Course outline
Module 1
Module 1: What Problem Solving Is
What Problem Solving Is
Knowledge check
Q1. Which of the following best describes a problem in the context of problem solving?
- A. A routine task that you complete the same way every time
- B. A gap between a current state and a desired goal with no obvious way to close it ✓
- C. Any task that takes a long time to complete
- D. A question that has already been answered by an expert
Why: A problem exists when there is a difference between where you are and where you want to be, and the path to closing that gap is not immediately clear. Routine tasks with known procedures are not problems in this sense.
Q2. What is the term for the mental representation of a problem, including the starting state, the goal state, and the possible actions in between?
- A. Heuristic
- B. Problem space ✓
- C. Algorithm
- D. Insight
Why: The problem space is the set of all states that can be reached through allowable operations, bounded by the initial state and the goal state. Searching this space is central to how problem solvers reason.
Q3. A well-defined problem differs from an ill-defined problem primarily because a well-defined problem:
- A. Has no known solution
- B. Has clear starting conditions, a clear goal, and specified allowable operations ✓
- C. Can only be solved by experts
- D. Requires creative insight rather than logic
Why: Well-defined problems, such as a math equation or a chess checkmate puzzle, specify the initial state, the goal, and the rules for moving between them. Ill-defined problems, like improving a company's culture, leave one or more of these elements vague.
Q4. Which step of a classic problem-solving process involves identifying what the problem actually is before attempting any solution?
- A. Implementing the solution
- B. Evaluating the outcome
- C. Problem representation ✓
- D. Generating random ideas
Why: Problem representation is the stage where the solver figures out what the problem is, what information is relevant, and how to frame it. Research shows that poor representation is a common cause of failed problem solving, even when the solver has good strategies.
Q5. Why is it useful to distinguish between the initial state and the goal state when approaching a problem?
- A. It guarantees that the solution will be found quickly
- B. It clarifies the gap that must be closed, which guides the choice of strategies ✓
- C. It eliminates the need to test any solutions
- D. It shows that the problem has only one correct answer
Why: Naming the initial and goal states makes the difference between them explicit, which helps the solver select operations that move toward the goal. This clarity supports means-ends analysis and other systematic approaches.
Module 2
Module 2: How the Brain Represents Problems
How the Brain Represents Problems
Knowledge check
Q1. In cognitive psychology, what is the 'problem space'?
- A. The physical room where a problem-solving experiment takes place
- B. The set of all states a problem solver can reach, including the initial state, goal state, and the operators that move between them ✓
- C. The amount of working memory a person has available for a task
- D. The emotional stress a person feels when facing a difficult question
Why: Newell and Simon defined the problem space as the representation of all possible states of knowledge and the operators (moves) that connect them, from the initial state to the goal state.
Q2. Which term describes the starting condition of a problem as the solver understands it?
- A. Goal state
- B. Operator
- C. Initial state ✓
- D. Heuristic
Why: The initial state is the situation as it is at the start of the problem, which the solver must transform through operators toward the goal state.
Q3. What is an 'operator' in the context of problem representation?
- A. A person who supervises a psychology experiment
- B. A permissible action or move that transforms one state of a problem into another ✓
- C. The final answer a problem solver produces
- D. A memory store for long-term facts
Why: Operators are the allowable actions that change the current state of a problem, such as moving a disk in the Tower of Hanoi.
Q4. Why do people often struggle with the 'Tower of Hanoi' puzzle even when the rules are simple?
- A. Because the rules are written in a confusing way
- B. Because the disks cannot be seen clearly
- C. Because the problem requires holding many subgoals and constraints in mind at once, which strains working memory ✓
- D. Because people cannot count past three moves
Why: The puzzle requires tracking several subgoals and rule constraints simultaneously, and the demands on working memory make it harder as the number of disks increases.
Q5. What does it mean when a problem solver is said to have a 'mental representation' of a problem?
