Chapter 13: Problem Solving and Creativity

Each of these people is describing a creative friend. Does the description suggest that the friend is skilled in convergent thinking or divergent thinking?

"I was just going to toss these old coffee filters that I never use, but Alex suggested dyeing them and making them into fake flowers as a decoration. They ended up really cute." = divergent "Peyton locked herself out of her car, but she cut a hole in a tennis ball and pushed it over the lock to exert enough pressure to open it. That hack is genius." = divergent "Berta is the best researcher in our lab. She always connects ideas from different articles and classes that she's taken to her experiments; it has led to some really interesting findings." = convergent

Alvin and two of his classmates are trying to come up with an idea for an experiment they will conduct for a biology assignment. Based on the discussion of brainstorming in your textbook, decide whether each of these brainstorming tips from his project partners are good suggestions or bad suggestions. good suggestion bad suggestion

"Let's sleep on it and see if we come up with anything tomorrow." = good "Let's try to only say one or two really good ideas out loud. If it's not great, think up a new one." = bad "Let's each engage in a little mind-wandering, just to see what comes to mind." = good "Let's keep brainstorming out loud together until we come up with something." = bad

Participants are more likely to solve the tumor problem if they are advised to use the "general and fortress" story as an aid. When participants are not explicitly advised to use this analogy, how many solve the tumor problem? (Go here to read the tumor problem and the "general and fortress" story.)

30%

Adam is participating in an experiment on "Aha!" moments during problem solving. As he works on each insight problem, he conveys his progress by providing warmth ratings ("I'm getting warmer . . . , I'm getting warmer . . . , I'm getting hot!") on a 0-10 scale. Based on the ratings, select the point on the graph when Adam suspected that he was about to solve this problem.

5th Dot.

In chess, which move is best at any point in the game depends on what your opponent will be able to do in response to your move, and then what you'll do next. To make sure you're choosing the best move, you need to think ahead through a few cycles of play. Once the game is under way, though, there will be roughly 700 million possibilities for how the game could unfold over only three cycles of play. What can we learn about the problem-solving process from this?

A problem solver needs a way to narrow the search through a problem space.

Identify the problems that are "insight problems."

A stranger approached a museum curator and offered him an ancient bronze coin. The coin had an authentic appearance and was marked with the date 544 B.C. The curator had happily made acquisitions from suspicious sources before, but this time he promptly called the police and had the stranger arrested. Why? = insight A landscape gardener is given instructions to plant four special trees so that each one is exactly the same distance from each of the others. How should the trees be arranged? = noni insight

If a problem is ill-defined, it cannot be solved.Press Space to opentruefalse Well-defined problems only have one solution.Press Space to opentruefalse An ill-defined problem can become well-defined.Press Space to opentruefalse The constraints or assumptions with which one defines a problem may be incorrect.

A strategy in which the person is guided by a step-by-step comparison of the current state and the goal state. The problem-solver will ask, "What means do I have to make these states more alike?" = means-end analysis If people use this strategy, they will choose the option that carries them closer to their goal whenever their problem-solving efforts give them a choice = hill-climbing strategy.

Each ____ in the figure shows a possible problem state. From the initial state, there are ___ legal moves one could make.

Circle Four

According to Wallas (1926), creative thought proceeds through four stages: preparation, incubation, illumination, and verification. Which of these more recent findings are consistent with Wallas's proposal and which are inconsistent?

Consistent: "Mind wandering" can make incubation effects more likely. Certain types of problems ("insight problems") are often solved in an "Aha!" moment.

____refers to the ability to find ways in which seemingly distinct ideas might be interconnected.

Convergent thinking

Which of these are characteristics of problem-solving sets?

Correct Blind you to useless strategies Blind you to useful strategies Narrow your search through the problem space

Dr. Castle has given his participants the tumor problem to solve. He has also given them the "general and fortress" story to read, but he has not told them that it is relevant to the tumor problem. Which of these participants will likely use the analogy anyway and solve the tumor problem? (Go here to read the tumor problem and the "general and fortress" story.)

