Problem Solving et al.

Phases in Problem Solving

Modelling ( Purpose and Types)

Problem Solving Techniques

Phases in Problem Solving

The goal of the Input phase is to gain a clearer understanding of the problem or situation. The first step is to identify the problem(s) and state it(them) clearly and concisely. Identifying the problem means describing as precisely as possible the gap between one's perception of present circumstances and what one would like to happen. Problem identification is vital to communicate to one's self and others the focus of the problem-solving/decision-making process. Arnold (1978) identified four types of gaps: 1) something is wrong and needs to be corrected; 2) something is threatening and needs to be prevented; 3) something is inviting and needs to be accepted; and 4) something is missing and needs to be provided. Tunnel vision (stating the problem too narrowly) represents the major difficulty in problem identification as it leads to artificially restricting the search for alternatives.

The second step of the Input phase is to state the criteria that will be used to evaluate possible alternatives to the problem as well as the effectiveness of selected solutions. During this step it is important to state any identified boundaries of acceptable alternatives, important values or feelings to be considered, or results that should be avoided. In addition, criteria should be categorized as either essential for a successful solution or merely desired.

The third step is to gather information or facts relevant to solving the problem or making a decision. This step is critical for understanding the initial conditions and for further clarification of the perceived gap. Most researchers believe that the quality of facts is more important than the quantity. In fact, Beinstock (1984) noted that collecting too much information can actually confuse the situation rather than clarify it.

The Processing Phase

In the Processing phase the task is to develop, evaluate, and select alternatives and solutions that can solve the problem.

The first step in this phase is to develop alternatives or possible solutions. Most researchers focus on the need to create alternatives over the entire range of acceptable options as identified in the previous phase (Schnelle, 1967). This generation should be free, open, and unconcerned about feasibility. Enough time should be spent on this activity to ensure that non-standard and creative alternatives are generated.

The next step is to evaluate the generated alternatives vis-a-vis the stated criteria. Advantages, disadvantages, and interesting aspects for each alternative (using the PMI technique) are written individually (introversion, sensing, judging), then shared and discussed as a group (extroversion, sensing, judging). Most researchers advocate written evaluation, if only in the form of personal notes. After discarding alternatives that are clearly outside the bounds of the previously stated criteria, both advantages and disadvantages should be considered in more detail. An analysis of relationships among alternatives should be completed (i.e., is an advantage of one a disadvantage for another) and consideration should be given to the relative importance of advantages and disadvantages. Only those alternatives the majority considers relevant and correct are considered further.

The third step of the processing phase is to develop a solution that will successfully solve the problem. For relatively simple problems, one alternative may be obviously superior. However, in complex situations several alternatives may likely be combined to form a more effective solution (simply selecting one alternative will appeal to sensing, judging; combining one or more alternatives to make a new alternative will appeal to intuition, perceiving). A major advantage of this process is that if previous steps have been done well then choosing a solution is less complicated (Simon, 1969).

Before leaving this phase it is important to diagnose possible problems with the solution and implications of these problems (what could go wrong--sensing, judging; implications--intuition, perceiving). When developing a solution it is important to consider the worst that can happen if the solution is implemented. In addition, the solution should be evaluated in terms of overall "feelings." That is, does the alternative match important values as previously stated (feeling).

The Output Phase

During the Output phase a plan is developed and the solution actually implemented. The plan must be sufficiently detailed to allow for successful implementation, and methods of evaluation must be considered and developed. When developing a plan, the major phases of implementation are first considered (intuition), and then steps necessary for each phase are generated. It is often helpful to construct a timeline and make a diagram of the most important steps in the implementation using a technique such as network analysis (sensing, judging). Backwards planning and task analysis are also useful techniques at this point. The plan is then implemented as carefully and as completely as possible, following the steps as they have been developed and making minor modifications as appropriate (sensing, judging).

The Review Phase

The next step, evaluating implementation of the solution, should be an ongoing process. Some determination as to completeness of implementation needs to be considered prior to evaluating effectiveness. This step is often omitted and is one reason why the problem-solving/decision-making process sometimes fails: the solution that has been selected is simply not implemented effectively. However, if the solution is not implemented then evaluation of effectiveness is not likely to be valid.

