After studying this chapter you should be able to:
•demonstrate an understanding of representation and describe the different building blocks of thinking
•identify and describe three different approaches to thinking and outline their different underlying assumptions
•discuss what cognitive psychology has contributed to our understanding of problem solving, reasoning and everyday cognition
•demonstrate an understanding of the tension that exists between seeing thinking as an internal mental process, as opposed to seeing it as a social process embedded in activities.
Melinda was always thinking about something, but it wasn’t always what she should be thinking about. As she tried to pay attention to her lecturer that morning, she was actually wondering whether her boyfriend was really committed to their relationship. He had been cold and critical recently. She had initially imagined that it was just exam stress, but then the exams had finished and his behaviour had not changed. With a guilty start, Melinda turned her attention back to what her lecturer was talking about, which was thinking. As she listened, she became absorbed in his discussion of the way that what we think about has to be represented in our minds. Melinda was not surprised to hear that there have been a number of different theories about thinking because she had already discovered that psychology has lots of theories! But she was very happy to learn a bit more about her everyday thinking.
Thinking is not one but many kinds of activities. For example, the terms ’paying attention’, ’wondering’, ’imagining’, ’visualising’, ’being aware’, ’deciding’ and ’concentrating’ all refer to some form of thinking.
Given its many forms, defining thinking is problematic. The above words, however, do have some things in common. They are all verbs and suggest an activity or process. They all suggest that this process occurs at an internal, mental level. They suggest that the outcome of the process leads to insight, understanding or the manipulation of ideas or knowledge. In general terms, then, thinking is the mental processes or capacities that enable people to solve problems, to reason, to make sense of things or to use their knowledge to understand situations, events, other people or even themselves.
As we go further we will see that the idea that thinking is only about mental processes is challenged by some psychologists, but this is an adequate working definition from which to start. As this chapter explores how psychologists have come to understand thinking, three themes are followed:
1.The problem of representation is examined. (If thinking happens at an internal level, then it is important to understand how objects and ideas are represented mentally.)
2.The constructivist, the information-processing and the socio-historical approaches to the study of thinking are discussed. (Each of these approaches opens very different windows onto thinking.)
3.Three different types of thinking are described: reasoning, problem solving and everyday thinking. (These types of thinking are discussed alongside the approaches to the study of thinking.)
Representation and thinking
Look at Figure 11.1. What do you see? A square and two different triangles? Would it surprise you if you were told that in a study conducted by Gilbert (1987) in rural KwaZulu-Natal, a number of respondents saw the square as a wall of a house, the equilateral triangle as a roof or poles for a house and the right-angled triangle as a saw needed to cut the poles? Figure 11.1 is nothing more than lines and shading on white paper, but mentally these come to represent different things for different people. When something stands in for or refers to the thing we are thinking about, this is called representation. How do humans represent things?
Figure 11.1 What are these?
One powerful way of representing the world is to place things that have similar characteristics or properties into categories. Shape, colour and form, for example, are three ways in which we classify objects.
The symbols in Figure 11.2 have the properties of shape, size and shading. How many different combinations of these images can you create using just three categories? If we were to group these symbols in terms of the category ’shape’, we would have three triangles, three circles and three squares. Do the same with the categories ’shading’ and ’size’. Afterwards you will find that in each case you grouped the symbols together in terms of their similar, pre-selected properties.
People use the term ’concept’ to refer to a mental category that classifies objects, events, processes or abstract ideas. Democracy, for example, is a concept used to describe a particular abstract quality of social and political life. For a number of reasons, concepts are important building blocks for thinking:
•They lead us into sets of linked knowledge. Using the concept of democracy to describe South Africa, for example, evokes the ideas of free speech, the rule of law and the right to free association.
•Concepts promote cognitive economy (Quinlan & Dyson, 2008; Rosch, 1978). Concepts on their own can be used for thinking instead of having to use all the separate ideas to which they are linked. Having a sense of all that the concept democracy means enables us to use the term ’democracy’ as the basis for the further development of ideas.
•Categories combine with other categories to form hierarchies, which then provide complex pictures of phenomena (see Figure 11.3).
Figure 11.2 Consider how complex categorisation can become, even with three simple categories
Botany is an excellent example of this. Linnaeus (1707— 1778) started classifying plants in terms of the structure of flowers and seeds. On this simple criterion, all known plants have now been incorporated into a hierarchical taxonomy. For example, a species of lily — the arum lily (Zantedeschia aethiopica) — is classified under the genus Zantedeschia within the family Araceae, within the division Alismatales, and the kingdom Plantae, which refers to all plants in the living world.
This taxonomy is now a powerful resource. A South African botanist, for instance, can visit the jungles of Panama and discover a new plant which, given its flower structure, may be categorised as being closely related to a rose. Once this is done, without any further information, a whole set of generalisations about the new species can be made, including: ’Beware of the thorns!’
Figure 11.3 Classification taxonomy
However, while categorisation is important in making assumptions about people, events and places, rigid and unfounded categorisations can be the source of racism, sexism and other forms of unfair discrimination.
Figure 11.4 Arum lilies
Concepts are not formed from a set of similar features, but from a representative example of the concept, whether it be an object, event, process or abstract idea. This representative example is called a prototype and exhibits the typical features of a particular category. Prototypes serve as reference points by which we categorise things. For example, you may find it difficult to define what a fruit is, but you would find it easy to think of an example of a fruit (and this would be a prototype).
