Cognitive Psychology - Stefan Fokuhl, Student Publications, Research, Projects, Investigation and Academic Work presented by Atlantic International University students, faculty and other contributors. Bachelor, master, doctoral degree programs by distance

Student Publications

Author: Stefan Fokuhl
Title: Cognitive Psychology
Area: Social and Human Science
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Program: Psychology
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	Abstract Cognitive psychology became more and more important during the last decades. It is involved also in other branches of psychology and has changed them. But also other parts of social science are being influenced. Thus, new knowledge about learning influences pedagogy. But even new sights about attention are important for completely other realms, such as marketing. This shows how important cognitive psychology is. The purpose of this thesis is to introduce some parts of cognitive psychology: topics such as attention, consciousness, memory, learning, thought and language are illustrated. There are also shown some methods that are used in mental processes: algorithm and heuristics. The properties, advantages and disadvantages of them are explained. A chapter about intelligence rounds this thesis off. 1 Introduction The term 'cognitive' or its noun 'cognition' is borrowed from the Latin expression 'cognoscere' which means 'to know'. Bought into psychology it is used for the branch cognitive psychology. It means here not just everything that deals with knowledge but with concepts like mind, reasoning, perception, intelligence, learning and like memory, attention, action, problem solving and mental imagery. Cognition is an abstract object that is not be able to investigate directly but only by observation others. There are a lot of similarities between how we process information and how modern technologies process information. In a very theoretical way it is even equal. Moreover, a computer is much faster, more reliable in processing given information. That is the reason why more and more computer replace erroneous human worker in our factories. Both - computer and human brain - uses either algorithm or heuristics to process high level information. These two method can be seen in several sections, such as problem solving, reasoning, comprehension of languages. They appear there independent on the section and accompany them like a leitmotif. They are introduced in the according chapters here. But human beings are not only able to process new or already existing information but they are able to create new ideas and make personal decisions. Insofar, cognitive processes are much more richer than 'just processing machines'. A good example for such a information processing machine is a roboter that can walk, receive input from the environment and process it but is never be able to have own desires or ideas. Here start the differences between a merely machine and a living creature. Such desires or ideas are build in the brain as cognitive processes. We combine stored information to new structures and create things as imagine first. No computer or roboter can do that. But since we construct computer and roboter we are able to evaluate how much cognitive effort our brain is able to perform. The goal of this thesis is to show how the human brain is able to accomplish the tremendous and difficult assignment of information processing in even different and disjunct partitions. How is our brain prepared do achieve them conveniently? 2 Definition This thesis consists of six parts: Consciousness/Attention, Memory, Learning, Thought, Language and Intelligence. Each component is here presented shortly now: Consciousness/Attention In order to interact to our environment, first, we must be able to receive information. That is the task of our senses. But the received information must be processed, that is, we must be aware of what is going on around us. This is the state is consciousness. If we cannot process it then we cannot notice our environment and act, react or even interact with it. Thus, consciousness it the base or precondition of any mental deliberately processing. However, there is too much input and we need to filter out useless and unimportant information. This is done by attention. Therefore, consciousness and attention are very important step for any cognitive process regarding incoming information from outside. They belong to cognitive psychology as the first steps of mental input information processing. Both terms, consciousness and attention, are introduced here. Memory After receiving such a huge amount of information be must encode, store and - retrieve - it in order to reuse it in a reasonable way. According to the theory of Richard Atkinson and Richard Shiffrin (1968) there are three different stores which are introduced in this chapter. Each part of the memory encodes, stores and retrieves information, but in different ways, duration and capacity. When the importance is high enough then it is transferred to the next part until finally it is stored in the last one. It is also mentioned how we can improve storing information. Memory is a part of cognitive psychology because we can only do mental tasks on information the is not volatile and - therefore - not existent. It were not possible to compare any information if it were not stored at any place. Learning In this chapter the two types of conditioning according to Pawlow, Thorndike and Skinner are introduced: Classical and Operant Conditioning. At the first sight they seem nothing to do with cognitive psychology but they are also based on mental processes. They require cognitive capability as well. While conditioning some utilities can be employed, such as reinforcement or punishment. There is also another type of learning that is based on observation of others and imitation - social learning. These kind of learnings are not based on behaviorism but on cognitive processes. Thought Our daily thinking is categorized by psychologists to problem solving, reasoning, and decision making. In this context, the first time the two important methods appear: algorithm and heuristics. But before, the question is answered how we encode our thinking: in language, imagery or even acoustic. Furthermore, it is shown how we categorize objects in a reasonable hierarchy in order to retrieve it faster at later access. Problem solving, reasoning, and decision making are obviously mental processes that belong to cognitive psychology. Language One of the greatest mastered tasks in the early childhood it the acquisition of the mother language. There is no grammar book, no vocabulary list but just the listening to people around the child. Thus, a child learns only from thinking about the just listened phrases and imitation. But it is also discussed what a language is, actually. It consists of several levels that are processed separately. In order to predict the continuation of a still listened sentences we apply heuristics as well. Another question is how far the own language influences the way of thinking. Does the own language form the thoughts? Acquiring an language and comprehend a sentence is a pure mental process. Language is an important part of cognitive psychology. Intelligence The last chapter in this thesis treated the ability or capability of any mental process that is a human being to perform. The definition of intelligence is somehow difficult if not impossible. Several approaches are done. Thus, some psychologists think that there is a multiple system of intelligences, others divide intelligence in three parts. Intelligence even seems to depend on the external environment: one culture put the emphasis on matters that are completely unimportant in other cultures. Some methods of measuring intelligence are explained. As result of such tests the IQ and normal distribution are introduced. 3 Consciousness / Attention 3.1 Consciousness While we are awake and while we sleep a huge amount of information arrives us. If we processed all those informations we would be overloaded and too busy to do something else. Consciousness allows us to filter the most important information and to drop silently the useless signals. We can decide what is important and can concentrate on what we think is essential for us. And we can combine the new information with the already memorized information in our brain to a useful structure. Thus, we can interpret, analyze current given data, and then merge them together with our experience to adequate activities (Marcel, 1983). First, we can monitor the environment and, second, we can control the resulting functions (Kihlstrom, 1984). The consciousness let us directly control our life, it even protects our life: If a danger approaches it let us know the danger and we can react in the right manner by using the current information combined with our experience. It let us be aware of positive and negative events. But the consciousness does not work like an input machine where all information is processed in the same way. There are personal and individual differences in how we process the same information. E.g., in the cinema all members of the audience see the same movie (= the same input), but all process it and think about it in a personal way. Thus, the conscious is not a bare instrument like a computer but it is a individual and complex instrument to let us survive in the world. 