- A. They have drawn a picture of the problem on paper
- B. They have an internal model of the problem's elements, relationships, and goals that they can manipulate in thought ✓
- C. They have memorized the answer to the problem
- D. They have asked someone else to explain the problem to them
Why: A mental representation is an internal, cognitive model of the problem's components and structure, which the brain uses to reason about possible solutions.
Module 3
Module 3: Heuristics and Mental Shortcuts
Heuristics and Mental Shortcuts
Knowledge check
Q1. Which term describes a mental shortcut that helps people solve problems quickly but may not always lead to the best answer?
- A. Algorithm
- B. Heuristic ✓
- C. Syllogism
- D. Hypothesis
Why: A heuristic is a mental shortcut or rule of thumb that speeds up problem solving and decision making. Unlike an algorithm, it does not guarantee a correct solution, though it is often good enough.
Q2. What is the key difference between an algorithm and a heuristic?
- A. An algorithm is always faster than a heuristic
- B. An algorithm guarantees a correct solution if followed exactly, while a heuristic offers a probable but not guaranteed solution ✓
- C. A heuristic requires complete information, while an algorithm does not
- D. Algorithms are only used by computers, while heuristics are only used by humans
Why: An algorithm is a step-by-step procedure that, when followed correctly, guarantees a solution, such as long division. A heuristic is a shortcut that usually works but can produce errors, such as guessing based on past experience.
Q3. A person judges how likely an event is based on how easily examples of it come to mind. Which heuristic is being used?
- A. Representativeness heuristic
- B. Anchoring heuristic
- C. Availability heuristic ✓
- D. Means-ends analysis
Why: The availability heuristic involves estimating the likelihood of an event based on how easily instances come to mind. For example, people often overestimate the risk of plane crashes because such events are vivid and widely reported.
Q4. Which heuristic involves working backward from the goal state to figure out the steps needed to reach it?
- A. Hill climbing
- B. Trial and error
- C. Working backward ✓
- D. Random search
Why: Working backward is a problem-solving strategy that starts from the desired end state and reasons back toward the starting conditions. It is especially useful in problems like mazes or logic puzzles where the goal is clearly defined.
Q5. When a person relies too heavily on the first piece of information they receive when making a decision, which bias or heuristic is at work?
- A. Confirmation bias
- B. Anchoring ✓
- C. Hindsight bias
- D. Functional fixedness
Why: Anchoring occurs when an initial value or piece of information serves as a reference point that unduly influences later judgments. For example, the first price mentioned in a negotiation often shapes the final agreed price.
Module 4
Module 4: Insight and Restructuring
Insight and Restructuring
Knowledge check
Q1. In insight problem solving, what is the term for the sudden restructuring of how a problem is represented that leads to a solution?
- A. Incubation
- B. Representational change ✓
- C. Algorithmic search
- D. Means-ends analysis
Why: Representational change theory holds that insight occurs when a solver abandons an initial, often faulty, mental representation of a problem and adopts a new one that makes the solution accessible.
Q2. Which of the following is a classic example of a problem that typically requires insight rather than systematic trial and error?
- A. Solving a 4x4 sliding tile puzzle
- B. Calculating the sum of a long list of numbers
- C. The nine-dot problem of connecting all dots with four straight lines without lifting the pencil ✓
- D. Finding the shortest route on a known map
Why: The nine-dot problem requires the solver to extend lines beyond the perceived boundary of the square, a constraint the solver imposes mentally. Recognizing and dropping this self-imposed constraint is a hallmark insight restructuring.
Q3. What does the term 'functional fixedness' refer to in the context of insight problems?
- A. The tendency to perceive an object only in terms of its typical use ✓
- B. The inability to recall past solutions
- C. A preference for risky over safe strategies
- D. Persistent attention to irrelevant details
Why: Functional fixedness, studied by Karl Duncker, is the tendency to see objects only in their conventional function, which blocks solutions that require using an object in a novel way, such as using a box as a platform.