In what ways are an elephant and a giraffe similar and different? Considering this, are you visualising these animals? Visual imagery (i.e. seeing the images of objects represented in your mind’s eye) is an important form of representation.
There has been considerable debate about whether mental representation is an actual picture of the image or the scene (Pylyshyn, 2002, in Quinlan & Dyson, 2008) or is more symbolic, like the well-known symbols for female and male (). The symbols (like the letters of the alphabet, as another example) are arbitrary, but people have agreed about what they represent. Interestingly, while there is strong evidence to support the symbols theory, there are nevertheless supporters of both ideas among cognitive theorists today (Quinlan & Dyson, 2008).
One common and fairly durable form of imagery is a cognitive map. This is an internal representation of the spatial arrangements of an environment (Quinlan & Dyson, 2008). If someone asks you for directions to a lecture venue on campus, you are likely to hold some image of the route in your head while giving directions. You would be using your cognitive map of the campus. Box 11.1 identifies some systematic distortions that appear to lie behind cognitive maps.
Schemas, scripts and models
Schemas refer to the over-arching ’packets’ of knowledge that are central in our thinking and that are stored in our semantic memory (Eysenck & Keane, 2010). For example, our schemas lead us to expect that a classroom will have desks and chairs for students and the teacher, and some form of chalkboard. Scripts and models refer to the more practical aspects of schemas as they deal with knowledge about specific contexts (Eysenck & Keane, 2010; Shore, 1996).
Think about the following example: Nomabaso entered the computer room at the university and sat down in front of a computer. She rummaged in her bag for her student card. ’Oh no,’ she said, ’I left my student card in the library.’ Can you understand why Nomabaso was looking for her student card? If you are familiar with working on a university computer and having to input your student number when you log on, then the above description will make complete sense to you. Nomabaso needs her student card because she has forgotten her student number and without it cannot use the computer. You have made sense of the scenario by using a script of working on a university computer.
11.1COGNITIVE MAP DISTORTIONS
Using your own internal cognitive map of South Africa, do the following tasks:
•In your head, draw a line directly south from Johannesburg until it crosses the coastline. Which coastal city is nearest to this line and about how far away is it?
•In your head, draw a line between Cape Town and Port Elizabeth. Draw another line between Port Elizabeth and Durban. How much of an angle is there between these lines when they meet at Port Elizabeth?
Get a map out and check your own cognitive map. Does it surprise you that neither Cape Town, Port Elizabeth nor Durban are close to being south of Johannesburg? East London is directly south of Johannesburg. Does it also surprise you that Port Elizabeth is almost as far south as Cape Town, so that a line drawn between the two is a horizontal one, whilst Durban is northeast of Port Elizabeth?
Tversky (2005) argues that while cognitive maps are reasonably accurate, they reflect systematic errors. We use heuristics, or rules of thumb, to estimate things, and these are biased to make things more orderly.
The rotation heuristic bias occurs when figures that are slightly tilted (such as the map of the coastline between Cape Town and Durban) are ’seen’ as more vertical or more horizontal than they really are. If you thought Cape Town, Port Elizabeth and Durban were on a straight line running northeast, this would be evidence of a rotation bias to the vertical.
A second bias is the alignment heuristic bias. In this bias there is a tendency to line up two objects in a straight line close to the lines of latitude or longitude. Pulling Cape Town or Durban closer to a southern line from Johannesburg than they actually are would be an example.
A script is an information set that provides guiding principles about what we would normally expect in a specific situation (Eysenck & Keane, 2010). A script is one kind of schema or network of knowledge about procedures, sequences of events or processes. For example, when we go to a restaurant, we expect to be welcomed and shown to a table, and then given a menu.
Models can be divided into two types:
•Task models provide a schedule for getting practical things done (Shore, 1996). For example, when cooking a meal, we peel and start cooking the potatoes before grilling the meat.
•Diagnostic models enable us to extract information from important phenomena. For example, meteorologists have models of cloud formations, which enable them to predict whether or not it is likely to rain.
Both scripts and models enable us to make assumptions about what will happen in particular situations. They can create problems, however, when they are used in the wrong context or are applied rigidly when a situation rapidly changes. For example, Nomabaso would have difficulty trying to log on to a computer at an internet café using her student card because this is a different setting and the university rules do not apply here.
•Thinking is involved in many mental activities. It can be defined as the mental processes or capacities that enable people to solve problems, to reason, to make sense of things or to use their knowledge to understand situations, events and people.
•Thinking is only possible because humans can make mental representations of things. These representations can be placed in categories which have similar characteristics or properties.
•A concept is a mental category that classifies objects, events, processes or abstract ideas. Concepts are important building blocks for thinking. Concepts and categories can be arranged hierarchically.
•A prototype is a representative example of a concept.
•Visual imagery (e.g. a cognitive map) provides an important form of representation.
•Schemas are over-arching bodies of knowledge used in thinking. Scripts are sets of information that provide guiding principles about what we would normally expect in a specific situation; scripts and models refer to the more practical aspects of schemas used in particular contexts. Both scripts and models enable us to make assumptions about what will happen in particular situations.