3.2 Attention As already said, the consciousness filters unimportant information and let enter important input. We are aware of only few signals. We can decide what is important for us by turning our attention toward a task, all other information is diminished but not totally. While we are concentrated the focus is on one task but all other things are excluded. 3.2.1 Attention on Several Tasks The interesting question arising here is whether we are able to concentrate on more than one task at the same time. We learned before that we focus on one task. Are we able to focus on several tasks simultaneously? It also clarifies the question how far the left information is filtered out. Several experiments are developed to investigate it. 3.2.1.1 Dichotic Presentation Colin Cherry (1953) developed an experiment to investigate how we select attention among multiple sources. A subject receives two different messages to each ear and must repeat them right after hearing them. So, he is forced to concentrate on one voice. This situation happens quite often at parties where multiple people talk at the same time and we want to follow a message. The subjects could recall the message from the focused ear but were not able to hear to the second message. But the second message was not completely ignored. At least, they noticed when the voice was replaced by a different gender or a tone. If the unattended message suddenly got identical to the first one, all subjects noticed it. This experiment checked the auditory channel, but there are tests that check the optic channel as well. 3.2.1.2 Stroop Effect One famous experiment is called stroop effect. Some words of colors are written in a table and the foreground color differs from the word. Thus, it is very difficult to say quickly the right color of the word. Red Green Yellow Blue Green Blue Red Yellow Blue Yellow Green Red The written word interferes with the foreground color. There are two stimulus and we have to decide at each word what we concentrate on. Sometimes it tilts and we say the wrong word. That is an indicator that we cannot ignore the non-attended signal completely. 3.2.1.3 Counting a Number Chain During a further experiment (Kahneman, 1970) the subjects were told to perform two tasks: First, they had to listen to a spoken chain of numbers (Example: 4-2-6-8). After a second they had to add a one to that chain and to speak them loud (5-3-7-9). Second, they had to identify a visual shown single letter and to tell the letter aloud after the added number chain. Thus, the sequence was: a) reading the single letter, b) listening to the number, c) repeating the number after one second, d) repeating the letter. The elapsed time between a) and b) was variable. Two depending variables were used: first, the average percentage of wrong repeated letters depending on the point in time of the display of the letter, second, the average percentage of errors while repeating the number chain as function of the point in time of the display of the letter. The figure 1 shows the result of the experiment. The most errors on repeating the letters were done during a thin line of time. Fig. 1: Chain of Numbers 3.2.1.4 Conclusions The tests (and some others) allow the following conclusions: 3.2.1.4.1 Attention is a Gradual Process One noticeable fact during the dichotic presentation was that the subjects recognized personal considerable or important messages on the unattended ear, though. If this were not possible a important information would never be able to get our attention (e.g. danger or a cry for help). That means that there must be an analyze of all received information, even the unattended. Of course, the attended information is more intensive processed and longer in memory (Norman 1968). 3.2.1.4.2 Input is analyzed by Experience Because of the above mentioned fact there must be a mechanism that checks the input whether there is a meaningful information even in the unattended input. This implies that they are compared with already known information from the memory. According to Neisser (1967), the new incoming input is combined with the information from the memory and then transported to the conscious. Thus, all information that reached the conscious level is already preprocessed. Or, in other words, it is impossible to get information at the conscious level that is not preprocessed already. 3.2.1.4.3 Attention is a limited Function The chain-of-numbers experiments proofs that we cannot perform more than one task or pay attention to multiple inputs at the very same time. If the elapsed time is long enough we are able to do two or more things at the same time. As long as the slice is wide enough we can distinguish easily two tasks but if the delay gets shorter we get problems to solve both tasks adequate. There is also a difference in what the two tasks are. The more similar the inputs are the more difficult they are to perform (Navon & Gopher, 1979). The famous example is to read and to dictate a text at the same time. It is almost impossible. But it can be trained a bit. After a certain time of training subjects were able to read an write a dictated text (Spelke, Hirst, & Neisser 1976) 3.2.1.4.4 Automation Yet, there is an exception how we can do even more than two tasks and inputs each. For a given task we can select the necessary input and this input seems to step forward. Thus, subjects can easily search for numbers among a heap of letters, or strokes or crosses under a crowd of check marks. The to be searched items seem to be emphasized. Exactly this emphasis is not controlled, the filtering process appears to be automated (Posner 1982; Schneider & Shiffrin, 1977). Another kind of automation happens if we do tasks that we are used to do. We do not need to concentrate on those processes any more. A vivid example is the driving of a car. While we learn to drive we are fully concentrated on the different subtasks and the corresponding inputs. Later, when we have learned it, we do not concentrate on the driving but do other things at the same time like talking or discussing to the passenger. Just if we need more attention to the driving (drive into a parking lot) we stop talking and concentrate on that. Moreover, we are able to do more trained and unattended tasks while we concentrate on a non trained and unknown task. 3.2.1.5 Decisions without Thinking Because of our ability to do things without our attention we are able to do more than one process. This is a big advantage. But there is a big disadvantage, too. We can decide or perform something without paying attention to it. While we are concentrated on a single process someone else might ask us an (for us) unimportant question and we answer or react without paying attention about what we answered. This effect is called compliance. In an experiment people in the subway were asked to give seat with a given meaningful "because". But, the people gave seat even if the because was a non sense phrase. (Langer, 1978). Later, when asked why we decided in that way we try to find a reason and find causes that did not exist in reality. We construct an excuse that never happened before (Zimbardo, 1995). Chapter summary In this chapter a short introduction about conscious is given, first. Second, the term attention is illustrated. Hereby, the question is whether we are able to pay attention to multiple input and if not, which parameter are used to decide what we pay attention to. After a lot of practice we are able to automate a task and no longer need to concentrate on it. Therefore, we are freed again for further tasks and can perform it unconsciously. And important mile stone to grow up and to be able to do more things at the same time. 4 Memory 4.1 Introduction To be able to survive we need not only a heart and other organs but we need a construct that allows us to store any kind of information. Meaningful information is always in need during our daily life. Without own storage we were not able even to go or eat. Every action that needs information were not possible to perform. Since we have computer it is easier to explain why we need such a construct called memory. The analogy between memory in general and a computer helps us to understand that a memory is necessary. No computer could work at all without memory. No person could survive without memory. In fact, the human memory is far more complex than any kind of computer. Our human memory is located in our head. In this chapter I provide an introduction about how our memory works. First of all some definitions. Memory is not only the place or storage where the information is stored, furthermore, it is the whole process or ability of encoding, storing and retrieving any kind of information. Again, this can be compared with a branch of computer technology: databases. A database stores and retrieves any kind of information. But the memory is far complexer, it realizes the encoding as well. A database needs already encoded information, but storing and retrieving are similar. Encoding is a process by which any kind of information is changed in that way that it is store able in the memory. Again, an analogon from computer technology: A picture in paper format is not storable in computer memory. First, it must be scanned in, digitalized, and changed in a certain format of bits. This last process is called encoding. Now, it is storable. Storage is the place where the information is held. Each stored information needs a storage unit. We only have a limited amount of such units. So, it could theoretically happen that the storage is full once. Here we have the same case when a hard drive is full: All storage units (here: sectors and cylinders) are used and no further information can be stored. The storage units and their limits in our memory I am going to explain later. Retrieval is the process of finding the already stored information again. This process is as important as the encoding and the storage for information that is only stored is useless. It needs to be found quickly in an effective way by using hints and indexes. 