Below is an essay I’ve written in a rush, which incidentally scored an 80.
Haa~
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“In the evolutionary line of the humans, we are faced with problems from the beginning of time. From the basics of finding shelter to the complexity of hunting as a group, we had progressed tremendously from then. However, in today’s context, we are far from able to solve problems efficiently as we thought we could. What is a problem? And why everyday people find it hard to solve problems? In this essay, we sought to understand different constraints involving solving a problem successfully.
A problem is defined as a situation where a person (the solver) implicitly, is faced without any means and/or information to achieve his goals. Though this may be temporal, it is rather frustrating for most of us. The constraints that we would face in any problem-solving situation can be broadly categorized into 4 main areas, namely; Linguistic skills, Visual perception, Memory and Problem Representation, which in most of the time; more than 1 element could be present as constraints. The following texts will bring us through each area and see how it affects us to solve problems successfully.
When posed with a problem in the form of written text or spoken language, we tend to interpret it as it is read or spoken. But in certain cases, we get misled by the words itself. The constraint we face here is the level of our linguistic skills versus the context of the problem, which is how well or ill-defined the problem is. If we couldn’t understand the problem well, we could not be able to find the means to solve it. Given a simple matter of a riddle, how well would a child and an adult measure up? With the child’s weak command of the language, compared to an adult’s, we could safely assume that the adult would fare better in comprehending the riddle than the child.
Furthermore, language plays an important part in successful problem solving. Being effectively versed in language, will be a plus. As noted in the previous paragraph, on the notion of being misled by words, it would take a person to understand a deeper underlying structure of the texts than to only scratch the surface structure of the problem. We would need an extensive array of understanding to able to interpret, analyse and finding the right words to comprehend the problem.
The way we perceive a problem visually is also one of the constraints we face in. For instance, given a situation of parking a car, we would need to visualise how would the car fit into the parking lot, how would we turn the steering wheel at the correct angle, consider will we hit the cars beside the lot or will we to find another lot. The way we perceive the problem visually is largely attributed to the way to the state space analysis we conceive in our problem solving process. Consider the Maier’s (1931) ‘two-string’ problem, where a participant is needed to tie two ends of two strings hanging from the ceiling. The problem is when a participant held on to one end of the string, they could not reach over and hold the other end of the other string. They perceive this as a seemingly impossible task. However, as a subtle hint to the participants before they hang themselves, the experimenter ‘apparently accidentally’ brushes across one of the string to set it swinging. Soon after, participants were found to devise ways to set one of the strings swinging by pendulum effect and successfully tie both strings together. By noticing that effect caused by the experimenter, participants were able to visualise and work out a solution by hindsight, after desperate attempts failing to notice the objects that are placed around them. This shows that by narrowing our attention to the problem, we fail to see that the solution is in the problem itself and/or around the problem.
In memory, we hold many past experiences of solving problems successfully. In every instance we solved a problem successfully; we commit the process and the end result into our memories and use it again in the future to solve related problems. However, this poses a rather constricting barrier. Should we be faced by another problem that is similar in surface structure but the goal is different in the deep structure, we tend to apply what we had remembered doing previously into the problem regardless whether it helps or not. We will feel stumped and puzzled. Past experiences have formed schemas that we fall back to in this instance. In the study conducted by Reed, Ernst and Banerji (1974), participants were ask to solve two problems – Missionaries and Cannibals and then Missionaries and Cannibals; or Jealous Husbands and Jealous Husbands again; or Missionaries and Cannibals and the Jealous Husbands; or Jealous Husbands and then Missionaries and Cannibals. Some of the participants are told hints about the relationship between the two problems. The results from the Reed et al. experiment shows that there is considerable improvement when previous experiment facilitates the solution of the second question if the second question is simpler than the first; that is, having a simpler deeper structure than the previous attempt. This goes on to that schemas are formed when we solved a problem. However, when faced with a harder problem, the schema we tried to apply on the problem will not applicable. We re-route our schema and assess the problem again and again till another pattern forms.
The way we represent a problem in our mind differs from each and every individual. Given the same problem to two participants for the first time, they will present two variations of what they think will be the solution. The way they represent the problem strongly influences their way of solving it, whether it could be done at all. The problem with representation is that it could simplify the problem into everyday context where participants are able to connect and relate to or, it could further complicate matters by confusing the participants. With the discussion of the previous 3 areas, representation is uniform across all areas. Consider that we represent what we hear or read with our internal lexicon, we represent what we see with past experiences and find similarities between and lastly, we when we are faced with a problem, we try to represent or visualise the problem in our mind to find means of solving it.
Hayes (1978) used two examples to illustrate the issue of problem representation, the 62-square checkerboard problem and the 62 young people problem. In the checkerboard problem, two diagonally opposite corners have been removed. The participant is tasked to place 31 dominoes over the 62 remaining squares; where each domino could cover exactly 2 squares and if not, explain why. In another similar problem of the 62 young people, there are 30 men and 32 women to be paired up. Most people will find it hard to answer both questions. However, Hayes finds out, when both problems were presented in more everyday terms, participants found it easier to answer the questions. He argues that “people do not always construct an optimal representation of a problem. But the way a problem is presented to help them to achieve a more useful representation.
To conclude, constraints in successful problem solving are present no matter how well-versed we are in our problem-solving skills. In comparison between novice programmers and expert programmers, their difference is where their experiences are. The expert programmer, being well-versed in the programming language (and probably debugged ten of thousands of lines before), will find it easier to relate to past experiences when they encounter a problem compared to the novice programmer. So this brings us a interesting point of whether does experiences help in finding solutions faster/better or does it constraints us further by restricting us into the well-trodden paths that we had taken every time?”
Dua Pai Lang