The constructivist approach to thinking
Piaget’s perspective on the development of thinking in childhood and adolescence
Jean Piaget (1896—1980), a Swiss scientist, is the central theorist in the constructivist approach to thinking. He started his scientific life as a zoologist, and was interested in how organisms transform in response to the demands of the environment. He used this idea of adaptation to explain how logical abstract thinking develops in humans.
Figure 11.5 Jean Piaget, one of the greatest thinkers of the 20th century
His metaphor for thinking is that it is internalised action. He argued that we are not born with the structure of our thought already in place; thinking is not innate (or inherited). We construct our ability to think as we interact with the world. For this reason, his approach is known as constructivism.
Piaget’s theory of developmental change concerned adaptation, which involves two related processes that change our thinking in opposite directions: assimilation and accommodation. Assimilation is ’the integration of external elements into evolving or completed structures’ (Piaget, 1970, p. 7). Coming across a new object and incorporating it into an existing category would be assimilation, for example discovering a new flower in Panama and classifying it in the genus Rosa. Sometimes, however, action requires the ’modification of a structure by the elements it assimilates’ (Piaget, 1970, p. 8). This is accommodation. In this process, new information transforms cognitive structures. Discovering a new flower that does not fit into any existing genus and requires a revision of plant taxonomy would be an example of accommodation.
Through these dual processes, Piaget argued, thinking is constantly transformed. At first, thinking involves thinking by doing, i.e. putting together simple patterns of action while manipulating objects (the sensorimotor stage). Out of this comes mental schemas — mental operations that are sequences of actions that have come to be represented mentally. Once such schemas are in place, the quality of thinking changes. Now a problem can be solved by thinking about the action rather than having to physically take the action. This is the concrete operational stage. Adding 104 and 250 in your head by imagining yourself doing it on paper, is an example of the concrete internalisation of action. Do the task outlined in Box 11.2 before going further.
Piaget goes one step further in arguing how thought is internalised action. Interacting with more complex phenomena (e.g. volume rather than area) requires the construction of new forms of thinking. Instead of thinking about action, thinking now involves manipulating the mental schemas that are in place. This requires thinking in terms of abstract, logical principles, making deductions and formulating hypotheses. Such thought is formal operational thinking — thinking based on abstract schemas and now free from the immediate physical context. (For more on Piaget’s ideas, refer back to the chapters in Part 2, where Piaget’s stage theory of development is discussed in more detail.)
Figure 11.6 Piaget’s theory of adaptation
Cut a piece of string so that you have a piece that is 60 cm long. Tie the two ends together. Place the loop on a table. Using the thumb and forefinger of both hands, make a square. Now reduce the space between your thumb and forefingers while moving your hands apart so that the square becomes a rectangle (see Figure 11.7). Do you think that, for the two shapes you created, the surface area enclosed by the string is approximately the same? Will the area always be roughly the same no matter what rectangle you create? Explain your answer.
Figure 11.7 Move your fingers to form a square and a rectangle with the string
If you said, ’Yes, the area is approximately the same because the length of string is always the same’, or ’because the area within the rectangles looks similar’, then you are making an error.
Let us work this out logically. A square made by string 60 cm long would have sides 15 cm by 15 cm (assuming that tying the knot does not shorten the string). The area of this square is 15 cm × 15 cm = 225 cm2. If you close up your fingers a little to make a rectangle 18 cm by 12 cm, then the area will be 18 cm × 12 cm = 216 cm2. This is still roughly the same area. If, however, you make a rectangle with sides 25 cm by 5 cm then the area is 25 cm × 5 cm = 125 cm2.
This task captures the Piagetian idea that as tasks become more complex, thinking has to become more distant from actual manipulations (as it is in the concrete operation stage — see Chapter 3) and must instead become more logical (as it is in the formal operational stage — see Chapter 4).
A number of methodological critiques have been aimed at Piaget’s theory (Hopkins, 2011). For example, he rarely described in detail how he selected his samples, nor indicated the size of the sample. In one instance, his sample was just three — his own children (Hopkins, 2011). In addition, apart from the ages of his participants, he did not conduct any statistical analysis. Despite this, Piaget’s method of in-depth interviews with children about their thinking ’has yielded enormously influential results’ (Hopkins, 2011).
Schaie’s perspective on the development of thinking in adulthood
The Piagetian approach was criticised for not considering how thinking develops beyond adolescence. In response, Schaie (1994) extended Piaget’s theory by maintaining that adult thinking develops in different progressive stages:
•Achieving stage. During young adulthood, individuals use their intellectual competencies in the areas of problem solving and decision making. For example, they choose a partner and/or decide on a career.
•Responsibility stage. Individuals are now required to be independent thinkers. They must use their own solutions, not only for personal and career decisions but also for problem solving and decision making that involves, for example their families and the broader community.
•Executive stage. Individuals in middle adulthood learn to apply their problem-solving and decision-making skills to management situations, such as in their families, careers and the broader community.
•Reintegration stage. Individuals in late adulthood now use their accumulated intellectual skills to assess life and to give meaning to their past.
Challenges to the constructivist perspective
The constructivist approach is concerned with establishing universal principles that lie behind thinking. It assumes that all humans of normal intellect are faced, at a general level, with the same forms of adaptation and will therefore move in the direction of more and more abstract thought. As the following sections reveal, not all psychologists share this view.