The second step of this phase is evaluating the effectiveness of the solution. It is particularly important to evaluate outcomes in light of the problem statement generated at the beginning of the process. Affective, cognitive, and behavioral outcomes should be considered, especially if they have been identified as important criteria. The solution should be judged as to its efficiency (thinking, judging), its impact on the people involved (feeling, judging), and the extent to which it is valued by the participants (feeling, judging).

The final step in the process is modifying the solution in ways suggested by the evaluation process. Evaluation of the solution implementation and outcomes generally presents additional problems to be considered and addressed. Issues identified in terms of both efficiency and effectiveness of implementation should be addressed.

Modeling

A model is a representation or pattern of an idea or problem. That is, a model is a way to describe or present a problem in a way that aids in understanding or solving the problem. Models serve several purposes

The Purpose of Modeling

1. To make an idea concrete. This is done by representing it pictorially or symbolically. We are very visually oriented creatures, and it is easy to bring about understanding or conceptualization through an image--much the way analogy works, only now you use a picture, drawing, map, boxes, circles. A drawing can show a relationship, connection, arrangement, hierarchy, and so forth much more quickly than words alone can.

Another use of representative modeling is to enhance creativity by converting an idea into something that can be experienced by the senses. "Okay, this salt shaker is our blocked plan, and these French fries are the people opposing the plan by holding up the rules--this napkin--in front of it. Well, what can we do? Lift the salt shaker, move it around, over, through, empty it."

2. To reveal possible relationships between ideas. Relationships of hierarchy, support, dependence, cause, effect, etc. can be revealed by constructing a visual model.

A fact that needs special emphasis is that the model one uses for understanding will have a profound effect on perception and conceptualization. In fact, to a large extent, a model will determine your perception of an idea or problem and control your thinking about possibilities, relationships between parts, and so on. That's why multiple models are often highly desirable: they allow a person to think of the same concept in several different ways without the unconscious controlling influence that a single model might have.

We have to be careful, then, how much we let our models control our thinking.

3. To simplify the complex to make it manageable or understandable. Almost all models are simplifications because reality is so complex. The whole economy, weather system, human personality, geological structure of the earth, air flow over airplane wings--all are too complex to be treated as is, so models are constructed that present simplifications that can be treated. Simplification is both benefit and danger, and when dealing with a model, one must always be sure not to forget that the model and reality might not match perfectly--and sometimes not well at all.

4. The main purpose of modeling, which often includes all of the above three purposes, is to present a problem in a way that allows us to understand it and solve it. That is, by seeing the problem in a different form or from a different angle, we can gain the insight necessary to find a solution. We take a problem and simplify it, make it visual, and provide a familiar pattern.

Types of Models

1. Categories. Models can be put into one of two categories, conceptual and structural. Of the types listed below, many of them can fall into either category depending on the use made of them.

A. Conceptual. Models used for concretizing or reifying an idea, used to aid conception or understanding. These can be ultimately symbolic or arbitrary, whatever is necessary or useful. Also models to aid memory or teaching and relationship models.

B. Structural. Physical models of physical structures--oil refineries, DNA helixes, buildings, architectural model, a new kind of record player or bicycle. A model is almost always constructed before a prototype is made for a product and models are usually made for all large construction projects.

2. Types. These are not fixed and exclusive boxes--they often overlap, as in visual symbolic.

A. Visual. Draw a picture of it. If the problem is or contains something physical, draw a picture of the real thing--the door, road, machine, bathroom, etc. If the problem is not physical, draw a symbolic picture of it, either with lines and boxes or by representing aspects of the problem as different items--like cars and roads representing information transfer in a company.

Visual models are among the most effective because we are highly visually oriented beings. Remember Confucius' saying that is now a cliche but a true statement nonetheless: A picture is worth a thousand words.

B. Physical. The physical model takes the advantages of a visual model one step further by producing a three dimensional visual model. Again, you can use a real model or a symbolic one.

C. Mathematical. Many problems are best solved mathematically, by using calculations for speed, area, projected income, national unemployment. Thinking beyond three dimensions visually or four dimensions physically is very difficult. But with math, ten or fifteen dimensions are no problem. Ideas of speed, acceleration, and accelerating acceleration are often more understandable mathematically.

