Well Defined and Ill-Defined Problems
A problem is defined as a process of changing from the initial state to the desired or goals state. Thus, this needs a set of actions to reach the desired solution. As far as problem-solving is concerned, there are two types of problems, that is, the well defined and the ill-defined problems. Ill-defined problems refer to the problems that do not have clear or well-defined goals, end states, set operations, or constraints. In most cases, these types of problems have restrictions and goals that must always be determined by those solving the problem (Reed,2002). Reed (2002) defined ill-defined problems as those that present ambiguity regarding the rules, concepts, and principles that are essential for the solution. This type of problem calls for learners to make judgments concerning the issue and defend verdicts by expressing personal beliefs or opinions. Ill-defined problems always have various solutions and solution paths or may have no solutions at all.
The opposite of ill-structured problems is the well-structured ones. Thus, well-structured problems are defined as those which their goal state, initial state or constraints are clearly defined. To solve these problems, procedural knowledge is required that and one is supposed to use the step by step procedure. A well-structured problem has a similar goal and is done in the same manner. In the first case where one is taking classes and is living a considerable distance from the campus and has a worn out car and has no means of getting a new one, which can be considered as both well-defined and ill-defined problem. If the area where the person is living has public transport, the problem can be regarded as well defined. The goal is finding the means of transport that can get one to the campus and the solution to that is asking about its timetable. In such as a case, the solution is very clear, and this can be regarded as a well-defined problem. On the other hand, it can be considered as an ill-defined problem if the person is residing in an area with no public transport. The primary reason why the problem is ill-defined is that the solution and also the corresponding steps that can be undertaken may not be clear, for instance, the person can ask the people who live next to him such as the neighbors and relatives and own cars to take him or her to the campus. The other option is to purchase a bicycle that is not as costly as a car. These are some of the answers to the problem but are not clear and that the person has to decide for him or her.
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In the second example, the problem can be regarded as well defined. First and foremost, the task is not new to the individual, and since it deals with the application of information processing theory, there might use an algorithm of managing it. Secondly, the steps that are required to handle the task are clear. The individual may follow some well-defined steps to accomplish the task. These include determining the topic that relies on the given subject matter, go to the internet or library to collect information, do an analysis of the sources, plan the structure of the essay, write it, and submit it to the teacher. Thus, the solution to the problem is based on the information that was provided.
In the last example, the two friends were planning to go for dinner, and one of the people fell asleep an hour before the agreed time of going out due to working late the previous night. That can thus be regarded as ill structures because it has multiple solutions. One of the solutions is waking up the “significant” and make a decision whether to attend the dinner or stay at home and continue sleeping. The second solution is not deciding to wake the “significant” and wait until the next meeting to rearrange the dinner. However, regardless of the solution, it is not obvious that the solution will be solved and this makes it ill-defined.
Aspects of Constructivist Theory, Problem Solving, and Critical Thinking
Constructivism is one of the major learning theories. Learning theories help in the explanation of how people improve their knowledge and have an understanding of new concepts (Jonassen & Land, 2012). The chief proponent of the theory is Jerome Bruner, and according to him, one aspect of the theory is that learning is considered as an active process where students construct new concepts and ideas based on the past or current knowledge (Jonassen & Land, 2012). Thus, the students select information and transform it, construct various hypotheses regarding the problem and finally make decisions by relying on the cognitive structures. The cognitive structures helps the learners provide organization and meaning of the experiences and go past the information that is provided.
This theory can be incorporated in my teaching where as a teacher, I would encourage the learners to try and discover principles by themselves. I would engage the students in dialogue or rather what is known as Socratic learning. As an instructor, my task would be translating the information that is about to be learned into a format that is appropriate to student’s present state of understanding.
When it comes to teaching, group activity is one of the learning activities that the learners often engage them in. Thus, as a sophomore literature teacher, I would guide the students to solve a problem rather than telling them how to solve it. For instance, when teaching rhyme in poetry, I would begin by asking them if they have ever heard the term rhyme and rhyme. If not, I would ask them to compose a short song that has similar sounds at the end of words. From that, I would then ask them to try and define rhyme. When it comes to rhythm, I would tell them to sing while tapping the table following the rhythm of the song. From that, I would ask them what they understand by the term rhythm. In such a case, I will have facilitated the discovery of the meaning of the two poetic terms without explaining them to the students in a direct manner.