Furthermore, while Piaget perceived logical reasoning to be the pinnacle of human thinking, D’Andrade’s (1995) experiment revealed that the picture may be more complex than this (see Box 11.3). When required to think abstractly we often fail to do so, but given a culturally appropriate context for such thinking, our ability to think in logical ways is revealed.
•Piaget is the central theorist in the constructivist approach to thinking. He saw thinking as internalised action.
•Piaget said developmental change includes assimilation (integration of new elements into existing structures) and accommodation (in which a mental structure is modified by the elements it incorporates).
•As children grow, they develop from thinking by doing (physically manipulating objects) to thinking about manipulating objects, to more abstract thinking which allows the person to make deductions and formulate hypotheses.
•Schaie criticised the Piagetian approach for not considering how thinking develops beyond adolescence. Schaie argued that adult thinking develops in different progressive stages: the achieving stage, the stage of responsibility, the executive stage and the reintegration stage.
•The constructivist approach attempted to establish universal principles that lie behind thinking. However, other theorists disagreed with this. It seems people do not always reason logically, although we are better at it in culturally appropriate contexts.
Piaget’s focus on abstract, logical thinking came out of his interest in the nature of scientific thinking. Reasoning, which is systematically drawing conclusions from statements or facts, is a characteristic of thinking in science. The study of this form of thinking has a history that goes back to the early Greek philosophers who developed the formal rules of logic. Modern philosophers and psychologists continue to see reasoning as thinking that works according to the principles of logic. Two kinds of reasoning have received considerable attention: deduction and induction.
Deduction involves working from general statements to draw particular conclusions that are true in relation to these statements. A syllogism is a particular form of deductive reasoning that has two premises (propositions) that are followed by a conclusion. The following sequence of reasoning would be deductive:
•Proposition 1: All humans die before they are thirty.
•Proposition 2: I am a human.
•Conclusion: I will die before I am thirty.
Logically, this conclusion is true, even though Proposition 1, from which it is derived, is obviously false. In deductive reasoning, the conclusion is certain to be true as long as the two propositions are true and as long as the conclusion is logically built on these propositions.
Tasks A and B are examples of a deductive reasoning task. They are adapted from a study conducted by D’Andrade (1995) and also appear in Gilbert (1997):
•Task A: Imagine you work at a label factory. Labels have either an X or a Y printed on the front and a 1 or 2 printed on the back. Unfortunately the printer has malfunctioned and some of the labels have been incorrectly printed. You have the job of checking to ensure that if a label had a Y on the front then a 1 is printed on the back. You have the following labels in front of you. Which labels would you turn over to be sure that every label with a Y on the front has a 1 on the back?
•Task B: Imagine you are employed by your local supermarket. You have to check receipts made out by sales staff. If any sale involves an amount of R100 or more, it has to be approved by the sales manager. The amount of the sale should be written on the front of the receipt and the manager’s approval on the back. You have the following receipts in front of you. Which would you turn over to be sure that the sales clerk has followed the rule?
In Task A, which of the labels did you decide you needed to turn over? Logically, the answer is labels ii and iv. (You need to turn over label iv to see if it has a 1 on the other side. You need to turn over label ii to check that it does not have a Y on the other side. You do not need to turn over labels i and iii because label i has an X on it and therefore will not have a Y on it at all, and label iii has a 1 on it, therefore it would be satisfactory both if it had a Y on it or an X on it.)
D’Andrade (1995), from whose study this task is taken, found that about 80 per cent of the graduates in his study got it wrong, so do not worry if you did as well!
What answer did you give to Task B? If you said iii and iv you would be correct. In contrast to Task A, D’Andrade (1995) found that more than 70 per cent of his students got the answer correct on this task.
Tasks A and B are identical in terms of logic, so why is there this discrepancy in responses? D’Andrade argues that while people can reason deductively, whether or not they use this form of thinking accurately will depend on the cultural schemas that they have available to them. The difference between the two tasks is that the second is a more familiar one and makes more sense because cultural schemas for this kind of task are present.
Induction is reasoning that draws conclusions from particular cases. It is the process whereby people project information from a known case or cases to an unknown case or cases (Heit, 2000). For example, every day you observe that the sun rises from the sea. Inductively you might, therefore, conclude that the sun will always rise from the sea. Similarly, your home is broken into one night; even though you previously felt safe, you now think that your house will be broken into again the next night or some night in the near future (example from Heit, 2000).
It is important to understand that conclusions from inductive reasoning are probabilities rather than certainties as is the case in deductive reasoning. The level of probability or certainty depends on a number of factors. For example, the similarity between the known case and the unknown case is important. Think of the sunrise example above — despite differences due to weather and season, the sun is the same and the sunrise is a similar event each day. On the other hand, when you think about the probability of a break-in, you may see some similarity between the known case (your home on the night of the break-in) and future cases (your home on future nights), you also need to consider all of the nights when your home was not broken into and whether or not there have been other break-ins nearby (Heit, 2000). Other factors that influence the probability are the number of observations made and the diversity of the observations. This is very similar to the research process where the more observations (and the more observations from different sources) are collected, the more reliable are your results.
