Problem Solving Skills
Another avenue of inquiry has recently started to look at the specific problems encountered by students in IT/CS programs. Students in these courses often encounter a level of abstraction in their subject matter unfamiliar to students in many other disciplines. Forming algorithms to solve computational problems often involves a number of different types of logical processing within the same problem space. Definitions in this knowledge domain often involve negation with conditional conjunction or disjunction. An example could be the definition of a “ball” in North American baseball: “A pitch at which the batter does not swing and which does not pass through the strike zone” (Goodwin & Johnson-Laird, 2010). For those familiar with the game, this definition seems self-evident, but for a person learning new skills (such as programming), the logic to conceptualize such an abstract concept can be daunting. Similarly, the definition that “x owns y” means that (in part), “it is permissible for x to use y, and not permissible for others to prevent x from using y” (Goodwin & Johnson-Laird, 2010).
Goodwin and Johnson-Laird hypothesize that people form mental models of these Boolean expressions that are not often correct in their logical representations. They found that people generally have a difficult time considering all the possibilities of such Boolean paradigms.
Stanovich (2002) argues that cognitive capacity (such as the ability to do well on an IQ test) is distinct from a person’s thinking disposition—a term that he uses to refer to the intersection of cognitive ability or intelligence, and personality traits such as will, desire and behaviour. Stanovich (2002) then suggests that “thinking dispositions can predict performance on reasoning and rational thinking tasks even after individual differences in measures of general cognitive ability have been partialled [sic] out” (p. 131). One type of thinking disposition, which Toplak and Stanovich (2002) call disjunctive reasoning or “as the tendency to consider all possible states of the world when deciding among options or when choosing a problem solution in a reasoning task” (p. 197), may be significant in identifying those people who can process complex logical problems. In a study involving nine disjunctive logic problems, a number of the problems tested generalized disjunctive thinking dispositions and these test items show a stronger association with thinking styles (or dispositions) than with cognitive ability and capacity, thus strengthening the argument in favour of a differentiation between the two constructs (Toplak & Stanovich, 2002).
A sub-type of complex reasoning problems known as “Analytical Reasoning” problems, have until recently been part of the Graduate Record Examination (GRE), an entrance test widely used for candidates to graduate schools throughout Europe and North America. They remain part of the Law School Admission Test (LSAT) and discussions are on-going about resurrecting their use in the GRE (Newstead, Bradon, Handley, Dennis, & Evans, 2006). In this class of problem, a narrative of the scenario contains the initial context and a list of the rules allowed in the problem space. The subject is then presented with a list of questions or problems. Successfully arriving at the solution involves a deep semantic understanding of the scenario and the ability to parse out the embedded rules. Only then can the subject start to solve the problem. Problem solving involves identifying which rule to apply first in order to reduce the number of possible options in the solution set as quickly as possible.