D. Metaphorical or Symbolic or Analogical. Remember what we said about metaphor and analogy, that the unfamiliar becomes understandable by comparing it to the familiar. That's how this kind of modeling works. Both understanding and structure can be established for a problem by using a metaphor or symbol. Here are some examples useful kinds:

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Problem Solving Techniques

The following techniques focus more on logic and critical thinking, especially within the context of applying the scientific approach:

A. Analysis--the identification of the components of a situation and consideration of the relationships among the parts (Bloom, Englehart, Furst, Hill, & Krathwohl, 1956);

B. Backwards planning--a goal selection process where mid-range and short-term conditions necessary to obtain the goal are identified (Case & Bereiter, 1984; Gagne, 1977; Skinner, 1954); this technique is related to the more general technique of means-ends analysis described by Newell and Simon (1972);

C. Categorizing/classifying--the process of identifying and selecting rules to group objects, events, ideas, people, etc. (Feuerstein, Rand, Hoffman, & Miller, 1980; Sternberg, 1988);

D. Challenging assumptions--the direct confrontation of ideas, opinions, or attitudes that have previously been taken for granted (Bransford & Stein, 1984; Brookfield, 1987);

E. Evaluating/judging--comparison to a standard and making a qualitative or quantitative judgment of value or worth (Bloom et al., 1956);

F. Inductive/deductive reasoning--the systematic and logical development of rules or concepts from specific instances or the identification of cases based on a general principle or proposition using the generalization and inference (e.g., Devine, 1981; Pelligrino, 1985; Sternberg, 1988);

G. Thinking aloud--the process of verbalizing about a problem and its solution while a partner listens in detail for errors in thinking or understanding (Whimby & Lochhead, 1982);

H. Network analysis--a systems approach to project planning and mangement where relationships among activities, events, resources, and timelines are developed and charted. Specific examples include Program Evaluation and Review Technique and Critical Path Method (Awani, 1983; Handy & Hussain, 1969);

I. Plus-Minus-Interesting (PMI)--considering the positive, negative, and interesting or thought-provoking aspects of an idea or alternative using a balance sheet grid where plus and minus refer to criteria identified in the second step of the problem-solving process (de Bono, 1976; Janis & Mann, 1977);

J. Task analysis--the consideration of skills and knowledge required to learn or perform a specific task (Gagne, 1977; Gardner, 1985).

The following problem-solving techniques focus more on creative, lateral, or divergent thinking (e.g., de Bono, 1983; Prince, 1970; Wonder & Donovan, 1984):

A. Brainstorming--attempting to spontaneously generate as many ideas on a subject as possible; ideas are not critiqued during the brainstorming process; participants are encouraged to form new ideas from ideas already stated (Brookfield, 1987; Osborn, 1963);

B. Imaging/visualization--producing mental pictures of the total problem or specific parts of the problem (Lazarus, 1978; McKim, 1980; Wonder & Donovan, 1984);

C. Incubation--putting aside the problem and doing something else to allow the mind to unconsciously consider the problem (Frederiksen, 1984; Osborn, 1963);

D. Outcome psychodrama--enacting a scenario of alternatives or solutions through role playing (Janis & Mann, 1977);

E. Outrageous provocation--making a statement that is known to be absolutely incorrect (e.g., the brain is made of charcoal) and then considering it; used as a bridge to a new idea (Beinstock, 1984); also called "insideouts" by Wonder and Donovan (1984);

F. Overload--considering a large number of facts and details until the logic part of the brain becomes overwhelmed and begins looking for patterns (Wonder & Donovan, 1984); can also be generated by immersion in aesthetic experiences (Brookfield, 1987), sensitivity training (Lakin, 1972), or similar experiences;

G. Random word technique--selecting a word randomly from the dictionary and juxtaposing it with problem statement, then brainstorming about possible relationships (Beinstock, 1984);

H. Relaxation--systematically relaxing all muscles while repeating a personally meaningful focus word or phrase (Benson, 1987); a specific example of the more general technique called "suspenders" by Wonder and Donovan (1984);

I. Synthesizing--combining parts or elements into a new and original pattern Bloom et al., 1956; Sternberg, 1988);

J. Taking another's perspective--deliberately taking another person's point of view (de Bono, 1976; referred to as "be someone else" by Wonder and Donovan (1984);

K. Values clarification--using techniques such as role-playing, simulations, self-analysis exercises, and structured controversy to gain a greater understanding of attitudes and beliefs that individuals hold important (Fraenkel, 1977; Johnson & Johnson, 1988; Kirschenbaum, 1977).

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