Inductive reasoning produces hypotheses, which are tentative conclusions, which can then be scientifically tested. This is the process that is followed in much psychology research (see Chapter 2). As in research, the process of induction may be open to biases like the confirmation bias discussed in Chapter 2. Both inductive reasoning and deductive reasoning are central to science.
The information-processing approach
In the 1960s, developments in the fields of computer science and information science began to revolutionise the world. Computers became highly efficient and effective processors of information. Unsurprisingly, psychologists then thought the computer might be a useful metaphor for understanding how humans process information. This produced the information-processing (IP) approach, which is the major perspective in cognitive psychology (see Chapter 15). But before you go further with this section try and solve the problem given in Box 11.4.
11.4HOW FAR DID THE FLY FLY?
Try and solve this problem (which is an adapted form of a problem proposed by Bransford & Stein, 1984).
Car A and Car B are travelling in a straight line towards each other at 50 km/h. When the cars are 100 km apart a fly takes off from Car A in the direction of Car B at the speed of 80 km/h. When it meets Car B it turns around and flies back to Car A, and then turns and flies back to Car B. It continues doing this between the two cars until they meet. How far does the fly travel? (Assume the cars and the fly travel at a constant speed and never have to slow down.)
In the IP approach, the challenge is to produce process models that describe the step-by-step ways that humans process information. Newell and Simon’s (1972) view of problem solving provides an example of this approach to thinking. They see problem solving as searching through a problem space, i.e. processing information to achieve a goal. This problem space is defined by a starting state and an end state (the goal of the task). Steps have to be taken (sub-goals achieved) to reach the end state. How these steps are sequenced forms the strategy that is used to solve the problem. Therefore, in the IP approach, a state—action analysis (a description of the states, steps and strategies taken within a problem space) would be a description of the thinking that has taken place.
A state action—analysis of the problem ’How far did the fly fly?’ is demonstrated in Box 11.5.
Comparing the thinking of experts and novices
The comparison of the thinking of experts and novices has been a useful source of information for the IP approach. Experts are people who perform well on a particular task. Novices are new to the task. Research has shown novices and experts across a wide range of domains of knowledge represent problems differently. Experts spend more time trying to understand the nature of the problem and often use their prior knowledge in solving problems (Brand- Gruwel, Wopereis & Vermetten, 2005). Experts also monitor themselves more during problem-solving tasks. In terms of mathematical problems, both experts and novices use visual representations; however, experts use visual representations for a wider variety of problems (Stylianou & Silver, 2009). In addition, experts use their visual representations more dynamically, using them to develop a better understanding of the problem. Brand-Gruwel et al. (2005) found that there was little difference in the way novices and experts searched the internet.
Figure 11.8 An expert—novice interaction?
11.5A STATE—ACTION ANALYSIS
Let us use the problem of ’How far did the fly fly?’ from Box 11.4 as an example of how the IP approach would construct a state— action analysis to understand your thinking.
You were required to calculate the distance the fly travels. This is the end state. The starting state is the information given in the problem: the speed of the cars and the fly, and the distance the cars are apart. The gap between these states creates the problem space. To solve the problem requires transforming the starting information into a form that provides an answer to the question: How far does the fly fly? There are a number of possible steps that can be taken. Here is one strategy:
Step 1:The starting state tells us the fly travelled at 80 km/h. So if we knew the amount of time the fly flew we would know the distance it travelled.
Step 2:From the starting state, we know the fly and the cars travelled for the same length of time. So if we know how long the cars travelled for, we will know how long the fly travelled for.
Step 3:From the starting state, we also know the speed of the cars. If we can calculate the distance the cars travelled then we can work out how long they travelled for.
Step 4:We know that the cars travelled in a straight line towards each other at 50 km/h and that they were 100 km apart. We can, therefore, calculate the distance the cars travelled. The cars must have met after 50 km.
Step 5:With this information, return to step 3. The cars travel at 50 km/h for 50 km. Therefore they travel for one hour.
Step 6:With this information, return to step 2. If the cars travel for one hour, the fly must have travelled for one hour.
Step 7:With this information return to step 1. We know that the fly travelled at a speed of 80 km/h. Therefore in an hour it must have travelled 80 km.
Problem solved! Does this description capture the way you thought?
Challenges for the information processing approach
Many of the insights from the IP approach have come from studies of problem solving. The reason for this is that it is possible to manipulate systematically the elements of problems in experiments. There are, however, at least two kinds of problems: well-defined and ill-defined problems. In a well-defined problem, the elements of the problem (the original state, the end state and the rules) are clearly defined. (The fly problem is a good example.) In an ill-defined problem, one or more of these elements is/are unclear. In everyday life, many problems are ill-defined because there are no clear solutions. Sometimes we do not even know what the starting point is or what kinds of questions we should be asking ourselves. This raises the question: ’How applicable are the findings of the IP approach for understanding the thinking behind the everyday problems of human life?’
A number of important insights into problem solving have come from the IP approach.