4.2 Encoding, Storage and Retrieval 4.2.1 Encoding The process of encoding is a bit complexer than computer's encoding and it compounds more subtasks. The input is analyzed first. It is compared with already stored patterns (is it a sound, picture or smell ?), thus, its not merely a 'stupid' encoding but an intelligent preprocessing. Many useless input is already filtered out. The input is categorized or classified into already known and general areas or is even recognized as important for later purposes. 4.2.2 Storage The Storage does not work like a machine. We do not store information like a computer that memorize each single word and never forgets it. Rather, the storing of information demands several processes before it is stored permanently. The more a information is connected to similar or neighbored items and the more it is practiced and repeated the more is the likelihood that we stored it permanently. Many psychologists believe that if an information is stored once it will never be lost again. The only thing that prevent us from remembering is that we cannot find it. And thus, we are at the last important process: 4.2.3 Retrieval The retrieval of information seems to be simple but it is the biggest problem among all processes. One information might be stored well in the memory but it is useless unless we find it again. The retrieval works better the more ways are built to the information. In other words the more indexes point to the information the more possibilities exists to find it quickly and reliable. One fact is unique: While we retrieve an information it is changed. Each hit of a memory unit changes the content but reinforces the retrieval. Thus, what we retrieve often is likely to retrieve the next time even better as if the way to the info is made wider. There are two way of retrieving information: recall and recognition. The recall is a completely self-made reconstruction is stored memory without any hints and the recognition is just a comparison between a given input and a stored information. Because is the given input a recognition is easier to perform than the recall. 4.3 Three Stores One view about how memory works is an approach of Richard Atkinson and Richard Shiffrin (1968). This view is widely accepted but other views are developed either. I will only describe the view of Atkinson and Shiffrin because of its acceptance. According to them the memory is divided in 3 different stores: the sensory memory, the short-term memory and the long-term memory. These three stores do not have a certain realm in the brain each, its rather a hypothetical structure.. The way of the information goes always from the sensory memory to the short-term to the long-term memory. One fact makes the whole memory process more complex: Each store or stage has their own encoding, storage and retrieval. 4.3.1 Sensory Memory The sensory memory is the first memory within the memory chain. Here, arrive all information from the senses. This memory gets in action directly after the input but before any process of recognition of pattern. Therefore, this memory is precategorial (Crowder & Morton, 1969). Each sense has its own part within the sensory memory. The visual part is called iconic memory, the auditive part is called echoic memory. The left parts are not as well investigated as the former one. The remembrance of the iconic memory lasts for nearly a half second, for the echoic memory around some seconds (Neisser, 1967). This kind of memory is needed for the recognition of the patterns. If we had not such a memory we would see or listen as long as the physical inputs lasts, there were no 'buffer', too short to process the input contiguously. 4.3.1.1 Encoding During the first encoding there is already a selection of which inputs are marked as important (not to mix up with a recognition of patterns). While a sportsman is performing the sport he/she does not notice injuries. Later, after finishing he/she get aware of those. Or, a soldier does not notice own wounds until he is off the battle field. These two examples show that there is a selection regarding the importance. How long and how much can the sensory memory store? According to the experiments of Sperling (1960) we can only store a limited time and amount of input. He presented some lines as shown below containing 3 randomly ordered consonants to subjects for the period of 50ms. F W X D N W F Q L After showing the complete table he asked to repeat one line that was chosen by an acoustic signal. He noticed that all subjects were almost always able to repeat the chosen line perfectly. He interpreted this result as evident that we can memorize within the sensory memory nine items. In further tests with four consonants and a larger delay he could ascertain the limit of the sensory memory. After a delay of one second the subject were significantly lesser able to repeat the chosen line. Later scientists enhanced the experiment by testing the acoustic ability to remember auditive input (Darwin, Turwey, & Crowder, 1972) They proved that we can store more acoustic information than we can normally report. This fact is probably necessary to process words and sentences to a semantic meaning. But why is a limit of one second useful? Or why just a second? Two considerations may give an answer. Firstly, if the time to remember were too short we could not process continuously the input. There were interruptions during our merging of the received input. Secondly, on the other side, if the time to remember were too long the old information would interfere with the new ones. We had an overlap of old and new inputs. An experiment of Averbach & Coriell (1961) gets us to see that. Two rows of eight letters each were presented briefly to subjects. A marker that indicated the location of a target letter was presented either simultaneously or at varying time intervals following the presentation of the letter array. Subjects were to report the identity of the marked target letter. The accuracy of identification of the target letter decreased with increases in the temporal interval between onset of the letter array and marker. During a certain time the subject 'sees' the marker instead of the previous letter. This phenomenon is called backward masking. During this very first time of processing there is a race of all input against the time. The most inputs loose that race and never reach the short-time nor the long-term memory: if the input is too short and directly interfered by next inputs. Thus, we need a certain time to receive and process successful useful and important information. 4.3.1.2 Conditions for a Transfer to the Short-term Memory We receive much more information than we can process. Therefore, the sensory memory filters the vast part. What are the conditions that an information is transferred to the short-term memory? First, we must pay attention to that input. Only if an input is important and worthy enough for us to pay attention to it is able to reach the next realm or level. If this is the case then we select that input and concentrate on it. This step or decision is called selective attention. We select one input out of a multiple amount of inputs and concentrate on it while we ignore the rest of inputs. This input is a candidate for further processing in the short-term memory. Second, while we perceive an input a pattern recognition takes place. If one input consists of pattern that we can recognize and process to useful information it is available for a longer time in the sensory memory and will we transferred to the short-term memory because it is regarded as important, useful, and helpful. 