Correct Hans searches his memory for things he knows about converging forces. Beatrice focused on the relationship between the soldiers and the fortress in the story. She realizes the relationship is the same between the rays and the tumor.

Which of these elements need to be clearly or exactly stated for a problem to be well-defined?

Correct Steps you cannot take the goal steps you can take

When confronted with an ill-defined problem, what can you do to make it more solvable?

Correct: Add assumptions Create well-defined subgoals

Which of these individuals are overcoming functional fixedness?

Correct: Ellen just moved and can't find her corkscrew in any of the moving boxes. To open a bottle of wine, she instead uses a bike pump, pumping air into the bottle until the cork dislodges. Alvin is trying to move a very heavy bookcase, but it won't budge. He slides a metal cookie sheet underneath it and now he can move it across the carpet easily!

Expert chess players, average players, and novice players were shown this and other similar arrangements of chess pieces on a board for 5 seconds. Which of these statements accurately describe the outcome of this study?

Correct: Experts remembered the pieces based on tactical plays. Average players and novices tried to remember the board as a whole.

Kennan has just started his engineering homework and has come across a particularly difficult problem. After 10 minutes, he is still stuck. Based on the discussion of incubation in your textbook, which of these tactics could you reasonably recommend?

Correct: Go do something else Keep trying Stop trying and daydream for a bit Take a nap, then try again

For which of these problems do participants typically demonstrate functional fixedness?

Correct: The candle problem The two-string problem

Participants often experience functional fixedness while trying to solve this two-string problem. The trick here is not to think of the pliers in terms of their usual function—squeezing or pulling. Instead, the trick is to think of them as a weight. Which of these actions could a researcher take during the experiment to reduce the likelihood that the participant experiences functional fixedness?

Correct: Use the pliers for an unusual purpose, like hammering in a loose nail on the table Direct a gentle fan toward one of the strings to make it swing slightly

____refers to the ability to move one's thoughts in novel, unanticipated directions

Divergent thinking

A problem solver's beliefs, habits, and preferred strategies are referred to as ____.

Einstellung

Identify the advantages that experts have over novices. If none of these are advantages, select the "No Advantages" button.

Experts' knowledge is more heavily cross-referenced. Experts have established routines that they can use for many tasks. Experts have more knowledge.

Relative to less creative people, highly creative people

Have relatively greater working memory capacity. Tend to generate more ideas. Are skilled in convergent and divergent thinking. Are usually more willing to take risk. Are better at searching their memories for ideas.

Identify each statement about ill-defined and well-defined problems as true or false.

If a problem is well-defined, it is easy to reach the solution = false If a problem is ill-defined, it cannot be solved = false Well-defined problems only have one solution = false An ill-defined problem can become well-defined = true The constraints or assumptions with which one defines a problem may be incorrect = true

Some problems—like "becoming a better person," "attaining world peace," and "saving money for retirement"—are ____.

Ill-defined

Which of these does a problem space include?

Includes States that do not lead to a solution. States that lead to a solution.

Identify each heuristic the problem solver is using in these descriptions.

Juan needs to move a heavy stack of barbell plates—stacked with the largest on the bottom and smallest on top—to the other side of the recreation space. First, he has to take the smaller plates off and put them to the side in order to move the bigger plates to the other side. Then, he picks up the smaller plates in reverse to stack them on top of the bigger ones = means-end analysis. Jax is trying to get from Chicago to D.C. for a business trip. A flight will get him from Chicago to D.C., but how to arrange the flight? He'll need to find a computer to book the ticket, then he'll need to arrange a ride to the airport. He makes a list of other tasks he needs to complete in order to make it to D.C. = means-end analysis Camilla is headed north to visit her mother in Santa Barbara. When she leaves her house, she drives north for an extra 15 minutes in order to get to the freeway even though there was an on-ramp 2 minutes south of her house = hill-climbing strategy Roscoe, an energetic beagle puppy, has gotten his leash wrapped around a street light. He keeps pulling forward trying to get free, but it doesn't occur to him to retrace his steps in order to unwrap the leash = hill climbing strategy.

