Important+Researchers+&+Their+Contributions

  **The Most Important Researchers & Their Contributions ** **To the Obstacles & Aids to Problem Solving** 

Obstacles:

The first factor that can become an obstacle in problem solving is a mental set, consider **entrenchment**. According to Sternberg and Sternberg (2012), this consists of “a frame of mind involving an existing model for representing a problem, a problem context, or a procedure for problem solving” (p. 460). Possessing an entrenched mental set, a problem solver will fixate on a strategy that has previously worked for them in other problems, yet it does not work well in solving the current problem at hand.
 * Mental Sets**

Mental sets have been shown to affect solutions of even routine problems, much like that of **Abraham S. Luchins’s** (1942) “water-jar” problems, in which participants measured different amounts water using three different jars (Sternberg & Sternberg, 2012, p. 460). //See figure below.//

Another type of mental set is **functional fixedness,** which is the inability to recognize that something, besides being used for its known operation, may also be used for performing other functions. For instance, an example would be thieves refashioning a hanger into a tool to break into a locked car (Sternberg & Sternberg, 2012, p. 460).

Consider the candle problem posed by cognitive psychologist **Karl Duncker**, “You are led into a room that contains a table. On the table are three objects: a candle, a BOX of matches, and a box of thumbtacks. Your job is to find an easy way to attach a candle to the wall of the room so that it burns properly, using no other objects on the table” (Whitten, 2013, para. 7). According to Duncker, functional fixedness was overcome if the subjects in his experiments used the empty match box to hold the candle up by tacking it to the wall (Biella & Luther, 2006, p. 23). I will elaborate on Duncker more in the analogies section.

The final type of mental set, to be discussed here, is an aspect of social cognition called stereotypes. “**Stereotypes** are beliefs that members of a social group tend more or less uniformly to have particular types of characteristics” (Sternberg & Sternberg, 2012, p. 460). According to research by **Neto**, **Williams**, and **Widner** (1991), and **Seguino** (2007), stereotypes form during childhood. In fact, cross-cultural studies show children obtaining knowledge about gender stereotypes throughout their childhood years (as cited in Sternberg & Sternberg, 2012, p. 460). Overgeneralizing leads to assumptions that further patterns will conclude the same instances, such as believing that all African-Americans are fast runners (Sternberg & Sternberg, 2012, p. 461). This action leads people to limit their thinking.

A **transfer** is knowledge or skill a person takes from one problem to the next; it can be negative or positive, the latter will be discussed as an aid to problem solving. **Negative transfer** occurs when a problem solver was on the wrong track for an earlier problem, thus making it harder to solve the next one. For instance, operating a new tool in a way they are already familiar with.
 * Transfers**

Other obstacles may include, but are not limited to incorrect or incomplete representation of the problem and a lack of domain knowledge ("Problem Solving PDF", p. 24)

Aids: As discussed earlier, transfers can be positive as well. **Positive transfer** is the exact opposite of negative transfer, and occurs when an earlier problem aids in solving a new problem. Interestingly, sometimes the transfer of a mental set can be an aid to problem solving. For example, learning simple math in grade school will allow you to complete more complex algebraic problems in high school. Many researchers have considered this topic in their studies, some of them include **Bassok** and **Holyoak** (1989); **Chen** and **Daehler** (1989); and **Campbell** and **Robert** (2008) (Sternberg & Sternberg, 2012, p. 462).


 * Gick and Holyoak’s** 1980s studies involve positive transfer using analogies; although, analogies were not noticed because the participants were not looking for them. To value the results of their work, you need to become familiar with a problem first used by Karl Duncker (1945), often called the “radiation problem.” //See figures below to compare the two studies.//



Algorithms and heuristics are cognitive procedures used for solving problems. When applied completely and correctly, **algorithms** are procedures that will guarantee a solution. p. 18). Another type of heuristic is a **mean-end heuristic**, which requires a reduction in the steps between the initial state of the problem and goal state by identifying the “ends.” Finally, **working backward** is just that, a heuristic in which one works from the goal to the initial state; this type is great for learning procedures (Whitten, 2013, para. 6).
 * Algorithms and Heuristics**
 * Heuristics** are “informal, intuitive, speculative strategies” that do not guarantee a solution, but within a limited amount of time provide a good chance ( "Problem Solving PDF",
 * Hill climbing** is one type of heuristic that causes someone to pick a solution based on the most direct way to achieve the goal. For instance, by picking the hill that has the steepest incline, the climber will get to the top of the mountain faster.

Research by psychologists, **Davidson** (1995) and **Sternberg** (1985), suggests a three-process theory, “according to which insights arise out of processes called selective encoding, selective combination, and selective comparison” (As cited in Davidson & Sternberg, 2003, p. 19). The possibility of an insight may result from a change in the problem deﬁnition or representation by any of the three processes (Davidson & Sternberg, 2003, p. 19).
 * Insight**

“**Smith**’s (1995; Smith & Blankenship, 1989) research on incubation suggests that a period of time spent away from the problem can allow the problem solver to let go of unfruitful approaches and to allow an appropriate representation to come to mind, thus culminating in a moment of insight” (Davidson & Sternberg, 2003, p. 19). The role of incubation, or taking a break from trying to solve the problem, allows the problem solver to produce different strategies for solving that problem, thereby eliminating a stalemate (Davidson & Sternberg, 2003, p. 162).
 * Incubation**