cognitive ch.13

1. Problem Solving

: a process in which a person begins with a goal and seeks some steps that will lead toward the goal. - is the process of cognition that occurs when a goal must be reached by thinking and behaving in certain ways. We use problem solving in order to reach a goal when the solution is not immediately obvious to us.

Factors that Influence Problem Solving

Factors that Influence Problem Solving Both bottom-up processing and top-down processing help us to understand certain factors that affect our problem solving ability. Those with expertise in an area demonstrate exceptional performance on tasks in that area. Top-down processing skills allow them to perform well on problem solving tasks in their area. Experts differ from novices in six main ways: A) *Knowledge Base*- Novices lack important information about the area. Experts have more extensive schemas in their area of expertise which are essential in helping us to understand the problem properly. B)* Memory* - Experts can use retrieval cues from their WM to access a large body of knowledge in their LTM. Their memory is also better than novices when the representation of the problem fits into a certain schema. C) *Representation* - Novices and experts have a different representation of the problem in their minds. Novices focus on surface features whereas experts have the knowledge and ability to focus on structural features (i.e., what something looks like compared to what something does). D) *Problem-Solving Strategies* - Experts are more likely to use the means-ends heuristic when solving a problem. In addition when they use the analogy approach, experts are better at solving the problem because they are able to focus on structural features more accurately than novices. E) *Speed and Accuracy *- Experts solve problems quicker than novices do and are very accurate Operations become automatic Certain problems trigger certain responses Experts use parallel processing and novices use serial processing F) *Metacognitive Skills* - Experts are better at monitoring their problem solving than novices. They are more aware of making errors and also more skilled at allocating their time for solving problems.

Mental set or Einstellung

Imagine you have three jars, A, B, and C. For each of the seven problems below, the capacity of the three jars is listed. Your job is to obtain an exact measurement of water, however, no jar's capacity is the exact amount of water that you need. In order to get the goal amount (far right column) you must use jars A,B & C in order to obtain the amount of liquid specified. You may obtain the goal amount by adding or subtracting the quantities listed in A, B and C. Try working out these problems as to how you would achieve the goal state. Were you able to solve the problems effectively? Did you notice a pattern in your problem solving? Problem solvers may exhibit mental sets when solving problems. This happens when we continuously solve a problem the same way even though there are easier ways of solving a problem. Mental set prevents us from thinking carefully about a problem and solving it effectively. Experts use top-down processing effectively because they can use previous knowledge to effectively solve problems. With mental sets we tend to overuse top-down processing so that we fail to use more effective solutions.

Nature of the Stereotype Threat

The problem with the stereotype threat is that if you belong to a group that is labeled with a negative stereotype and you associate yourself with that group your performance on certain tasks may decrease (i.e., A girl taking the math section of her GRE's). This effect is demonstrated through experiments where individuals are primed to associate themselves with a certain group. In experimental groups participants performance will generally decrease. In control groups where no priming occurs there is usually no decrease in performance. Shih et al., (1999) conducted research with Asian females. They conducted a study examining mathematical abilities. Society has stereotypes that Asian-Americans are good at math and women typically are not good in math. Shih divided participants into three main groups: A) Ethnicity-emphasis condition: Participants were asked to indicate their ethnicity and answer several questions about their ethnicity and then complete a math test. B) Gender-emphasis condition: Participants were asked to indicate gender and answer several questions regarding their gender identity and then complete a math test. C) Control group condition: Participants did not answer any questions before taking the math test. Shih found that the ethnicity emphasis condition Answered 54% of the questions correctly, the control condition answered 49% of the questions correctly and the gender emphasis condition answered 43% of the questions correctly. Participants who were primed to think about ethnicity performed relatively well, compared to p's that were primed to think about their gender. Shih's (1999) study has also been replicated with young Asian-American females attending elementary school - as young as school children in kindergarten. European American women have also shown a decrease in math problem solving skills when primed to think about gender - in that study women who were told that they were taking a math test designed to highlight gender differences performed worse than women who were told nothing. So why does this happen? Two main factors attempt to explain this effect. 1) Thinking about the stereotype increases arousal. This has been shown through elevated blood pressure in participants who are in the experimental condition. We know from previous research that when we have high levels of arousal our performance decreases on tasks. High arousal interferes with our WM. 2)Females taking a difficult math test may be working to suppress the thought that females are inferior to males on mathematical problem solving ability. What have we learned about thought suppression? When we are suppressing thoughts our WM capacity is reduced. The more we try not to think about something the more we tend to think about it.

i. Dunkers candle problem

Think about this problem by Dunker (1945). You are given three objects: 1) A candle, 2) a box of matches and 3) a box of thumbtacks. You are asked to attach the candle to the wall so that it burns properly using no other objects than what you are given. How do you do this? When participants tried to solve Dunker's candle problem they attempted to attach the candle to the wall using tacks. The candle failed to burn properly. Here participants have displayed functional fixedness. The correct solution would be to tack the match box to the wall creating a candle holder thus placing the candle holder on the matchbox. Sometimes we have to think outside of the box or the realm of what we know in order to come up with a solution. These mistakes in cognitive processing can be traced to rational strategies. We are too rigid and fail to notice sensible solutions

Ill-defined problem

a problem for which the goal state is specified only in general terms and the operations available for reaching the goal state are not obvious at the start.