4.3.2 Short-term Memory The short-term memory is according to Richard Atkinson and Richard Shiffrin the second kind or realm of memory. In the order of processes of memorizing is lays between the sensory and the long- term memory. As already mentioned the flow goes from sensory via short-term to the long-term memory. Some interesting properties differs it from the other two, sensory and long-term memory (Zimbardo, 1995). � The capacity of the short-term memory is very limited. Compared to the other two memories it is negligible. � The duration is also very limited, around 20 seconds, unless it is kept conscious. � Only in this stage information is processed consciously, the other two are never conscious for us. � This part of memory is the only one that is able to assemble subsequent pieces of input to a context such as a conversation or a fluent input of visual or auditory input from a speech. We can also follow and adapt to a changing situation by the short-term memory. Only here we are aware of any flow or change. One example: We sit in a restaurant and are talking concentrated. The waiter passes by our table. After a while resounds a loud clangor. Even though we haven't seen the cause we know that is was not caused by a tree or car or whatever but by the waiter. The short-term memory accesses the just received input including information from the long-term memory to interpret the cause of it. (Baddeley & Hitch, 1974). 4.3.2.1 Encoding As already said, only selected and regarded as important information reaches the short-term memory. But the question is how it will be encoded there. Two kinds of encoding are used: articulatory-acoustic or semantic encoding. 4.3.2.1.1 Articulatory-acoustic Encoding One method of encoding is the articulatory-acoustic encoding. We rather hold the label of the item in the short-term memory if it is labeled. Even verbal patterns that are received in visual input (=reading) are stored in an acoustic form. Experiments dealing with lists of letters have proved it. Subject were presented an amount of letters like CBTPEGFSYX for a short time. Mistakes of memorizing were done with letters which sound similar (D and T), but not which are written similar (D and O) (Conrad, 1964). During the test no one read or spoke those letters. This proves that we think and memorize in acoustic or language form, not in visual pictures like the form of the letter. But there is still the question whether we use an acoustic code (= using the description of its sound) or an articulatory code (= using the way how to pronounce the word), but in both cases it has something to do with the sound of the item, hence the term 'articulatory-acoustic' is used in order to pay attention to the still existing uncertainty. Tests with deaf subjects show that we are able to use other encodings as well: visual and semantic encoding, but as healthy people much lesser. (Bellugi, Klima & Siple, 1975; Frumkin & Anisfeld, 1977). 4.3.2.1.2 Semantic Encoding Keppel & Underwood (1962) made further investigations of the paradigm of Peterson & Peterson (1959) and pointed out that the very first try was recalled even after 18 seconds error free. They observed that these results worsened down to 10% after the third or fourth trial. This phenomenon is called proactive inhibition. It refers to the fact that new information is interfered by old information and thus prevent memorizing them. Wickens et al. refined the paradigm of Peterson & Peterson (1959) again by using even different meanings of 3-letter words. They told the subject now a completely different code after the 3rd or 4th try, not a 3-letter-code but a 3-digit-number. Surprisingly the ability to memorize was again at the level of nearly 100%. Wickens et al. thought that such a dramatical improvement always takes place on the forth trial no matter what kind of information. In other words is that phenomenon more general? This is indeed the case and it shows that a change in the meaning influence the memorizing. This implies again that we use semantic encoding as well because just acoustic encoding would never take care of the meaning. The subjects do not have to be aware of the change of the meaning, therefore the change is not conscious. (Wickens, 1972; Wicken, Born, & Allen, 1963). The processing of the meaning not only the acoustic means that there must be a close connection between the short-term and the long-term memory because recognizing the meaning implies a use of the long-term memory. 4.3.2.2 Storing The process of storing into the short-term memory is like a bottleneck. Here we can store only very few information. The maximal amount of information is around 7 items. It seems to differ between 5 and 9 items. This limit is very strict. It is not possible to store one item more than usual. If we need to store a new item the first stored will be deleted. George Miller (1956) found the limit of the short-term memory and it is confirmed by many scientists. A list of coincidental numbers or letters was shown to subjects who were asked to read and repeat right away. All were able to repeat around seven numbers or letters. Some person can repeat only five, some others even nine items. 5 8 3 4 9 5 0 8 6 5 4 8 G J R X O M A Y I P E S V Fig. 2: Available Space in Short-Term Memory It is easy to confirm by ourself that there is a limit. We can only store around seven items. More is not possible, even if we work hard at it. 4.3.2.2.1 Processing in Short-term Memory The limit seems to be too low. How can we memorize longer information, though? There are two ways how we are able to store longer information: chunking and repeating. Chunking Chunking means to pool or merge several items to a larger one, that is like to merge e.g. four numbers (2 0 0 7) to a larger item (2007) or 'i n f o r m a t i o n' (=11 letters) to 'information' (=1 item). Chunking is not limited just to numbers or letters. Each pattern or information can be reorganized to few items. Those items do not necessarily have to have a meaning, but the new structure must be recognizable. Here are some examples given: 19451939191819141871 1945 1939 1918 1914 1871 GMIBMUNESCOUSAWHO GM IBM UNESCO USA WHO THISISANORMALSENTENCE THIS IS A NORMAL SENTENCE Fig. 3: Chunking The big advantage is that the short-term memory can store seven items. In this case each word is an item, not just the letters of a word. Thus, we are able to store far more real letters than only seven. It is just a matter of reorganizing. When we merge them together in a reasonable, traceable way we are able to place more information in here. This chunking can be nested, so we can even regard a whole sentence as one chunk. Hereby, the length of the content of one chunk is not important. Of course, this nesting is not infinite, there is still a genetic limit. Lehrl and Fischer (1988) argued in their theoretical framework of information psychology mental power that the capacity C of the short-term memory can be calculated by the product of the individual mental speed Ck of information processing (in bit/s) and the duration time D (in s) of information. C (bit) = Ck(bit/s) � D (s) But Chi (1976) and Simon (1972) argued that the limit also depends on the age of the subject. An adult has his limits beyond a child's limit. It might be caused by a more limited structure of its short-term memory. The real limit cannot be seized into a fixed formula. Those attempts are just approximations. The real limit probably depends on more parameters and is still unclear. The important point of how much we can store in the short-term memory is how much information we are able to reorganize them into chunks. A adequate example is how much chess pieces a novice and a chess master are able to recall after seeing them for few seconds. While a novice is able to recall around seven pieces, a chess master is able to recall around 25 pieces. He reorganize all given pieces to traceable chunks. This shows, that the ability of chunking can be trained. (Simon, 1974; Simon & Chase, 1973) This fact is applied to learn or memorize more efficient. Repeating The question was how to enlarge the very limited capacity of the short-term memory. One way is to reorganize information into items. The second way is to repeat the information. An insightful experiment shows clearly how far we are able to maintain information without repeating it. Subject were shown 3 coincidental consonants like TBX. They were told to repeat them after a signal. The time between showing and repeating them varied from 3 - 18 sec. In order to prevent a rehearsal the subjects were asked to count down aloud a 3-digit-number three-step-wise until the signal resounded. Thus, they were kept concentrated. Already after an interval of three seconds the consonants were repeated unreliable and after 18 seconds nearly no subject was able to repeat them (Peterson & Peterson, 1959). No one was able to recall them without repeating. There are two ways to perform such a repeating: maintenance rehearsal and elaborative rehearsal. Maintenance Rehearsal The easiest way to keep information in the short-term memory is just to repeat it several times. Thus, we can prevent new inputs to interfere and to kick out our wanted information. It is also a matter of concentration: what we repeat we concentrate on and block other inputs from entering the short-term memory. One big disadvantage of maintenance rehearsal is that the information do not necessarily enter the long-term memory. Elaborative Rehearsal To ensure that information enters the long term-memory elaborative rehearsal has to be done. Hereby, the input is analyzed and bound to already existent information from the long-term memory. Practically, elaborative rehearsal takes place when we process the input in such a way that we combine it other useful information. One example shows this process: A phone number (25365869) is memorizable in (at least) two ways: 1) when we build a calculation (2536+3333=5869). Here we combine the new information with an mathematical addition that is already known in the long term-memory. 