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).