Three main Features

a. Initial state : this is the situation at the beginning of the problem. b. Goal state : this state is reached when we solve the problem. c. The obstacles: these are the restrictions that we must overcome between the initial state and the goal state

Divergent thinking

ability to move one's thoughts in novel, unanticipated direction. Here there is no right answer, success in divergent thinking is reflected in an ability to come up with a large number of new ideas, ideas that can then be evaluated to see if they're of any value. ( *brainstorming*)

- Convergent thinking

ability to spot ways in which seemingly distinct ideas might be interconnected. This ability is sometimes measured through the remote associates test. Given trio if words, and you need to find one more word that fits with each of the three. For example trio cross, rain, tie the correct answer is bow ( crossbow, rainbow, bowtie)

a. Well-defined problem

add some structure to the problem by including

Insight problems

are when the problem initially seems impossible to solve but then an alternative approach pops into your mind that seems both plausible and correct. For example, you are driving a jeep in the Sahara Dessert. You come across a dead man lying face down in the desert. You see no tracks nearby and there have been no winds to erase the tracks. You look in the man's backpack - What do you find? The Answer: A parachute. There is really no logical steps that you can take to get to the answer - rather it will just pop into your head sooner or later. Answers to insight problems are described as 'aha' moments - when the answer just pops into your head.

Non-insight problems

are when we solve a problem gradually using our memory, reasoning skills and a routine set of steps. It is "non-insight" because we achieve our answer through logical steps. Those who experience insight when solving a problem usually are using top-down processing. If they are considering the wrong set of alternatives then the misleading information needs to be disregarded before the problem can be solved. In addition, research has shown that it is difficult to solve insight problems if we think aloud. Studies have illustrated that that language interferes with problem solving.

Wallas' four stages of creativity

i. Preparation : the problem solver gathers information and does some work on the problem, but with little progress. ii. Incubation: the problem solver sets the problem aside and seems not to be working on it. The problem solver continuous to work the problem unconsciously during this stage, so actually the problems solution is continuing to develop, unseen. iii. Illumination : a key insight or new idea emerges iv. Verification : in which the person confirms that the new idea really does lead to a solution and works out the details.

c. Functional Fixedness

- A tendency to be rigid in how one think about an objects function. This generally involves a strong tendency to think of an object only in terms of its typical function. - The tendency to be rigid in how one thinks about an objects function. With fixedness on place, the problem was rarely solved. Two strings hang from the ceiling but are too far apart to allow a person to hold one and walk to the other. On the table are a book of matches, a screwdriver, and a few pieces of cotton. How could the strings be tied together? Come up with an answer before reading any further. Solution: You could tie the screwdriver to the end of one rope and swing it. You could then grab the still rope and catch the swinging rope as it moves towards you. Did you think of using the screwdriver as a weight on the end of a rope? Functional fixedness occurs when functions or uses we assign to objects remain fixed or stable (i.e., a hammer is only meant to pound things into wood). This phenomenon occurs when we rely too heavily on previous concepts, expectations and memory, we fail to look at features of an object that might be helpful in solving our problem. To overcome functional fixedness we need to learn to think flexibly.

Nine dot problem

- Asked to draw straight line passing through all nine of these dots, without lifting your pencil from the page. Most had difficulty with this problem, probably because of an inappropriate problem solving.

Heuristics

- are our second method of problem solving. This is when we use general rules that we typically know to be correct to solve our problems. It is an educated guess based on prior experiences. This decision strategy helps to narrow down possible solutions for a problem. It is also known as a "rule of thumb". Heuristics are cognitive shortcuts. It is much quicker however there is no guarantee that we will solve a problem correctly. i.e., make as many words as you can using ejkwfhpwierjhsdf If we are faced with this question we are most likely to put together letter combinations that we know to have worked in the past (pier, we. wire etc...).

The Analogy Approach

-is when we use a solution from an earlier problem to solve a new problem. In order to do this we first determine the underlying structure of the problem. We must be careful to focus on structural features rather than surface features. People often fail to see the analogy between old and new problems based on structural features. For example : 2+4 and 2-4 look very similar on the surface but are structurally different requiring different problem solving strategies. Whereas, 10+6 and 1+8 may look different on the surface but have the same structure.

