Definitions

problem

problem play

or thesis play

Type of drama that developed in the 19th century to deal with controversial social issues in a realistic manner, expose social ills, and stimulate thought and discussion. It is exemplified by the works of Henrik Ibsen, who exposed hypocrisy, greed, and hidden corruption of society in a number of masterly plays. His influence encouraged others to use the form. George Bernard Shaw brought it to an intellectual peak with his plays and their long, witty prefaces. More recent examples include works of Sean O'Casey, Athol Fugard, Arthur Miller, and August Wilson.

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In epistemology, the problem of explaining how it is possible for one person to know anything about the quality of another person's inner experience, or even that other people have inner experiences at all. According to a standard example, because each person's pain sensation is private, one cannot really know that what another person describes as pain is really qualitatively the same as what one describes as pain oneself. Though the physical manifestations the other person exhibits can be perceived, it seems that only the other person can know the contents of his mind. The traditional justification for belief in other minds, the argument from analogy, was given its classic formulation by John Stuart Mill: because my body and outward behaviour are observably similar to the bodies and behaviour of others, I am justified by analogy in believing that others have feelings like my own and are not simply automatons. In the mid-20th century the argument from analogy was severely criticized by followers of the later Ludwig Wittgenstein. An approach to the problem of other minds from the perspective of existentialism is contained in Being and Nothingness (1943), by Jean-Paul Sartre.

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Metaphysical problem of the relationship between mind and body. The modern problem stems from the thought of René Descartes, who is responsible for the classical formulation of dualism. Descartes's interactionism had many critics even in his own day. Thomas Hobbes denied the existence of mental substance. Materialism of a sort was also supported by Descartes's correspondent Pierre Gassendi (1592–1655). Benedict de Spinoza posited a single substance of which the mental and the material are attributes; his theory is known as psycho-physical parallelism. More recent views include the double-aspect theory, identity theory, eliminative materialism (which denies the reality of the familiar categories of mental state posited in so-called folk psychology), and theories of supervenience.

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Problem of justifying the inductive inference from the observed to the unobserved. It was given its classic formulation by David Hume, who noted that such inferences typically rely on the assumption that the future will resemble the past, or on the assumption that events of a certain type are necessarily connected, via a relation of causation, to events of another type. (1) If we were asked why we believe that the sun will rise tomorrow, we would say that in the past the Earth turned on its axis every 24 hours (more or less), and that there is a uniformity in nature that guarantees that such events always happen in the same way. But how do we know that nature is uniform in this sense? We might answer that, in the past, nature has always exhibited this kind of uniformity, and so it will continue to be uniform in the future. But this inference is justified only if we assume that the future must resemble the past. How do we justify this assumption? We might say that in the past, the future turned out to resemble the past, and so in the future, the future will again turn out to resemble the past. The inference is obviously circular: it succeeds only by tacitly assuming what it sets out to prove, namely that the future will resemble the past. (2) If we are asked why we believe we will feel heat when we approach a fire, we would say that fire causes heat—i.e., there is a “necessary connection” between fire and heat, such that whenever one occurs, the other must follow. But, Hume asks, what is this “necessary connection”? Do we observe it when we see the fire or feel the heat? If not, what evidence do we have that it exists? All we have is our observation, in the past, of a “constant conjunction” of instances of fire being followed by instances of heat. This observation does not show that, in the future, instances of fire will continue to be followed by instances of heat; to say that it does is to assume that the future must resemble the past. But if our observation is consistent with the possibility that fire may not be followed by heat in the future, then it cannot show that there is a necessary connection between the two that makes heat follow fire whenever fire occurs. Thus we are not justified in believing that (1) the sun will rise tomorrow or that (2) we will feel heat when we approach a fire. It is important to note that Hume did not deny that he or anyone else formed beliefs about the future on the basis of induction; he denied only that we could know with certainty that these beliefs are true. Philosophers have responded to the problem of induction in a variety of ways, though none has gained wide acceptance.

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In topology, a long-standing conjecture asserting that no more than four colours are required to shade in any map such that each adjacent region is coloured differently. First posed in 1852 by Francis Guthrie, a British math student, it was solved by Kenneth Appel and Wolfgang Haken using a computer-assisted proof in 1976.

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Problem-based learning (PBL) is a student-centered instructional strategy in which students collaboratively solve problems and reflect on their experiences. It was pioneered and used extensively at McMaster University, Hamilton, Ontario, Canada. Characteristics of PBL are:

  • Learning is driven by challenging, open-ended problems.
  • Students work in small collaborative groups.
  • Teachers take on the role as "facilitators" of learning.