When constructivism is used in learning activities, it allows the learners discover new things on their own that the internet cannot provide them with. Constructivism is also useful in learning in that it makes make associations and connections by relating the topic to real life situations.
Critical thinking is the application of high order and rational thinking skills such as analysis, synthesis of the problem, recognition of the problem, solving the problem, and evaluation. In simple terms, it means making reasonable judgments. Critical thinking is made of eight aspects such as asking questions, definition of the problem, examination of evidence, analysis of biases and assumptions, avoidance of emotional reasoning, avoidance of oversimplification, considerations of other interpretations, and being able to tolerate ambiguity.
Critical thinking can be used in learning activities where the teacher guides the learners to think critically and creatively (Jonassen & Land, 2012). Discussion is a learning activity that can be used to stimulate the students’ creativity. As a sophomore instructor, I can use discussion in my literature class to promote critical thinking among the learners. For instance, I can present a story to the students without giving a conclusion. Thus, I can use structured questions to lead the learners through a discussion and allowing them to give a conclusion to the story. Besides, I can also use dialogues to enhance their thinking. Thus, I can achieve that by using both written and group dialogue. I would extract a dialogue from one of the literary texts such as a play and then ask them to analyze various viewpoints of the people involved in the dialogue, after analyzing these viewpoints, I can then ask them to act the dialogue and give an explanation of the analysis. I could also use spontaneous dialogue where I assign various students different roles to play. All the aspects would enhance the learners’ critical skills.
When a teacher applies this concept well in learning by choosing the appropriate learning activities, the learners develop better critical thinking skills that help them solve various concepts in different subjects.
Problem-solving is an approach that challenges the learners to learn through engaging themselves in the real problem. Problem-based learning uses the power of problem-solving to actively engage the students in learn and also motivate them to learn more. Problem-based learning is one that starts with the introduction of ill-structured problems where learning is mostly centered. When it comes to problem-solving, most of the learning occurs in small groups rather than in lectures. The role of a teacher thus shifts from being on the stage to being the guide on the side. Thus, this means that the teacher is a coach and a facilitator of student learning and in most times, he or she acts as resource person rather than disseminator or holder of knowledge. The student then becomes more active as he or she is being engaged as a decision-maker, problem solver rather than being a note taker and a passive listener
Problem-solving can be applied in learning activities and most cases; it goes hand in hand with critical thinking (Savery & Duffy, 1995). For instance, literature is a subject that leaves the learners puzzled and asked numerous questions about theme, character, symbol, event, or structure. Moralistic or predictable literary texts that have flat characters do not a lot of questions. When the texts are complex, they questions that arise from them present numerous engaging problems that require the learners employ the problem-solving approach. In learning problem solving is very effective since it makes the learners find solutions to problems with the guidance of the teacher. When teaching English, I would use a problem-solving approach where I would use real life problems when explaining things such as themes. Besides, poetry calls for learners to apply critical thinking skills and also be problem solvers. Thus, when teaching the students poems of nature such as those of William Wordsworth, I would provoke their problem solving skills by asking them what certain words represent according to a particular poem.
To sum up, teachers need to shift from traditional teaching approaches to the contemporary ones. Traditional methods are the ones where teaching was teacher centered much of the information was provided the teacher. Thus, teachers should focus on making teaching learner-centered rather than teacher centered. Learner-centered learning is that which allows the learners provide much of the information and not the teacher-centered. Constructivist theory, problem-solving and critical thinking are the aspects that for the basis of learner-centered learning.
Jonassen, D., & Land, S. (Eds.). (2012). Theoretical foundations of learning environments . Routledge.
Reed, D. (2002). The use of ill-defined problems for developing problem-solving and empirical skills in CS1. Journal of Computing Sciences in Colleges , 18 (1), 121-133.
Savery, J. R., & Duffy, T. M. (1995). Problem based learning: An instructional model and its constructivist framework. Educational technology , 35 (5), 31-38.