolic "information processing systems" (IPSs), abstracted entirely from physiological bases. Modeling subjects with IPSs yields predictive theories of their problem-solving behavior and performance, and psychological insight into their heuristics and methods. Newell and Simon's previous epoch-making collaborations included the General Problem Solver, the Logic Theorist, and the Information Processing Language. This book is a careful application of those ideas from artificial intelligence - the ideas of AI's first golden age - to cognitive psychology. The authors first develop the formal theory of information processing systems. They then report studies of three symbolic reasoning tasks, and analyze that data using the information processing paradigm. In the final section, they state their comprehensive theory of human problem-solving. The success of the models of cognition given in this work was a major piece of evidence for the physical symbol system hypothesis, which Newell and Simon would first state a few years later. Newell went on to co-develop the Soar cognitive architecture, and Simon to receive the Nobel Prize in Economics. The two jointly received the Turing Award in 1975 for the research program of which Human Problem Solving was the culmination.

• Print length 938 pages
• Language English
• Publisher Echo Point Books & Media
• Publication date February 5, 2019
• Dimensions 6.69 x 1.94 x 9.61 inches
• ISBN-10 1635617928
• ISBN-13 978-1635617924
• See all details

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Stumped five ways to hone your problem-solving skills.

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Respect the worth of other people's insights

Problems continuously arise in organizational life, making problem-solving an essential skill for leaders. Leaders who are good at tackling conundrums are likely to be more effective at overcoming obstacles and guiding their teams to achieve their goals. So, what’s the secret to better problem-solving skills?

1. Understand the root cause of the problem

“Too often, people fail because they haven’t correctly defined what the problem is,” says David Ross, an international strategist, founder of consultancy Phoenix Strategic Management and author of Confronting the Storm: Regenerating Leadership and Hope in the Age of Uncertainty .

Ross explains that as teams grapple with “wicked” problems – those where there can be several root causes for why a problem exists – there can often be disagreement on the initial assumptions made. As a result, their chances of successfully solving the problem are low.

“Before commencing the process of solving the problem, it is worthwhile identifying who your key stakeholders are and talking to them about the issue,” Ross recommends. “Who could be affected by the issue? What is the problem – and why? How are people affected?”

He argues that if leaders treat people with dignity, respecting the worth of their insights, they are more likely to successfully solve problems.

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Best 5% interest savings accounts of 2024, 2. unfocus the mind.

“To solve problems, we need to commit to making time to face a problem in its full complexity, which also requires that we take back control of our thinking,” says Chris Griffiths, an expert on creativity and innovative thinking skills, founder and CEO of software provider OpenGenius, and co-author of The Focus Fix: Finding Clarity, Creativity and Resilience in an Overwhelming World .

To do this, it’s necessary to harness the power of the unfocused mind, according to Griffiths. “It might sound oxymoronic, but just like our devices, our brain needs time to recharge,” he says. “ A plethora of research has shown that daydreaming allows us to make creative connections and see abstract solutions that are not obvious when we’re engaged in direct work.”

To make use of the unfocused mind in problem solving, you must begin by getting to know the problem from all angles. “At this stage, don’t worry about actually solving the problem,” says Griffiths. “You’re simply giving your subconscious mind the information it needs to get creative with when you zone out. From here, pick a monotonous or rhythmic activity that will help you to activate the daydreaming state – that might be a walk, some doodling, or even some chores.”

Do this regularly, argues Griffiths, and you’ll soon find that flashes of inspiration and novel solutions naturally present themselves while you’re ostensibly thinking of other things. He says: “By allowing you to access the fullest creative potential of your own brain, daydreaming acts as a skeleton key for a wide range of problems.”

3. Be comfortable making judgment calls

“Admitting to not knowing the future takes courage,” says Professor Stephen Wyatt, founder and lead consultant at consultancy Corporate Rebirth and author of Antidote to the Crisis of Leadership: Opportunity in Complexity . “Leaders are worried our teams won’t respect us and our boards will lose faith in us, but what doesn’t work is drawing up plans and forecasts and holding yourself or others rigidly to them.”

Wyatt advises leaders to heighten their situational awareness – to look broadly, integrate more perspectives and be able to connect the dots. “We need to be comfortable in making judgment calls as the future is unknown,” he says. “There is no data on it. But equally, very few initiatives cannot be adjusted, refined or reviewed while in motion.”

Leaders need to stay vigilant, according to Wyatt, create the capacity of the enterprise to adapt and maintain the support of stakeholders. “The concept of the infallible leader needs to be updated,” he concludes.

4. Be prepared to fail and learn

“Organisations, and arguably society more widely, are obsessed with problems and the notion of problems,” says Steve Hearsum, founder of organizational change consultancy Edge + Stretch and author of No Silver Bullet: Bursting the Bubble of the Organisational Quick Fix .

Hearsum argues that this tendency is complicated by the myth of fixability, namely the idea that all problems, however complex, have a solution. “Our need for certainty, to minimize and dampen the anxiety of ‘not knowing,’ leads us to oversimplify and ignore or filter out anything that challenges the idea that there is a solution,” he says.

Leaders need to shift their mindset to cultivate their comfort with not knowing and couple that with being OK with being wrong, sometimes, notes Hearsum. He adds: “That means developing reflexivity to understand your own beliefs and judgments, and what influences these, asking questions and experimenting.”

5. Unleash the power of empathy

Leaders must be able to communicate problems in order to find solutions to them. But they should avoid bombarding their teams with complex, technical details since these can overwhelm their people’s cognitive load, says Dr Jessica Barker MBE , author of Hacked: The Secrets Behind Cyber Attacks .

Instead, she recommends that leaders frame their messages in ways that cut through jargon and ensure that their advice is relevant, accessible and actionable. “An essential leadership skill for this is empathy,” Barker explains. “When you’re trying to build a positive culture, it is crucial to understand why people are not practicing the behaviors you want rather than trying to force that behavioral change with fear, uncertainty and doubt.”

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