2) we compare the number with the layout of the keyboard of the computer. We type 2536 and then we shift up the finger one row and type 5869. Here we combine the new input with the known layout of a keyboard. Of course, there is no limit in building such ways and every individual has his own preferences. Often elaborative rehearsal is even combined with chunking. Thus, elaboration is used to construct new chunks. Chase & Ericsson (1981) investigated this process by training a student to remember as much as possible numbers. After 2.5 years of training this student was able to recall numbers with a length of 80. His method was simple: He was a former long-distance runner and compared the numbers with the times for different runnings. Hereby, he used already known information from his long-term memory (=elaborative rehearsal) and constructed new groups of numbers (=chunking). His limitation of the short-term memory was still the same, he was still not able to recall more than seven characters. 4.3.2.3 Retrieval Once the information is stored we need to retrieve it reliable. Sternberg (1966) tested subjects by a simple experiments and used the speed of retrieval to point out how we retrieve information from the short-term memory. A short list of letters (lesser than 6 items) was presented to subjects. After few seconds one letter was shown to them and they had to decide whether it existed in the list or not and to tell it as soon as possible.. The only parameter was the length of the list and only the time was measured. Theoretically there are two algorithms of finding the information. Parallel or serial searching. Parallel searching means that all parts of the set are checked at the same time. Serial searching means that the pieces are checked one by one. But there are two different serial (sub-) algorithms again. The list could be checked completely (exhaustive scanning) or after finding the searched pieces it stops (self-terminating scanning). The latter is more intelligent because it stops right after the first letter in best case. So, the run time is O(1) in computer science notation. In the worst case all items must be checked. Then, the run time is equal to the exhaustive scanning because the algorithm must go though the entire list. Thus, the run time is O(n). It is interesting that Sternberg found out that we use the exhaustive scanning algorithm. This use is not optimal, but we can afford the wasted time since the list is never longer than 7 +/- 2 items. 4.3.3 Long-term Memory The long-term memory is that part of memory where we keep all kind of information since we were born. Again, this part is divided in three sections: encoding, storing and retrieval. 4.3.3.1 Encoding The long-term memory encodes different than the short-term memory. The reason is that the long- term memory has different tasks and needs more possibilities to retrieve the information. Long-term memory is not just a big box where information is stored but it is able to solve problems and to create new ideas and to apply old experience to sort new input. This encoding is done semantically. 4.3.3.1.1 Semantic Encoding Different to the short-term memory where information is subsequent stored, here all information is stored like in a library or in a filing cabinet, which means that all information is stored parallel and ordered according to their meaning. Often the data has more than on meaning. This fact is represented in multiple indices. Therefore, there are more than one way to retrieve the data. One evidences prove that data is stored here according to their meanings. It is very likely that sentences are not stored literally like a file on an audio tape and recalled literally but rather the meaning and content of a sentence (Bransford & Franks, 1971). Furthermore, a sentence that someone has not understood is not recallable as contributing item for further synthesis. There are some ways to organize such an index or sorting. But here we see that chunking and elaborative rehearsal are preparations for a creation of such an index: � Find an adequate headline for a topic. If we find something recapitulating for a given topic or context or if it is given we can handle this fact easier and make it more to a sortable and comprehensible unit. � Grouping. Supposing that there are several items it is easier to group them into several categories. We do that daily but it is the art to group them efficient and intelligent. If a new item has to be added we can either append it to an existing group or create a new group. Basically, an item is supposed to be processed in such a way that encoding, storing and retrieving is matched, balanced or aligned as much as possible. The more data is processed accordingly the more it is likely that it will be utilizable later (Zimbardo, 1995). 4.3.3.2 Storing The long-term memory stores not only input from outside but also thoughts and creative ideas. Thus, it stores more than the merely information from the world outside. All combinations and connections from mental production are hold here as well. To fulfill this high requirement the long- term memory is divided in several sections according to Tulving (1972): The procedureal memory, the declarative memory, whereas the declarative memory is divided again in semantic and episodic memory. 4.3.3.2.1 Procedural Memory In this part of memory there is information stored about how we make things and do tasks, either concerning cognition or movement or perception. (Anderson, 1982; Tulving, 1983) Each acquired skill is basically a sequence of subsequent actions. Those subsequent actions are stored as single unit and are gained by a lot of practice (Bandura, 1986). They require a lot of practice which means they are difficult to obtain but even more difficult to forget. Once we can swim we can swim forever even after may be 20 years or longer. We probably just need a very short time to get used to it again, but actually we still know how to do it. Once we have learned a skill we don't need to pay attention on how we do it, we can concentrate on other things, moreover paying attention on it again is even going to disturb the automated skill. 4.3.3.2.2 Declarative Memory Again, the declarative memory is divided in two parts: the semantic memory and the episodic memory. The declarative memory contains facts that we have to recall consciously. Semantic Memory The semantic memory is like a encyclopedia or a library. All abstract or theoretical information is stored in here. Here are not stored personal information or own remembrances rather facts which are valid for a general range like history or formulas of natural science. Episodic Memory This part is just the opposite of the semantic memory. In here are all personal remembrances are stored. Here is hold not just the fact but also the time and the context of an event. But often, we remember a fact (that belongs to the semantic memory) via a personal event, such as we remember a fact about history via the lesson at school when the teacher dealt with that subject. In such a case there are connections between the semantic and the episodic memory. It is very interesting that we with each recall from the episodic memory even more save in the memory. We save the remembrance on the remembrance as well. This additional saving contaminate the existing information and veil it. Therefore, the more we remember a personal event the more it becomes unreal. 4.3.3.3 Retrieval Like the short-term memory the stored information must be retrieved in order to use it for further tasks. The question is just how we retrieve them. Many scientists believe that no information is lost or forgotten but we no longer know how to retrieve them (Linton, 1975). We have two kinds of remembering from the long-term memory: free recall and recognition. 4.3.3.3.1 Free Recall A free recall from memory means a complete self-constructed report or repetition of stored information. We only got a command to reproduce it (by others or by ourself) and start recording what we know unless we don't remember any more because of the lack of indices. The problem here is that we do not have any cues from outside. Thus, if there is not path at all to the information or we cannot find it then we will never be able to recall them. As a test of an exam it refers to a own written description or article out of the memory without any cues like dictionaries or encyclopedias. 