Problem Solving: Well-Defined and Ill-Defined Problems

• Problem Solving is a multistage process involving discovering a problem, developing strategies, and effectively storing a solution.

Well-Defined vs Ill-Defined Problems

• Well-defined and ill-defined problems differ in the number of solutions, solution paths, and cognitive load.
• Strategies help to navigate the problem space and avoid combinatorial explosion in well-defined problems.

Ill-Defined Problems

• Ill-defined problems are situations lacking a clear path to move from the problem to the goal state.
• Ill-defined problems have very few task constraints, which are limitations regarding how to solve the problem.
• Multiple solutions can exist for ill-defined problems.

Solving Ill-Defined Problems

• Solving ill-defined problems are associated with uncertainty.
• Strategies, not scripted solutions, must fit the situation to solve them.
• Solutions include recombining related memories to form imagined hypothetical solutions and remembering past experiences related to a problem.

Analogical Problem Solving

• Analogical problem solving involves making comparisons across scenarios and applying solutions from past situations to current problems.
• Target problems are the problems a person is trying to solve.
• This an be something like, "What to cook for a dinner party"
• Source problems share similarity with the target problem, and an example question might be "How was this resolved in past similar scenarios?"
• Noticing a relationship involves recognizing an analogous relationship between a source problem (familiar) and target problem (unfamiliar).
• The correspondence is mapped by identifying what is similar between the target and source problems, requiring inferences and generalization.
• When you apply the mapping, generate a parallel solution for the target problem.

The "Tumor" Problem

• To solve requires creativity.
• A doctor has a patient with a malignant tumor in their stomach, and it is impossible to operate. The tumor is deadly.
• There is a kind of ray to destroy the tumor.
• If the rays reach the tumor all at once at a sufficiently high intensity, the tumor will be destroyed.
• The healthy tissue that the rays pass through on the way to the tumor will also be destroyed. At lower intensities, the rays are harmless to healthy tissue, but they will not affect the tumor either.

The Fortress Story

• A small country was ruled from a strong fortress by a king.
• The fortress was situated in the middle of the country surrounded by farms and villages, with many roads radiating outward.
• A rebel general vowed to capture the fortress, knowing that an attack would capture the fortress, and gathered an army at the head of one of the roads.
• The general learned that the king had planted mines on each of the roads that would detonate with a large force.
• It seemed impossible to mount an attack on the fortress because detonating mines would blow up the road, render it impassable, and destroy neighboring villages.
• The general knew just what to do, dividing his army into small groups dispatched to the head of a different road.
• Each group marched down a different road once the signal given. So the entire army finally arrived at the fortress at the same time, the fortress fell, and the king was forced to flee into exile.
• After reading a similar problem story and the solution, people are more likely to solve the “Tumor” Problem

Analogical Transfer and Similarity

• People don't naturally engage in analogical transfer without a hint and low surface similarity.
• Surface details are the content of scenarios.
• It is easier to use a school-related problem to solve a current school-related problem than a related current relationship-related problem.
• Structural similarity stores the essence of the problem solution .
• It is a generalized relationship between problem and solution.
• When more focus is put on structural similarity, the source scenario expands in creavity.

Sleep and Analogical Transfer

• Sleep facilitates analogical transfer.
• Wake groups left the lab for 120 mins
• Nap groups slept for 110 mins while EEG was recorded, they were given 10 mins after waking to clean up
• Both groups attempted to solve target problems and completed similarity ratings.

Additional Considerations

• Analogies make unfamiliar problems familiar and benefit from sleep.
• Superficial similarity influences mapping between a source and target problem but can confine this form of problem-solving.
• Structural similarity is more important for drawing analogical inferences, especially creative and insightful ones.

The Einstellung Effect

• Familiarity leads to the Einstellung effect, causing bias to use familiar methods to solve a problem.
• Rigid Thinking is an inability to seek out a better method to solve a given problem.
• Different types of blocks in problem solving include Functional and Mental Fixedness.

Functional Fixedness

• Functional fixedness is the inability to see beyond the most common use of a particular object.
• “Fixed” on the known function of an object.
• A classic test of functional fixedness found that only 39% of people can find the solution within 10 minutes.
• Solution hints help: prior to the task, swinging arms in a solution-relevant manner led to the solution.
• The candle problem is another common test relating to functional fixedness.
• You must attach the candle to the wall using tools.
• There is not fixedness in children without "pre-utilization" (experience with objects).
• Too much experience leads to fixedness and the Einstellung effect.

Alternate Uses Task

• This task can link to creativity.

Mental Fixedness

• Mental fixedness is overusing mental sets.
• In mental fixedness, people are responding with previously learned rule sequences even when they are inappropriate or less productive.
• Additionally, it is the tendency to respond inflexibly to a particular type of problem and not later your response.
• This equation could be applied to all remaining problems: Solution: Amount = B - A - 2C

Insight Problem Solving

• A productive thinking process forms new patterns or ways to view a problem, the opposite is reproductive thinking.
• Restructuring a problem leads to a sudden solution known as "the Aha moment".
• Gestalt switches are the experience of having a sudden switch in how you see something.
• Mental impasse, which means you stuck in a solution path.

Four Features of Insight

• Suddenness: solution pops into mind with surprise.
• Ease: The solution comes quickly and fluently.
• Positive: A pleasant experience, even before assessing if the solution is effective.
• Confidence: The solution is believed to be the right one.

Insight vs Non-insight

• Insight problem solving is involuntary, happens suddenly, and comes with 'pleasure'.
• Non-insight problem solving happens gradually, and there is an awareness of incremental success.
• Participants rate their 'warmth' around problems every 15 seconds.
• Warmth ratings predicted performance on algebra but not insight problems.

Insight Defined by Experience

• Participants shown problems and asked to rate feeling of knowing ("Do you feel that you will know the answer to this problem?") These feelings predicted algebra but not insight problem solving ability.
• Metacognitive assessments (What you know about what you know) are unaccurate for insight problems.
• People cannot accurately predict performance (finding solution) in solving insight problems.
• Focus is shifted toward problem-solving restructuring and definition in insight problems.
• Non-insight problem-solving comes with awareness and algorithms help predict the performance.

The Right Temporal Lobe

• TDCS to right ATL (anterior temporal lobe) improves performance on creativity problem-solving tasks (RAT) compared to other TDCS locations or sham.
• TDCS assists at semantic integration.

Walking and Insight

• Studies found that: walking has a large effect on creative insight.