Q4. According to Gestalt psychologists, what best describes the moment of insight?
- A. Gradual accumulation of small improvements
- B. A sudden restructuring of the problem's perceptual or cognitive organization ✓
- C. Recall of a memorized formula
- D. Applying a step-by-step procedure without error
Why: Gestalt theorists such as Wertheimer and Köhler argued that insight involves a sudden reorganization of the elements of a problem into a new whole, rather than incremental learning through reinforcement.
Q5. Why do insight problems often feel like they are solved suddenly with an 'aha' experience?
- A. Because the solver has been consciously working step by step the entire time
- B. Because the solution emerges after unconscious processing reorganizes the problem representation ✓
- C. Because the problem is always easier than it appears
- D. Because the solver guesses randomly until succeeding
Why: Incubation and unconscious processing are thought to reorganize problem representations, so when the solution finally emerges it appears sudden, producing the characteristic 'aha' feeling of insight.
Module 5
Module 5: Analogy and Transfer
Analogy and Transfer
Knowledge check
Q1. A student solves a physics problem about a ball rolling down a ramp by using conservation of energy. Later, they face a problem about a pendulum swinging and recognize they can also use conservation of energy. What problem-solving process is this an example of?
- A. Brute-force trial and error
- B. Transfer of a solution strategy across problems with similar underlying structure ✓
- C. Means-ends analysis with no prior knowledge
- D. Random guessing informed by intuition
Why: Transfer occurs when a strategy learned in one context is applied to a new context that shares the same underlying structure. Both the rolling ball and the swinging pendulum convert potential energy into kinetic energy, so the same principle applies.
Q2. Which of the following best describes an analogy in problem solving?
- A. A direct copy of a previously solved problem with the same numbers
- B. A mapping between a familiar source situation and an unfamiliar target situation based on shared relational structure ✓
- C. A rule memorized without understanding its purpose
- D. A guess that happens to produce the correct answer
Why: An analogy maps the relationships in a known source domain onto a target domain. Its power comes from the shared relational structure, not from surface features like specific objects or numbers.
Q3. A student solving a new math problem notices it has the same structure as a problem they solved last week, even though the story context is entirely different (a bakery versus a farm). What is this an example of?
- A. Surface-level similarity matching
- B. Near transfer based on structural similarity ✓
- C. Coincidence with no learning involved
- D. Overfitting to irrelevant details
Why: Recognizing a shared underlying structure despite different surface details reflects structural (deep) similarity. Transfer that relies on deep structure is often more robust than transfer based on surface features.
Q4. Why do students often fail to transfer a solution they learned in one class to a problem in a different class?
- A. They lack any memory of the solution at all
- B. They focus on surface features such as the topic labels or story details rather than the underlying principles ✓
- C. Transfer is impossible between different subjects
- D. The solution is always too complex to remember
Why: Students commonly categorize problems by surface features, so a problem labeled as chemistry may not trigger a principle learned in physics even when the principle applies. Teaching students to identify deep structure helps overcome this barrier.
Q5. Which strategy most effectively encourages transfer of problem-solving skills to new situations?
- A. Having students practice many problems that all look identical
- B. Asking students to compare problems with different surface features but the same underlying solution, and to explain what they share ✓
- C. Giving students only the final answers to memorize
- D. Restricting practice to a single problem type until mastered
Why: Comparing contrasting cases that share deep structure helps learners abstract the key principle away from surface details, which supports transfer to novel problems.
Module 6
Module 6: Biases That Block Solutions
Biases That Block Solutions
Knowledge check
Q1. A team has already invested heavily in a software project that is clearly failing. Leaders decide to keep funding it, mainly because of the money already spent. Which bias is most at work?
