Type of Operation/Skill. Some situations require simple operations, such as addition or subtraction, or simple measurement (e.g., finding the length of a shelf ), or recognition of shape. These are usually easier to analyze mathematically than situations that require multiplication or division, and than situations that require using exponents. While the difficulty of recognizing and carrying out the operation implied by a situation (be it additive, multiplicative, etc.) has direct bearing on task complexity, there may be exceptions that occur when alternative approaches are obvious. There are some tasks that combine both interpretive and generative skills and may involve a deeper conceptual understanding than merely carrying out a procedure. Other more complex tasks may involve an explanation of one's reasoning. The interpretation of information appearing in graphs, for example, becomes more complex if comparisons, conjecturing, or "reading beyond the information given" is required.

This factor requires that a task will be analyzed in terms of the question: How complex is the mathematical action that is required?

Expected Number of Operations. Tasks that require acting upon the mathematical information given may call for one application (step) of an operation, or for one action (e.g., literal reading of information in a table, or measurement). More complex tasks will demand more than one operation, which may be the same or similar to one another, such as the steps involved in multiple passes on the data or text. Still more complex tasks are those that involve the integration of several different operations.

This factor requires that a task will be analyzed in terms of the question: How many steps and types of steps are required?

4.3 Overall complexity level

It is possible to estimate the overall difficulty level of a specific item by first scoring the item on each of the five factors of complexity, according to the levels described in Appendix 2, and then summing together the scores for each factor. Figure 1 below explains the process; Appendix 2 describes each level of the five factors in detail. The total summary score can range between 5 (easiest) and 19 (most difficult).

The estimation process outlined in Figure 1 suggests that each factor has a separate contribution to an item's overall difficulty or complexity. However, it can be hypothesized that as tasks become more complex, actual performance on items may increasingly depend not only on each factor by itself, but also on the interplay or interaction between them. Hence, the computational process suggested in Figure 1 can provide only approximate information about an item's anticipated difficulty level.

Further, the difficulty of a task cannot in some cases be predicted without taking into account characteristics of the person who interacts with the task. The same task may be more difficult for some individuals and less difficult for other individuals, depending on factors such as their familiarity with the context in which a task is situated, knowledge of formal mathematical notations, background world knowledge, as well as general literacy, problem-solving, and reasoning skills. For example, it could be predicted that a task that involves the composition of a fertilizer would be more difficult for an urban apartment dweller than for a rural farmer whereas a task that uses a bus schedule would be more difficult for the farmer. For the above reasons, the prediction of the difficulty of a task in isolation of detailed knowledge about the respondent himself can only be an estimate.