Accordingly, students are encouraged to take responsibility for their group and organize and direct the learning process with support from a tutor or instructor. Advocates of PBL claim it can be used to enhance content knowledge and foster the development of communication, problem-solving, and self-directed learning skill.

Presenting problems to learners


Guidance is progressively faded. [adapted from Merrill (2002)]

Problem-based learning (PBL) is typically organized with small groups of learners, accompanied by an instructor, faculty person, or facilitator. During this process, a series of problems are provided to learners with guidance early in the PBL process (with introductory problems), and then later guidance is faded as learners gain expertise (Merrill, 2002). Guidance is faded as group members feel more confident with the subject matter and become more competent with the learned procedures.

Merrill (2007) suggests beginning with worked examples and then later, introduce students to smaller less complex problems. But as the process progresses, Merrill suggests changing problems by adding components to make them more realistic (Merrill, 2002, 2007). Thus it is important to begin with simplified versions of real world problems to progressively add components. This progression and fading motivates learners as they slowly gain expertise and take ownership.

During the PBL process learners should discuss problems, define what they know, generate hypotheses, derive learning goals and organize further work. Results may be subsequently presented to larger groups (under guidance from an instructor). A PBL cycle should conclude with learners reflecting on the learning that has taken place.

From a constructivist perspective [Problem-based learning (PBL)], the role of the instructor is to guide the learning process rather than provide knowledge (Hmelo-Silver & Barrows, 2006). From this perspective, feedback and reflection on the learning process and group dynamics are essential components of PBL.

Problem-based learning and cognitive load

Sweller and many others have published a series of studies over the past twenty years that is relevant to problem based learning but concerning cognitive load and what they describe as the guidance-fading effect (Sweller, 2006). Sweller and his associates conducted several classroom-based studies with students studying algebra problems (Sweller, 1988). These studies have shown that active problem solving early in the learning process, is a less effective instructional strategy than studying worked examples (Sweller and Cooper, 1985; Cooper and Sweller, 1987). Certainly active problem solving is useful as learners become more competent, and better able to deal with their working memory limitations. But early in the learning process, learners may find it difficult to process a large amount of information in a short amount of time. Thus the rigors of active problem solving may become an issue for novices. Once learners gain expertise the scaffolding inherent in Problem based learning helps learners avoid these issues.

Sweller (1988) proposed cognitive load theory to explain how novices react to problem solving during the early stages of learning. Sweller and his associates suggests a worked example early, and then a gradual introduction of problems to be solved. They propose other forms of learning early in the learning process (worked example, goal free problems, etc.); to later be replaced by completions problems, with the eventual goal of solving problems on their own (Sweller, Van Merrienboer, & Paas, 1998). This problem based learning becomes very useful later in the learning process.

Many forms of scaffolding have been implemented in problem based learning to reduce the cognitive load of learners. These are most useful to fade guidance during problem solving. As an example, consider the fading effect helps learners to slowly transit from studying examples to solving problems. In this case backwards fading was found to be quite effective.

Cognitive effects of Problem based learning

The acquisition and structuring of knowledge in PBL is thought to work through the following cognitive effects (Schmidt, 1993):

  • initial analysis of the problem and activation of prior knowledge through small-group discussion
  • elaboration on prior knowledge and active processing of new information
  • restructuring of knowledge, construction of a semantic network
  • social knowledge construction
  • learning in context
  • stimulation of curiosity related to presentation of a relevant problem

Some theories suggest that learning occurs as students collaboratively engage with concepts in meaningful problem solving. In this view, knowledge is seen as a tool for thinking and for enabling learners to participate in meaningful activity.

Problem-based learning is often referred to as a form of Inquiry-based learning (IBL), which describes an environment in which learning is driven by a process of inquiry owned by the student.

Evidence supporting problem-based learning

Hmelo-Silver, Duncan, & Chinn cite several studies supporting the success of the constructivist problem-based and inquiry learning methods. For example, they describe a project called GenScope, an inquiry-based science software application. Students using the GenScope software showed significant gains over the control groups, with the largest gains shown in students from basic courses.

Hmelo-Silver et al also cite a large study by Geier on the effectiveness of inquiry-based science for middle school students, as demonstrated by their performance on high-stakes standardized tests. The improvement was 14% for the first cohort of students and 13% for the second cohort. This study also found that inquiry-based teaching methods greatly reduced the achievement gap for African-American students.

A systematic review of the effects of problem-based learning in medical school on the performance of doctors after graduation showed clearly positive effects on physician competence. This effect was especially strong for social and cognitive competencies such as coping with uncertainty and communication skills.

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