Figure 8.1: Domain of Business Math

An academic discipline such as Basic Math, Algebra, or Business Math is represented as a particular set of problems or questions that comprehensively embody the knowledge of the discipline. That set is called the domain, and the problems are called items. A symbolic representation of the domain of Business Math uses dots standing for items (Fig. 8.1). One of the items, which might be entitled "Word problem with percentages," is indicated by a line. The problem in the rectangle is an instance of that item.

Each item, or problem type, has at least dozens, more often hundreds or thousands of instances. Full mastery of the subject implies the ability to solve problems corresponding to all the items making up the domain.

Determining the set of items that make up the domain is the first step in constructing a "knowledge structure" for that domain. This is done by research in instructional materials and standards and systematic consultation with professionals. Substantial agreement is achieved among expert pedagogues on the choice and definition of items. The set of items finally arrived at and forming the domain must be comprehensive, that is, it must cover all the concepts that are included in the particular academic discipline.