4.3.3.3.2 Recognition The main difference to a free recall is that we receive an input from outside first and then we just need to compare it with already existent knowledge. If there is no knowledge we cannot recognize it and have no result (even not a negative result), but if we know it we can answer a result. As a test of an exam it refers to a multiple choice task. The recognition seems to me easier because we "just" compare a given input to a stored item but sometimes if the inputs are very similar it is almost as difficult to remind as a free recall because it approximates to a free recall. If we slow down and stagnate in an oral exam - that is a free recall - and the examiner gives us a cues and we can continue fluently then it changes from a free recall to recognition, or in other words the cues provides us a path to the actually lost knowledge. Chapter Summary In this chapter the memory is introduced. After providing some explanations about basic expressions, each memory is presented in detail. Most in detail explained is the short-term memory for several reasons, First, it is the last step before entering the long-term memory and, second, it is the only memory that we experience consciously. It is, so to speak, the connection between the external and the internal world. Different types of encodings and the - very limited- way of storing in chunks is mentioned but also the ways of improvements to increase this limits. In long-term memory the different kind of encoding and retrieval is described. The memory theory of Atkinson-Shiffrin is only one way to explain how our memory works. The problem is that we cannot look inside the memory and see while it work how it works. Only experiments from outside can provide us an idea. But even the results have to be interpreted. Thus, some theories are made and accepted, as long as they are plausible and can explain the memory in an more easy way. Modern technological devices are very helpful to look inside a memory, but the memory or thinking itself is still concealed. Here, we ought to have a machine that works in the same way like the memory, that can decode memory's information before it is already decoded by the memory. Thereby, to make such a machine we have to know the code first. But, if we already know the code we no longer need to construct such a machine. This means, we will never be able to understand completely how our memory works. 5 Learning The type of learning treated here is not a continuation of the last chapter. It is rather a description of how we learn behavior, habituation, and our character. Thus, the meaning of learning here is not an increase of knowledge but a stable change in the behavior caused by experience from the result of a certain action. The first and pioneering experiments performed Iwan Petrowitsch Pawlow 5.1 Classical Conditioning He studied the behavior of a dog that was presenting food. He found out the following generalized phenomenon: The first step (A) is an already known and normal unconditional reaction (UCR) of a subject to a unconditional stimulus (UCS) like here a salivating dog after presenting it some food. At the same time a different stimulus that has nothing to do with the first one or the reaction is presented (B). This happened several times. In our example a bell is ringed while presenting the food. After a while just the second stimulus is presented and the subject shows the same reaction like to the first stimulus (C). Thus, the unconditional reaction changed to a conditional reaction (CR). The learned conditional stimulus (CS) is an actually neutral stimulus. The dog in Pawlow's experiment salivated after the ringing bell alone. A UCS UCR UCS B UCR UCS C CS CR Fig. 4: Classical Conditioning The conditional reaction is not learned right after the first occurrence of both stimuli. The more they are presented together the more is the likelihood that the conditioning is more stable. This process is called acquisition. But the conditional reaction might not necessarily last forever. After a while the subject 'learns' again that the reaction is in vain and is going to loose it. This phase is called extinction. Another parameter of a successful conditioning is the time between the two stimuli. The optimal time interval is zero. But a tolerance is permitted depending on the kind of stimuli. Some stimuli might have a time delay of up to a minute, others must take place within a second. If a subject is conditioned and suddenly a completely other conditional stimulus is presented the subject shows no reaction. The more the conditional stimulus resembles the original conditional stimulus the more likely the subject reacts. He generalizes the stimulus. Or, the other direction, the lesser the similarity the more the subject discriminates and the lower is the likelihood of a conditional reaction. Thus, generalization and discrimination are the two counterparts of how a subject reacts to a third stimulus. 5.2 Operant Conditioning Nearly at the same time like Pawlow, Thorndike (1898) experimented with cats. But he did not pay attention to reaction to given stimuli but to responses to own actions within a given environment. He presented not a second stimuli to a first one but just the first one beyond an obstacle and observed what the cats would have done. After some trial and errors the cats have overcome it. Skinner (1938) refined the experiments and was able to teach subject almost any kind of behavior. The learning is possible by using rewards after any wanted action (=operant). Operant conditioning means the change of the probability of a behavior to a wanted direction. 5.2.1 Feedbacks Such a reward or - more general - feedback can be a reinforcement or even a punishment and motivates the individual to repeat or to avoid the behavior. 5.2.1.1 Reinforcement We learn what be will rewarded. Such a reward reinforces the subject to do the action again, or increases the likelihood that that action will be repeated. Such a reinforcement does not necessarily be a feedback from outside. Already, the knowledge that the behavior is right is a reinforcement. There are positive and negative reinforcers. 5.2.1.1.1 Positive Reinforcement A positive reinforcer provides a pleasant atmosphere or gives a comfortable feeling. Therefore, it increases the motivation to do the very same again or even to improve the action in order to receive a more positive feedback. Such a positive reinforcer from outside might be a smile, a praise or a compliment. The action and positive reinforcer together as a pair are called positive reinforcement. 5.2.1.1.2 Negative Reinforcement The result of negative reinforcement is the same , namely the motivation to repeat the action, but it is based on the withdrawal of a displeasing stimulus or situation. For example, if a student does the homework concentrated then it is done more quickly. Here, the action is the performing of the assignments, and the unpleasant situation is the feeling not be able to be free, the reinforcer is the knowledge that it can be done more quickly. When he is ready the situation changes to a more pleasant one. 5.2.1.2 Punishment The opposite site of feedback is punishment. This is necessary when the individual does not act in the wanted way. Thus, this action is to be diminished. The negative feedback helps that the action disappears. Hereby, the likelihood of a repeat decreases because the individual excepts again the negative consequence. As well, there are two different kind of punishment. 5.2.1.2.1 Positive Punishment A positive punisher appears when a unpleasant stimulus is given or a unhappy situation takes place. Such a positive punisher might be a scolding, a hit, a laugher or extra work after an unsolicited action. 5.2.1.2.2 Negative Punishment Similar to negative reinforcement negative means a withdrawal of a stimulus. Here, it is the withdrawal of a pleasant stimulus such as the opportunity to watch TV or playing games with friends. The punishment leads to avoid a situation. It is also called aversive conditioning because the individual tries to escape of something by an aversive stimulus. 5.2.2 Differences to Operational Conditioning There are some basic differences between classical and operant conditioning. The individual is in classical conditioning rather passive. He reacts on a stimulus and has no own proactive initiative. In operant conditioning he acts and try to find a solution to a given environment. He even interact with it in order to find a solution. In classical conditioning there is always a pair of stimuli, one unconditional and one conditional, whereas in operant conditioning there is no stimulus at all. Of course, there is the environment providing stimuli but not an active emphasized stimulus. In operant conditioning the motivation is caused by reinforcement or punishment. Classical conditioning does not know such feedback. Operant conditioning is far more important for our daily life: We use it for others (like our children) and others apply it to us (like colleagues or the boss) but often not in an optimal way. 5.3 Cognitive Influences In conditional and operant conditioning come behavior, stimuli, interaction and consequences to the fore. Each kind of learning is eventually a act of cognition because the just observed stimuli or input must be remembered and interpreted but here the behavior is in the foreground (Bandura, 1976; Miller & Dollard, 1941). But there are some kind of learning that are based on cognitive activities. Some of them are introduced here. 5.3.1 