We first present a theoretical analysis of the role of dual-task problem solving and cognitive fit in well-structured problem areas. We then apply the theory to a study of problem solving on the well-structured problem of understanding conceptual schemas (Khatri et al., 2006).
When the problem is well-structured, both the external IS problem representation and the IS task itself are sufficiently well formalised for problem solution to occur directly; that is, with reference to the problem statement alone and the associated representations, and without reference to the application domain. In terms of the dual-task problem-solving model presented in Figure 1, problem solving can take place in terms of the cognitive fit model related to the IS task alone (presented at the lower left of the model). In this case, the second task, that of forming a mental representation of the application domain, is not essential to forming the mental representation for task solution and therefore plays only a minor role in solving such a problem.
We use the theory of cognitive fit to understand the interrelationship between knowledge of the IS and application domains and the role of each in well-structured problem domains.
Because only IS domain knowledge is required to solve well-structured problems, any effect of application domain knowledge will occur in addition to the effect of IS domain knowledge. There will therefore be no interaction between the two types of knowledge and each therefore has independent effects on performance. We state the following proposition.
Proposition WS-1: In well-structured IS problem areas, the effects of IS and application domain knowledge are independent.
We can now explore the independent effects of both IS and application domain knowledge on performance. Because IS domain knowledge is essential to solving well-structured problems, we expect that it will influence performance on all types of well-structured problems. We state the following proposition.
Proposition WS-2: IS domain knowledge influences performance on all tasks in well-structured IS problem areas.
From the viewpoint of the application domain, although application domain knowledge is not essential to the solution of well-structured problems, we expect that its effect will be contingent upon the nature of the task in the well-structured problem area under investigation. Two situations may arise. First, in addressing certain tasks, the knowledge required for task solution can be acquired directly from the external IS problem representation; that is, cognitive fit exists. The problem solving that takes place is therefore both accurate and timely (Vessey, 1991). Hence knowledge of the application domain does not influence performance. We state the following proposition.
Proposition WS-3: When cognitive fit exists, problem solvers addressing tasks in well-structured IS problem areas are equally accurate irrespective of their knowledge of the application domain.
Second, while all of the information essential to solving well-structured problems is available in the external IS problem representation, it may not always be available directly. In this case, the knowledge required to address the task and that available for task solution do not match; that is, cognitive fit does not exist. Problem solvers must transform either knowledge emphasised in the external IS problem representation to match that emphasised in the IS task, or vice versa, in order to form a mental representation of the IS task and ultimately a mental representation that facilitates task solution (mental representation for task solution). The need to transform such knowledge to solve the task effectively increases the complexity of the task at hand. In this situation, the presence of application domain knowledge may play a role in problem solution, thereby effectively reducing the complexity of the task under consideration. In terms of the dual-task problem-solving model presented in Figure 1, the formulation of the mental representation for task solution may be aided by the presence of application domain knowledge. Hence the cognitive fit model to the upper left of Figure 1 may also play a role in such problem-solving situations. We state the following proposition.
Proposition WS-4: When cognitive fit does not exist, problem solvers solving tasks in well-structured IS problem areas are more accurate when they have knowledge of the application domain.
For our application of dual-task problem solving to well-structured problem areas, we draw on Khatri et al. (2006), who examined conceptual schema understanding in the context of high and low application domain knowledge. Note that, in what follows, we use the practical term ‘schema’ to denote the external IS problem representation.
We first address the well-structured nature of conceptual schema understanding, followed by theory on conceptual schema understanding tasks so that we can then examine the situations of fit and lack of fit that may arise.
A conceptual schema represents the structure and inter-relationships in a set of data. The structure of data has been subject to extensive formalisation over the past four decades (see, among others, Chen, 1976; Codd, 1970; Elmasri and Navathe, 1994). As a result, all of the information required to solve conceptual schema understanding tasks (IS task) can be gained from the schema itself, which, from the viewpoint of the model of dual-task problem solving, is represented by the external IS problem representation. There is, therefore, a clearly-defined initial state, a well-defined goal state, a formal set of transformation and evaluation paths, as well as a well-defined solution path. Conceptual schema understanding can therefore be addressed using IS domain knowledge alone and we can characterise conceptual schema understanding as a well-structured problem area.
In keeping with the cognitive theories we use to explain the role of application domain knowledge in IS problem solving, we characterise conceptual schema understanding tasks based on the cognitive nature of the task.
Based on prior IS research we can identify two basic types of conceptual schema understanding tasks: comprehension tasks and problem-solving tasks. Comprehension tasks are supported by the education literature, which identifies two different types of knowledge, syntactic and semantic (Shneiderman and Mayer, 1979; Mayer, 1991).[2] We therefore refer to such tasks as syntactic and semantic comprehension tasks. Syntactic knowledge involves understanding the vocabulary specific to a modelling formalism, for example, the ER model. Syntactic comprehension tasks are therefore those that assess the understanding of just the syntax of the formalism (conceptual model) associated with a schema. For example, the syntax for an entity type is a rectangle. Semantic knowledge refers to a set of mappings from a representation language to agreed-upon concepts in the real world. Thus, semantic comprehension tasks are those that assess the understanding of the data semantics conveyed through constructs in the schema; for example, a rectangle, the symbol for an entity type, represents a collection of entity instances, that is, objects, things, events, or places (in the ‘real world’) (Elmasri and Navathe, 1994).
Problem-solving tasks require a deeper level of understanding than comprehension tasks (see Gemino, 1999). Khatri et al. (2006) refer to a problem-solving task that can be solved using knowledge represented in the schema as a schema-based problem-solving task. Such tasks resemble query tasks; respondents are requested to determine whether, and how, certain information is available from the schema (see also, Shanks et al., 2003). A further type of problem-solving task, which Khatri et al. (2006) refer to as an inferential problem-solving task, requires conceptual modellers to use information beyond what is provided in the schema (see, for example, Bodart et al., 2001; Burton-Jones and Weber, 1999; Gemino and Wand, 2003; Shanks et al., 2002; Shanks et al., 2003).
In this study, we examined syntactic and semantic comprehension tasks and schema-based problem-solving tasks (in order of increasing complexity) based on their relevance to practicing conceptual modellers.
Khatri et al. (2006) investigated the effects of IS and application domain knowledge on conceptual schema understanding using problem solvers with high and low IS knowledge in both familiar and unfamiliar application domains.
The study findings were as follows. First, there was no interaction between IS and application domain knowledge supporting our theory, as presented in Proposition WS-1, that tasks in well-structured problem areas can be solved using IS knowledge alone.[3] Second, as expected, IS domain knowledge influenced the solution of all types of conceptual schema understanding tasks, supporting Proposition WS-2. Third, application domain knowledge did not influence the solution of syntactic and semantic comprehension tasks because the information required for their solution is available directly from the external IS problem representation. Hence Proposition WS-3 is supported. The solution of schema-based problem-solving tasks is, however, influenced by the presence of application domain knowledge because the information represented in the schema requires transformation to support the formulation of a consistent mental representation for task solution. As we have seen, the presence of application domain knowledge aids in the transformation process, effectively reducing the complexity of these types of tasks. Hence Proposition WS-4 is supported.