When presented with a problem that needs to be solved, often the most difficult task is knowing where to start. However, once a problem is clearly stated, finding a solution may be more easily accomplished (Goldstein, 2005). People use a number of strategies in problem solving. These include algorithms, heuristics, analogies, working backwards and means—end analysis. Algorithms have been found to assist problem solving. An algorithm is a step-by-step process that will always provide the solution. The formula for calculating the average of a set of scores by adding up all the scores, and dividing by the number of scores in the set, is an algorithm. The seven steps for solving the fly problem in Box 11.5 constitute an algorithm. Applying known algorithms to problems helps to solve them.
When a problem space is large (i.e. when the number of possible solutions to a problem is large), then applying an algorithm may be too time consuming. In such instances, people may decide to be more selective in the possible solutions they consider; they may use heuristics. A heuristic is a short-cut method, a rule of thumb that reduces the problem space. Unlike algorithms, heuristics do not guarantee success, although they can be very useful.
Analogies are heuristic devices that involve seeing a similarity between a current problem and one that has been encountered in the past. When using an analogy, a person must locate the previous problem, compare the two problems, adapt the procedures used to solve the previous problem to the current one, and develop a schema that can then be applied to a whole class of problems of which the current one and the previous one are examples (Quinlan & Dyson, 2008).
Another useful heuristic device involves working backwards from the end state to the starting state. An example taken from Cox (2001) explains this. Let us try to solve the problem of how magicians pull a rabbit out of a hat. If you start with the idea of an empty hat, this will be a difficult problem to solve. However, if you start at the end — from the rabbit being pulled out of the hat — the solution becomes clear. First, the rabbit must have been put in the hat either before or during the performance. Second, as this is difficult to manage during the performance, you realise the rabbit must have been put in the hat before the performance. Therefore, there must be a compartment where the rabbit has been hidden. (Did you apply this strategy when solving the fly problem?)
Means—end analysis is a heuristic strategy that involves breaking down a problem into a series of sub-problems. Each sub-problem is solved until a final solution to the original problem is arrived at. For example, suppose your psychology textbook is stolen. The solution to your problem could be to follow these steps: visit the psychology course coordinator, make a list of all students who did the course previously, contact them, arrange to buy one of their textbooks.
Barriers to problem solving
Problem solving would not be a problem if we were always able to choose the best strategy for the problem at hand. Unfortunately, previously used problem-solving ideas may persist and inhibit the development of new, more appropriate problem-solving ideas.
A mental set occurs when problem-solvers continue to use the same solution they have used with previous problems, even though there may be more efficient ways of solving a particular problem. Similarly, functional fixedness occurs when problem-solvers focus on a particular characteristic of an object, and fail to see alternative characteristics of the object that would assist in solving the problem at hand.
•The 1960s saw revolutionary developments in the fields of computer and information science. The information-processing approach emerged; this saw the computer as a useful metaphor for understanding how humans process information.
•The IP approach worked to produce models to describe the step-by-step ways that humans solve problems.
•Problem solving involves searching through a problem space, which is defined by a starting state and the steps to be taken to reach the end state (the goal). A state—action analysis provides a description of the states, steps and strategies taken within a problem space.
•The IP approach has gained useful information by comparing the thinking of experts and novices. Experts use more abstract ideas and interpret what they see in terms of rules and principles. Experts also spend more time trying to understand the nature of the problem before starting to solve it and are more aware of errors.
•The IP approach has been helpful for understanding how people solve well-defined problems; however, in everyday life many problems are ill-defined.
The socio-historical approach
One of the major criticisms of Piaget’s approach was that it did not take into consideration the developing child’s social context (Holt et al., 2012). In contrast to the constructivist and IP approaches, the socio-historical approach suggests that thinking is a social process, which is linked to the interaction between the individual and the setting in which the thinking occurs (Davey, 2004). However, it does not deny the existence of internal mental processes. This view is also known as the situated-cognition approach. Lev Vygotsky (1896—1934), a Russian psychologist, is often regarded as the founder of this approach. He argued that thinking has its origins in the social world within which people live (Vygotsky, 1978). His idea can be captured in the phrase ’thinking is internalised culture’. In describing the cognitive development of children, Vygotsky said that any function appears twice: ’first, on the social level, and later, on the individual level; first between people (inter-psychologically) and then inside the child (intra-psychologically). All the higher functions [of thinking] originate as actual relations between human beings’ (Vygotsky, 1978, p. 57).
Two important ideas are contained in this statement. First, that thinking has its origins in interaction with others. Second, that what is learned in interaction with others is taken over by the individual and used as the base for their own thought. In other words, the symbols, schemas and scripts for thinking that are internalised become the tools for our own thinking. (For more on Vygotsky, see Chapter 3.)
This view suggests that thinking cannot be separated from the social context in which it is used. The social setting often provides the structure and resources for thinking. Complete the task in Box 11.7.
Box 11.8 contains an example of everyday thinking. Such thinking does not happen in experiments or laboratories, but occurs in the everyday settings of daily life, so it needs to be studied in these settings.
Studies of everyday thinking have revealed that it differs from the kind of thinking that is studied in more formal settings. Everyday thinking incorporates aspects of the task environment into problem solving. Scribner (1986) reports, for example, that dairy workers in the US required to fulfil an order for 31 bottles of chocolate milk, restructured the problem in relation to the way the milk was packaged. Working with crates that contained 32 bottles, they saw the problem as one crate minus one bottle. In other words, the way they calculated arithmetic problems in the work situation was not based on standard mathematical algorithms, but on the way the items were packaged. Similar findings of everyday thinking were found among child street vendors in Brazil, as demonstrated in Box 11.8.