Hill-Climbing strategy

< common used strategy in problem solving. If people use this strategy, then whenever their efforts toward solving a problem give them a choice, they will choose the option that carries them closer to the goal. - entails selecting the alternative at each choice point that appears to lead most directly to one's goal. The name for this heuristic derives from the notion that if you need to climb a hill with many choice points along the pathway (and limited ability to see ahead), one simple strategy would be to always choose the path with the steepest upward slope. The hill-climbing heuristic is a logical strategy that works much of the time, but it can also backfire. Sometimes the optimal solution to a problem involves an indirect pathway or even moving backward, away from one's goal. We may fail to choose other alternatives which have greater long-term benefits (i.e., getting a job after you receive your B.A). This heuristic works best for short term goals rather than long term goals.

Means-ends analysis

A strategy used in problem solving in which the person is guided, step by step, by a comparison of the difference between the current state and then goal state, and by a consideration of the operations available for reducing that difference. is a heuristic that involves a two step process. There are two components: 1) Divide the problem into sub problems 2) Create solutions for each of the sub problems. The means-ends heuristic requires you to identify the "ends" you want and then figure out the "means" you will use to reach the ends. For example, if your car breaks down on the way to work you may face multiple sub problems - need to fix the car, need to call a friend for a ride, need to call work to tell them you will be late etc... We then figure out the means to get to the ends. This problem-solving technique is more sophisticated than the hill-climbing heuristic. it is also a more effective and flexible problem-solving strategy.

Algorithm

An algorithm is a methodical, step-by-step procedure for trying all possible alternatives in searching for a solution to a problem, which guarantees a solution. This is a method that always produces a solution for the problem. Even though we will always find the solution to our problem, it is a rather unsophisticated way of problem solving. It is also very time consuming. i.e., make as many words as you can using the letters: ejkwfhpwierjhsdf If we were to use the algorithm method, we would go through every possible letter combination even if it doesn't make sense to us (i.e., ej, ew, ek, ef, eh...). Eventually we will find all possible words because we will have exhausted every possible option.

Understanding the Problem

Attention is important in understanding a problem. We have limited attention so we must decide on the most relevant information in a problem and focus on that. Once we recognize that there is a problem, we need to find a good method to represent the problem. The most effective methods include symbols, matrices, diagrams and visual images. *Symbols* - sometimes it is effective if we can translate the words in a problem into symbols. This is most common in algebraic problems (i.e., Tom is 27 years old ~ T=27). Reducing the number of words can help to clarify the information we need to focus on. However, if we are relying on symbols, we need to be careful to translate the information correctly. *Matrices* - A matrix is a chart that shows all possible combinations of items. For example: Five people are in a hospital. Each person has only one disease. Each person occupies a separate room; the room numbers are 101-105... If you are given a list of information with a series of clues it may be helpful to organize that information and work through all of the combinations to see what is and what is not possible. An example of a matrix would be: *Diagrams* - can aid in problem solving if we are presented with a large amount of information. We can organize information in a hierarchical structure to specify various possible options to solve a problem. For example, if an electronic device has a malfunction and you consult the troubleshooting guide you may see a diagram - i.e., is the power on? if yes go here, if no, press the button... *Visual Images* - When problems take the form of stories they may be solved faster if we visualize them as a story

i. Luchin's water jar problem

Luchin (1942) found the majority of students demonstrated mental set in the water jar problem when they started out with the series of complex problems. When the students started out with problems like number 6 they did not demonstrate mental set because they had no previous experience with the problems. They solved problems the easier way (A-C). My dad exhibits metal set when paying the bills every month. When all of the bills come in, he writes out checks for all of them and then drives to each place to pay each bill. I try to tell him that he can pay all of his bills in about 10 minutes over the internet but he refuses. His method has worked for him in the past and he doesn't care to look for other more efficient methods. Mental set belongs to a larger category known as mindlessness. Mindlessness is referred to as automatic thinking in which we continue to focus on old categories rather than new ones and are not aware of new information in the environment. Mindfullness is when we make an effort to create new categories. We attempt to look at the same information from a different point of view i.e., using new study strategies to learn material for an exam. This takes a little longer in the beginning put leads to more efficient problem solving in the long run.

Stereotypes and Problem Solving

Sometimes stereotypes aimed towards us or others can affect the way we solve problems. Errors occur due to overactive top-down processing. Our top-down processes are overactive due to beliefs about our own abilities based on stereotypes. Some research regarding this has been conducted on ethnic group stereotypes and social group stereotypes however most research has been conducted on gender stereotypes. Gender Stereotypes are an organized set of beliefs about the characteristics of males and females. Everyone has stereotypes to some extent. Can you think of any stereotypes that you may have about gender? We often hear that men have better mathematical skills, women have better verbal skills, men are better drivers, women are better at asking for directions etc... Stereotypes may be partially valid however they are not true for every member of both genders (i.e., many women score higher than men on a test of mathematical problem solving ability). However, because of these stereotypes, women have tended not to associate themselves with mathematics in the past.