“It must be a trick,” he said to himself, because he knew from experience that problems posed in this way often were not what they first appeared to be. So he set out to question what the teacher had meant by the word line, and came up with an acceptable solution as a result. If information is misunderstood or used inappropriately, then mistakes are likely—if indeed the problem can be solved at all. For students working on the nine-dot matrix described in the last section, the notion of “drawing” a line was also initially fixed; they assumed it to be connecting dots but not extending lines beyond the dots. She had also seen other drawing-related puzzles and knew that their solution always depended on making the lines longer, shorter, or differently angled than first expected. Teachers can assist this process, as you might expect, by suggesting reasonable, helpful analogies for students to consider. 47–62. Several problem-solving interventions that utilise a “circle” approach have been applied within the field of educational psychology, for example, Circle Time, Circle of Friends, Sharing Circles, Circle of Adults and Solution Circles. Problem-solving transfer. Just as there are cognitive obstacles to problem-solving, there are also general strategies that help the process be successful, regardless of the specific content of a problem (Thagard, 2005). For students working on the nine-dot matrix described in the last section, the notion of “drawing” a line was also initially fixed; they assumed it to be connecting dots but not extending lines beyond the dots. When a problem is well-structured, so are its solution procedures likely to be as well. But two volunteers tried doing it at the board, but were unsuccessful. A well-defined procedure for solving a particular kind of problem is often called an algorithm; examples are the procedures for multiplying or dividing two numbers or the instructions for using a computer (Leiserson, et al., 2001). With the nine-dot matrix problem, for example, construing the instruction to draw four lines as meaning “draw four lines entirely within the matrix” means that the problem simply could not be solved. Although it can date back as early as the days of Plato and Aristotle, educational psychology was not considered a specific practice. He had not, however, seen this particular problem. This approach is especially helpful when a problem is well-structured but also has elements that are distracting or misleading when approached in a forward, normal direction. This story illustrates two common features of problem solving: the effect of degree of structure or constraint on problem solving, and the effect of mental obstacles to solving problems. Problems vary in how much information they provide for solving a problem, as well as in how many rules or procedures are needed for a solution. The solution of each subproblem contributes the solution of the whole, though of course is not equivalent to a whole solution. Somewhat less open-ended than creative thinking is problem-solving, the analysis and solution of tasks or situations that are complex or ambiguous and that pose difficulties or obstacles of some kind (Mayer & Wittrock, 2006). ), https://open.umn.edu/opentextbooks/BookDetail.aspx?bookId=153. Her solution looked exactly like Willem’s. In that situation it pretty much guarantees a correct solution. Problem solving happens in classrooms when teachers present tasks or challenges that are deliberately complex and for which finding a solution is not straightforward or obvious. A first grade student can partially decode unfamiliar printed words by analogy to words he or she has learned already. Three alternatives are described in Scenes #3 (for Alicia) and 4 (for Willem and Rachel). But not all necessary information was given: students needed to consider lines that were longer than implied in the original statement of the problem. Mind: Introduction to Cognitive Science, 2nd edition. Alicia stared at the teacher blankly, but then smiled and said, “Hmm! This story illustrates two common features of problem-solving: the effect of degree of structure or constraint on problem-solving, and the effect of mental obstacles to solving problems. & Luchins, E. (1994). Problem solving happens in classrooms when teachers present tasks or challenges that are deliberately complex and for which finding a solution is not straightforward or obvious. The example also illustrates two common problems that sometimes happen during problem-solving. Cambridge, MA: MIT Press. The teacher walked by Alicia’s desk and saw what Alicia was doing. Luchins, A. We have numbered and named the paragraphs to make it easier to comment about them individually: A teacher gave these instructions: “Can you connect all of the dots below using only four straight lines?” She drew the following display on the chalkboard: The problem itself and the procedure for solving it seemed very clear: simply experiment with different arrangements of four lines. Toulmin’s model and the solving of ill-structured problems. The teacher walked by Alicia’s desk and saw what Alicia was doing. Another helpful strategy is working backward from a final solution to the originally stated problem. In devising a plan to improve bicycling in the city, for example, an analogy of cars with bicycles is helpful in thinking of solutions: improving conditions for both vehicles requires many of the same measures (improving the roadways, educating drivers). Functional fixedness in a technologically sparse culture. An ill-structured problem has the converse qualities: the information is not necessarily within the problem, solution procedures are potentially quite numerous, and a multiple solutions are likely (Voss, 2006). Algorithms are only effective when a problem is very well-structured and there is no question about whether the algorithm is an appropriate choice for the problem. Video 5.4.1. In the nine-dot problem, most students began in Scene #1 with a simple algorithm that can be stated like this: “Draw one line, then draw another, and another, and another.” Unfortunately this simple procedure did not produce a solution, so they had to find other strategies for a solution. “The lines need to be no longer than the distance across the square,” she said to herself. Functional fixedness sometimes is also called response set, the tendency for a person to frame or think about each problem in a series in the same way as the previous problem, even when doing so is not appropriate to later problems. For another, consider this problem: “The number of water lilies on a lake doubles each day. If the child cannot yet read the word screen, for example, he can note that part of this word looks similar to words he may already know, such as seen or green and from this observation derive a clue about how to read the word screen. Algorithms are only effective when a problem is very well-structured and there is no question about whether the algorithm is an appropriate choice for the problem. Identifying the problem seems like the obvious first stem, but it’s not exactly as simple as it sounds. When beginning research for a term paper, for example, a useful heuristic is to scan the library catalogue for titles that look relevant. CC licensed content, Specific attribution, https://courses.lumenlearning.com/edpsy/chapter/problemsolving, CC BY-NC-SA: Attribution-NonCommercial-ShareAlike, https://courses.lumenlearning.com/educationalpsychology, Identify the problem. Problem Solving explains strategies used for solving problems. When no one seemed to be getting it, the teacher asked, “Think about how you’ve set up the problem in your mind—about what you believe the problem is about. A well-structured problem provides much of the information needed and can in principle be solved using relatively few clearly understood rules. But not all necessary information was given: students needed to consider lines that were longer than implied in the original statement of the problem. If information is misunderstood or used inappropriately, then mistakes are likely—if indeed the problem can be solved at all. These steps can be explicitly taught to enhance problem-solving skills. In D. Berliner & R. Calfee (Eds. Problem-solving is a mental process that involves discovering, analyzing, and solving problems. Bassok, J. When beginning research for a term paper, for example, a useful heuristic is to scan the library catalog for titles that look relevant. Over time, we get so used to one particular purpose for an object that we overlook other uses. Working backward in this case encourages reframing the extra information in the problem (i. e. the size of each water lily) as merely distracting, not as crucial to a solution. Several others worked at it at their seats, but also without success. (The answer, incidentally, is that the lake is half covered in 99 days; can you think why?). As it happened, Willem loved puzzles of all kinds and had ample experience with them. Continued to think about how long the lines could be no longer than the!! To himself: “ think outside the box, ” as Willem this! 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