Social Learning This kind of learning is very common, too. Social learning or observational learning starts with the simple observation what others do. First, the individual is not performing directly but only watching passive. Compared to the conditioning types no learning is to expect. Despite, learning is in effect. Bandura (1965, 1969, 1986) tested in numerous experiments that already children learn by observing adult's behavior. They just imitate the featured actions. During the most famous experiment, Bandura divided children in three groups and presented all of them a video clip. All children saw a man who punched or kicked a bobo doll. Later in the film shown to the first group, the man was rewarded, in the second film he was punished, and in the third film he experienced no consequences. Right after the film, the subjects were asked to play with such a doll. The children of the first and third group copied that man. Children of the second group played the most less aggressive. Four depending processes are necessary to learn by observing. � First of all, the individual must pay attention to the happening. Again, such a paying depends on the personal structure of the individual: is it attractive enough? does it have a adequate level to concern about? what is the own state? � Second, the model behavior must be stored in the memory. Sometimes, this period of time might be very long, until a adequate opportunity to perform is given. � Third, the motor action must be reproduced out of the memory. No own practice is possible because it is the first time he acts in that way � Fourthly, the subject must be motivated enough to perform and to imitate the former seen action. Now, the question arises what and how can increase the motivation. But this question is not discussed here. 5.3.2 The Cognitive Map Some situation are not explainable by merely stimuli and behavior structures. Tolman & Honzik (1930) performed some experiments with rats that were to find a way in a maze to their food. Several ways were possible. These ways had different lengths. After closing the easiest and shortest way by imposing the lock B, the rats went without any doubt and error the longest way (way 3). They must have learned a cognitive map of the maze before. There was no certain stimulus that lead them to the food, all ways looked the same. Thus, they were not able to distinguish the right way from the others by a unique stimulus. Fig. 5: Cognitive Map But not only rats - also human beings - use cognitive processes to solve problems. Suppose, there is a problem to solve that we cannot touch or try and error. We can only analyze the problem in our brain and synthesize a solution virtually. This is a clear cognitive process. This matter is introduced in the next chapter. Even the conditioning is a cognitive process. The subject must � process information in an active way � scans the environment for significant events � memorizes many properties in the memory � organizes and integrates the new information from outside is in a beneficial way � decides what is to do based on the new information combined with old information from the long-term memory This changes the point of view from a behavioral learning to a cognitive learning. Behavioral learning emphasizes the physical stimulus and the environment, cognitive learning emphasizes the internal process necessary to perform such a task. (Spada, Ernst, & Ketterer, 1992). Such a change in researcher's thinking took place in the last 30 years and changed the aspects of learning, thinking and memorizing. Also, neurological processes became more important (Garcia & Garcia y Robertson, 1985; McGaugh, Weinberg, Lynch & Granger, 1985; Thompson, 1986). Chapter Summary This section about learning start with the two kind of conditioning. At the first sight they are behavioral but they demand a tremendous cognitive effort to be performed. Actually, from the internal point of view they are cognitive tasks. In operant conditioning the two feedbacks - reinforcement and punishment - are explained more deeply. The third kind of learning - social learning - that is a merely cognitive process as well is introduced next. The memorizing of a cognitive map round this chapter off. 6 Thought In our daily life we think nearly every second. Psychologists define a thought or thinking in a different, more precise way. Thinking is a conscious and controlled concern in order to reach a certain goal. Thus, thinking can we applied by solving problems, finding a decision or a jugdement, and reasoning. These three parts are discussed in this chapter. But first, the structures in which we think are illustrated. Which methods and concepts do we use to progress such tasks? 6.1 Cognitive Structures During a day we receive numerous signals and inputs from outside. The brain were unable to process such a tremendous amount of information if there were not special filters that allow to pass only useful information. But not only the first filter are necessary, also we need to catalogize and organizes the input into classes. 6.1.1 Conceptual Thinking Each individual, not only human beings, is different. Each tree, each animal differs from the next. Again, each situation differs to the former one. If we considered each case as a single and unique case it were each time a brand new situation and we could newer use already learned solutions. That is not only impossible, it were even dangerous. We could not escape a danger because also each dangerous situation is different. Therefore, we need a technique to organize and classify each new input and to add it in a reasonable way to the already existing information. Already little babies are able to categorize objects of the environment. We have (an already built) class of, for example, 'games'. Each game is different but we sorted them to a class because there is a certain similarity. We have created a set of concepts which we have ordered all objects, ideas or situations in. But we build not only classes, we build a hierarchy as well. The 'game' we can organize in a tree with a root, vertices and leafs. The figure 6 shows such a hierarchical tree using the example game. Games Videogames Olympic Games Parlor Games Card Games Simulator Winter Games Summer Games Flightsim. Trainsim. Biathlon Run Shotput Monopoly Taboo Poker Skat Fig. 6: A Hierarchy of the Term 'game' If we receive an input that does not fit in any concept we have two ways to organize it: First, we interpret the new item by sort it into already existing classes. This process is called assimilation. Second, we enhance a very similar class or even create a new structure until the new item fits well and accordingly. This way is called accommodation. We always apply both ways to integrate new information into old knowledge in order to use both in the future. The right balance between assimilation and accommodation is important. But also for retrieving such a classification is important. It helps us to find an element much fast as if it were unorganized. But not all elements in such a set are regarded equal. We find a typical member of a class faster than an untypical (Kintsch, 1981; Rosch, Mervis, Gray, Johnson & Boyes- Braem, 1976). Moreover, we find a element faster if we search in the right or next higher level of the category. We are able to answer faster when we are asked to find the 'Poker' under 'card games' then under 'games' (Rosch, 1987) 6.1.2 Non-language Thinking While we are thinking we use our language to express what we want to say in order to reach our goal. A thought is composed of the language we use daily. But we can/must think without language sometimes (Steinberg, 2000), E.g. when we have to imagine an observed object or a spatial item. Those imageries cannot be represented by any verbal language. 6.1.2.1 Visual Imagery Subjects were coincidentally presented a letter in different spatial order. They were to be identified as real image or mirror image as soon as possible. The more the letters are turned around the more time took it to decide whether it is a mirror image or not. This time delay depends on the rotation and is a proof the we turn mentally the image back upright in order to decide it. Hence, this is a proof that we also think imaginary (Shepard & Cooper, 1982). Fig. 7: Turned Letter Fig. 8: Scan of an Image During another experiment subjects were shown a boat for a short moment. Shortly after seeing them, they were asked to emphasize on the motor of the boat. When the subject pay attention to the motor they were asked to decide whether there is a wind shield. As next question, there were asked whether there is a anchor. The anchor was at the other end of the boat, it took them longer to decide whether there is an anchor than to decide whether there is a wind shield. The reaction time was slightly longer. Obviously, they scanned the boat in their mind from the end to the top (Kosslyn, 1980). This is dealt as another evidence for a mental image. There are still visual problems that we cannot resolve picturally. Suppose to have a sheet of paper, how thick is it after being folded once? how think is it after two foldings? And now, how thick is it when it is folded 50 times? Our image of that paper let us underestimate the total result. We use not only language and visual imageries but also smell, sounds, and sense according to the input. A melody could never be represented in language or an image. Those different kinds of representation enriches our cognitive actions and often, we understand faster and more clear with the aid of diagrams or drawings. But mainly we express our thoughts - especially abstract ideas - in language. 