There are two different types of problems: ill-defined and well-defined; different approaches are used for each. Well-defined problems have specific end goals and clearly expected solutions, while ill-defined problems do not. Well-defined problems allow for more initial planning than ill-defined problems. Solving problems sometimes involves dealing with pragmatics, the way that context contributes to meaning, and semantics, the interpretation of the problem. The ability to understand what the end goal of the problem is, and what rules could be applied represents the key to solving the problem. Sometimes the problem requires abstract thinking or coming up with a creative solution.
Various categorizations of questions have been proposed. With regard to research projects, one system distinguishes:
- descriptive questions, used primarily with the aim of describing the existence of some thing or process
- relational questions, designed to look at the relationships between two or more variables
- causal questions, designed to determine whether certain variables affect one or more outcome variables
Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state or object (a cause) contributes to the production of another event, process, state or object (an effect) where the cause is partly responsible for the effect, and the effect is partly dependent on the cause. In general, a process has many causes, which are also said to be causal factors for it, and all lie in its past. An effect can in turn be a cause of, or causal factor for, many other effects, which all lie in its future. Some writers have held that causality is metaphysically prior to notions of time and space.
A keystone (or capstone) is the wedge-shaped stone at the apex of a masonry arch or typically round-shaped one at the apex of a vault. In both cases it is the final piece placed during construction and locks all the stones into position, allowing the arch or vault to bear weight.
Problem-framing emphasizes focusing on the problem definition. Since how one defines a problem determines one’s understanding of and approach to that problem, being able to redefine or reframe a problem and to explore the “problem space” can help broaden the range of alternatives and solutions examined.
Ideally the shutter opens instantaneously, remains open as long as required, and closes instantaneously.
In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system can result in large differences in a later state.
Extraversion and introversion are typically viewed as a single continuum, so to be high in one necessitates being low in the other.
The vesica piscis is a type of lens, a mathematical shape formed by the intersection of two disks with the same radius, intersecting in such a way that the center of each disk lies on the perimeter of the other.
CULTURAL WRITING PATTERNS
In a typology of cultural writing patterns of ESL students, Robert Kaplan identifies fivemodels for organizing a paper and structuring an argument:
(1) North American (English) argumentative writing is linear, direct and to the point, with the thesis statement/claim at the beginning of the argument, and supporting arguments arranged hierarchically.
( 2) Semitic argumentative writing (Jewish, Arabic, Armenian) presents the argument in parallel propositions, or embedded in stories, not in hierarchical progression.
(3) Oriental (Asian) argumentative writing approaches the argument in a circular, respectful, indirect, non-assertive, but authoritative way.
(4) Romance (and German) argumentative writing favor a digressive style that requires readers to follow the argument to its conclusion.1
(5) Russian argumentative writing follows the Romance model, but with more freedom for dividing the pieces of the argument as the author proceeds to the conclusion.