Describe and give an example of how a problem could be solved in each of the following ways: (A) mechanically by rote, (B) through understanding, (C) by using a random search strategy, (D) by using heuristics, and (E) through insight

Question

What will be an ideal response?

Answer 1

Answer will include that (A) for routine problems, a mechanical solution may be adequate. Mechanical solutions are achieved by trial and error or by rote. When a problem is solved by rote, thinking is guided by an algorithm, or learned set of rules that always leads to an answer. A simple example of an algorithm is the steps needed to divide one number into another. (B) Many problems cannot be solved mechanically. In that case, understanding or a deeper comprehension of a problem is necessary. To solve a problem through understanding, you must discover the general properties of a correct solution. Problem solving through understanding usually is accomplished by first developing a general solution, which defines the requirements for success, but not

in enough detail to guide further action. Then, you propose a number of functional (workable) solutions and select the best one. An example might involve understanding the general properties of the card game so that you can play with ease rather than mechanically. (C) If the number of alternatives is small, a random search strategy may work. This is another example of trial-and-error thinking in which all possibilities are tried, more or less randomly. For example, you are trying to read a phone number written on a sheet of paper but you cannot determine the last number. You could dial the first digit and then randomly add a number between 0 and 9 as the last number.
(D) Regarding this phone number example, if you can tell the last number is either a 4, 8, or 9, then you have reduced your number of alternatives and would be using a heuristic to solve this phone number problem. A heuristic is a "rule of thumb" that reduces the number of alternatives thinkers must consider. Although this raises the odds of success, it does not guarantee a solution. Other ways to reduce alternatives would be to (1) Try to identify how the current state of affairs differs from the desired goal. Then find steps that will reduce the difference. (2) Try working backward from the desired goal to the starting point or current state. (3) If you can't reach the goal directly, try to identify an intermediate goal or subproblem that at least gets you closer. (4) Represent the problem in other ways, with graphs, diagrams, or analogies. (6) Generate a possible solution and test it. Doing so may eliminate many alternatives, or it may clarify what is needed for a solution. (E) A thinker who suddenly solves a problem has experienced insight. Insight is so rapid and clear that we may wonder why we didn't see the solution sooner. Insights are usually based on reorganizing a problem. This allows one to see problems in new ways and makes their solutions seem obvious. An example may be when you are caught in the rain at a picnic, you might suddenly realize that you can use the blanket on the ground or a garbage bag as a raincoat.