6.1.2.2 Cognitive Maps As already mentioned in section 5.3.2 we represent images and geographic items in cognitive maps. If we have to answer questions like 'What is the best route from our home to our work?', 'What way can we go if this optimal way is blocked?', 'Which city is more in the north: New York or Shanghai?', or 'Which countries flows the Mekong through?' then we must access our cognitive maps that represent our spatial environment. Orientation, path finding - or more general geographic problems - and even walking in darkness depend on the existence of such maps in your memory. (Hart & Moore, 1973; Thorndyke & Hayes-Roth, 1987), Yet, a computer algorithm would solve such geometric problem in a different - for us unusual - way. If a computer looks for a closest pair it might use a geometric algorithm that ascertain it deterministically by using a sweep line (Hinrichs, Nievergelt, & Schorn, 1988). For us, such a mechanical way were too unhandy (see below: Algorithm and Heuristics in 6.2.2) 6.2 Problem Solving In our daily life we meet problems that need to be solved. Here, the problems are discussed are problems we can solve by goal-oriented and analytically thinking. Basically, a problem is a discrepancy between that what we know and that what we ought to know, or a situation that we are in and a situation that we suppose to be in. Problem solving is , therefore, to find a way to overcome those discrepancies. We are at the beginning at a starting point and have to go to the goal by allowed operations. In information technology a problem consists of a initial point, the allowed operations and the target state. These three components compose the problem space (Newell & Simon, 1972): Suppose PS is the space of problem solving, begin is the initial state, operation the allowed and performed operation and end is the target state. PS(begin operation end): begin end Operation The operation might be divided in multiple sub-operations and sub-targets: PS(begin operation end): begin sub-target sub-target end Sub-Operation Sub-Operation Sub-Operation 6.2.1 Well- / Ill- structured Problems While we face problems we come across well-structured and ill-structured problems (Simon, 1973). A well-structures problem has a clear ans precise defined initial state, clear defined operations and a distinct target state. Sometimes, there are more than one way to change the state (Anderson, 1988). In a ill-structured problem either one of them is not clear defined or even ambiguous, or two, or all of them, so that the problem is based on uncertainties. Therefore, the solution of the problem is very likely wrong or unsure. If the way is long and difficult to solve the problem then we might use sub-operations to approach a sub-ordinate target - or in other words - we achieve our goal step by step. Two important tools are very helpful to understand and to find a way out: analysis and synthesis. Analysis mean that we break down the complexity to smaller parts and make it more easy to handle. Synthesis is the complementary process: We join the pieces together to a complex one. Naturally, the analysis takes place in the very beginning and the synthesis at the very end. An example for a well-structured problem is any mathematical problem like: "What is 567,643 divided by 456?" The initial point is clear defined (the numbers are distinct), the target state is clear (the result) and the operations as well (dividing). An example for a ill-structured problem is (Gardner, 1978; Weisberg, 1995): "The Schneeville Wolverines won the championship basketball game 72:49, yet not one man on the team scored match as a single point. How is that possible?" 6.2.2 Algorithm and Heuristics So far the problem space is illustrated. We know now what a problem is, but we still don't know how to solve it. How do we find the way to the goal? There are two different strategies we can apply to the problem: algorithm or heuristic. 6.2.2.1 Algorithm An algorithm is a methodical procedure composed of single subsequent steps that leads guaranteed to a solution (If the problem has a solution). It has the following properties (Six, 1999): � The complete procedure must be described in an finite text. The elementary components are called steps. � Each step must be performable. � The procedure must end after finite steps. � Each step is strong prescribed at any time. No coincidence is allowed (deterministic). Here is given an example: Suppose, we must calculate the factorial of a number (n!). One algorithm could look like this: 1) Set a counter to 0 and a result variable to 1 2) Increase the counter by 1 3) Multiply the counter by the result variable and save the result in the result variable. 4) Go back to step 2) until the counter is equal or bigger than n 5) The result is stored in the result variable An algorithm looks inflexible and stiff but find the solution always. However, some algorithm are very time-consuming. One example is the famous traveling-salesman-problem. A salesman wants to visit all locations once as a round-trip and wants to return to the start position. He wants to find out what is the best route. Thus, this problem is a geographic problem. The algorithm has to check all possible routes and decide at the end which is the ideal. This is so time consuming that it takes the permutation of n locations (O(n!)). This problem is NP-hard and even NP-complete (Gary & Johnson, 1979). It would take years to find a route if n is bigger. 6.2.2.2 Heuristics Practically, such a algorithm is not usable. Therefore, an informal and shorter way is searched for. We use heuristics to make the way of problem solving shorter. Heuristics are not exactly defined ways like algorithms. They are rules of thumb. Even coincidence is allowed. Thus, they are shorter and not deterministic, but a big disadvantage is that they not necessarily find a solution. And if they find a solution it might not be exactly, it's just a approximation. We have to accept such a unsure solution if the costs for an algorithm are too high. We human beings use often heuristics because it is not our nature to think so strict and deterministic. 6.2.2.2.1 Problems with Heuristics A heuristic is a subjective rule of thumb that might lead to a solution. However, there are some traps that prevent us to find a solution. The heuristic itself is not wrong but we apply the heuristic in a wrong way. Functional Fixedness Often we trust our experience and memory and look for similar ways to solve a problem that helped in the past. But such an analogy might even prevent us from finding the right way because the set of possible ways is limited to the already-known ways - the range is shorter. We see an object only in that way how we use it daily but not necessarily in other - unusual - ways. A matchbox is not only a container for matches. We could use it even as pedestal (Duncker, 1945) or a hammer is not only a tool to drive a nail into the wall but could also be used as end of a pendulum (Maier, 1930; 1931; Birch & Rabinowitz, 1951). Cognitive Set Such a fixation does not refer to the item itself but also to the use of operations or combinations of operations. Based on our experience we prefer certain operations more than unusual operations. Luchins and Luchins (1959) proved that in the nice water-pitcher problem. We tend to solve each problem in the same way and this way is not always the best, sometimes even unsolvable in the former ways. People who apply for a job are often tested during an interview whether they are fixed thinking or not. In one example the candidate was lead into an empty room. Just a burning lamb was inside but no switch. He was asked to turn the light off. One solution were to rotate the bulb, but it was hot. One candidate took his shoe and throw it toward the bulb in order to destroy it. This candidate got the job. He was the only one who used his shoes in a different way but not as the usual function. Perceptual Set Before we start to solve a problem, we observe and view the problem from a point of view in order to understand what the problem is. Often, he doesn't change this point of view later but another point of view might be better. We perceive or encode the problem just from one side - may be another or even the opponent side might be lead to a quicker and more smarter solution. This obstacle is called perceptual set. Moreover, these sets or hindrances influence each other and the definitions are not so strict. The perceptual set could also be defined as functional fixedness, namely, when we 'perceive' an object only as an object having one function. Or it could be a cognitive set because we see only the well- used function. The borders are flowing, but they are distinct to emphasize the