- A. Confirmation bias
- B. Sunk cost fallacy ✓
- C. Availability heuristic
- D. Anchoring bias
Why: The sunk cost fallacy is the tendency to continue an endeavor because of resources already invested, even when future costs outweigh future benefits. Past spending should not influence the decision to continue.
Q2. A manager believes her new hiring method works, so she only notices and remembers the successful hires while overlooking the poor ones. Which bias does this illustrate?
- A. Hindsight bias
- B. Framing effect
- C. Confirmation bias ✓
- D. Status quo bias
Why: Confirmation bias is the tendency to search for, interpret, and remember information in ways that support existing beliefs. Selectively noticing the successes while ignoring the failures reinforces her belief about the method.
Q3. When brainstorming a solution to a budget shortfall, a team fixates on the first number mentioned in the meeting and makes all later estimates close to it. Which bias is this?
- A. Anchoring bias ✓
- B. Bandwagon effect
- C. Dunning-Kruger effect
- D. Optimism bias
Why: Anchoring bias occurs when an initial piece of information, even an arbitrary one, disproportionately influences subsequent judgments. Estimates then cluster around the first number rather than the true evidence.
Q4. A problem solver rejects a promising solution simply because it was proposed by a colleague they dislike. Which bias is most likely operating?
- A. Availability heuristic
- B. Groupthink
- C. Ad hominem-driven bias, often called the source bias ✓
- D. Planning fallacy
Why: Source bias is the tendency to judge an idea based on who proposed it rather than on its merits. Rejecting a good solution because of the messenger blocks effective problem solving.
Q5. After a project succeeds, a team member says, 'We obviously knew this would work all along.' Which bias does this statement reflect?
- A. Hindsight bias ✓
- B. Loss aversion
- C. Recency bias
- D. Halo effect
Why: Hindsight bias is the tendency to believe, after an outcome is known, that the outcome was predictable. This distorts learning because it hides the real uncertainty that existed at decision time.
Module 7
Module 7: Testing and Refining Solutions
Testing and Refining Solutions
Knowledge check
Q1. Why is it important to test a proposed solution before fully committing to it?
- A. Testing guarantees the solution will never need changes
- B. Testing reveals flaws or unintended consequences before they become costly ✓
- C. Testing is only required for solutions that involve mathematics
- D. Testing replaces the need to define the problem clearly
Why: Testing exposes flaws, errors, and unintended side effects early, when they are cheaper and easier to fix than after full implementation.
Q2. What is the main purpose of a pilot test in problem solving?
- A. To prove the solution is perfect before any analysis
- B. To try the solution on a small scale to gather evidence before wider rollout ✓
- C. To avoid collecting feedback from users
- D. To eliminate the need for a problem statement
Why: A pilot test applies the solution in a limited setting so you can observe results and learn what to improve before scaling up.
Q3. Which of the following best describes an iterative refinement cycle?
- A. Implementing a solution once and never changing it
- B. Testing, evaluating results, adjusting the solution, and testing again ✓
- C. Choosing the first idea generated and accepting it without review
- D. Repeating the same test with identical conditions to confirm the result
Why: Iterative refinement involves repeated cycles of testing, evaluating outcomes, making adjustments, and retesting until the solution meets its goals.
Q4. A team changes two things at once in their solution and sees improved results. Why is this a weakness in their testing approach?
- A. Changing two things always makes results worse
- B. It is impossible to tell which change caused the improvement ✓
- C. Testing must never produce positive results
- D. Two changes require twice as much budget, which is always forbidden
Why: Changing one variable at a time, a controlled approach, lets you isolate which change produced the effect. Changing two at once leaves the cause ambiguous.
Q5. What should a problem solver use to decide whether a tested solution succeeded?
- A. Personal feelings about how the solution looks
- B. The opinion of the person who proposed the solution alone
- C. Predefined success criteria measured against the test results ✓
- D. Whether the test took a long time to complete
Why: Defining success criteria before testing gives an objective standard, so the evaluation is not biased by hopes or personal preference.