Figure 11.9 Dairy workers calculated arithmetic problems in the work situation based not on standard mathematical algorithms, but on the way the items were packaged
11.7A WEIGHT-WATCHER’S DILEMMA
Imagine you want to lose weight. You use a Weight Watcher’s recipe to make a meal, which includes cottage cheese as an ingredient. The recipe says that you should use two-thirds of a cup. You go to the fridge and fill a cup two-thirds full with cottage cheese. Just before you are about to use it you remember that your diet table says that today you are allowed only three-quarters of what the recipe says. How would you go about working out threequarters of two-thirds of a cup of cottage cheese (example taken from Lave, 1988)?
How did you arrive at an answer? Seen as a mathematical problem, the solution is simple. Three-quarters of two-thirds of a cup can be represented arithmetically as ¾ × 2/3 = ½ cup!
It is that easy. Perhaps, however, you were like the weight watcher reported by Lave (1988), who solved the problem as follows. He filled the measuring cup two-thirds full with cottage cheese then turned up the cup onto a chopping board. He then patted it into a circle, marked a cross on it and scooped away one of the quarters. The remaining portion was his allocation. What is interesting about this person’s action was that Lave reports that the man had sophisticated mathematical skills but did not think about using them. Such behaviour is not uncommon. In this case, the setting provided a structure for his thinking, in which his standard mathematical skills were not called upon. It also provided resources for resolving the problem in novel ways — the board and the utensils. These formed part of his thinking.
11.8CHILD STREET VENDORS IN BRAZIL
Carraher, Carraher and Schliemann (1985) have done interesting research on everyday thinking. They studied the way child vendors in Brazil solved the day-to-day problems of marketing their products — sweets and fruit. They found numerous examples of how the manner in which items were structured in their environment was used as a resource for solving problems. Thus, for example, coconuts, which were priced at 35 cruzeiros, were normally sold in lots of three. When a customer (the researcher) asked for the price of 10 coconuts, the child vendor would use this knowledge as the base for their thinking. Their calculation, therefore, took the following line of reasoning: ’Three coconuts are 105 cruzeiros, three more will be 210, three more will be 315 and then one more to make ten will be 350’. As with the weight watcher, the vendors used the way the items were naturally structured in their environment, rather than alternate algorithms, such as ten times 35, to solve the problem.
What the study of everyday thinking suggests is that thinking is not just a mental activity; it is spread across the context in which the thinking takes place and cannot be separated from it. The term ’distributed cognition’ describes this idea.
Challenges to the socio-historical approach
In contrast to the constructivist approach, which argues for a domain-general approach to thinking, the socio-historical approach argues that thinking will change across contexts and will be affected by the resources for thinking that are available in that context. This kind of thinking is regarded as domain-specific thought — thinking that is tied to a particular sphere of life or context. The term ’local knowledge’ is often used for this kind of thinking (Corburn, 2003).
The socio-historical approach raises the question: ’If thinking is tied to context, does this mean people from different contexts will think differently?’ This issue is the cultural relativism debate, which is examined in the chapter on language (Chapter 14). While the socio-historical approach argues that thinking is tied to context, it also suggests that thinking is flexible, for as we change contexts so does our thinking. From this position, the socio-historical approach provides a positive view of human thought, since it suggests that given opportunities to understand what is required in new situations and access to new tools for thinking, people can overcome the limitations to thinking that they may have. Corburn (2003) used this approach to study the role that local knowledge can play in improving environmental and health-risk planning in affected communities. In these communities, people from within the community use their first-hand knowledge to engage with and challenge input from planners and scientists.
•The socio-historical approach argues that thinking is a social process, and is linked to the interaction between the individual and the setting in which the thinking occurs. Vygotsky is regarded as the founder of this approach.
•This approach argues that as thinking develops in children, any function appears twice: first, on the social level, and later, on the individual level. Thus, the symbols, schemas and scripts for thinking that are internalised from social interactions become the tools for our own thinking.
•Thinking cannot be separated from the social context in which it is used.
•Studies of everyday thinking show that it differs from the kind of thinking that is studied in more formal settings. In everyday thinking, people incorporate aspects of the task environment into their problem solving.
•The socio-historical approach argues that thinking is domain specific; i.e. thought will change across contexts and will be affected by the resources for thinking that are available in that context. This raises the cultural relativism debate; it also suggests that thinking is flexible and that local knowledge should be accessed.
Thinking is not only one kind of activity and does not have only one form. There are many kinds of thinking, and the structure and nature of thought changes depending on the context within which it occurs. It is inevitable, then, that psychologists will approach thinking from different perspectives and each approach will tend to investigate the type or form of thinking that relates to that approach.