According to Wallas (1926), creative thought proceeds through four stages. Identify the stage in which each problem solver seems to be at the moment.

Kyra looked all over for the book that she borrowed from her professor, but she can't find it anywhere. During a conversation the next day about nearby restaurants, it suddenly hits her: She left it in the dining hall restroom! = illumination. J.J. is trying to write his English Literature term paper, but he's experiencing "writer's block." He gives up after a couple of hours to go to the gym instead = incubation Lena has been struggling to figure out a proof for her Calculus class for several days, but she thinks she finally has the solution. She double-checks her work—seems to be correct! = verification Monroe needs to move to Ohio to start his new job next month. He searches online for different moving companies to get quotes and he starts to look around his apartment for things he can donate instead of taking with him = preparation

Identify the traits that are generally either true or false of creative people.

Motivated by the work itself = true Tend to follow trends = false Refuse to tolerate ambiguous findings = Willing to take risks = Willing to ignore criticism =

Functional fixedness arises because of what?

Ones problem solving set

Participants were given a candle, a book of matches, and a box of tacks. Their task was to find a way to attach the candle to the wall of the room, at eye level, so that it would burn properly and illuminate the room. One group of participants received a box full of tacks, while the other group received the tacks alongside the empty box. Which group was able to solve the problem?

Participants who were provided with the matches, the candle, a pile of tacks, and an empty box.

According to Wallas (1926), creative thought proceeds through four stages. Place these stages in order according to Wallas's proposal.

Preparation Incubation Illumination Verification

The general process by which a person begins with a goal and seeks some steps that will lead toward that goal is referred to as ____.

Problem solving

The starting assumptions that a person uses when trying to solve a new problem are referred to as the solver's ____.

Problem-solving set

Select the incorrect assumptions participants tend to make when solving this nine-dot problem, thus preventing them from reaching a solution.

The lines must begin and end on dots. Each line should cancel out a full row or columns of dots.

According to Wallas (1926), creative thought proceeds through four stages. Match each stage to the correct description.

The problem solver gathers information and does some work on the problem, but with little progress = preparation The problem solver sets the problem aside and seems not to be working on it = incubation. A key insight or new idea emerges = illumination. The problem solver confirms that the new idea really does lead to a solution and works out the details = verification.

Dr. Ana Logue is studying potential ways to make analogy use more likely. She has participants read the "general and fortress" story before trying to solve the tumor problem. (Go here to read the tumor problem and the "general and fortress" story.) Across her participants, she attempts to induce a "relational mindset" at different stages of the task. Which group of her participants is most likely to solve the tumor problem?

Those who had a relational mindset inducted while reading the fortress story

Which of these statements about individual differences in problem solving are true?

True: Experts are more likely than novices to think about a problem's deep structure. People who are better problem solvers are more likely to use analogies.

Map the components of the "general and fortress" story onto the tumor problem. (Go here to read the tumor problem and the "general and fortress" story.) Note that not all items will have a match.

Tumor = Fortress Intensity of the rays = # of soldiers Healthy tissue = neighboring villages The doctor = the general Rays = soldiers Directions of the rays = roads with mines

Identify these problem-solving behaviors as more characteristic of experts, more characteristic of novices, or equally characteristic.

Use problem-solving heuristics = equally Categorize new problems based on deep features = experts Set sub goals = experts. Frequently use analogies = experts. Categorize new problems based on surface features = novices

People generally solve this problem correctly if they start by doing what?

Visualizing the arrangement of the books

Other problems—like the tumor problem, the candle problem, and the water-jar problem—are ___.

Well-defined

In one study, participants were given a series of "insight problems" to solve. As participants worked on each problem, they rated their progress by using a judgment of "warmth" ("I'm getting warmer . . . , I'm getting warmer . . .").

When you say "Aha!" it means that you've discovered a new approach.