Video Module 29: Problem-Solving

Question 1

four components of a problem

Answer 1

1. initial state
2. goal state
3. operators
4. constraints

Question 2

operators of a problem

Answer 2

the set of operations or actions that you can take to reach the goal state

Question 3

goal state of a problem

Answer 3

the end product; the thing you want to achieve

Question 4

initial state of a problem

Answer 4

the resources you currently have; your current situation

Question 5

constraints of a problem

Answer 5

rules that cannot be violated

Question 6

the problem space

Answer 6

the total set of possible moves within the constraints of the problem
- all of the possible moves you could make at any point while solving the problem

Question 7

heuristics for problem solving

Answer 7

informal, intuitive strategies that sometimes lead to effective solutions, and sometimes don’t
1) hill-climbing heuristic
2) means-ends heuristic

Question 8

algorithms

Answer 8

a procedure for inspecting every possible move in the problem space
- A series of operations applied over the problem space that may be represented over and over again, continuing until a final state is reached
- slow, resource consuming
- guaranteed to produce a correct answer
- e.g. Computers play chess while using an algorithm to represent every possible move they could make in response to an opponent, and every possible move they could make after that depending on what their opponent does

Question 9

heuristics for problem solving

Answer 9

informal, intuitive strategies that sometimes lead to effective solutions
1) hill climbing heuristic
2) means-ends heuristic

Question 10

hill-climbing heuristic

Answer 10

taking a step in the direction that most reduces the distance between your present state and your end state
- each step in between the initial state and the goal state must take you closer to the goal state
- good when there is a straightforward path to the solution
- can lead people to get stuck when the solution requires briefly moving away from the goal

Question 11

means-ends heuristic

Answer 11

dividing the problem into smaller problems, then solving the smaller problems in any order to get to the end state
- You do not have to think of the first step first: means-ends only requires that you take all of the steps necessary to reach the end state
—you acknowledge that not all of the steps will necessarily bring you closer to the end goal
- e.g. Tower of Hanoi puzzle

Question 12

How might working backwards help us solve problems? How is this an example of the means-ends heuristic?

Answer 12

Working backwards can help us solve problems that seem as though they require many steps in between the initial state and the end state
- e.g. Lily pads problem
- This is an example of using the means-ends heuristic, because with backwards thinking, you are only thinking of how to get to the end state—not how to move sequentially from the initial state to the end state

Question 13

analogical reasoning

Answer 13

using structural similarities between a well-known base and an unfamiliar target domain to make inferences about the target domain
- In other words, comparing a problem to another, structurally similar problem that you’ve already solved, in order to find the solution

Question 14

What did Gick & Holyoak (1980) discover about people’s ability to use analogical reasoning?

Answer 14

Gick & Holyoak (1980) designed a study in which participants were given stories to read, one of which included a general attacking a fortress using divided forces.
—When given the radiation problem initially, only about 10% of people were able to spontaneously generate the answer.
—After reading the story of the fortress, about 40% of participants could solve the radiation problem without further help
—After being told the story of the fortress was relevant to the radiation problem, an additional 40% of participants could solve the problem

Question 15

convergence schema

Answer 15

A schema that outlines the initial state goal, resources, operators, constrains, solution, and outcome of two structurally similar problems
- Using a convergence schema allows you to explicitly see the similarities between two problems

Question 16

Why is it difficult for people to use analogical reasoning?

Answer 16

people tend to focus on surface features of problems, rather than deep structures of problems
—surface features are typically superficial in identifying the solution of a problem
- Our ability to use analogies often depends on our expertise within the relevant domain

Question 17

How do novices and experts differ in how they approach problems?

Answer 17

1) experts think of problems in terms of deep structure rather than superficial features
2) experts may take longer to determine the kind of problem they’re facing and decide on what method to use to solve the problem, however they typically end up solving the problem faster than novices once they’ve decided on the correct way

Question 18

How can people support analogical thinking?

Answer 18

1) Comprehending the deep structure of a problem: allows you to focus on more broad strategies rather than small details of the problem
2) Paying attention to a problem’s structure
3) Prompting participants to compare two problems, or asking participants to explain a problem