As a result, there is no simple answer to the question: what is thinking? This chapter has tried to capture some of the fascinating and insightful ways psychologists answer this question. They all add up to a rich picture of the complex and changing nature of the human cognition.
accommodation: a process in which new information transforms existing cognitive structures
achieving stage: a stage in adult thinking that occurs during young adulthood where individuals use their intellectual competencies in the areas of problem solving and decision making
adaptation: the process whereby thinking is changed by means of assimilation, where new information is integrated into previous information, and/or accommodation, where new information changes previous information
algorithm: a step-by-step process that will always provide the solution to a problem
alignment heuristic bias: a tendency to line up two objects in a straight line close to the lines of latitude or longitude
analogy: a heuristic device that involves seeing a similarity between a current problem and one that has been encountered in the past
assimilation: the incorporation of a new object into an existing category
cognitive map: an internal representation of the spatial arrangements of the environment
concept: a mental category by which people classify objects, events, processes or abstract ideas
deduction: a form of reasoning that involves working from general statements to draw particular conclusions that are true in relation to these statements
diagnostic models: over-arching bodies of knowledge that are central to thinking and that enable the evaluation of important phenomena
everyday thinking: the kind of thinking that occurs as we deal with the mundane, practical things of life
executive stage: a stage in adult thinking where, through increasing knowledge, individuals in middle adulthood learn to apply their problem-solving and decision-making skills to management situations, such as in their families, careers and the broader community
functional fixedness: a barrier to problem solving that occurs when problem-solvers focus on a particular characteristic of an object, and fail to see alternative characteristics of the object that would assist in solving the problem at hand
heuristic: a short-cut method to problem solving that reduces the problem space and often, but not always, works
induction: a form of reasoning that draws conclusions from particular cases, and is based on relationships between real events
information-processing (IP) approach: a major perspective in cognitive psychology where the computer is thought to be a useful metaphor for understanding how humans process information
means—end analysis: an heuristic strategy that involves breaking down a problem into a series of sub-problems
mental set: a barrier to problem solving that occurs when problem-solvers continue to use the same solution they have used with previous problems, even though there may be more efficient ways of solving a particular problem
problem space: the starting state and the end state of a problem
prototype: a representative example of an object, event, abstract idea or process
reasoning: systematically drawing conclusions from statements or facts
reintegration stage: a stage in adult thinking during old age where individuals use their accumulated intellectual skills to assess life and to give meaning to their pasts
representation: when something stands in for or refers to the thing a person is thinking about
responsibility stage: a stage in adult thinking where individuals use their own solutions, not only for personal and career decisions, but also for problem solving and decision making that involves, for example, their families and the broader community
rotation heuristic bias: when figures that are slightly tilted are ’seen’ as more vertical or more horizontal than they really are
schemas: the more over-arching networks of knowledge that are central in our thinking
script: one kind of schema or network of knowledge about procedures, sequences of events or processes
socio-historical approach: an approach to thinking that suggests that thinking is a social process and linked to the interaction between the individual and the setting in which the thinking occurs
state—action analysis: a description of the states, steps and strategies taken within a problem space
syllogism: a particular form of deductive reasoning that has two premises (propositions) that are followed by a conclusion
task models: over-arching bodies of knowledge that are central to thinking and comprise schedules for getting practical things done
thinking: the mental processes or capacities that enable people to solve problems, to reason, to make sense of things or to use their knowledge to understand situations, events, other people or themselves
working backwards: a heuristic device that involves working backwards from the end state of a problem to the starting state
Multiple choice questions
1.Representing objects by classifying them into categories:
a)assists in the creation of complex hierarchies
b)connects the object or idea to a body of related knowledge
c)places an object into a taxonomy.
d)all of the above are correct.
2.Sitting in a lecture and having a fairly accurate idea of the sequence of events that will happen during the lecture period would be evidence of:
b)a state—action analysis
3.Which one of the following is a characteristic of the way novices think in comparison to experts?
a)Novices use more abstract ideas.
b)Novices spend more time trying to think about a problem before starting to solve it.
c)Novices are more aware of making an error.
d)Novices group problems on the basis of the similarity of the information available rather than the underlying principles.
4.Which one of the following is associated with the socio-historical approach to thinking?
5.Seeing a new object and including it in an existing classification system is an example of:
c)concrete operational thinking
d)none of the above is correct.
6.Which approach in cognitive psychology would support the view that thinking and knowing are linked to relations between people and the activity they are engaged in?
a)the information-processing approach
b)the constructivist approach
c)the behaviourist approach
d)the socio-historical approach.
7.Which one of the following is the term used for a step-by-step process that will ensure the achievement of a goal?
8.Persistent use of an inappropriate heuristic is known as:
a)a rotation heuristic bias
b)an alignment bias
c)a mental set
9.A model that identifies the states, steps and strategies used in solving a problem would be characteristic of which one of the following approaches to thinking?
a)the constructivist approach
b)the information-processing approach
c)the behaviourist approach
d)the socio-historical approach.
10.You observe that every morning the sun rises in the east, from the sea. If you hypothesise, therefore, that the sun will rise tomorrow from the sea, this would be an example of what kind of thinking?
1.Give three reasons why representing the world in terms of concepts can be regarded as the building block for thinking, and give an example for each reason.
2.Experts and novices differ in the way they think. What does this tell us about how humans process information?
3.Briefly give an example of ’everyday thinking’ in your life. Why is it important to study such thinking in comparison to the study of formal reasoning?
4.What is the difference between an algorithm and a heuristic? Give an example of when you would use each one of these when solving a problem.
5.Using an example, explain how Piaget argues that thinking is constantly transformed by the processes of assimilation and accommodation.