# Problem-Solving Methods

 chapter 13 Problem Solving and Intelligence

General Problem-Solving Methods People solve problems all the time. Some problems are pragmatic (“I want to Tom borrowed my car. How can I get there?”). Others are social (“I really want Amy to notice me; how should I arrange it?”). Others are academic (“Im trying to prove this theorem. How can I do it, starting from these axioms?”). What these situations share, though, is the desire to figure out how to reach some goal-a configuration that defines what we call problem solving. How do people solve go to the store, but problems?  Problem Solving as Search  Researchers compare problem solving to a process of search, as though you were navigating through a maze, seeking a path toward your goal (see Newe & Simon, 1972; also Bassok & Novick, 2012 Mayer, 2012). To make this point concrete, consider the Hobbits and Orcs problem in Figure 13.1. For this problem, you have choices for the various moves you can make (transporting creatures back and forth), but you’re limited by the size of the boat and the requirement that Hobbits can never be outnumbered (lest they be eaten). This situation leaves you with a set of options shown graphically in Figure 13.2. The figure shows the moves available early in the solution and depicts the options as a tree. with each step leading to more branches. All the branches together form the problem space- that is, the set of all states that can be reached in solving the problem.

It seems, then, that the masters-experts in chess-memorize the board in terms of higher-order units, defined by their strategic function within the game. This perception of higher-order units helps to organize the experts’ thinking. By focusing on the units and how they’re related to one another, the experts keep track of broad strategies without getting bogged down in the details. Likewise, these units set subgoals for the experts. Having perceived a group of pieces as a coordinated attack, an expert sets the subgoal of preparing for the attack. Having perceived another group of pieces as the early deevelopment of a pin (a situation in which a player cannot move without exposing a more valuable piece to an attack), the expert creates the subgoal of avoiding the pin. It turns out, though, that experts also have other advantages, including the simple fact that they know much more about their domains of expertise than novices do. Experts also organize their knowledge more effectively than novices. In particular, studies indicate that experts’ knowledge is heavily cross-referenced, so that each bit of information has associations to many other bits (e.g., Bédard & Chi, 1992; Bransford, Brown & Cocking, 1999; Reed, 2017). As a result, experts have better access to what they know. It’s clear, therefore, that there are multiple factors separating novices from experts, but these factors all hinge on the processes we’ve already discussed-with an emphasis subproblems, and memory search. Apparently, then, we can use our theorizing so far to describe on analogies, how people (in particular, novices and experts) differ from one another. e. Demonstration 13.1: Analogies  Analogies are a powerful help in solving problems, and they are also an excellent way to convey new information. Imagine that you’re a teacher, trying to explain some points about astronomy. Which of the following explanations do you think would be more effective?

Literal Version

Collapsing stars spin faster and faster as they fold in on themselves and their size decreases. This principle called phenomenon of spinning faster as the star’s size shrinks occurs because of a “conservation of angular momentum.”

Analogy Version

Collapsing stars spin faster as their size shrinks. Stars are thus like ice skaters, who pirouette faster as they pull in their arms. Both stars and skaters operate by a principle called “conservation of angular momentum”

Which version of the explanations would make it easier for students to answer a question like the following one?

What would happen if a star “expanded” instead of collapsing?

a) Its rate of rotation would increase.

b) Its rate of rotation would decrease.

c) Its orbital speed would increase.

d) Its orbital speed would decrease.

Other participants were given the same tools, but configured differently. They were given some matches, a pile of tacks, the box (now empty), and a candle. In this setting, the participants were less they to solve the problem (Duncker, 1945). (Also see were less likely to think of the box likely to think of the box as a container for the tacks, and so likely as a container. As a result, they were more Figure 13.10; for more on fixedness, see McCaffrey, 2012.)

“Thinking outside the Box”  A related obstacle derives from someone’s problem-solving set-the collection of beliefs and assumptions a person makes about a problem. One often-discussed example involves the nine-dot problem (see Figure 13.11). People routinely fail to solve this problem, because-according to some interpretations-they (mistakenly) defined by the dots. In fact, this problem is probably the source of the cliché “You need to think assume that the lines they draw need to stay inside the “square” outside the box.”