Cognitive Psychology Problem Solving Notes PDF

## Cognitive Psychology Lecture Seven - Problem Solving <3 ### You should understand - Types of problems - History of problem solving research - What makes problems hard to solve? - Problem space theory - Heuristics - Problem solving strategies - Overcoming obstacles ### Types of problems - Knowl...

## Cognitive Psychology Lecture Seven - Problem Solving <3 ### You should understand - Types of problems - History of problem solving research - What makes problems hard to solve? - Problem space theory - Heuristics - Problem solving strategies - Overcoming obstacles ### Types of problems - Knowledge-lean problems require little knowledge to be solved e.g. puzzles - Knowledge-rich problems require a lot of knowledge in order to be solved e.g. problem solving behaviour of experts - In research we need to combine studies of both types of problems in order to gain understanding of problem solving behaviour - Well-defined problems - clear path to solution, with initial and goal states clear - Ill-defined - no clear path to solution, initial and goal states less precise ### Here's a typical problem - Three men want to cross the river - They find a boat, but it is very small and will only hold 200 pounds - The men are named Mr Large, Mr Medium, and Mr Small - Mr Large weighs 200 pounds, Mr Medium weighs 120 pounds, and Mr Small weighs 80 pounds - How can they all get across? ### Behaviourist psychology - Thorndike - learning by trial-and-error - Hungry cats were placed in a cage with food outside and had to learn how to open the cage - Random behaviour would lead to an accidental solution, which would have to be reinforced over a number of trials in order to be remembered - Cumulativeness of learning, lack of insight ### Wolfgang Köhler - Mentality of apes (1927) - study of problem solving in primates - Stack boxes to reach objects on the ceiling - It was argued that this demonstrated evidence of 'insight', resulting from 'productive' problem solving behaviour ### Gestalt theory of problem solving - Problem solving behaviour is both reproductive and productive - Reproductive problem solving involves the re-use of previous experience (sometimes can be bad for successful problem solving) - Productive problem solving is characterised by insight into the structure of the problem and by productive restructuring of the problem - Insight often occurs suddenly accompanied by an “ah-ha” experience - it might result from - Extended unconscious leaps in thinking - Greatly accelerated mental processing - Some kind of “short-circuiting” of normal reasoning process - Fundamentally what the Gestalt psychologists referred to as 'restructuring' ### What makes problems hard to solve? - Functional fixedness - Tendency to use objects and concepts in the problem environment only in their customary and usual way - Mental set (entrenchment) - A bias or a tendency to solve problems in one particular way, using a single specific approach, even when a different approach would be more productive ### Problem space - Newell and Simon - labyrinth (maze) metaphor - problems are solved through exploration of different paths to a solution - Objective structure of the problem can be characterised as a set of states - Initial knowledge state - Many intermediate states - Goal knowledge state - Operators are actions used to move from one state to another - There is a whole space of possible states and paths through this space (only some of them lead to the goal) ### The Tower of Hanoi - Operators (rules) - Only one disk can be moved at a time - Larger disk cannot be placed on the top of a smaller disk ### Problem space - Problem space describes the abstract structure of the problem - For any given problem, there are a number of alternative paths from an initial state to a goal state; the total set of such states, as generated by the legal operators, is called the basic problem space - People's problem solving behaviour can be viewed as the production of knowledge states by the application of mental operators, moving from an initial knowledge state to a goal knowledge state ### Heuristics - Heuristics - Intuitive strategies to reduce the number of stages one has to pass through to reach the goal - They are "rules-of-thumb" that do not guarantee a solution, but usually work and save a lot of time ### Algorithms - A formal procedure that will definitely solve the problem - would involve thinking through all of the problem space ### Means-ends analysis (example of heuristic) - Note the difference between the current and goal state - Create the sub-goal to reduce the difference - Select an operator that will solve this sub-goal - Often used in The Tower of Hanoi ### Not always successful... - Sweller and Levine (1982) - Means-ends analysis proved highly unsuccessful in solving this problem - Participants who were aware of the end point were far slower than those who were not ### Hobbits and Orcs problem - Three Hobbits and three Orcs arrive at a riverbank, and they all wish to cross to the other side. - Fortunately, there is a boat, but unfortunately, the boat can hold only two creatures at one time. - There is another problem, Orcs are vicious creatures, and whenever there are more Orcs than Hobbits on one side of the river, the Orcs will immediately attack the Hobbits and eat them up. Consequently, you should be certain that you never leave more Orcs than Hobbits on any riverbank. How should the problem be solved? It must be added that the Orcs, though vicious, can be trusted to bring the boat back! - Only two or fewer can crops at a time - Someone must return the boat back - There can't be more orcs than hobbits on the same riverbank at any time ### Hobbits and Orcs Solution - Step 0 - Right Bank bHHHOOO - Journey - Left Bank - Step 1 - Right Bank HHOO - Journey bHO → Left Bank - Step 2 - Right Bank - HHOO - Journey ← bH - Left Bank - O - Step 3 - Right Bank - HHH - Journey bOO → Left Bank - Ο - Step 4 - Right Bank - HHH - Journey ← bO - Left Bank - OO - Step 5 - Right Bank - HO - Journey bHH → Left Bank - OO - Step 6 - Right Bank - HO - Journey ← bHO - Left Bank - НО - Step 7 - Right Bank - OO - Journey bHH → Left Bank → HO - Step 8 - Right Bank - OO - Journey ← bO - Left Bank - HHH - Step 9 - Right Bank - O - Journey bOO → Left Bank - HHH - Step 10 - Right Bank - O - Journey ← bH - Left Bank HHOO - Step 11 - Right Bank - Journey bHO → Left Bank HHOO - Step 12 - Right Bank - Journey - Left Bank - HHHOOO - People struggle at Step 6 - it appears to be a backward step - evidence shows participants thinking carefully at this point ### Availability Heuristic - The term was first coined in 1973 by psychologists Tversky and Kahneman - Relies on immediate examples that come to mind when evaluating a specific topic, concept, method or decision - Occurs unconsciously and operates under the principle that “if you can think of it, it must be important" - Things that come to mind more easily are believed to be far more common and more accurate reflections of the real world - This is not always true - media coverage can help fuel a person's bias with widespread and extensive coverage of unusual events ### Problem solving strategies - Breaking down the problem and generating appropriate sub-goals leads to successful problem solving - Experience is one of the main sources of such sub-goals - in successive attempts strategies become progressively more efficient - In order to benefit from our experience, we often need to look beyond the surface aspect of the problem ### Isomorphic problems - Two problems are isomorphic when their formal structure is the same, but their contents differ - they can have the same form or the same relational structure - E.g. The Hobbits and Orcs puzzle is sometimes presented as book-lovers and book-burners puzzle - isomorphism here is very obvious - But even slight differences in presenting the problem may lead to a decrease in success - different surface characteristics tend to obscure underlying structural isomorphism ### Monster-globe problem - Initial state - MG, MG, MG - Goal state - MG, MG, MG - But monster etiquette demands that - Only one globe is transferred at a time - If a monster is holding two, only the bigger globe is transferred - A globe cannot be transferred to a monster who is holding a larger globe - The monster-globe problem is a 'move problem' with a problem space isomorphic with The Tower of Hanoi - It has a 'change version' that tends to be more difficult - The change version rules are - Only one globe can be changed at a time - If two globes are the same size only the one held by the largest monster can be changed - A globe may not be changed to the same size as the globe of a larger monster ### Rule application hypothesis - Predicts 'move' version easier than 'change' version - 'Change version' twice as hard as the 'move' version - Change rules are harder to apply (require more thinking about the 'legal' operations) than 'move' rules - This is known as the rule application hypothesis (Hayes & Simon, 1977) ### Rule learning hypothesis (Kotovsky, Haynes, & Simon, 1985) - General ease of rule learning and application is likely to be influenced by - Consistency with real-life knowledge - Memory load inherent in the problem - Ease of representing rules with mental imagery - Kotovsky et al. (1985) found that it took participants longer to simply learn change rules compared to move rules ### Overcoming problem solving obstacles - Working backwards - Finding an analogy - Restructuring - Creative thinking ### Working backwards - Water lilies double in area every 24 hours, on the first day of summer there is one lily on the lake, in 60 days the lake is covered - on what day is the lake half covered? - Starting with a goal state and seeking the path back - Effective when one doesn't know how to reach a goal, or doesn't understand a problem structure - More used by novices than experts ### Using analogies - Relies on using similarities with problems solved in the past - Detecting similarities is not always easy - according to Chen (2002) - Superficial similarity - solution irrelevant, details are common in two problems - Structural similarity - causal relationships among main components are shared by two problems - Procedural similarity - actions for turning the solution principle into concrete operations is common for two problems ### Finding an analogy - A patient has a stomach tumour and the only way to treat it is with rays of deadly intensity - What can the doctor do to save his patient? - Half of the participants are told a story about a general trying to capture a fortress - Initially, 90% of participants fail to solve this problem, but after hearing the story about the general 80% successfully solve the problem - The use of analogies relies on focusing on the underlying structure of the problem, rather than superficial features ### Restructuring - Looking for alternative ways to conceptualise the problem - Breaking the mental set - "Thinking outside the box" - Insight ### Creative thinking - The use of analogy is common here - George de Mestral in 1984 examined why it is that burrs stick to clothes so readily - What he found was then used, creatively, to lead to his invention of Velcro ### Good things about research on puzzles - Gives us a normative theory that deals with "ideal” behaviour and can help us evaluate "normal" behaviour - As puzzles are well-defined problems behaviour can be formalised and implemented in a computational model (application in AI) - Advances our understanding of basic problem solving processes (representations, learning, etc) - Allows integration with models of other cognitive processes (e.g. memory) ### Limitations of research on puzzles - Ecological (or external) validity - Puzzles are unfamiliar problems about which we have little knowledge - Knowledge required for the solution is present in the puzzle - Requirements in puzzles are relatively unambiguous - Puzzles are well-defined problems with operators, initial and goal states well specified - In life, we often deal with ill-defined problems that are under-specified and require domain-specific knowledge ### Summary - Different types of problems - We use various heuristics to solve problems, with mixed success - Our thinking can be 'blocked' by prior experience - Restructuring can be helpful here - Problem solving research tells us something, but can also be considered limited